Write excel journal. It’s about Theory of Corporate Finance. You should know excel, finance. The person with FRM will be perfect for this work
1.
(a)The formula of discount factor is . r is the interest rate, and it is constant at 0.0
3
. t is the period number. First, getting the discount rate of each year. Second,based on the discount rate, getting the discount factor for each year.
(b)(i) Getting the PV through the discount factor, I use . The present value of the receiving the rent for 88 years is $30.86.
(ii) Using formula which from the class, I get $30.86. The result is the same as (i).
(c) Formula can be used to get the present value of receiving the rent forever .
(d) In (b), I have found the PV of 88-year lease. Following (b), I get the PV of 22 and 10-year lease. Using the PV of lease sell to divided the full market value, then getting the percentages.
(e)
A
n 88-year lease would sell for 97 per cent of its full market price. We have formula , then . Canceling both side, 0.. To get r, . r=0.0
4
06
5
.
2.
(a) The earning for each year is $100K. I consume 30% of my earning, then I can saving $70K ever year. I put my saving to saving account at beginning of a year with 0.04 interest rate. Through , I get column 4 & 5. When i need to withdraw $70000 at beginning of T, I need to get the capital through .
b. As there is 5% saving rate, all previous years’ saving will increase by 5%. For example, in year 0, the total saving will be $5000 as the income is assumed to be saved at the end of year 0, thus no compounding. In year 1, the $5000 earned in year 0 will earn an interest rate of 5%. Total saving in year 1 will thus become I created a column to find the compounded saving each year,
c. Let saving rate be and earning be E. At t=T, the capital KT would be
As and E = $10000 in this question,
d. NPV of perpetuity of future consumption at t=T is .
B
y equating KT and . we get . By solving for T, T=13.96 years.
Part 2:
e. As illustrated in part c, the amount of capital at the end of year T-1 would be , which would be equal to .
f. . Since E cancels out on both sides and the expression is independent of E, the minimum capital we need at the beginning of period T is E>0.
g. By equating and , we get
When s = 0.5, T = 13.96, which is the same as part d.
3
A
1.Use function =norminv(probability, mean, standard_dev) to generate 400 random rate of return with mean 10.7% and variance 3.2%.
2.To get arithmetic rate of return, the variance over 400 years, and the geometric rate of return, I use excel function =average(), =var.s(), =geomean(). For the geometric rate of return, I add 1 to each random rate to let them be positive.
3. Yes. I get the half of the variance, then get the difference of the arithmetic rate & geometric rate of return. I resample several times, and the half of the variance is close to the difference; so, the statement holds.
B
1. Following A1, I get other two column random rate of return. Using to get the holding rate over two periods.
2.
I used “varS” function to calculate variances of one-period holding rate of return and two-periods holding rate of return. The variance of two-periods holding rate of return is approximately 2 times of the variance of one-period holding rate of return. This implies that the standard deviation of two-periods rate of return is approximately times of the standard deviation of one-period rate of return. Thus, the conclusion that ‘Risk grows approximately with the square root of time’ is verified.
4
1. 1-day T-statistics = 2/50, N-day T-statistics = 2. I get the formula , so N= days.
2.Using the function IF (RAND()<0.5,-1,1), -1 & 1 have the same probability to show in the column.
3. Using the function 2+IF(RAND()<0.5,-1,1)*50 to get the signal.
4.(a) Using question 3 as the basis point change every year. Using the function to get 5000-days’ realized compounded rate of return.
(b) Using the function . Getting the compound rate of return from a 2bq drift alone by multiplying the drift in year T-1.
1. I used the function “=2+IF(RAND()<0.5,-1,1)*70” to find the basis point change in each year. I then generate rate of return in column C and F with 5000 entries of daily rate of return. (a) Then I plot a scatter plot for column C as the time series plot of the realized rate of return. (b) I generated column D of year T by multiplying the drift in year T-1 by 2bp drift. I then plot a scatter plot for column D as the time series plot of the compounded rate of return from 2bp drift alone.
2. By drawing many samples of 5000 observations, I would expect to see that there are more positive rate of returns in columns C and F. I repeated the analysis using 4bp drift and 200 bp noise. The difference between two signals are sensible. It is harder to detect a drift in the case where drift is 4 bp and noise is 200 bp as there is less positive numbers in column I as compared to column C and F.
5
I chose AMZN as my company to compute beta.
1) I computed beta for AMZN using 2-year daily return, 2-year monthly return, and 4-year daily return data. I computed beta using , where Rs is the rate of return for stock and Rm is the rate of return for markets. After getting beta, I shrink it to by using the formula to allow beta to converge to 1 in the long run.
2) The result is as following: , , . The beta for AMZN provided by Yahoo Finance is 1.63. It matters to choose daily data rather than monthly data because stock returns are very noisy. By having daily data rather than monthly data, we can get more observations over the same period and thus we can have better estimates. Also, the longer the period of study, the less reliable the estimate as over a long horizon, the unobserved underlying true betas themselves tend to move around. Thus, we need to shrink the computed beta even more (50%-60%) when the horizon is longer (>5 years).
3) There is difference between the result obtained by calculation and the result provided by Yahoo Finance. This is probably because the beta provided by Yahoo Finance is not shrunk and it is computed using three-year data. The beta I computed using 2-year daily data is less than 1.63, which implies that the stock return of AMZN fluctuates less with the market return than what is predicted Yahoo Finance.
>2
> :
.0 iscount Rate
PV .33
0 1 1 0. 0 7 8 .8 0
08 9 0 D 0.9 5 91 594
27
0.91 94 8 9
88 6 1
8 04 0878 9
7 91
27 7 0.8 6087844 842 7
10 02
9060 1
40 65
0.8 8425 915 3
7 6 0.81 15 409 43
00814
0.7894092 3 64 3
Lease Years % Interest Rate: 773 38
0.7664167 88 0.97 4
0651 13
91 7 0.74409 49 6
8707
0.7 2 66 98802
6088 0.701 8802 8533 0.68095134 1 8058
97 0.66 78058 74
74 0.6418619474 6 0.6 669392 8
476323
0.6050164458 6076
12
0.5873946076 0 60531
0.5702860268 57542
0.5536757542 49 9
5717
0.5375492759 09
4089
0.5 925009 84
65111
0.5066917484 37 4 5
0.4919 363 79 0.4776055693 47 59 75
0.4636947274 90056
0.4501890558 767532
9276757
0.4370767532 3
565506
0.4243463623 867595
6 12
0.41 67595 987 2
3
0. 9871452 3370 7557
0.3883370341 7
4
0.3770 467 0448997
5 5
0.3660448997 38 78
6 44
0.355 8 51
0.3450 98 69
6778
0.3 829369 26 4
0. 2 524 5 6
825
0. 753546 7792
0.3065568408 008
8989258
0.2976280008 959224
0.288959224 0.280542936 25
34
0.272 7825 4 238
0.2644386238 7 279
0.2567365279 950 0.249258765 88009
25 93
0. 9988009 950 2
4356
0.2349502922 0798
60187
0.2 070798 3 3
2 93
0.2 6 43 128003
0. 0128003 750 5
721
0.2087502915 670 9
463
0.20 01859 767 8
5917
0.1967671708 0 882
0.1910360882 09
0.1854719303 0698 09841
0.1800698352 030 0.1748250827 9
3 0.16973309 2
0.1647894078 31
0.1599897163 3 51
0.155 8216 11986
0.1508056521 4
8 46
0.1464132544 1487907
8 66
0.1421487907 085347
0.1380085347 9888686
0.13 88686 862802
7399
0.1300862802 0.1262973594 6187956
0.1226187956 0 666
0.1190473743 5799751
846
0.1155799751 68
0.112 568 9452 0.108945 7 0.1057720502 6913 408
0.10269 09 8
0059908 0.0997003018 0.0967964095 0.0939770966 98996
0.091 8996 913
0.0885824268 62
085495
0.0810654691 9
0.0787043 02
0.0764119795 9
62
0.0741863879 857
3655566
48
065233
99
9319
6398
99
106
5043
3
343077
1 9
089903
2
978999
4251455
807238
76
638095
736015
8
7497
555489
646106
49
967093
474797
5
4615
9651988
799463
68411
794
2787
09
20879
03
506
0947
281197
49
1309
2 Interest Rate at beginning of T and do not work
70000 0.0 0.0 1 1 1 342.6
1 1 1 1 1 1 1 1 78.6
1 33.8
1 1 1 1 1 1 0 5044.1
0 3 Number Variance SD 0.032 1 1 5
861353
2 0635113
3211
3 4 19
04
7172
5 746482
366
6 7 8 973051
9 84618
10 11 12 13 14 583
15 16 17 18 29
19 20 21 032
22 23 7993157
24 1318
25 5308987
26 27 28 29 30 31 32 21051
33 34 35 36 102449
37 38 1435241
39 904
14
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 888027
217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 911821
314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 4 -0.0048 0.0002 4(b)The compounded rate of return from 2bq drift alone
2.0000000000000001E-4 4.0003999999993489E-4 6.0012000799991583E-4 8.0024003200152016E-4 1.0004000800079016E-3 1.2006001600239902E-3 1.4008402800560482E-3 1.6011204481121144E-3 1.8014406722017817E-3 2.0018009603361975E-3 2.2022013205282853E-3 2.4026417607923012E-3 2.6031222891444994E-3 2.8036429136022445E-3 3.0042036421848994E-3 3.2048044829133815E-3 3.4054454438099402E-3 3.6061265328986014E-3 3.8068477582051674E-3 4.0076091277567727E-3 4.2084106495823281E-3 4.4092523317122989E-3 4.6101341821787045E-3 4.8110562090151188E-3 5.0120184202568918E-3 5.2130208239409281E-3 5.4140634281056865E-3 5.6151462407911801E-3 5.8162692700394203E-3 6.0174325238933069E-3 6.2186360103979599E-3 6.4198797376000538E-3 6.6211637135475954E-3 6.8224879462903676E-3 7.0238524438797079E-3 7.2252572143685079E-3 7.4267022658114357E-3 7.6281876062644915E-3 7.8297132437856742E-3 8.0312791864343147E-3 8.2328854422715203E-3 8.4345320193599527E-3 8.6362189257638278E-3 8.8379461695489159E-3 9.0397137587827636E-3 9.2415217015344719E-3 9.4433700058746961E-3 9.6452586798758677E-3 9.8471877316117506E-3 1.0049157169158107E-2 1.025116700059181E-2 1.0453217233991952E-2 1.0655307877438736E-2 1.0857438939014141E-2 1.1059610426801925E-2 1.1261822348887174E-2 1.1464074713356975E-2 1.1666367528299526E-2 1.1868700801805243E-2 1.2071074541965654E-2 1.2273488756874062E-2 1.2475943454625327E-2 1.2678438643316303E-2 1.2880974331044959E-2 1.3083550525911036E-2 1.3286167236016277E-2 1.3488824469463534E-2 1.3691522234357434E-2 1.3894260538804382E-2 1.4097039390912114E-2 1.4299858798790366E-2 1.4502718770550205E-2 1.4705619314304252E-2 1.4908560438167129E-2 1.5111542150254786E-2 1.5314564458684732E-2 1.551762737157647E-2 1.5720730897050839E-2 1.5923875043230229E-2 1.6127059818238809E-2 1.6330285230202524E-2 1.6533551287248649E-2 1.6736857997506016E-2 1.6940205369105454E-2 1.7143593410179347E-2 1.7347022128861411E-2 1.7550491533287138E-2 1.7754001631593797E-2 1.7957552431919988E-2 1.816114394240631E-2 1.8364776171194697E-2 1.8568449126428854E-2 1.8772162816254045E-2 1.8975917248817309E-2 1.9179712432267015E-2 1.9383548374753534E-2 1.9587425084428567E-2 1.9791342569445369E-2 1.9995300837959196E-2 2.0199299898126855E-2 2.0403339758106487E-2 2.060742042605801E-2 2.0811541910143116E-2 2.1015704218525055E-2 2.1219907359368628E-2 2.1424151340840414E-2 2.1628436171108545E-2 2.1832761858342709E-2 2.2037128410714368E-2 2.2241535836396542E-2 2.2445984143563802E-2 2.2650473340392496E-2 2.2855003435060528E-2 2.3059574435747576E-2 2.3264186350634652E-2 2.3468839187904766E-2 2.367353295574226E-2 2.3878267662333474E-2 2.408304331586586E-2 2.4287859924529087E-2 2.4492717496513938E-2 2.4697616040013193E-2 2.4902555563221185E-2 2.5107536074333803E-2 2.5312557581548711E-2 2.5517620093064908E-2 2.5722723617083387E-2 2.59278681618067E-2 2.6133053735438949E-2 2.6338280346186016E-2 2.6543548002255335E-2 2.6748856711855673E-2 2.6954206483198018E-2 2.7159597324494689E-2 2.736502924395956E-2 2.7570502249808282E-2 2.7776016350258281E-2 2.7981571553528317E-2 2.8187167867838925E-2 2.8392805301412416E-2 2.8598483862472657E-2 2.8804203559245067E-2 2.9009964399956845E-2 2.9215766392836739E-2 2.9421609546115279E-2 2.9627493868024546E-2 2.9833419366798175E-2 3.0039386050671579E-2 3.0245393927881725E-2 3.0451443006667356E-2 3.0657533295268768E-2 3.0863664801927815E-2 3.1069837534888123E-2 3.1276051502395097E-2 3.1482306712695474E-2 3.1688603174037988E-2 3.1894940894672708E-2 3.2101319882851698E-2 3.2307740146828134E-2 3.2514201694857414E-2 3.2720704535196266E-2 3.2927248676103194E-2 3.3133834125838479E-2 3.3340460892663515E-2 3.3547128984842134E-2 3.3753838410639059E-2 3.3960589178321232E-2 3.4167381296156929E-2 3.4374214772416201E-2 3.4581089615370653E-2 3.4788005833293667E-2 3.4994963434460402E-2 3.5201962427147349E-2 3.5409002819632773E-2 3.561608462019672E-2 3.5823207837120785E-2 3.6030372478688122E-2 3.623757855318388E-2 3.6444826068894542E-2 3.6652115034108368E-2 3.685944545711517E-2 3.7066817346206538E-2 3.7274230709675837E-2 3.7481685555817768E-2 3.7689181892928802E-2 3.7896719729307415E-2 3.8104299073253189E-2 3.8311919933067706E-2 3.8519582317054324E-2 3.8727286233517733E-2 3.8935031690764399E-2 3.9142818697102566E-2 3.9350647260842031E-2 3.9558517390294146E-2 3.976642909377226E-2 3.9974382379591056E-2 4.0182377256066992E-2 4.0390413731518082E-2 4.0598491814264337E-2 4.08066115126271E-2 4.1014772834929492E-2 4.1222975789496408E-2 4.1431220384654299E-2 4.1639506628731171E-2 4.1847834530056804E-2 4.2056204096962757E-2 4.2264615337782141E-2 4.2473068260849622E-2 4.2681562874501866E-2 4.2890099187076647E-2 4.309867720691396E-2 4.3307296942355356E-2 4.3515958401743715E-2 4.3724661593424141E-2 4.3933406525742846E-2 4.4142193207048042E-2 4.4351021645689492E-2 4.4559891850018518E-2 4.47688038283 88437E-2 4.4977757589154121E-2 4.5186753140671998E-2 4.5395790491300048E-2 4.560486964939825E-2 4.5813990623328138E-2 4.60231534214528E-2 4.6232358052137101E-2 4.644160452374746E-2 4.6650892844652292E-2 4.6860223023221126E-2 4.7069595067825709E-2 4.7279008986839344E-2 4.7488464788636664E-2 4.7697962481594303E-2 4.7907502074090669E-2 4.8117083574505504E-2 4.8326706991220325E-2 4.8536372332618649E-2 4.8746079607085102E-2 4.8955828823006531E-2 4.9165619988771114E-2 4.9375453112768808E-2 4.9585328203391343E-2 4.9795245269032007E-2 5.0005204318085861E-2 5.0215205358949522E-2 5.0425248400021383E-2 5.0635333449701392E-2 5.0845460516391272E-2 5.1055629608494524E-2 5.1265840734416201E-2 5.1476093902563136E-2 5.1686389121343712E-2 5.189672639916787E-2 5.2107105744447768E-2 5.2317527165596678E-2 5.2527990671029867E-2 5.2738496269164159E-2 5.294904396841793E-2 5.3159633777211557E-2 5.3370265703966968E-2 5.3580939757107648E-2 5.379165594505908E-2 5.4002414276248079E-2 5.4213214759103234E-2 5.4424057402055137E-2 5.4634942213535487E-2 5.4845869201978203E-2 5.505683837581854E-2 5.5267849743493747E-2 5.5478903313442407E-2 5.5689999094105103E-2 5.5901137093923969E-2 5.6112317321342697E-2 5.6323539784806975E-2 5.6534804492763824E-2 5.6746111453662262E-2 5.6957460675952865E-2 5.716885216808798E-2 5.7380285938521514E-2 5.7591761995709145E-2 5.7803280348108332E-2 5.8014841004177864E-2 5.822644397237875E-2 5.843808926117311E-2 5.8649776879025284E-2 5.8861506834401167E-2 5.9073279135767987E-2 5.9285093791595189E-2 5.9496950810353555E-2 5.970885020051564E-2 5.9920791970555776E-2 6.013277612894985E-2 6.0344802684175525E-2 6.055687164471224E-2 6.0768983019041212E-2 6.0981136815644987E-2 6.1193333043008113E-2 6.1405571709616691E-2 6.1617852823958597E-2 6.1830176394523262E-2 6.2042542429802117E-2 6.2254950938288145E-2 6.2467401928475885E-2 6.2679895408861652E-2 6.2892431387943315E-2 6.3105009874220963E-2 6.3317630876195796E-2 6.3530294402371013E-2 6.3743000461251365E-2 6.3955749061343603E-2 6.4168540211155811E-2 6.4381373919198071E-2 6.4594250193981795E-2 6.4807169044020618E-2 6.5020130477829507E-2 6.5233134503924983E-2 6.5446181130825787E-2 6.5659270367051992E-2 6.5872402221125448E-2 6.6085576701569559E-2 6.6298793816909951E-2 6.6512053575673358E-2 6.6725355986388513E-2 6.6938701057585703E-2 6.7152088797797216E-2 6.7365519215556668E-2 6.7578992319399678E-2 6.7792508117863637E-2 6.8006066619487271E-2 6.8219667832811082E-2 6.8433311 766377569E-2 6.8646998428730788E-2 6.8860727828416568E-2 6.9074499973982295E-2 6.928831487397713E-2 6.9502172536952012E-2 6.9716072971459431E-2 6.9930016186053656E-2 7.0144002189290733E-2 7.0358030989728482E-2 7.05721025959265E-2 7.0786217016445718E-2 7.1000374259849064E-2 7.121457433470102E-2 7.1428817249567844E-2 7.1643103013017795E-2 7.1857431633620461E-2 7.2071803119947209E-2 7.228621748057118E-2 7.2500674724067293E-2 7.2715174859012022E-2 7.2929717893983836E-2 7.3144303837562541E-2 7.3358932698329937E-2 7.3573604484869604E-2 7.3788319205766451E-2 7.4003076869607609E-2 7.4217877484981543E-2 7.4432721060478491E-2 7.4647607604690469E-2 7.4862537126211492E-2 7.5077509633636685E-2 7.5292525135563393E-2 7.5507583640590514E-2 7.5722685157318503E-2 7.5937829694350034E-2 7.6153017260288891E-2 7.6368247863740857E-2 7.6583521513313491E-2 7.6798838217616128E-2 7.7014197985259658E-2 7.7229600824856748E-2 7.7445046745021617E-2 7.7660535754370708E-2 7.787606786152157E-2 7.8091643075093753E-2 7.8307261403708806E-2 7.8522922855989608E-2 7.8738627440560816E-2 7.8954375166048862E-2 7.9170166041081957E-2 7.9386000074290086E-2 7.9601877274305011E-2 7.9817797649759825E-2 8.0033761209289844E-2 8.0249767961531715E-2 8.0465817915124083E-2 8.0681911078707147E-2 8.0898047460922884E-2 8.1114227070415046E-2 8.1330449915829162E-2 8.1546716005812314E-2 8.1763025349013363E-2 8.1979377954083166E-2 8.2195773829673913E-2 8.2412212984439792E-2 8.2628695427036547E-2 8.2845221166121918E-2 8.3061790210355202E-2 8.3278402568397247E-2 8.3495058248910903E-2 8.3711757260560571E-2 8.3928499612012653E-2 8.4145285311935103E-2 8.4362114368997432E-2 8.4578986791871147E-2 8.4795902589229533E-2 8.5012861769747428E-2 8.5229864342101447E-2 8.544691031496976E-2 8.5663999697032756E-2 8.5881132496972157E-2 8.6098308723471462E-2 8.6315528385216167E-2 8.6532791490893102E-2 8.6750098049191315E-2 8.696744806880119E-2 8.7184841558414883E-2 8.7402278526726551E-2 8.7619758982431906E-2 8.7837282934228433E-2 8.8054850390815176E-2 8.8272461360893395E-2 8.8490115853165463E-2 8.8707813876335972E-2 8.8925555439111292E-2 8.9143340550199124E-2 8.9361169218309167E-2 8.9579041452152897E-2 8.9796957260443344E-2 9.0014916651895316E-2 9.0232919635225617E-2 9.0450966219152606E-2 9.066905641239642E-2 9.0887190223678971E-2 9.1105367661723724E-2 9.1323588735256145E-2 9.1541853453003252E-2 9.1760161823693842E-2 9.1978513856058486E-2 9.2196909558829754E-2 9.2415348940741548E-2 9.2633832010529771E-2 9.2852358776931876E-2 9.3070929248687317E-2 9.3289543434537103E-2 9.3508201343224018E-2 9.3726902983492622E-2 9.3945648364089251E-2 9.4164437493762021E-2 9.438327038126082E-2 9.4602147035337092E-2 9.4821067464744058E-2 9.5040031678236936E-2 9.52590396845725E-2 9.5478091492509298E-2 9.569718711080788E-2 9.5916326548230124E-2 9.6135509813539688E-2 9.6354736915502448E-2 9.6574007862885614E-2 9.679332266445817E-2 9.7012681328991102E-2 9.7232083865256946E-2 9.7451530282030019E-2 9.767102058808641E-2 9.7890554792203988E-2 9.8110132903162395E-2 9.8329754929743052E-2 9.8549420880728933E-2 9.8769130764905011E-2 9.8988884591058035E-2 9.9208682367976309E-2 9.9428524104449911E-2 9.9648409809270699E-2 9.9868339491232527E-2 0.1000883131591308 0.10030833082176271 0.100528392487927 0.10074849816642462 0.10096864786605786 0.10118884159563102 0.10140907936395016 0.10162936117982291 0.10184968705205888 0.10207005698946925 0.10229047100086719 0.10251092909506743 0.10273143128088646 0.10295197756714258 0.10317256796265606 0.1033932024762485 0.10361388111674374 0.10383460389296717 0.10405537081374572 0.10427618188790855 0.10449703712428615 0.10471793653171102 0.10493888011901742 0.10515986789504117 0.10538089986862009 0.10560197604859378 0.10582309644380339 0.10604426106309206 0.10626546991530472 0.10648672300928785 0.10670802035388971 0.10692936195796054 0.10715074783035217 0.10737217797991816 0.10759365241551411 0.10781517114599715 0.10803673418022641 0.10825834152706237 0.10847999319536772 0.10870168919400669 0.10892342953184553 0.10914521421775181 0.1093670 4326059532 0.10958891666924742 0.10981083445258122 0.11003279661947163 0.11025480317879555 0.1104768541394312 0.11069894951025905 0.11092108930016109 0.11114327351802111 0.11136550217272467 0.11158777527315911 0.11181009282821375 0.11203245484677926 0.11225486133774853 0.11247731231001601 0.1126998077724779 0.11292234773403242 0.11314493220357913 0.11336756119001978 0.11359023470225771 0.11381295274919823 0.11403571533974799 0.11425852248281587 0.1144813741873123 0.1147042704621497 0.11492721131624206 0.11515019675850535 0.11537322679785711 0.11559630144321664 0.11581942070350526 0.11604258458764605 0.11626579310456364 0.11648904626318446 0.11671234407243714 0.11693568654125164 0.11715907367855993 0.11738250549329554 0.1176059819943942 0.11782950319079299 0.11805306909143121 0.11827667970524947 0.1185003350411904 0.11872403510819862 0.11894777991522032 0.11917156947120344 0.11939540378509772 0.11961928286585466 0.11984320672242776 0.12006717536377232 0.12029118879884515 0.12051524703660488 0.12073935008601211 0.12096349795602923 0.12118769065562041 0.12141192819375157 0.12163621057939022 0.12186053782150608 0.1220849099290704 0.12230932691105623 0.12253378877643839 0.12275829553419371 0.12298284719330055 0.12320744376273929 0.12343208525149185 0.12365677166854216 0.12388150302287593 0.1241062793234804 0.12433110057934504 0.1245559667994609 0.12478087799282078 0.12500583416841926 0.12523083533525292 0.1254558815023199 0.12568097267862033 0.12590610887315612 0.12613129009493074 0.12635651635294964 0.1265817876562203 0.1268071040137515 0.12703246543455426 0.12725787192764115 0.12748332350202674 0.12770882016672713 0.12793436193076047 0.12815994880314663 0.12838558079290729 0.12861125790906591 0.12883698016064771 0.1290627475566799 0.12928856010619127 0.12951441781821238 0.12974032070177599 0.12996626876591622 0.13019226201966938 0.13041830047207337 0.13064438413216783 0.13087051300899422 0.13109668711159594 0.13132290644901823 0.13154917103030805 0.13177548086451418 0.13200183596068715 0.13222823632787928 0.13245468197514487 0.1326811729115398 0.13290770914612215 0.13313429068795135 0.13336091754608881 0.13358758972959794 0.13381430724754373 0.13404107010899313 0.1342678783230149 0.13449473189867955 0.13472163084505917 0.13494857517122805 0.13517556488626226 0.1354025999992394 3 0.13562968051923918 0.13585680645534293 0.13608397781663406 0.13631119461219732 0.13653845685111965 0.13676576454248979 0.13699311769539824 0.13722051631893728 0.13744796042220098 0.13767545001428538 0.13790298510428811 0.13813056570130899 0.13835819181444919 0.1385858634528121 0.13881358062550264 0.13904134334162777 0.13926915161029596 0.13949700544061794 0.13972490484170597 0.13995284982267431 0.14018084039263878 0.14040887656071721 0.14063695833602941 0.14086508572769652 0.14109325874484213 0.14132147739659118 0.14154974169207057 0.14177805164040902 0.14200640725073699 0.14223480853218717 0.1424632554938936 0.1426917481449923 0.1429202864946213 0.14314887055192016 0.14337750032603047 0.14360617582609558 0.14383489706126085 0.14406366404067317 0.1 4429247677348123 0.14452133526883593 0.14475023953588972 0.14497918958379685 0.14520818542171354 0.1454372270587978 0.14566631450420964 0.14589544776711039 0.14612462685666383 0.14635385178203508 0.14658312255239148 0.1468124391769019 0.14704180166473724 0.14727121002507015 0.14750066426707509 0.14773016439992848 0.14795971043280853 0.14818930237489503 0.14841894023536994 0.14864862402341705 0.14887835374822167 0.14910812941897134 0.14933795104485514 0.14956781863506419 0.14979773219879111 0.15002769174523078 0.15025769728357985 0.1504877488230365 0.15071784637280117 0.15094798994207581 0.15117817954006418 0.15140841517597226 0.15163869685900733 0.15186902459837914 0.15209939840329878 0.15232981828297931 0.15256028424663581 0.15279079630348513 0.1530213544627459 0.1532519587336385 0.15348260912538514 0.1537133056472102 0.15394404830833963 0.15417483711800117 0.15440567208542477 0.15463655321984193 0.15486748053048593 0.15509845402659206 0.15532947371739736 0.15556053961214089 0.15579165172006326 0.1560228100504073 0.15625401461241739 0.15648526541533991 0.15671656246842303 0.15694790578091666 0.15717929536207276 0.15741073122114524 0.15764221336738937 0.15787374181006286 0.15810531655842475 0.15833693762173651 0.15856860500926073 0.15880031873026246 0.15903207879400849 0.1592638852097672 0.15949573798680916 0.15972763713440652 0.15995958266183341 0.16019157457836575 0.16042361289328144 0.16065569761586018 0.16088782875538343 0.16112000632113443 0.16135223032239865 0.16158450076846309 0.16181681766861677 0.16204918103215049 0.16228159086835681 0.16251404718653051 0.16274654999596772 0.16297909930596699 0.16321169512582823 0.16344433746485332 0.16367702633234615 0.16390976173761262 0.16414254368996017 0.16437537219869824 0.16460824727313805 0.1648411689225926 0.16507413715637709 0.1653071519838083 0.165540213414205 0.16577332145688772 0.16600647612117903 0.16623967741640322 0.1664729253518864 0.16670621993695667 0.16693956118094411 0.16717294909318037 0.16740638368299887 0.16763986495973549 0.16787339293272741 0.16810696761131383 0.16834058900483617 0.16857425712263718 0.16880797197406161 0.16904173356845642 0.16927554191517014 0.16950939702355305 0.1697432989029577 0.16997724756273835 0.17021124301225088 0.17044528526085334 0.17067937431790559 0.17091351019276924 0.171147 69289480769 0.17138192243338657 0.17161619881787327 0.17185052205763673 0.17208489216204814 0.17231930914048044 0.17255377300230856 0.17278828375690902 0.17302284141366031 0.17325744598194293 0.17349209747113936 0.17372679589063367 0.17396154124981167 0.17419633355806163 0.17443117282477316 0.17466605905933807 0.17490099227114997 0.17513597246960422 0.17537099966409819 0.17560607386403104 0.17584119507880391 0.17607636331781973 0.17631157859048319 0.17654684090620121 0.17678215027438249 0.17701750670443728 0.17725291020577805 0.17748836078781927 0.17772385845997674 0.1779594032316687 0.17819499511231496 0.17843063411133731 0.17866632023815954 0.17890205350220723 0.17913783391290772 0.17937366147969036 0.17960953621198628 0.17984545811922859 0.18008142721085241 0.18031744349629464 0.18055350698499395 0.18078961768639101 0.18102577560992827 0.18126198076505018 0.18149823316120317 0.18173453280783547 0.18197087971439707 0.18220727389033997 0.18244371534511794 0.18268020408818697 0.18291674012900461 0.18315332347703039 0.18338995414172587 0.18362663213255415 0.18386335745898053 0.18410013013047233 0.18433695015649842 0.18457381754652968 0.18481073231003897 0.18504769445650093 0.18528470399539221 0.18552176093619122 0.18575886528837837 0.18599601706143609 0.18623321626484834 0.18647046290810132 0.18670775700068298 0.18694509855208308 0.18718248757179357 0.18741992406930796 0.18765740805412179 0.18789493953573255 0.18813251852363977 0.1883701450273445 0.18860781905635005 0.18884554062016123 0.18908330972828513 0.1893211263902308 0.18955899061550885 0.1897969024136319 0.19003486179411455 0.19027286876647342 0.19051092334022668 0.1907490255248947 0.19098717532999965 0.19122537276506568 0.19146361783961874 0.19170191056318653 0.19194025094529921 0.19217863899548826 0.1924170747232874 0.1926555581382321 0.19289408924985962 0.19313266806770968 0.1933712946013233 0.19360996886024351 0.19384869085401557 0.19408746059218629 0.19432627808430469 0.19456514333992159 0.19480405636858955 0.19504301717986317 0.19528202578329901 0.19552108218845565 0.19576018640489323 0.1959993384421741 0.1962385383098626 0.19647778601752464 0.19671708157472811 0.19695642499104293 0.19719581627604121 0.19743525543929641 0.19767474249038419 0.19791427743888224 0.19815386029436999 0.1983934910664289 0.1986331697646 4218 0.19887289639859507 0.19911267097787477 0.19935249351207029 0.19959236401077263 0.19983228248357476 0.20007224894007147 0.20031226338985952 0.20055232584253746 0.20079243630770605 0.2010325947949676 0.20127280131392666 0.20151305587418933 0.20175335848536413 0.20199370915706116 0.20223410789889251 0.20247455472047227 0.20271504963141629 0.20295559264134244 0.20319618375987059 0.20343682299662258 0.20367751036122184 0.20391824586329399 0.20415902951246667 0.20439986131836907 0.20464074129063281 0.20488166943889086 0.20512264577277861 0.20536367030193303 0.2056047430359933 0.20584586398460036 0.20608703315739718 0.2063282505640287 0.20656951621414144 0.20681083011738433 0.20705219228340788 0.20729360272186459 0.20753506144240896 0.2077765684546975 0.20801812376838846 0.20825972739314214 0.20850137933862078 0.20874307961448846 0.20898482823041142 0.2092266251960575 0.20946847052109674 0.20971036421520095 0.20995230628804396 0.21019429674930157 0.21043633560865138 0.21067842287577299 0.21092055856034819 0.21116274267206014 0.21140497522059443 0.21164725621563862 0.21188958566688165 0.21213196358401509 0.21237438997673186 0.21261686485472708 0.2128593882276979 0.21310196010534344 0.21334458049736438 0.21358724941346385 0.21382996686334654 0.21407273285671913 0.21431554740329051 0.21455841051277114 0.21480132219487369 0.21504428245931262 0.21528729131580437 0.2155303487740674 0.21577345484382215 0.21601660953479085 0.21625981285669771 0.21650306481926895 0.2167463654322328 0.21698971470531925 0.21723311264826028 0.2174765592707899 0.2177200545826441 0.21796359859356063 0.21820719131327926 0.21845083275154198 0.21869452291809233 0.21893826182267584 0.21918204947504027 0.21942588588493517 0.21966977106211205 0.21991370501632446 0.22015768775732769 0.22040171929487906 0.22064579963873809 0.22088992879866587 0.22113410678442547 0.22137833360578241 0.22162260927250355 0.22186693379435796 0.22211130718111671 0.22235572944255289 0.22260020058844132 0.22284472062855909 0.22308928957268481 0.22333390743059933 0.22357857421208549 0.2238232899269279 0.22406805458491319 0.22431286819583018 0.22455773076946928 0.22480264231562308 0.2250476028440862 0.22529261236465503 0.22553767088712795 0.22578277842130534 0.22602793497698959 0.22627314056398506 0.22651839519209793 0.22676369887113634 0.22700905161091045 0.22725445342123263 0.2274999043119168 0.22774540429277912 0.22799095337363773 0.22823655156431233 0.22848219887462506 0.22872789531439985 0.22897364089346262 0.22921943562164127 0.2294652795087655 0.22971117256466722 0.22995711479918013 0.23020310622213991 0.23044914684338424 0.23069523667275282 0.23094137572008733 0.23118756399523122 0.23143380150803017 0.23168008826833164 0.23192642428598531 0.23217280957084241 0.23241924413275661 0.23266572798158314 0.23291226112717944 0.23315884357940475 0.23340547534812051 0.23365215644319015 0.23389888687447868 0.23414566665185355 0.23439249578518395 0.2346393742843409 0.23488630215919781 0.23513327941962969 0.23538030607551352 0.23562738213672851 0.23587450761315587 0.23612168251467858 0.23636890685118139 0.23661618063255152 0.23686350386867794 0.23711087656945162 0.23735829874476555 0.23760577040451447 0.23785329155859536 0.23810086221690696 0.23834848238935025 0.23859615208582818 0.23884387131624529 0.23909164009050854 0.23933945841852666 0.2395873263102104 0.2398352437754725 0.24008321082422746 0.24033122746639224 0.24057929371188558 0.24082740957062798 0.24107557505254218 0.24132379016755268 0.2415720549255862 0.24182036933657125 0.24206873341043855 0.2423171471571206 0.24256561058655191 0.24281412370866917 0.2430626865334109 0.24331129907071758 0.2435599613305317 0.24380867332279776 0.24405743505746225 0.24430624654447364 0.24455510779378242 0.24480401881534108 0.24505297961910411 0.24530199021502797 0.24555105061307092 0.24580016082319345 0.24604932085535802 0.24629853071952912 0.24654779042567299 0.24679709998375809 0.24704645940375491 0.24729586869563569 0.24754532786937489 0.24779483693494875 0.24804439590233573 0.24829400478151609 0.24854366358247226 0.24879337231518872 0.2490431309896517 0.24929293961584964 0.24954279820377279 0.24979270676341359 0.25004266530476627 0.25029267383782727 0.25054273237259483 0.25079284091906939 0.25104299948725317 0.25129320808715061 0.25154346672876793 0.25179377542211356 0.25204413417719795 0.25229454300403331 0.25254500191263407 0.25279551091301666 0.2530460700151993 0.2532966792292024 0.25354733856504819 0.25379804803276107 0.2540488076423677 0.25429961740389606 0.25455047732737679 0.25480138742284231 0.25505234770032681 0.25530335816986693 0.25555441884150087 0.25580552972526904 0.25605669083121407 0.25630790216938037 0.25655916374981413 0.25681047558256398 0.25706183767768054 0.25731325004521599 0.25756471269522496 0.25781622563776407 0.2580677888828915 0.25831940244066809 0.25857106632115623 0.25882278053442054 0.25907454509052741 0.25932635999954545 0.25957822527154528 0.25983014091659951 0.26008210694478273 0.26033412336617157 0.26058619019084484 0.26083830742888292 0.26109047509036865 0.26134269318538661 0.26159496172402363 0.26184728071636831 0.26209965017251147 0.26235207010254591 0.26260454051656645 0.26285706142466969 0.26310963283695465 0.26336225476352193 0.26361492721447455 0.26386765019991731 0.26412042372995725 0.26437324781470317 0.26462612246426609 0.26487904768875881 0.26513202349829657 0.26538504990299616 0.26563812691297684 0.26589125453835938 0.26614443278926703 0.26639766167582479 0.26665094120815991 0.2669042713964016 0.26715765225068089 0.26741108378113099 0.26766456599788713 0.26791809891108676 0.26817168253086887 0.26842531686737492 0.26867900193074834 0.26893273773113435 0.26918652427868062 0.26944036158353635 0.26969424965585298 0.26994818850578417 0.27020217814348535 0.27045621857911395 0.27071030982282984 0.27096445188479445 0.27121864477517144 0.27147288850412643 0.27172718308182731 0.2719815285184437 0.27223592482414727 0.27249037200911208 0.27274487008351378 0.27299941905753045 0.27325401894134194 0.27350866974513011 0.27376337147907903 0.27401812415337479 0.27427292777820544 0.27452778236376107 0.27478268792023375 0.27503764445781775 0.27529265198670938 0.27554771051710669 0.27580282005920997 0.27605798062322173 0.27631319221934625 0.27656845485779002 0.27682376854876156 0.27707913330247136 0.27733454912913191 0.27759001603895772 0.2778455340421655 0.27810110314897396 0.27835672336960382 0.27861239471427779 0.27886811719322058 0.27912389081665911 0.27937971559482233 0.27963559153794137 0.27989151865624895 0.2801474969599802 0.28040352645937228 0.28065960716466409 0.28091573908609702 0.28117192223391418 0.28142815661836096 0.2816844422496847 0.28194077913813453 0.28219716729396205 0.28245360672742081 0.28271009744876618 0.28296663946825595 0.28322323279614947 0.28347987744270875 0.28373657341819736 0.28399332073288086 0.28425011939702749 0.28450696942090681 0.28476387081479104 0.28502082358895398 0.28527782775367183 0.28553488331922261 0.28579199029588653 0.2860491486939456 0.28630635852368447 0.28656361979538914 0.28682093251934826 0.28707829670585205 0.28733571236519317 0.28759317950766627 0.28785069814356778 0.28810826828319658 0.28836588993685308 0.28862356311484039 0.28888128782746336 0.28913906408502887 0.28939689189784579 0.28965477127622541 0.2899127022304806 0.29017068477092667 0.29042871890788091 0.29068680465166241 0.29094494201259269 0.29120313100099526 0.29146137162719543 0.29171966390152093 0.29197800783430128 0.29223640343586821 0.29249485071655545 0.29275334968669875 0.29301190035663605 0.29327050273670729 0.29352915683725467 0.29378786266862211 0.2940466202411558 0.29430542956520389 0.294564290651117 0.29482320350924729 0.29508216814994914 0.29534118458357916 0.29560025282049596 0.29585937287106012 0.29611854474563426 0.29637776845458341 0.2966370440082744 0.29689637141707603 0.29715575069135935 0.29741518184149762 0.29767466487786587 0.29793419981084135 0.29819378665080354 0.29845342540813369 0.29871311609321527 0.29897285871643398 0.29923265328817727 0.29949249981883486 0.29975239831879863 0.30001234879846228 0.30027235126822194 0.30053240573847551 0.30079251221962311 0.30105267072206709 0.30131288125621158 0.3015731438324627 0.30183345846122922 0.30209382515292149 0.30235424391795207 0.30261471476673574 0.30287523770968905 0.303135812757231 0.30339643991978238 0.30365711920776639 0.30391785063160781 0.30417863420173408 0.3044394699285744 0.30470035782256 0.30496129789412452 0.30522229015370339 0.30548333461173405 0.30574443127865636 0.30600558016491197 0.30626678128094498 0.30652803463720124 0.30678934024412863 0.30705069811217744 0.30731210825179978 0.30757357067345015 0.30783508538758486 0.30809665240466244 0.30835827173514341 0.3086199433894905 0.30888166737816847 0.30914344371164404 0.3094052724003864 0.30966715345486651 0.30992908688555754 0.31019107270293467 0.31045311091747529 0.31071520153965881 0.31097734457996662 0.31123954004888255 0.31150178795689221 0.31176408831448366 0.3120264411321465 0.3122888464203728 0.31255130418965682 0.31281381445049483 0.31307637721338488 0.31333899248882746 0.31360166028732528 0.31386438061938282 0.31412715349550657 0.31438997892620568 0.31465285692199085 0.31491578749337523 0.31517877065087396 0.31544180640500419 0.31570489476628505 0.31596803574523835 0.31623122935238746 0.31649447559825794 0.31675777449337761 0.31702112604827626 0.31728453027348591 0.31754798717954058 0.31781149677697651 0.31807505907633193 0.31833867408814709 0.31860234182296465 0.3188660622913293 0.31912983550378748 0.31939366147088832 0.31965754020318249 0.31992147171122309 0.32018545600556525 0.32044949309676629 0.32071358299538555 0.32097772571198457 0.32124192125712692 0.32150616964137835 0.32177047087530664 0.32203482496948177 0.32229923193447574 0.32256369178086253 0.32282820451921856 0.32309277016012228 0.32335738871415431 0.3236220601918971 0.3238867846039355 0.32415156196085615 0.32441639227324837 0.32468127555170301 0.32494621180681338 0.32521120104917478 0.32547624328938451 0.32574133853804232 0.32600648680574995 0.32627168810311113 0.32653694244073184 0.32680224982922002 0.32706761027918585 0.32733302380124174 0.32759849040600186 0.32786401010408306 0.32812958290610394 0.32839520882268514 0.32866088786444969 0.32892662004202244 0.32919240536603089 0.32945824384710409 0.32972413549587354 0.32999008032297272 0.33025607833903736 0.33052212955470517 0.33078823398061608 0.33105439162741224 0.33132060250573758 0.33158686662623871 0.33185318399956398 0.33211955463636378 0.33238597854729113 0.33265245574300062 0.33291898623414928 0.33318557003139615 0.33345220714540247 0.33371889758683149 0.3339856413663489 0.33425243849462216 0.33451928898232097 0.33478619284011746 0.33505315007868552 0.3353201607087013 0.3355872247408429 0.33585434218579113 0.33612151305422833 0.33638873735683905 0.33665601510431031 0.33692334630733112 0.33719073097659247 0.33745816912278781 0.33772566075661237 0.33799320588876358 0.33826080452994134 0.3385284566908473 0.33879616238218535 0.33906392161466181 0.33933173439898479 0.33959960074586459 0.33986752066601378 0.34013549417014688 0.34040352126898088 0.34067160197323454 0.34093973629362906 0.34120792424088786 0.34147616582573592 0.34174446105890111 0.34201280995111283 0.34228121251310295 0.34254966875560555 0.34281817868935671 0.34308674232509451 0.34335535967355946 0.34362403074549408 0.34389275555164311 0.34416153410275352 0.34443036640957403 0.34469925248285582 0.3449681923333523 0.34523718597181885 0.3455062334090131 0.34577533465569488 0.34604448972262603 0.3463136986205706 0.34658296136029465 0.34685227795256668 0.34712164840815718 0.34739107273783887 0.34766055095238646 0.34793008306257689 0.34819966907918931 0.3484693090130051 0.34873900287480764 0.34900875067538251 0.34927855242551753 0.34954840813600252 0.34981831781762973 0.3500882814811932 0.35035829913748939 0.35062837079731679 0.35089849647147631 0.35116867617077063 0.35143890990600468 0.35170919768798581 0.35197953952752337 0.35224993543542893 0.35252038542251607 0.35279088949960058 0.35306144767750047 0.35333205996703598 0.35360272637902934 0.35387344692430522 0.35414422161369008 0.3544150504580128 0.35468593346810429 0.35495687065479786 0.35522786202892886 0.35549890760133462 0.35577000738285491 0.35604116138433151 0.35631236961660839 0.35658363209053179 0.3568549488169499 0.35712631980671317 0.35739774507067446 0.35766922461968864 0.3579407584646126 0.35821234661630541 0.35848398908562862 0.35875568588344575 0.35902743702062234 0.35929924250802636 0.35957110235652801 0.35984301657699924 0.36011498518031471 0.36038700817735081 0.36065908557898618 0.3609312173961019 0.36120340363958103 0.36147564432030888 0.36174793944917294 0.36202028903706274 0.36229269309487022 0.36256515163348912 0.36283766466381584 0.36311023219674854 0.36338285424318784 0.36365553081403634 0.36392826192019911 0.3642010475725832 0.36447388778209766 0.36474678255965398 0.36501973191616588 0.36529273586254907 0.36556579440972148 0.36583890756860349 0.36611207535011725 0.36638529776518713 0.36665857482474018 0.3669319065397052 0.367205292921013 0.36747873397959707 0.36775222972639288 0.36802578017233811 0.36829938532837248 0.3685730452054381 0.36884675981447912 0.36912052916644189 0.36939435327227521 0.36966823214292965 0.36994216578935823 0.37021615422251597 0.37049019745336054 0.37076429549285117 0.37103844835194977 0.37131265604162023 0.37158691857282844 0.37186123595654297 0.37213560820373415 0.37241003532537476 0.37268451733243979 0.37295905423590625 0.37323364604675335 0.37350829277596276 0.3737829944345179 0.37405775103340488 0.37433256258361158 0.37460742909612832 0.37488235058194741 0.37515732705206384 0.37543235851747414 0.37570744498917752 0.3759825864781754 0.37625778299547097 0.3765330345520701 0.37680834115898043 0.37708370282721226 0.37735911956777768 0.3776345913916912 0.37791011830996957 0.37818570033363152 0.37846133747369826 0.37873702974119294 0.37901277714714121 0.37928857970257068 0.3795644374185112 0.37984035030599483 0.38011631837605608 0.38039234163973124 0.38066842010805924 0.38094455379208081 0.38122074270283912 0.38149698685137956 0.38177328624874973 0.38204964090599947 0.38232605083418059 0.38260251604434736 0.38287903654755628 0.38315561235486584 0.38343224347733673 0.38370892992603212 0.38398567171201736 0.38426246884635984 0.38453932134012914 0.38481622920439706 0.38509319245023788 0.38537021108872782 0.38564728513094559 0.38592441458797166 0.38620159947088917 0.38647883979078324 0.38675613555874144 0.38703348678585314 0.38731089348321035 0.38758835566190686 0.38786587333303912 0.3881434465077056 0.38842107519700719 0.38869875941204657 0.38897649916392885 0.38925429446376159 0.38953214532265434 0.3898100517517189 0.39008801376206925 0.39036603136482162 0.39064410457109466 0.39092223339200882 0.3912004178386872 0.39147865792225489 0.39175695365383922 0.39203530504456996 0.39231371210557886 0.39259217484799991 0.39287069328296953 0.39314926742162615 0.39342789727511041 0.39370658285456539 0.39398532417113619 0.39426412123597032 0.39454297406021754 0.3948218826550296 0.39510084703156068 0.39537986720096696 0.39565894317440709 0.3959380749630419 0.39621726257803447 0.39649650603055009 0.39677580533175627 0.39705516049282252 0.39733457152492102 0.39761403843922594 0.39789356124691366 0.39817313995916304 0.39845277458715489 0.39873246514207228 0.3990122116351007 0.39929201407742765 0.39957187248024306 0.3998517868547391 0.40013175721210992 0.40041178356355234 0.40069186592026496 0.40097200429344904 0.40125219869430762 0.4015324491340464 0.40181275562387309 0.40209311817499782 0.40237353679863275 0.40265401150599245 0.40293454230829351 0.40321512921675517 0.40349577224259847 0.40377647139704687 0.40405722669132627 0.40433803813666458 0.40461890574429193 0.40489982952544068 0.40518080949134583 0.40546184565324417 0.40574293802237471 0.40602408660997913 0.4063052914273011 0.40658655248558651 0.40686786979608369 0.40714924337004277 0.40743067321871673 0.40771215935336036 0.40799370178523109 0.40827530052558814 0.40855695558569316 0.40883866697681026 0.40912043471020554 0.40940225879714753 0.40968413924890701 0.40996607607675672 0.41024806929197211 0.41053011890583058 0.41081222492961178 0.41109438737459758 0.41137660625207251 0.41165888157332287 0.4119412133496374 0.41222360159230731 0.41250604631262577 0.4127885475218882 0.41307110523139245 0.41335371945243859 0.41363639019632914 0.41391911747436838 0.41420190129786327 0.41448474167812277 0.41476763862645827 0.41505059215418361 0.4153336022726144 0.41561666899306893 0.41589979232686747 0.41618297228533274 0.41646620887978969 0.4167495021215657 0.41703285202198992 0.41731625859239418 0.41759972184411254 0.41788324178848124 0.41816681843683901 0.41845045180052631 0.41873414189088631 0.41901788871926438 0.41930169229700809 0.41958555263546748 0.41986946974599459 0.42015344363994367 0.42043747432867162 0.42072156182353737 0.42100570613590205 0.42128990727712923 0.42157416525858471 0.42185848009163629 0.42214285178765465 0.42242728035801225 0.42271176581408376 0.42299630816724654 0.42328090742887992 0.42356556361036568 0.42385027672308762 0.42413504677843217 0.42441987378778778 0.42470475776254535 0.42498969871409775 0.42527469665384054 0.42555975159317128 0.42584486354348994 0.42613003251619852 0.42641525852270168 0.42670054157440629 0.42698588168272122 0.4272712788590578 0.42755673311482956 0.42784224446145247 0.42812781291034474 0.42841343847292679 0.42869912116062125 0.42898486098485344 0.42927065795705044 0.42955651208864176 0.42984242339105938 0.43012839187573748 0.43041441755411269 0.43070050043762342 0.43098664053771096 0.43127283786581838 0.43155909243339141 0.43184540425187801 0.43213177333272834 0.43241819968739481 0.43270468332733225 0.43299122426399772 0.4332778225088505 0.4335644780733523 0.43385119096896685 0.43413796120716053 0.43442478879940194 0.43471167375716169 0.43499861609191304 0.43528561581513148 0.43557267293829449 0.43585978747288201 0.43614695943037662 0.4364341888222627 0.43672147566002706 0.43700881995515894 0.43729622171914984 0.43758368096349365 0.4378711976996863 0.43815877193922614 0.43844640369361398 0.43873409297435262 0.43902183979294751 0.43930964416090612 0.43959750608973835 0.43988542559095634 0.44017340267607441 0.44046143735660959 0.44074952964408087 0.44103767955000972 0.4413258870859198 0.441614152263337 0.44190247509378966 0.44219085558880833 0.44247929375992601 0.44276778961867791 0.4430563431766017 0.44334495444523703 0.443633623436126 0.44392235016081316 0.44421113463084527 0.44449997685777132 0.44478887685314294 0.44507783462851358 0.44536685019543931 0.44565592356547845 0.44594505475019153 0.44623424376114151 0.4465234906098936 0.44681279530801565 0.4471021578670773 0.44739157829865062 0.44768105661431035 0.44797059282563323 0.44826018694419822 0.44854983898158696 0.44883954894938327 0.44912931685917301 0.44941914272254491 0.44970902655108946 0.44999896835639963 0.4502889681500708 0.45057902594370081 0.45086914174888948 0.45115931557723932 0.45144954744035481 0.45173983734984291 0.45203018531731276 0.45232059135437619 0.45261105547264702 0.45290157768374151 0.45319215799927814 0.45348279643087808 0.45377349299016423 0.45406424768876219 0.45435506053829999 0.45464593155040767 0.45493686073671769 0.45522784810886496 0.45551889367848664 0.45580999745722228 0.4561011594567137 0.45639237968860491 0.45668365816454259 0.45697499489617543 0.45726638989515456 0.45755784317313353 0.45784935474176813 0.45814092461271638 0.45843255279763895 0.4587242393081985 0.45901598415606015 0.45930778735289124 0.45959964891036176 0.45989156884014371 0.46018354715391174 0.46047558386334253 0.46076767898011517 0.46105983251591121 0.4613520444824144 0.46164431489131075 0.46193664375428889 0.4622290310830397 0.46252147688925627 0.46281398118463413 0.46310654398087103 0.46339916528966718 0.46369184512272499 0.46398458349174954 0.4642773804084479 0.46457023588452961 0.46486314993170641 0.4651561225616927 0.46544915378620511 0.46574224361696226 0.46603539206568567 0.46632859914409885 0.46662186486392754 0.46691518923690034 0.46720857227474766 0.46750201398920255 0.46779551439200029 0.4680890734948786 0.46838269130957766 0.46867636784783961 0.46897010312140908 0.46926389714203331 0.4695577499214616 0.46985166147144586 0.47014563180374003 0.4704396609301007 0.47073374886228669 0.47102789561205904 0.47132210119118145 0.47161636561141962 0.47191068888454191 0.47220507102231868 0.47249951203652318 0.47279401193893045 0.47308857074131816 0.47338318845546645 0.47367786509315746 0.47397260066617597 0.47426739518630923 0.47456224866534646 0.47485716111507958 0.47515213254730249 0.47544716297381195 0.47574225240640677 0.47603740085688795 0.47633260833705937 0.47662787485872671 0.47692320043369851 0.47721858507378512 0.47751402879079974 0.47780953159655781 0.478105093502877 0.47840071452157762 0.47869639466448199 0.47899213394341489 0.47928793237020351 0.4795837899566775 0.47987970671466873 0.48017568265601174 0.48047171779254283 0.4807678121361012 0.4810639656985285 0.48136017849166812 0.48165645052736639 0.48195278181747181 0.48224917237383536 0.48254562220830999 0.48284213133275156 0.48313869975901813 0.48343532749897 0.48373201456446968 0.48402876096738257 0.48432556671957605 0.48462243183291998 0.48491935631928662 0.48521634019055049 0.48551338345858852 0.48581048613528011 0.48610764823250707 0.48640486976215347 0.48670215073610579 0.48699949116625296 0.48729689106448615 0.48759435044269894 0.48789186931278739 0.48818944768664996 0.48848708557618736 0.48878478299330252 0.48908253994990125 0.48938035645789113 0.48967823252918263 0.48997616817568845 0.4902741634093235 0.49057221824200536 0.49087033268565383 0.49116850675219093 0.49146674045354133 0.49176503380163195 0.49206338680839234 0.49236179948575409 0.4926602718456512 0.49295880390002034 0.4932573956608004 0.49355604713993251 0.49385475834936043 0.49415352930103018 0.49445236000689041 0.49475125047889179 0.49505020072898764 0.49534921076913352 0.49564828061128741 0.49594741026740974 0.49624659974946317 0.49654584906941301 0.49684515823922681 0.49714452727087455 0.49744395617632864 0.49774344496756395 0.49804299365655735 0.49834260225528859 0.49864227077573964 0.49894199922989468 0.49924178762974059 0.49954163598726642 0.49984154431446393 0.50014151262332684 0.50044154092585158 0.50074162923403676 0.50104177755988344 0.50134198591539536 0.50164225431257847 0.50194258276344095 0.50224297127999362 0.50254341987424955 0.50284392855822446 0.50314449734393607 0.50344512624340476 0.50374581526865336 0.50404656443170714 0.50434737374459337 0.50464824321934221 0.50494917286798602 0.50525016270255962 0.50555121273510006 0.50585232297764704 0.50615349344224247 0.50645472414093096 0.50675601508575907 0.50705736628877629 0.50735877776203409 0.50766024951758637 0.50796178156748995 0.50826337392380339 0.50856502659858815 0.50886673960390794 0.50916851295182863 0.50947034665441904 0.50977224072374994 0.51007419517189456 0.51037621001092881 0.51067828525293102 0.51098042090998153 0.51128261699416355 0.51158487351756232 0.51188719049226572 0.51218956793036408 0.51249200584395016 0.51279450424511897 0.51309706314596792 0.51339968255859714 0.51370236249510892 0.51400510296760782 0.51430790398820125 0.51461076556899887 0.51491368772211255 0.51521667045965702 0.51551971379374883 0.51582281773650762 0.5161259823000548 0.51642920749651489 0.51673249333801419 0.51703583983668167 0.5173392470046489 5 0.51764271485404989 0.51794624339702056 0.5182498326456999 0.51855348261222911 0.51885719330875157 0.51916096474741336 0.51946479694036274 0.51976868989975067 0.52007264363773054 0.52037665816645795 0.52068073349809119 0.52098486964479074 0.52128906661871977 0.52159332443204343 0.52189764309692976 0.52220202262554904 0.5225064630300742 0.52281096432268015 0.52311552651554472 0.52342014962084771 0.52372483365077183 0.52402957861750199 0.52433438453322556 0.52463925141013212 0.52494417926041415 0.52524916809626609 0.52555421792988533 0.52585932877347119 0.52616450063922593 0.52646973353935378 0.52677502748606164 0.52708038249155886 0.52738579856805723 0.52769127572777075 0.52799681398291631 0.52830241334571282 0.52860807382838182 0.52891379544314 754 0.5292195782022362 0.52952542211787668 0.52983132720230031 0.53013729346774063 0.53044332092643409 0.53074940959061934 0.53105555947253746 0.53136177058443201 0.53166804293854897 0.53197437654713675 0.53228077142244623 0.53258722757673072 0.53289374502224596 0.53320032377125037 0.5335069638360046 0.53381366522877172 0.53412042796181747 0.53442725204740982 0.53473413749781917 0.53504108432531861 0.53534809254218363 0.53565516216069198 0.53596229319312405 0.53626948565176269 0.53657673954889296 0.5368840548968028 0.53719143170778216 0.53749886999412366 0.53780636976812235 0.53811393104207594 0.53842155382828438 0.53872923813905005 0.53903698398667776 0.53934479138347502 0.53965266034175174 0.53996059087382009 0.54026858299199487 0.5405766367085 9313 0.54088475203593478 0.54119292898634197 0.54150116757213929 0.54180946780565375 0.54211782969921485 0.5424262532651547 0.54273473851580767 0.54304328546351077 0.54335189412060347 0.54366056449942746 0.54396929661232729 0.54427809047164977 0.54458694608974412 0.54489586347896202 0.54520484265165781 0.54551388362018804 0.54582298639691196 0.54613215099419121 0.54644137742438992 0.54675066569987485 0.54706001583301478 0.54736942783618137 0.54767890172174849 0.5479884375020927 0.54829803518959297 0.54860769479663096 0.54891741633559032 0.54922719981885737 0.54953704525882108 0.54984695266787287 0.55015692205840638 0.55046695344281793 0.55077704683350648 0.55108720224287322 0.55139741968332179 0.55170769916725848 0.55201804070709182 0.55232844431 52332 0.55263891000409626 0.55294943778609706 0.55326002767365434 0.55357067967918905 0.5538813938151248 0.55419217009388788 0.55450300852790657 0.55481390912961204 0.55512487191143789 0.55543589688582018 0.5557469840651974 0.5560581334620105 0.55636934508870284 0.55668061895772047 0.55699195508151189 0.55730335347252824 0.55761481414322267 0.55792633710605122 0.55823792237347236 0.55854956995794702 0.55886127987193857 0.55917305212791302 0.55948488673833863 0.55979678371568631 0.56010874307242942 0.56042076482104397 0.56073284897400821 0.56104499554380305 0.56135720454291183 0.56166947598382033 0.56198180987901702 0.5622942062409928 0.562606665082241 0.5629191864152574 0.56323177025254045 0.56354441660659083 0.56385712548991207 0.564169896915009 96 0.56448273089439294 0.56479562744057188 0.56510858656605989 0.56542160828337296 0.56573469260502951 0.56604783954355042 0.56636104911145901 0.56667432132128126 0.56698765618554559 0.56730105371678263 0.56761451392752593 0.56792803683031146 0.5682416224376774 0.56855527076216483 0.56886898181631729 0.5691827556126805 0.56949659216380311 0.56981049148223573 0.5701244535805321 0.57043847847124818 0.57075256616694237 0.57106671668017572 0.57138093002351176 0.57169520620951642 0.57200954525075831 0.5723239471598085 0.57263841194924048 0.57295293963163019 0.57326753021955645 0.57358218372560033 0.57389690016234551 0.57421167954237795 0.57452652187828646 0.57484142718266207 0.57515639546809849 0.57547142674719209 0.57578652103254147 0.576101678336747 86 0.57641689867241519 0.5767321820521496 0.57704752848855989 0.57736293799425753 0.57767841058185643 0.57799394626397271 0.5783095450532254 0.57862520696223596 0.57894093200362828 0.57925672019002894 0.57957257153406694 0.57988848604837373 0.58020446374558343 0.5805205046383326 0.58083660873926024 0.58115277606100801 0.58146900661622025 0.5817853004175435 0.58210165747762699 0.58241807780912258 0.58273456142468438 0.58305110833696938 0.58336771855863678 0.58368439210234846 0.58400112898076895 0.584317929206565 0.58463479279240627 0.5849517197509646 0.58526871009491477 0.58558576383693373 0.58590288098970111 0.58622006156589901 0.58653730557821215 0.58685461303932773 0.5871719839619356 0.58748941835872803 0.58780691624239978 0.58812447762564823 0.58844210252117324 0.58875979094167752 0.5890775428998658 0.5893953584084457 0.58971323748012727 0.59003118012762323 0.59034918636364875 0.59066725620092142 0.59098538965216152 0.59130358673009198 0.59162184744743795 0.59194017181692749 0.59225855985129083 0.59257701156326115 0.59289552696557379 0.59321410607096681 0.59353274889218088 0.59385145544195939 0.59417022573304767 0.59448905977819422 0.59480795759014993 0.59512691918166793 0.59544594456550426 0.59576503375441736 0.59608418676116814 0.5964034035985204 0.59672268427924013 0.59704202881609603 0.59736143722185919 0.59768090950930364 0.59800044569120536 0.59832004578034348 0.59863970978949954 0.59895943773145732 0.59927922961900348 0.59959908546492735 0.59991900528202025 0.6002389890830766 0.60055903688089307 0.60087914868826919 0.60119932451800673 0.60151956438291032 0.60183986829578684 0.60216023626944604 0.60248066831669989 0.60280116445036325 0.6031217246832532 0.60344234902818972 0.60376303749799543 0.60408379010549496 0.60440460686351605 0.60472548778488866 0.60504643288244564 0.60536744216902205 0.60568851565745585 0.60600965336058721 0.60633085529125919 0.60665212146231751 0.60697345188660989 0.60729484657698718 0.60761630554630264 0.60793782880741176 0.60825941637317316 0.60858106825644787 0.60890278447009916 0.60922456502699318 0.60954640993999853 0.60986831922198648 0.61019029288583093 0.61051233094440804 0.61083443341059684 0.61115660029727903 0.61147883161733851 0.61180112738366188 0.61212348760913859 0.6124459123066603 4 0.61276840148912171 0.61309095516941947 0.61341357336045332 0.61373625607512539 0.61405900332634045 0.61438181512700574 0.61470469149003115 0.61502763242832903 0.61535063795481459 0.61567370808240551 0.6159968428240219 0.61632004219258674 0.61664330620102525 0.61696663486226533 0.61729002818923773 0.61761348619487544 0.61793700889211434 0.61826059629389274 0.61858424841315141 0.61890796526283398 0.61923174685588656 0.61955559320525766 0.61987950432389871 0.62020348022476335 0.62052752092080832 0.62085162642499236 0.62117579675027734 0.62150003190962733 0.62182433191600928 0.62214869678239237 0.62247312652174891 0.62279762114705317 0.62312218067128256 0.62344680510741668 0.62377149446843805 0.62409624876733161 0.62442106801708497 0.6247459522306 8841 0.62507090142113442 0.62539591560141861 0.6257209947845388 0.6260461389834957 0.62637134821129226 0.6266966224809345 0.62702196180543068 0.62734736619779174 0.62767283567103127 0.62799837023816552 0.62832396991221318 0.62864963470619561 0.62897536463313686 0.62930115970606337 0.62962701993800452 0.62995294534199209 0.63027893593106055 0.6306049917182468 0.63093111271659041 0.63125729893913363 0.63158355039892133 0.6319098671090011 0.63223624908242293 0.63256269633223927 0.63288920887150568 0.63321578671327994 0.63354242987062248 0.63386913835659664 0.63419591218426796 0.63452275136670488 0.63484965591697828 0.6351766258481617 0.63550366117333135 0.63583076190556587 0.63615792805794702 0.63648515964355856 0.63681245667548714 0.637139819166822 27 0.6374672471306555 0.63779474058008168 0.63812229952819766 0.63844992398810319 0.63877761397290067 0.63910536949569519 0.63943319056959425 0.63976107720770803 0.6400890294231496 0.64041704722903425 0.64074513063847993 0.6410732796646077 0.64140149432054061 0.64172977461940461 0.64205812057432854 0.64238653219844344 0.64271500950488303 0.64304355250678391 0.64337216121728513 0.64370083564952862 0.64402957581665854 0.64435838173182192 0.64468725340816824 0.64501619085884987 0.64534519409702162 0.64567426313584098 0.64600339798846806 0.64633259866806569 0.64666186518779933 0.64699119756083689 0.64732059580034895 0.64765005991950897 0.64797958993149285 0.64830918584947916 0.64863884768664892 0.64896857545618625 0.64929836917127748 0.64962822884511 162 0.64995815449088057 0.65028814612177865 0.65061820375100288 0.65094832739175312 0.6512785170572315 0.651608772760643 0.65193909451519505 0.65226948233409798 0.65259993623056478 0.65293045621781087 0.65326104230905435 0.6535916945175162 0.65392241285641961 0.6542531973389909 0.65458404797845859 0.65491496478805433 0.65524594778101197 0.65557699697056804 0.65590811236996216 0.65623929399243619 0.65657054185123465 0.65690185595960493 0.65723323633079689 0.65756468297806303 0.65789619591465853 0.65822777515384145 0.65855942070887208 0.6588911325930138 0.65922291081953244 0.65955475540169628 0.65988666635277649 0.6602186436860471 0.66055068741478418 0.66088279755226709 0.66121497411177743 0.66154721710659969 0.66187952655002102 0.66221190245533101 0.66254434483582214 0.66287685370478933 0.66320942907553015 0.66354207096134532 0.66387477937553752 0.66420755433141254 0.66454039584227886 0.66487330392144739 0.66520627858223169 0.66553931983794801 0.66587242770191546 0.66620560218745584 0.66653884330789337 0.66687215107655495 0.66720552550677015 0.6675389666118714 0.66787247440519382 0.66820604890007473 0.66853969010985481 0.66887339804787671 0.6692071727274862 0.66954101416203171 0.66987492236486412 0.67020889734933697 0.67054293912880691 0.67087704771663259 0.67121122312617598 0.67154546537080129 0.67187977446387537 0.6722141504187682 0.67254859324885197 0.67288310296750176 0.67321767958809531 0.67355232312401281 0.67388703358863755 0.67422181099535528 0.67455665535755438 0.6748915666886259 3 0.67522654500196366 0.67556159031096397 0.67589670262902612 0.67623188196955186 0.67656712834594579 0.67690244177161496 0.67723782225996931 0.67757326982442123 0.67790878447838598 0.67824436623528173 0.67858001510852883 0.67891573111155057 0.67925151425777286 0.6795873645606243 0.67992328203353636 0.68025926668994297 0.68059531854328092 0.68093143760698949 0.68126762389451079 0.68160387741928963 0.68194019819477347 0.68227658623441245 0.68261304155165936 0.68294956415996966 0.68328615407280169 0.68362281130361624 0.68395953586587699 0.68429632777305005 0.68463318703860465 0.68497011367601224 0.68530710769874736 0.68564416912028703 0.68598129795411111 0.68631849421370195 0.68665575791254474 0.68699308906412715 0.68733048768193994 0.6876679537794 7632 0.68800548737023215 0.6883430884677062 0.68868075708539966 0.68901849323681663 0.68935629693546385 0.68969416819485097 0.69003210702848983 0.69037011344989541 0.69070818747258533 0.6910463291100799 0.69138453837590186 0.69172281528357704 0.69206115984663374 0.69239957207860314 0.69273805199301886 0.69307659960341739 0.69341521492333813 0.6937538979663227 0.69409264874591603 0.69443146727566507 0.69477035356912009 0.69510930763983381 0.69544832950136182 0.69578741916726194 0.69612657665109534 0.6964658019664256 0.69680509512681876 0.69714445614584419 0.69748388503707326 0.69782338181408066 0.69816294649044353 0.69850257907974167 0.69884227959555756 0.69918204805147655 0.69952188446108687 0.699861788837979 0.70020176119574651 0.700541801547985 62 0.70088190990829524 0.70122208629027694 0.70156233070753493 0.70190264317367634 0.70224302370231095 0.70258347230705143 0.70292398900151287 0.70326457379931306 0.70360522671407288 0.70394594775941566 0.7042867369489676 0.70462759429635735 0.70496851981521669 0.70530951351917959 0.70565057542188336 0.70599170553696777 0.70633290387807524 0.70667417045885084 0.70701550529294255 0.707356908394001 0.70769837977567973 0.70803991945163491 0.70838152743552518 0.70872320374101228 0.70906494838176037 0.70940676137143677 0.70974864272371097 0.71009059245225559 0.71043261057074591 0.71077469709286012 0.71111685203227859 0.71145907540268505 0.71180136721776566 0.71214372749120924 0.71248615623670752 0.71282865346795488 0.71317121919864834 0.71351385344248 808 0.71385655621317645 0.71419932752441895 0.71454216738992371 0.71488507582340155 0.71522805283856616 0.71557109844913391 0.7159142126688236 0.71625739551135736 0.71660064699045956 0.71694396711985764 0.71728735591328152 0.71763081338446422 0.71797433954714118 0.71831793441505054 0.71866159800193352 0.7190053303215338 0.71934913138759815 0.71969300121387558 0.72003693981411843 0.72038094720208123 0.72072502339152167 0.72106916839619983 0.72141338222987894 0.72175766490632487 0.72210201643930616 0.72244643684259402 0.72279092612996254 0.72313548431518848 0.72348011141205149 0.72382480743433386 0.72416957239582058 0.72451440631029973 0.72485930919156183 0.72520428105340007 0.72554932190961074 0.7258944317739926 0.72623961066034726 0.7265848585824 7923 0.7269301755541957 0.72727556158930651 0.72762101670162438 0.72796654090496471 0.72831213421314556 0.72865779663998809 0.72900352819931613 0.72934932890495596 0.72969519877073696 0.73004113781049118 0.73038714603805333 0.73073322346726099 0.73107937011195445 0.73142558598597684 0.73177187110317399 0.73211822547739458 0.73246464912248999 0.73281114205231446 0.73315770428072491 0.73350433582158092 0.73385103668874518 0.73419780689608283 0.73454464645746209 0.73489155538675344 0.73523853369783065 0.7355855814045702 0.73593269852085097 0.73627988506055519 0.73662714103756732 0.73697446646577469 0.73732186135906774 0.73766932573133959 0.73801685959648577 0.73836446296840497 0.73871213586099871 0.73905987828817077 0.73940769026382847 0.73975557180 188112 0.74010352291624137 0.74045154362082455 0.74079963392954862 0.74114779385633445 0.74149602341510557 0.74184432261978861 0.74219269148431244 0.74254113002260924 0.74288963824861365 0.7432382161762634 0.74358686381949868 0.74393558119226255 0.74428436830850098 0.74463322518216257 0.74498215182719907 0.74533114825756441 0.74568021448721589 0.74602935053011321 0.74637855640021922 0.74672783211149918 0.74707717767792148 0.74742659311345694 0.74777607843207949 0.74812563364776596 0.74847525877449539 0.74882495382625014 0.74917471881701525 0.74952455376077864 0.74987445867153069 0.75022443356326485 0.75057447844997749 0.75092459334566741 0.75127477826433653 0.75162503321998941 0.75197535822663331 0.75232575329827855 0.75267621844893817 0.75302675 369262784 0.75337735904336633 0.75372803451517489 0.75407878012207785 0.75442959587810221 0.75478048179727786 0.75513143789363735 0.75548246418121612 0.75583356067405227 0.75618472738618703 0.75653596433166426 0.7568872715245305 0.75723864897883542 0.75759009670863109 0.75794161472797272 0.75829320305091819 0.75864486169152823 0.75899659066386649 0.75934838998199927 0.75970025965999555 0.76005219971192761 0.76040421015186999 0.7607562909939003 0.76110844225209906 0.76146066394054945 0.76181295607333754 0.76216531866455228 0.76251775172828506 0.76287025527863062 0.76322282932968633 0.76357547389555225 0.76392818899033132 0.76428097462812938 0.76463383082305492 0.76498675758921952 0.76533975494073725 0.76569282289172547 0.76604596145630377 0.766399 17064859508 0.76675245048272478 0.76710580097282133 0.76745922213301587 0.76781271397744244 0.76816627652023795 0.76851990977554197 0.76887361375749697 0.76922738848024852 0.76958123395794442 0.76993515020473602 0.77028913723477688 0.7706431950622239 0.77099732370123619 0.77135152316597644 0.77170579347060952 0.77206013462930367 0.77241454665622955 0.77276902956556071 0.7731235833714738 0.77347820808814816 0.77383290372976576 0.77418767031051172 0.77454250784457379 0.77489741634614262 0.77525239582941174 0.77560744630857759 0.77596256779783923 0.77631776031139865 0.77667302386346093 0.77702835846823359 0.77738376413992727 0.77773924089275526 0.77809478874093374 0.77845040769868179 0.77880609778022158 0.77916185899977752 0.77951769137157734 0.7798 7359490985164 0.7802295696288335 0.78058561554275929 0.78094173266586786 0.78129792101240092 0.7816541805966033 0.78201051143272249 0.78236691353500909 0.78272338691771615 0.78307993159509959 0.78343654758141867 0.78379323489093489 0.78414999353791304 0.7845068235366206 0.78486372490132794 0.78522069764630809 0.78557774178583739 0.78593485733419444 0.78629204430566113 0.78664930271452227 0.78700663257506509 0.78736403390158016 0.7877215067083605 0.78807905100970221 0.7884366668199041 0.78879435415326804 0.7891521130240986 0.78950994344670344 0.78986784543539268 0.79022581900447975 0.79058386416828053 0.79094198094111423 0.79130016933730252 0.79165842937116992 0.79201676105704411 0.79237516440925537 0.79273363944213715 0.79309218617002553 0.793450 80460725947 0.79380949476818086 0.79416825666713442 0.7945270903184678 0.79488599573653151 0.79524497293567875 0.7956040219302658 0.79596314273465185 0.79632233536319874 0.79668159983027143 0.79704093615023752 0.79740034433746754 0.79775982440633508 0.79811937637121622 0.79847900024649032 0.79883869604653968 0.79919846378574899 0.79955830347850609 0.79991821513920169 0.80027819878222939 0.80063825442198588 0.80099838207287033 0.80135858174928476 0.80171885346563454 0.8020791972363277 0.80243961307577494 0.80280010099839005 0.80316066101858974 0.80352129315079335 0.80388199740942357 0.80424277380890552 0.80460362236366723 0.80496454308814003 0.80532553599675771 0.80568660110395696 0.80604773842417776 0.80640894797186258 0.80677022976145696 0.80713 158380740913 0.80749301012417063 0.80785450872619546 0.80821607962794073 0.8085777228438662 0.80893943838843496 0.80930122627611256 0.80966308652136765 0.81002501913867198 0.81038702414249975 0.81074910154732827 0.81111125136763773 0.81147347361791122 0.81183576831263471 0.81219813546629727 0.81256057509339041 0.812923087208409 0.81328567182585054 0.81364832896021566 0.81401105862600764 0.81437386083773289 0.81473673560990045 0.81509968295702229 0.81546270289361367 0.81582579543419231 0.81618896059327906 0.81655219838539761 0.81691550882507458 0.81727889192683945 0.81764234770522481 0.81800587617476572 0.81836947735000054 0.81873315124547053 0.8190968978757196 0.81946071725529479 0.8198246093987458 0.82018857432062542 0.82055261203548957 0.820916 72255789661 0.82128090590240821 0.82164516208358873 0.82200949111600541 0.82237389301422859 0.82273836779283149 0.82310291546639003 0.8234675360494832 0.82383222955669311 0.82419699600260432 0.82456183540180472 0.82492674776888508 0.82529173311843884 0.82565679146506255 0.82602192282335563 0.82638712720792018 0.82675240463336164 0.82711775511428831 0.82748317866531118 0.82784867530104411 0.8282142450361043 0.82857988788511139 0.82894560386268834 0.82931139298346079 0.82967725526205749 0.83004319071310984 0.83040919935125235 0.83077528119112265 0.83114143624736081 0.83150766453461022 0.83187396606751718 0.83224034086073062 0.83260678892890283 0.83297331028668853 0.83333990494874577 0.83370657292973549 0.8340733142443213 0.83444012890717012 0.83480 701693295156 0.83517397833633811 0.83554101313200535 0.83590812133463177 0.83627530295889874 0.8366425580194905 0.83700988653109443 0.83737728850840054 0.8377447639661022 0.83811231291889543 0.83847993538147914 0.83884763136855534 0.83921540089482893 0.83958324397500794 0.83995116062380282 0.84031915085592757 0.84068721468609864 0.84105535212903582 0.84142356319946154 0.84179184791210138 0.84216020628168375 0.84252863832294 0.84289714405060456 0.84326572347941475 0.84363437662411056 0.8440031034994353 0.84437190412013519 0.84474077850095908 0.84510972665665918 0.84547874860199057 0.84584784435171101 0.84621701392058135 0.84658625732336534 0.84695557457483006 0.84732496568974502 0.84769443068288286 0.8480639695690193 0.84843358236293298 0.84880326 907940562 0.8491730297332214 0.84954286433916804 0.84991277291203593 0.85028275546661836 0.8506528120177117 0.85102294258011524 0.85139314716863113 0.85176342579806485 0.85213377848322436 0.8525042052389209 0.85287470607996863 0.85324528102118458 0.85361593007738867 0.85398665326340417 0.85435745059405677 0.85472832208417548 0.85509926774859224 0.85547028760214183 0.85584138165966217 0.85621254993599405 0.85658379244598115 0.85695510920447027 0.85732650022631107 0.85769796552635635 0.85806950511946156 0.85844111902048548 0.85881280724428954 0.85918456980573832 0.85955640671969946 0.8599283180010433 0.8603003036646435 0.86067236372537637 0.86104449819812134 0.86141670709776097 0.86178899043918045 0.86216134823726831 0.86253378050691576 0.862906287 2630171 0.86327886852046976 0.8636515242941738 0.86402425459903265 0.86439705944995238 0.86476993886184239 0.86514289284961476 0.86551592142818468 0.86588902461247019 0.86626220241739271 0.86663545485787608 0.86700878194884767 0.86738218370523734 0.86775566014197825 0.86812921127400666 0.86850283711626153 0.86887653768368467 0.86925031299122146 0.86962416305381973 0.8699980878864304 0.87037208750400774 0.87074616192150844 0.87112031115389277 0.87149453521612341 0.87186883412316663 0.87224320788999132 0.87261765653156931 0.87299218006287549 0.87336677849888811 0.87374145185458785 0.87411620014495872 0.87449102338498763 0.87486592158966459 0.87524089477398248 0.87561594295293732 0.87599106614152777 0.87636626435475606 0.87674153760762707 0.87711688 591514858 0.87749230929233146 0.87786780775418993 0.87824338131574065 0.87861902999200381 0.87899475379800207 0.87937055274876164 0.87974642685931137 0.88012237614468325 0.88049840061991214 0.880874500300036 0.88125067520009592 0.88162692533513587 0.88200325072020291 0.88237965137034702 0.88275612730062103 0.88313267852608113 0.88350930506178638 0.88388600692279873 0.88426278412418324 0.88463963668100809 0.88501656460834432 0.88539356792126589 0.88577064663485006 0.88614780076417698 0.88652503032432972 0.88690233533039464 0.88727971579746079 0.88765717174062031 0.88803470317496846 0.8884123101156034 0.88878999257762659 0.88916775057614217 0.88954558412625739 0.88992349324308262 0.89030147794173109 0.89067953823731938 0.89105767414496673 0.8914358 856797957 0.89181417285693154 0.89219253569150281 0.89257097419864118 0.89294948839348076 0.89332807829115946 0.89370674390681759 0.89408548525559883 0.89446430235264995 0.89484319521312039 0.89522216385216291 0.89560120828493339 0.89598032852659037 0.89635952459229573 0.89673879649721422 0.89711814425651371 0.89749756788536494 0.89787706739894202 0.89825664281242168 0.89863629414098423 0.8990160213998124 0.89939582460409229 0.89977570376901306 0.90015565890976679 0.90053569004154865 0.90091579717955694 0.90129598033899283 0.9016762395350606 0.90205657478296764 0.90243698609792422 0.90281747349514374 0.90319803698984269 0.90357867659724067 0.90395939233256017 0.90434018421102658 0.90472105224786881 0.90510199645831824 0.90548301685760979 0.905864 11346098128 0.9062452862836734 0.90662653534093018 0.90700786064799832 0.90738926222012783 0.90777074007257186 0.90815229422058641 0.90853392467943039 0.90891563146436627 0.90929741459065916 0.90967927407357729 0.91006120992839201 0.91044322217037754 0.91082531081481166 0.91120747587697459 0.91158971737214989 0.91197203531562421 0.91235442972268732 0.91273690060863188 0.91311944798875366 0.91350207187835131 0.91388477229272702 0.91426754924718545 0.9146504027570348 0.91503333283758614 0.91541633950415369 0.91579942277205451 0.91618258265660879 0.91656581917314006 0.91694913233697473 0.91733252216344208 0.91771598866787474 0.91809953186560822 0.91848315177198137 0.91886684840233568 0.919250621772016 0.91963447189637026 0.92001839879074954 0.920402 40247050775 0.92078648295100174 0.92117064024759188 0.92155487437564143 0.92193918535051655 0.92232357318758651 0.92270803790222389 0.92309257950980439 0.92347719802570638 0.92386189346531156 0.9242466658440045 0.92463151517717335 0.92501644148020867 0.92540144476850461 0.92578652505745818 0.92617168236246972 0.92655691669894225 0.92694222808228188 0.9273276165278983 0.92771308205120384 0.92809862466761395 0.9284842443925474 0.92886994124142586 0.9292557152296741 0.92964156637272 0.93002749468599455 0.93041350018493163 0.93079958288496867 0.93118574280154554 0.93157197995010588 0.93195829434609578 0.9323446860049649 0.93273115494216574 0.93311770117315418 0.93350432471338873 0.93389102557833148 0.93427780378344716 0.93466465934420384 0.9350515922 7607271 0.93543860259452782 0.93582569031504659 0.9362128554531095 0.93660009802420019 0.93698741804380492 0.93737481552741353 0.93776229049051896 0.93814984294861703 0.93853747291720668 0.93892518041179018 0.93931296544787246 0.939700828040962 0.94008876820657017 0.94047678596021145 0.94086488131740342 0.94125305429366679 0.94164130490452558 0.94202963316550647 0.9424180390921395 0.94280652269995779 0.94319508400449781 0.94358372302129867 0.94397243976590284 0.94436123425385587 0.94475010650070668 0.9451390565220068 0.94552808433331115 0.94591718995017771 0.94630637338816759 0.94669563466284523 0.94708497378977774 0.94747439078453555 0.94786388566269242 0.948253458439825 0.94864310913151284 0.94903283775333902 0.94942264432088974 0.9498125288497 5387 0.95020249135552382 0.95059253185379489 0.95098265036016549 0.95137284689023738 0.95176312145961539 0.95215347408390727 0.95254390477872408 0.95293441355967978 0.95332500044239166 0.9537156654424801 0.95410640857556861 0.95449722985728358 0.95488812930325495 0.95527910692911555 0.95567016275050132 0.9560612967830513 0.95645250904240786 0.95684379954421628 0.95723516830412514 0.95762661533778592 0.95801814066085345 0.95840974428898562 0.95880142623784348 0.95919318652309093 0.95958502516039546 0.95997694216542739 0.96036893755386044 0.96076101134137115 0.96115316354363944 0.9615453941763481 0.96193770325518324 0.96233009079583431 0.96272255681399344 0.96311510132535627 0.96350772434562137 0.96390042589049041 0.96429320597566837 0.964686064616 86335 0.96507900182978679 0.96547201763015278 0.96586511203367875 0.96625828505608546 0.96665153671309656 0.96704486702043924 0.96743827599384336 0.96783176364904211 0.9682253300017718 0.96861897506777206 0.96901269886278563 0.96940650140255813 0.96980038270283853 0.9701943427793791 0.97058838164793504 0.97098249932426461 0.97137669582412944 0.97177097116329425 0.97216532535752687 0.97255975842259823 0.97295427037428261 0.9733488612283574 0.97374353100060307 0.97413827970680322 0.97453310736274457 0.97492801398421713 0.97532299958701385 0.97571806418693119 0.97611320779976851 0.97650843044132851 0.97690373212741677 0.97729911287384219 0.97769457269641702 0.97809011161095616 0.97848572963327829 0.97888142677920498 0.97927720306456068 0.97967305850 517361 0.98006899311687468 0.98046500691549809 0.9808610999168812 0.98125727213686442 0.98165352359129177 0.98204985429600988 0.98244626426686898 0.98284275351972239 0.9832393220704263 0.98363596993484026 0.98403269712882713 0.98442950366825288 0.98482638956898638 0.98522335484690005 0.98562039951786939 0.98601752359777284 0.98641472710249234 0.98681201004791275 0.98720937244992224 0.98760681432441211 0.98800433568727697 0.98840193655441433 0.98879961694172525 0.98919737686511344 0.98959521634048642 0.98999313538375455 0.99039113401083134 0.99078921223763339 0.99118737008008084 0.99158560755409675 0.99198392467560748 0.9923823214605425 0.99278079792483465 0.9931793540844196 0.99357798995523638 0.99397670555322737 0.99437550089433802 0.99477437599 45169 0.99517333086971571 0.99557236553588968 0.99597148000899671 0.99637067430499848 0.99676994843985933 0.99716930242954716 0.99756873629003295 0.99796825003729084 0.99836784368729825 0.99876751725603574 0.99916727075948697 0.99956710421363892 0.9999670176344817 1.0003670110380085 1.0007670844402159 1.0011672378571039 1.0015674713046754 1.0019677847989361 1.002368178355896 1.0027686519915671 1.0031692057219654 1.0035698395631099 1.0039705535310226 1.0043713476417286 1.0047722219112569 1.0051731763556391 1.0055742109909103 1.0059753258331083 1.0063765208982751 1.0067777962024547 1.007179151761695 1.0075805875920474 1.0079821037095655 1.0083837001303073 1.0087853768703332 1.0091871339457072 1.0095889713724961 1.0099908891667706 1.010392887344604 1.0107949659220727 1.0111971249152569 1.0115993643402401 1.0120016842131081 1.0124040845499507 1.0128065653668608 1.0132091266799339 1.0136117685052697 1.0140144908589708 1.0144172937571425 1.0148201772158938 1.0152231412513371 1.0156261858795874 1.0160293111167631 1.0164325169789863 1.0168358034823819 1.0172391706430783 1.0176426184772067 1.0180461470009021 1.0184497562303023 1.0188534461815482 1.0192572168707845 1.0196610683141585 1.0200650005278211 1.0204690135279266 1.0208731073306323 1.0212772819520985 1.0216815374084889 1.0220858737159704 1.0224902908907136 1.0228947889488915 1.0232993679066813 1.0237040277802625 1.0241087685858186 1.0245135903395357 1.0249184930576036 1.0253234767562152 1.0257285414515662 1.0261336871598563 1.026538913897288 1.0269442216800675 1.0273496105244035 1.0277550804465085 1.028160631462598 1.0285662635888904 1.0289719768416079 1.0293777712369763 1.0297836467912238 1.030189603520582 1.0305956414412862 1.0310017605695743 1.0314079609216882 1.0318142425138723 1.032220605362375 1.0326270494834473 1.0330335748933441 1.0334401816083227 1.0338468696446443 1.0342536390185733 1.0346604897463769 1.0350674218443263 1.0354744353286951 1.0358815302157609 1.036288706521804 1.0366959642631084 1.0371033034559609 1.0375107241166521 1.0379182262614752 1.0383258099067274 1.0387334750687085 1.0391412217637224 1.0395490500080751 1.0399569598180767 1.0403649512100404 1.0407730242002824 1.0411811788051226 1.041 5894150408835 1.0419977329238916 1.0424061324704765 1.0428146136969705 1.0432231766197098 1.0436318212550337 1.0440405476192849 1.0444493557288088 1.0448582455999547 1.0452672172490747 1.0456762706925247 1.0460854059466631 1.0464946230278525 1.0469039219524578 1.0473133027368484 1.0477227653973959 1.0481323099504753 1.0485419364124655 1.048951644799748 1.0493614351287079 1.0497713074157335 1.0501812616772166 1.050591297929552 1.0510014161891377 1.0514116164723752 1.0518218987956698 1.0522322631754291 1.0526427096280639 1.0530532381699893 1.0534638488176231 1.0538745415873865 1.054285316495704 1.054696173559003 1.0551071127937148 1.0555181342162734 1.0559292378431167 1.0563404236906853 1.0567516917754234 1.0571630421137783 1.0575744747222009 1.0579859896171451 1.0583975868150683 1.0588092663324313 1.0592210281856977 1.0596328723913349 1.0600447989658131 1.0604568079256063 1.0608688992871915 1.061281073067049 1.0616933292816624 1.0621056679475185 1.0625180890811081 1.0629305926989243 1.0633431788174641 1.0637558474532276 1.0641685986227181 1.0645814323424427 1.0649943486289111 1.065407347498637 1.0658204289681366 1.06623359305393 1.0666468397725408 1.0670601691404955 1.0674735811743234 1.0678870758905581 1.068300653305736 1.0687143134363972 1.0691280562990846 1.0695418819103444 1.0699557902867265 1.0703697814447839 1.0707838554010727 1.0711980121721529 1.0716122517745874 1.0720265742249424 1.0724409795397873 1.0728554677356952 1.0732700388292424 1.0736846928370083 1.0740994297755755 1.0745142496615308 1.074929152511463 1.0753441383419653 1.0757592071696336 1.0761743590110675 1.0765895938828698 1.0770049118016463 1.0774203127840067 1.0778357968465633 1.0782513640059324 1.0786670142787336 1.0790827476815892 1.0794985642311254 1.0799144639439717 1.0803304468367605 1.0807465129261278 1.0811626622287132 1.0815788947611589 1.0819952105401112 1.0824116095822189 1.0828280919041355 1.0832446575225165 1.083661306454021 1.0840780387153117 1.0844948543230548 1.0849117532939192 1.0853287356445778 1.0857458013917065 1.086162950551985 1.0865801831420954 1.0869974991787239 1.0874148986785594 1.0878323816582953 1.0882499481346271 1.0886675981242537 1.0890853316438784 1.08950314 87102074 1.0899210493399494 1.0903390335498173 1.0907571013565271 1.0911752527767984 1.0915934878273537 1.0920118065249191 1.0924302088862241 1.0928486949280014 1.093267264666987 1.0936859181199203 1.0941046553035441 1.0945234762346048 1.0949423809298517 1.0953613694060378 1.0957804416799188 1.0961995977682548 1.0966188376878083 1.0970381614553459 1.0974575690876369 1.0978770606014545 1.0982966360135746 1.0987162953407772 1.0991360385998452 1.0995558658075653 1.0999757769807266 1.1003957721361228 1.1008158512905499 1.1012360144608082 1.1016562616637002 1.102076592916033 1.1024970082346162 1.102917507636263 1.1033380911377901 1.1037587587560176 1.1041795105077687 1.1046003464098701 1.1050212664791519 1.1054422707324476 1.1058633591865941 1.1062845318584311 1.1067057887648026 1.1071271299225556 1.10754855534854 1.1079700650596096 1.1083916590726215 1.108813337404436 1.1092351000719169 1.1096569470919313 1.1100788784813496 1.1105008942570458 1.1109229944358971 1.1113451790347844 1.1117674480705912 1.1121898015602052 1.1126122395205171 1.1130347619684211 1.1134573689208147 1.1138800603945986 1.1143028364066776 1.114725696973959 1.1151486421133536 1.1155716718417761 1.1159947861761443 1.1164179851333795 1.1168412687304063 1.1172646369841526 1.1176880899115496 1.1181116275295317 1.1185352498550376 1.1189589569050087 1.1193827486963897 1.1198066252461287 1.1202305865711777 1.1206546326884919 1.1210787636150297 1.1215029793677527 1.121927279963626 1.1223516654196186 1.1227761357527024 1.1232006909798531 1.1236253311180491 1.1240500561842728 1.1244748661955097 1.124899761168749 1.1253247411209828 1.1257498060692068 1.1261749560304208 1.1266001910216268 1.1270255110598311 1.1274509161620432 1.1278764063452758 1.1283019816265449 1.12872764202287 1.1291533875512747 1.1295792182287849 1.1300051340724306 1.1304311350992449 1.1308572213262646 1.1312833927705297 1.1317096494490837 1.1321359913789735 1.1325624185772494 1.1329889310609649 1.133415528847177 1.1338422119529463 1.134268980395337 1.1346958341914162 1.1351227733582543 1.1355497979129261 1.1359769078725086 1.1364041032540833 1.1368313840747342 1.137258750351549 1.1376862021016194 1.1381137393420397 1.1385413620899083 1.1389690703623261 1.1393968641763985 1.1398247435492337 1.1402527084979437 1.1406807590396433 1.1411088951914512 1.1415371169704893 1.1419654243938835 1.1423938174787622 1.1428222962422581 1.1432508607015066 1.1436795108736471 1.1441082467758217 1.1445370684251768 1.1449659758388617 1.1453949690340295 1.1458240480278361 1.1462532128374416 1.1466824634800092 1.1471117999727052 1.1475412223326997 1.1479707305771663 1.1484003247232817 1.1488300047882265 1.1492597707891843 1.1496896227433422 1.1501195606678909 1.1505495845800242 1.1509796944969404 1.1514098904358399 1.1518401724139271 1.1522705404484097 1.1527009945564992 1.1531315347554103 1.1535621610623612 1.1539928734945737 1.1544236720692727 1.1548545568036865 1.1552855277150473 1.1557165848205901 1.1561477281375541 1.1565789576831813 1.1570102734747181 1.1574416755294128 1.1578731638645188 1.1583047384972915 1.1587363994449911 1.15916814672488 1.159599980354225 1.1600319003502957 1.1604639067303655 1.1608959995117116 1.1613281787116141 1.1617604443473564 1.162192796436226 1.1626252349955131 1.1630577600425123 1.1634903715945208 1.1639230696688396 1.1643558542827734 1.1647887254536298 1.1652216831987205 1.1656547275353604 1.1660878584808674 1.1665210760525637 1.1669543802677742 1.1673877711438276 1.1678212486980564 1.1682548129477959 1.1686884639103852 1.1691222016031673 1.1695560260434879 1.1699899372486966 1.1704239352361463 1.1708580200231933 1.1712921916271979 1.1717264500655231 1.172160795355536 1.172595227514607 1.1730297465601098 1.1734643525094217 1.1738990453799234 1.1743338251889992 1.174768691954037 1.1752036456924277 1.175638686421566 1.1760738141588503 1.1765090289216822 1.1769443307274665 1.177379719593612 1.1778151955375304 1.1782507585766377 1.1786864087283528 1.1791221460100987 1.1795579704393004 1.1799938820333882 1.1804298808097946 1.1808659667859565 1.1813021399793135 1.1817384004073093 1.1821747480873905 1.1826111830370079 1.1830477052736152 1.1834843148146699 1.1839210116776329 1.1843577958799685 1.1847946674391445 1.1852316263726324 1.1856686726979069 1.1861058064324466 1.186543027593733 1.1869803361992517 1.1874177322664914 1.1878552158129447 1.1882927868561071 1.1887304454134782 1.1891681915025609 1.1896060251408613 1.1900439463458894 1.1904819551351586 1.1909200515261857 1.1913582355364909 1.1917965071835983 1.1922348664850348 1.1926733134583318 1.1931118481210237 1.1935504704906479 1.193989180584746 1.1944279784208631 1.1948668640165474 1.1953058373893506 1.1957448985568284 1.1961840475365397 1.1966232843460469 1.1970626090029159 1.1975020215247163 1.197941521929021 1.1983811102334068 1.1988207864554532 1.1992605506127441 1.1997004027228666 1.2001403428034112 1.2005803708719718 1.2010204869461463 1.2014606910435353 1.2019009831817438 1.2023413633783799 1.2027818316510555 1.2032223880173856 1.2036630324949891 1.2041037651014879 1.2045445858545083 1.2049854947716789 1.2054264918706332 1.20586 75771690073 1.2063087506844412 1.2067500124345782 1.2071913624370652 1.2076328007095527 1.2080743272696948 1.2085159421351488 1.2089576453235757 1.2093994368526406 1.2098413167400111 1.2102832850033591 1.2107253416603596 1.2111674867286917 1.2116097202260372 1.2120520421700824 1.2124944525785164 1.212936951469032 1.2133795388593258 1.2138222147670978 1.2142649792100513 1.2147078322058933 1.2151507737723346 1.215593803927089 1.2160369226878744 1.2164801300724122 1.2169234260984267 1.2173668107836462 1.2178102841458029 1.2182538462026322 1.2186974969718727 1.219141236471267 1.2195850647185611 1.2200289817315046 1.220472987527851 1.2209170821253568 1.2213612655417818 1.2218055377948902 1.2222498989024491 1.2226943488822295 1.2231388877520057 1.223583515529556 1.2240282322326617 1.224473037879108 1.2249179324866839 1.2253629160731814 1.225807988656396 1.2262531502541272 1.2266984008841781 1.227143740564355 1.2275891693124681 1.2280346871463306 1.2284802940837598 1.2289259901425766 1.229371775340605 1.229817649695673 1.230263613225612 1.230709665948257 1.2311558078814469 1.2316020390430231 1.2320483594508316 1.2324947691227215 1.2329412680765461 1.2333878563301615 1.2338345339014274 1.2342813008082074 1.234728157068369 1.2351751026997828 1.2356221377203229 1.2360692621478671 1.2365164760002965 1.2369637792954964 1.2374111720513556 1.2378586542857657 1.2383062260166229 1.2387538872618262 1.2392016380392787 1.2396494783668865 1.2400974082625598 1.2405454277442121 1.2409935368297607 1.2414417355371268 1.2418900238842343 1.2423384018890111 1.2427868695693887 1.2432354269433024 1.2436840740286912 1.2441328108434968 1.2445816374056653 1.2450305537331463 1.245479559843893 1.2459286557558618 1.2463778414870128 1.24682711705531 1.2472764824787212 1.247725937775217 1.2481754829627718 1.2486251180593642 1.2490748430829761 1.2495246580515929 1.2499745629832031 1.2504245578957995 1.2508746428073785 1.2513248177359397 1.2517750826994867 1.2522254377160267 1.2526758828035698 1.2531264179801305 1.2535770432637263 1.2540277586723789 1.2544785642241134 1.254929459936958 1.2553804458289455 1.2558315219181111 1.2562826882224947 1.2567339447601391 1.2571852915490909 1.2576367286074008 1.2580882559531221 1.2585398736043127 1.2589915815790333 1.259443379895349 1.2598952685713281 1.2603472476250421 1.260799317074567 1.2612514769379821 1.2617037272333698 1.2621560679788164 1.262608499192412 1.2630610208922506 1.2635136330964292 1.2639663358230484 1.2644191290902129 1.2648720129160309 1.2653249873186141 1.2657780523160778 1.2662312079265408 1.2666844541681259 1.2671377910589596 1.2675912186171714 1.2680447368608947 1.268498345808267 1.2689520454774286 1.2694058358865239 1.2698597170537012 1.2703136889971121 1.2707677517349114 1.2712219052852585 1.2716761496663156 1.2721304848962487 1.2725849109932277 1.2730394279754265 1.2734940358610216 1.2739487346681937 1.2744035244151273 1.27485840512001 1.275 3133768010341 1.2757684394763942 1.2762235931642896 1.2766788378829226 1.2771341736504991 1.277589600485229 1.2780451184053261 1.278500727429007 1.2789564275744927 1.2794122188600077 1.2798681013037796 1.2803240749240401 1.2807801397390248 1.2812362957669725 1.2816925430261259 1.2821488815347313 1.2826053113110381 1.2830618323733001 1.2835184447397747 1.2839751484287225 1.2844319434584084 1.2848888298471 1.2853458076130693 1.2858028767745919 1.2862600373499466 1.2867172893574166 1.287174632815288 1.2876320677418511 1.2880895941553994 1.2885472120742305 1.2890049215166455 1.2894627225009487 1.2899206150454487 1.290378599168458 1.2908366748882916 1.2912948422232691 1.2917531011917136 1.2922114518119519 1.292669894102314 1.2931284280811344 1.2935870537667506 1.2940457711775037 1.294504580331739 1.2949634812478052 1.295422473944055 1.2958815584388437 1.2963407347505314 1.2968000028974815 1.2972593628980609 1.2977188147706404 1.2981783585335944 1.298637994205301 1.299097721804142 1.2995575413485025 1.3000174528567721 1.3004774563473434 1.3009375518386128 1.3013977393489804 1.30185801889685 1.3023183905006293 1.3027788541787295 1.303239409949565 1.3037000578315547 1.3041607978431209 1.3046216300026896 1.3050825543286901 1.3055435708395557 1.3060046795537237 1.3064658804896343 1.306927173665732 1.307388559100465 1.307850036812285 1.3083116068196472 1.3087732691410112 1.3092350237948396 1.3096968707995984 1.3101588101737582 1.3106208419357928 1.3110829661041801 1.3115451826974009 1.3120074917339402 1.3124698932322869 1.3129323872109335 1.3133949736883759 1.3138576526831134 1.3143204242136499 1.3147832882984924 1.3152462449561519 1.3157092942051429 1.3161724360639839 1.3166356705511966 1.3170989976853069 1.3175624174848437 1.3180259299683406 1.3184895351543342 1.3189532330613649 1.319417023707977 1.3198809071127187 1.3203448832941413 1.3208089522708 1.3212731140612539 1.3217373686840661 1.322201716157803 1.3226661565010347 1.3231306897323347 1.3235953158702811 1.324060034933455 1.3245248469404416 1.3249897519098295 1.3254547498602114 1.3259198408101835 1.3263850247783457 1.3268503017833013 1.3273156718436581 1.3277811349780269 1.3282466912050226 1.3287123405432637 1.3291780830113722 1.3296439186279745 1.3301098474117001 1.3305758693811822 1.3310419845550583 1.3315081929519694 1.3319744945905598 1.3324408894894777 1.3329073776673757 1.333373959142909 1.3338406339347375 1.3343074020615244 1.3347742635419366 1.3352412183946449 1.3357082666383238 1.3361754082916515 1.3366426433733096 1.3371099719019841 1.3375773938963644 1.3380449093751436 1.3385125183570188 1.33898022086069 1.3394480169048619 1.3399159065082427 1.3403838896895444 1.3408519664674823 1.3413201368607757 1.3417884008881478 1.3422567585683254 1.3427252099200389 1.343193754962023 1.3436623937130152 1.3441311261917579 1.344599952416996 1.3450688724074795 1.3455378861819609 1.3460069937591972 1.3464761951579489 1.34694549 03969806 1.34741487949506 1.3478843624709591 1.3483539393434532 1.3488236101313218 1.3492933748533482 1.3497632335283187 1.3502331861750245 1.3507032328122595 1.3511733734588218 1.3516436081335135 1.3521139368551403 1.3525843596425111 1.3530548765144395 1.3535254874897422 1.3539961925872399 1.3544669918257575 1.3549378852241225 1.3554088728011671 1.3558799545757272 1.3563511305666425 1.3568224007927556 1.3572937652729142 1.3577652240259686 1.3582367770707737 1.358708424426188 1.3591801661110732 1.3596520021442955 1.3601239325447243 1.3605959573312334 1.3610680765226997 1.361540290138004 1.3620125981960314 1.3624850007156706 1.3629574977158136 1.3634300892153566 1.3639027752331998 1.3643755557882464 1.364848430899404 1.365321400585584 1.3657944648657012 1.3662676237586742 1.366740877283426 1.3672142254588824 1.367687668303974 1.3681612058376347 1.368634838078802 1.3691085650464179 1.369582386759427 1.3700563032367787 1.3705303144974259 1.3710044205603253 1.3714786214444374 1.3719529171687261 1.3724273077521598 1.3729017932137104 1.373376373572353 1.3738510488470674 1.3743258190568368 1.3748006842206482 1.3752756443574921 1.3757506994863635 1.3762258496262607 1.3767010947961857 1.3771764350151448 1.3776518703021479 1.3781274006762083 1.3786030261563433 1.3790787467615746 1.3795545625109269 1.380030473423429 1.3805064795181137 1.3809825808140173 1.3814587773301801 1.381935069085646 1.3824114560994629 1.3828879383906827 1.3833645159783607 1.3838411888815565 1.3843179571193329 1.3847948207107565 1.3852717796748988 1.3857488340308337 1.3862259837976398 1.3867032289943992 1.387180569640198 1.3876580057541261 1.3881355373552768 1.3886131644627477 1.3890908870956404 1.3895687052730596 1.3900466190141141 1.3905246283379169 1.3910027332635844 1.3914809338102372 1.3919592299969992 1.3924376218429986 1.3929161093673672 1.3933946925892404 1.393873371527758 1.3943521462020634 1.3948310166313038 1.3953099828346298 1.3957890448311967 1.3962682026401629 1.396747456280691 1.3972268057719472 1.3977062511331018 1.3981857923833285 1.3986654295418051 1.3991451626277134 1.399624991660239 1.4001049166585711 1.4005849376419026 1.4010650546294308 1.4015452676403566 1.4020255766938847 1.4025059818092234 1.4029864830055851 1.4034670803021863 1.4039477737182464 1.4044285632729898 1.4049094489856442 1.4053904308754412 1.4058715089616163 1.4063526832634086 1.4068339538000614 1.4073153205908215 1.4077967836549394 1.4082783430116703 1.4087599986802726 1.4092417506800086 1.4097235990301447 1.4102055437499508 1.4106875848587008 1.4111697223756727 1.4116519563201479 1.4121342867114119 1.4126167135687542 1.4130992369114677 1.4135818567588498 1.4140645731302017 1.4145473860448279 1.4150302955220369 1.4155133015811412 1.4159964042414575 1.4164796035223057 1.4169628994430101 1.4174462920228987 1.4179297812813032 1.4184133672375596 1.4188970499110072 1.4193808293209895 1.4198647054868538 1.4203486784279513 1.4208327481636367 1.4213169147132692 1.4218011780962119 1.4222855383318311 1.4227699954394972 1.4232545494385849 1.4237392003484723 1.4242239481885419 1.4247087929781794 1.4251937347367751 1.4256787734837224 1.4261639092384191 1.4266491420202665 1.4271344718486705 1.42761989874304 1.4281054227227887 1.4285910438073333 1.4290767620160945 1.4295625773684977 1.4300484898839714 1.430534499581948 1.4310206064818645 1.4315068106031608 1.4319931119652813 1.4324795105876742 1.4329660064897918 1.4334525996910896 1.4339392902110277 1.4344260780690701 1.4349129632846838 1.4353999458773408 1.4358870258665162 1.4363742032716895 1.4368614781123439 1.4373488504079663 1.437836320178048 1.4383238874420834 1.4388115522195717 1.4392993145300155 1.4397871743929214 1.4402751318278 1.4407631868541655 1.4412513394915361 1.4417395897594343 1.4422279376773863 1.4427163832649219 1.4432049265415747 1.4436935675268829 1.4441823062403882 1.4446711427016363 1.4451600769301765 1.4456491089455623 1.4461382387673516 1.4466274664151051 1.447116791908388 1.4476062152667697 1.4480957365098228 1.4485853556571247 1.449075072728256 1.4495648877428016 1.4500548007203502 1.4505448116804942 1.4510349206428304 1.451525127626959 1.4520154326524843 1.4525058357390148 1.4529963369061627 1.4534869361735439 1.4539776335607786 1.4544684290874907 1.4549593227733082 1.4554503146378628 1.4559414047007904 1.4564325929817303 1.4569238795003265 1.4574152642762264 1.4579067473290817 1.4583983286785474 1.4588900083442828 1.4593817863459515 1.4598736627032207 1.4603656374357614 1.4608577105632485 1.461349882105361 1.4618421520817821 1.4623345205121985 1.4628269874163009 1.4633195528137839 1.4638122167243468 1.4643049791676916 1.4647978401635253 1.4652907997315578 1.4657838578915041 1.4662770146630826 1.4667702700660152 1.4672636241200285 1.4677570768448525 1.4682506282602215 1.4687442783858735 1.4692380272415506 1.4697318748469987 1.4702258212219679 1.4707198663862124 1.4712140103594895 1.4717082531615615 1.472202594812194 1.4726970353311564 1.4731915747382227 1.4736862130531705 1.4741809502957812 1.4746757864858404 1.4751707216431376 1.4756657557874662 1.4761608889386237 1.4766561211164113 1.4771514523406344 1.47764 68826311024 1.4781424120076285 1.4786380404900301 1.4791337680981282 1.4796295948517479 1.4801255207707182 1.4806215458748722 1.4811176701840472 1.4816138937180838 1.4821102164968272 1.4826066385401266 1.4831031598678348 1.4835997804998082 1.4840965004559084 1.4845933197559993 1.4850902384199505 1.4855872564676345 1.4860843739189278 1.4865815907937114 1.48707890711187 1.4875763228932923 1.4880738381578711 1.4885714529255027 1.4890691672160878 1.4895669810495309 1.4900648944457409 1.4905629074246298 1.4910610200061147 1.4915592322101161 1.492057544056558 1.4925559555653694 1.4930544667564822 1.4935530776498336 1.4940517882653634 1.4945505986230163 1.4950495087427407 1.495548518644489 1.4960476283482178 1.4965468378738875 1.4970461472414622 1.4975455564709104 1.4980450655822044 1.4985446745953208 1.4990443835302396 1.4995441924069457 1.5000441012454271 1.5005441100656762 1.5010442188876891 1.5015444277314667 1.5020447366170129 1.5025451455643362 1.503045654593449 1.5035462637243677 1.5040469729771124 1.5045477823717079 1.5050486919281822 1.5055497016665678 1.5060508116069009 1.5065520217692221 1.5070533321735757 1.5075547428400102 1.508056253788578 1.5085578650393359 1.5090595766123438 1.5095613885276662 1.5100633008053719 1.5105653134655328 1.5110674265282258 1.5115696400135312 1.5120719539415339 1.5125743683323223 1.5130768832059887 1.5135794985826299 1.5140822144823463 1.5145850309252427 1.5150879479314279 1.5155909655210142 1.5160940837141186 1.5165973025308612 1.5171006219913674 1.5176040421157655 1.5181075629241887 1.5186111844367733 1.5191149066736607 1.5196187296549954 1.5201226534009264 1.5206266779316064 1.5211308032671926 1.5216350294278462 1.5221393564337315 1.5226437843050182 1.523148313061879 1.5236529427244911 1.5241576733130362 1.5246625048476989 1.5251674373486686 1.5256724708361382 1.5261776053303056 1.5266828408513717 1.5271881774195419 1.5276936150550258 1.5281991537780368 1.5287047936087923 1.5292105345675142 1.5297163766744277 1.5302223199497624 1.5307283644137524 1.5312345100866351 1.5317407569886523 1.5322471051400499 1.532753554561078 1.5332601052719901 1.5337667572930442 1.5342735106445029 1.5347803653466316 1.5352873214197009 1.5357943 788839847 1.5363015377597615 1.5368087980673133 1.5373161598269265 1.537823623058892 1.5383311877835038 1.5388388540210602 1.5393466217918643 1.5398544911162229 1.5403624620144463 1.540870534506849 1.5413787086137503 1.541886984355473 1.542395361752344 1.5429038408246947 1.5434124215928597 1.5439211040771781 1.5444298882979934 1.5449387742756531 1.5454477620305083 1.5459568515829143 1.5464660429532309 1.5469753361618213 1.5474847312290536 1.5479942281752992 1.5485038270209341 1.5490135277863382 1.5495233304918954 1.5500332351579935 1.5505432418050251 1.5510533504533859 1.5515635611234764 1.5520738738357012 1.5525842886104684 1.5530948054681906 1.5536054244292843 1.5541161455141701 1.554626968743273 1.5551378941370215 1.5556489217158487 1.5561600515001919 1.5566712835104917 1.5571826177671939 1.5576940542907471 1.5582055931016052 1.5587172342202256 1.5592289776670696 1.5597408234626031 1.5602527716272956 1.5607648221816208 1.5612769751460571 1.5617892305410863 1.5623015883871947 1.5628140487048721 1.5633266115146132 1.5638392768369158 1.5643520446922832 1.5648649151012215 1.5653778880842415 1.5658909636618583 1.5664041418545906 1.5669174226829616 1.567430806167498 1.5679442923287312 1.568457881187197 1.5689715727634344 1.5694853670779869 1.5699992641514027 1.5705132640042327 1.5710273666570336 1.5715415721303647 1.5720558804447906 1.5725702916208797 1.5730848056792039 1.5735994226403398 1.5741141425248677 1.5746289653533725 1.575143891146443 1.5756589199246722 1.5761740517086569 1.5766892865189988 1.5772046243763027 1.577720065301178 1.578235609314238 1.5787512564361008 1.5792670066873882 1.5797828600887258 1.5802988166607435 1.5808148764240757 1.5813310393993603 1.5818473056072402 1.5823636750683616 1.5828801478033752 1.5833967238329358 1.5839134031777022 1.5844301858583378 1.5849470718955097 1.5854640613098887 1.5859811541221505 1.5864983503529748 1.5870156500230452 1.5875330531530496 1.5880505597636803 1.5885681698756331 1.589085883509608 1.5896037006863097 1.5901216214264471 1.5906396457507324 1.5911577736798823 1.5916760052346182 1.5921943404356651 1.5927127793037523 1.593231321859613 1.5937499681239848 1.5942687181176094 1.5947875718612328 1.595306529375605 1.5958255906814802 1.5963447557996164 1.5968640247507762 1.5973833975557263 1.5979028742352375 1.5984224548100845 1.5989421393010463 1.5994619277289064 1.599981820114452 1.600501816478475 1.6010219168417708 1.6015421212251391 1.6020624296493842 1.6025828421353139 1.6031033587037409 1.6036239793754814 1.6041447041713566 1.6046655331121906 1.6051864662188131 1.6057075035120567 1.606228645012759 1.6067498907417614 1.6072712407199097 1.6077926949680537 1.6083142535070474 1.6088359163577488 1.6093576835410204 1.6098795550777285 1.6104015309887441 1.6109236112949419 1.6114457960172008 1.6119680851764042 1.6124904787934393 1.6130129768891979 1.6135355794845756 1.6140582866004722 1.6145810982577924 1.6151040144774438 1. 615627035280339 1.6161501606873951 1.6166733907195328 1.6171967253976764 1.6177201647427557 1.618243708775704 1.6187673575174593 1.6192911109889625 1.6198149692111601 1.6203389322050024 1.6208629999914432 1.6213871725914415 1.6219114500259599 1.6224358323159649 1.622960319482428 1.6234849115463246 1.6240096085286337 1.6245344104503392 1.625059317332429 1.6255843291958954 1.6261094460617347 1.6266346679509471 1.6271599948845372 1.6276854268835139 1.6282109639688906 1.6287366061616844 1.6292623534829165 1.6297882059536128 1.6303141635948033 1.6308402264275221 1.6313663944728076 1.6318926677517021 1.6324190462852521 1.632945530094509 1.6334721192005279 1.6339988136243679 1.6345256133870927 1.6350525185097702 1.635579529013472 1.6361066449192747 1.6366338662482587 1.6371611930215084 1.6376886252601128 1.6382161629851648 1.6387438062177617 1.6392715549790053 1.639799409290001 1.640327369171859 1.6408554346456934 1.6413836057326225 1.6419118824537691 1.6424402648302596 1.6429687528832257 1.6434973466338025 1.6440260461031291 1.6445548513123498 1.6450837622826122 1.6456127790350688 1.6461419015908758 1.6466711299711938 1.647200464197188 1.6477299042900273 1.6482594502708854 1.6487891021609395 1.6493188599813715 1.6498487237533679 1.6503786934981184 1.6509087692368181 1.6514389509906655 1.6519692387808638 1.6524996326286199 1.6530301325551457 1.6535607385816569 1.6540914507293731 1.6546222690195189 1.6551531934733226 1.6556842241120173 1.6562153609568395 1.6567466040290308 1.6572779533498365 1.6578094089405062 1.658340970822294 1.6588726390164585 1.6594044135442618 1.6599362944269704 1.6604682816858558 1.6610003753421929 1.6615325754172612 1.6620648819323445 1.6625972949087311 1.6631298143677129 1.6636624403305862 1.6641951728186521 1.6647280118532159 1.6652609574555863 1.6657940096470774 1.6663271684490066 1.6668604338826962 1.6673938059694726 1.6679272847306663 1.6684608701876122 1.6689945623616498 1.6695283612741219 1.6700622669463767 1.6705962793997657 1.6711303986556456 1.6716646247353766 1.6721989576603238 1.6727333974518559 1.6732679441313461 1.6738025977201723 1.6743373582397161 1.674872225711364 1.6754072001565063 1.6759422815965377 1.6764774700528569 1.6770127 655468672 1.6775481680999764 1.6780836777335963 1.6786192944691432 1.679155018328037 1.6796908493317027 1.6802267875015691 1.6807628328590694 1.681298985425641 1.6818352452227261 1.6823716122717705 1.682908086594225 1.6834446682115436 1.683981357145186 1.6845181534166151 1.6850550570472986 1.6855920680587082 1.68612918647232 1.6866664123096142 1.6872037455920763 1.6877411863411949 1.6882787345784629 1.6888163903253783 1.6893541536034435 1.689892024434164 1.6904300028390509 1.6909680888396186 1.6915062824573863 1.6920445837138778 1.6925829926306206 1.6931215092291465 1.6936601335309924 1.6941988655576985 1.6947377053308101 1.6952766528718763 1.6958157082024505 1.696354871344091 1.6968941423183597 1.6974335211468232 1.6979730078510524 1.6985126024526225 1.699052304973113 1.6995921154341076 1.7001320338571944 1.7006720602639658 1.7012121946760184 1.7017524371149535 1.7022927876023766 1.702833246159897 1.7033738128091289 1.7039144875716907 1.7044552704692051 1.7049961615232987 1.7055371607556031 1.706078268187754 1.7066194838413913 1.7071608077381595 1.707702239899707 1.7082437803476869 1.7087854291037563 1.7093271861895771 1.7098690516268151 1.7104110254371405 1.710953107642228 1.7114952982637566 1.7120375973234094 1.7125800048428741 1.7131225208438425 1.7136651453480112 1.7142078783770809 1.7147507199527561 1.7152936700967465 1.7158367288307659 1.716379896176532 1.7169231721557674 1.7174665567901983 1.7180100501015563 4(a)The realized compounded rate of return
-4.7999999999999996E-3 3.7503999999999316E-4 5.5769902080000655E-3 7.5022065500163215E-4 5.9541218024077303E-3 1.1185083235780269E-2 1.6443245668606332E-2 1.1564318089396952E-2 6.7088093625677914E-3 1.8766070776274901E-3 7.0863654344313076E-3 1.2323214534690541E-2 7.4640631049240902E-3 1.2702876233069871E-2 1.7968931189481951E-2 1.3082680319772333E-2 8.2198834542372978E-3 3.3804280136568998E-3 8.5980062393280487E-3 1.3842715871772659E-2 8.9762708355880516E-3 4.1331847355772222E-3 -6.8665455115357599E-4 -5.4833586093080422E-3 -3.1187207407634698E-4 4.8865061911385066E-3 1.0111916023332501E-2 1.5364497986653847E-2 2.0644393376184622E-2 2.5951744221740958E-2 2.1027175849476665E-2 2.6336517163894069E-2 2.1410101881507382E-2 2.6721434411291378E-2 2.1793171526117261E-2 1.6888564302791842E-2 2.2176384837166552E-2 1.7269938189948153E-2 1.2387042486636357E-2 1.7651455107567049E-2 1.2766728123050797E-2 1.8033115109290732E-2 2.3326887307859145E-2 1.8414918248781387E-2 2.3710675823675142E-2 1.8796864579721406E-2 1.3906639629738704E-2 1.9178954155813388E-2 1.4286895175865455E-2 9.4183180790212706E-3 4.5731101522419326E-3 9.7968903250336137E-3 4.9498652514734509E-3 1.2610589826644869E-4 -4.6744994100452741E-3 -9.452061812877055E-3 -1.4206691916175296E-2 -1.8938499794977637E-2 -2.3647594995961807E-2 -1.8570562489940712E-2 -2.3281423789988986E-2 -1.8202487193696881E-2 -1.3097140127104057E-2 -7.9652452557649189E-3 -2.8066645310947935E-3 2.3787408133435495E-3 -2.4326771425605687E-3 2.7546729362981637E-3 -2.0585494937961357E-3 3.1307460488361194E-3 -1.6842815321983506E-3 -6.4761969808437847E-3 -1.3098732051440853E-3 -6.1035858137594712E-3 -9.3532445999089386E-4 4.259811852817208E-3 9.4819628744520212E-3 1.4731269081399212E-2 9.8605589898084212E-3 5.0132283066572914E-3 1.0239297093852073E-2 5.3901484678016143E-3 1.0618177239834381E-2 1.5873391761481503E-2 1.0997199481026287E-2 6.1444129235173062E-3 1.3149197414843439E-3 -3.4913918732748517E-3 -8.2746331922831651E-3 -1.3034914952960275E-2 -1.7772347361186047E-2 -2.2487040093852384E-2 -1.7403972702340287E-2 -1.2294473360392355E-2 -1.7035459888262494E-2 -1.1924044279681412E-2 -6.7860493099356489E-3 -1.1553476273247987E-2 -1.6298019587136392E-2 -2.1019789093118191E-2 -2.5718894105471235E-2 -3.0395443413764989E-2 -3.5049545285378958E-2 -3.0031802920862827E-2 -3.4687650266842729E-2 -2.9668026048230267E-2 -2.4622299783681023E-2 -1.9550335742556046E-2 -2.4256494130991846E-2 -1.9182627900472871E-2 -1.4082377565555193E-2 -1.8814782153240506E-2 -1.37126190204373E-2 -8.5839246393434321E-3 -1.3342721801074653E-2 -8.2121039544401642E-3 -1.2972685855458854E-2 -7.8401438219071196E-3 -2.6809125697809799E-3 -7.4680441894460214E-3 -1.2232197577336734E-2 -7.095805004738831E-3 -1.186174514071614E-2 -1.6604808764040691E-2 -2.1325105681973322E-2 -1.6235996231519501E-2 -1.1120423411923319E-2 -5.9782496136652208E-3 -1.0749554015519691E-2 -1.5497956156245274E-2 -1.0378545528257677E-2 -1.5128728509722023E-2 -1.0007397897972448E-2 -4.8594363670417806E-3 3.1529456384959964E-4 -4.4862188500569555E-3 6.9045281192292585E-4 -4.1128613615742937E-3 -8.8931196270387591E-3 -1.3650432652828948E-2 -1.838491057609537E-2 -2.3096663005330087E-2 -1.8016765652957734E-2 -1.2910452834352992E-2 -7.7775871890914949E-3 -1.2540254770583847E-2 -7.4054640953907791E-3 -2.2439725086866869E-3 -7.0332014406450094E-3 -1.179944207372996E-2 -1.6542804751776052E-2 -2.1263399288967588E-2 -2.5961334972380623E-2 -3.0636720564513276E-2 -3.5289664305803603E-2 -3.9920273917135818E-2 -4.4528656602333627E-2 -3.9560205616665622E-2 -4.4170316629705608E-2 -3.9200002276180035E-2 -3.4203842288016095E-2 -3.8839663845033678E-2 -4.3453233458577545E-2 -3.847919027256208E-2 -3.3479282061979365E-2 -2.8453374328701542E-2 -3.3116798131923808E-2 -2.8089005482209717E-2 -2.3035068310717111E-2 -1.795485066593272E-2 -2.2668667382736318E-2 -1.7586544453126463E-2 -1.2477994484282662E-2 -7.3428800556007978E-3 -1.2107634231333986E-2 -1.6849517587023577E-2 -1.1737135078475958E-2 -1.6480796830099287E-2 -1.1366496973615692E-2 -1.6111937788 14235E-2 -1.0995719864640652E-2 -1.5742940409290362E-2 -2.0467374295325746E-2 -2.5169130898708203E-2 -2.9848319070394425E-2 -2.4803530329560397E-2 -1.9732508687274053E-2 -2.4437792645575218E-2 -2.9120491240876456E-2 -2.4071917795328912E-2 -2.8756372589911372E-2 -2.3705905727378851E-2 -2.8392117379887449E-2 -2.3339756390262756E-2 -1.826112312349204E-2 -1.3156080963734107E-2 -8.0244925847454684E-3 -2.8662199461860771E-3 2.3188757100938151E-3 -2.492254893314616E-3 2.6947853812402389E-3 -2.1181495885896906E-3 -6.9079824705644555E-3 -1.1674824154705776E-2 -6.5355332403101984E-3 -1.3695180131597651E-3 -6.1629443266966177E-3 -9.9499163719529715E-4 -5.7902156773368407E-3 -6.2032479885887337E-4 -5.4173472398243439E-3 -2.4551744547129939E-4 4.9532058638124266E-3 1.2943047566604804E-4 -4.6711907906171746E-3 -9.448769074822283E-3 -4.2979026740113113E-3 8.7974823208392117E-4 -3.9244745594301245E-3 1.2551181728608363E-3 -3.5509063943689467E-3 -8.3338620436760324E-3 -1.309385950586639E-2 -7.9619475752967794E-3 -2.8033497026882515E-3 -7.5898936241153292E-3 -1.2353462134719551E-2 -1.7094165516472914E-2 -2.1812113521993859E-2 -2.6507415377088339E-2 -2.1445253937049102E-2 -1.6356769257521719E-2 -1.1241824457660754E-2 -1.598786370026406E-2 -2.0711121954502865E-2 -2.5411708569121227E-2 -2.0343849453680618E-2 -1.5249637470839628E-2 -1.0128935585687948E-2 -1.4880316694876661E-2 -9.7576943416899375E-3 -4.6084343522666549E-3 -9.3863138673757618E-3 -1.4141259560812358E-2 -9.0147941105285234E-3 -3.8616710399032028E-3 -8.643135018911674E-3 -3.4880793210099181E-3 -8.2713365402691252E-3 -3.1143474902783908E-3 2.0694579027722426E-3 7.2802190838667791E-3 2.4452740322642441E-3 7.6579894572321727E-3 1.2897811002409831E-2 1.8164879619622543E-2 1.3277688197448345E-2 1.8546732176075276E-2 1.3657707861630008E-2 1.8928727942510548E-2 2.4227157327811666E-2 1.9310866972638063E-2 1.441817481116936E-2 9.5489675720756839E-3 4.7031325277298031E-3 9.9275888168741666E-3 5.0799363905531525E-3 2.555526958785137E-4 -4.5456739570617355E-3 6.3068853836156791E-4 -4.1723387666225964E-3 1.0059650717910706E-3 6.2111960901645169E-3 1.3813823489317034E-3 -3.4252482863431633E-3 -8.2088070945687264E-3 -3.051492891460339E-3 2.132639345504117E-3 7.3437290701008351E-3 2.5084791705642928E-3 7.7215232622513952E-3 2.8844599505926105E-3 8.0994591423357853E-3 3.2605817384525615E-3 8.4775367634926102E-3 3.6368445870278432E-3 8.8557561788804584E-3 1.4101806111010751E-2 1.9375135502788021E-2 1.4482134852374706E-2 9.6126206050832774E-3 1.4862606232229902E-2 9.9912657223151236E-3 1.5243220304071325E-2 2.0522485049652595E-2 2.5829201971910853E-2 3.1163513822164868E-2 3.6525564094040286E-2 3.1550241386388844E-2 2.6598800227734198E-2 3.1937113988918409E-2 3.7303186981660907E-2 3.2324131684148938E-2 3.7692217168906694E-2 3.2711294526496015E-2 3.8081393258033946E-2 4.347941650297571E-2 3.8470715303761338E-2 4.3870763023341031E-2 4.9298890991062549E-2 5.4755245224216154E-2 6.0239972499382066E-2 5.51508206313851E-2 6.0637604898668318E-2 6.6152920444141561E-2 7.1696915630451219E-2 6.6552770435424957E-2 7.2098844841689269E-2 6.6952770386449201E-2 6.1831397088594198E-2 5.6734606382568886E-2 6.2229626335758237E-2 5.7130924129346505E-2 6.2628004934819126E-2 6.8153670560480384E-2 6.3026532941790059E-2 6.8554270913087523E-2 6.342521 0412704658E-2 5.8320769402723682E-2 5.3240829709590543E-2 5.8717682024080453E-2 5.3635837150364907E-2 4.8578385132043156E-2 5.4030992734729777E-2 4.8971643969603074E-2 5.4426296518245154E-2 5.990931326014004E-2 6.5420841689092901E-2 6.0306821648985265E-2 6.5820417121560171E-2 6.0704479119376709E-2 5.5613097619603646E-2 6.1102285727225647E-2 5.6008994755734953E-2 5.0940151580907367E-2 4.5895638853318932E-2 5.1334296175356231E-2 5.6801234515468257E-2 5.1728588589794011E-2 4.6680291364562976E-2 4.165622596601315E-2 4.7072838341036594E-2 4.2046888716999575E-2 4.746553253832797E-2 4.2437697982143918E-2 3.7433997031829591E-2 4.2828653816395112E-2 4.8251362816240428E-2 4.3219756274722521E-2 4.8644499007351127E-2 5.4097450402189384E-2 4.903778264025882E-2 5.4492779109988287E-2 4.9431213770260385E-2 4.4393943944163183E-2 4.9824792452672906E-2 5.528388137342688E-2 5.0218518742834339E-2 5.5679655040297149E-2 6.1169189246506717E-2 5.6075577138123389E-2 6.1567170139241734E-2 5.6471647722573293E-2 6.1965300290730774E-2 5.6867866849335202E-2 5.1794901088458412E-2 5.7264234574118555E-2 5.2189366248162727E-2 4.7138857290171421E-2 4.2112590775178482E-2 4.7531576247209495E-2 4.2503424681222812E-2 4.7924442489565289E-2 4.2894405165615268E-2 3.7888512020820331E-2 3.2906647163120306E-2 3.827776172836872E-2 4.3676806089356424E-2 4.9103925481021271E-2 5.4559265893522779E-2 4.9497381417233921E-2 4.4459793986431073E-2 3.9446386975296122E-2 4.4851508187567779E-2 3.9836220948267442E-2 3.4845007087715762E-2 4.0226201124571981E-2 4.5635377370419894E-2 5.1072681332746228E-2 5.6538259275676683E-2 5.1466875631153375E-2 4.6419834628123713E-2 4.1397019421908654E-2 3.6398313728683407E-2 3.1423601822785807E-2 2.6472768534036462E-2 3.1810426930413582E-2 2.6857736881147565E-2 3.2197397112929682E-2 2.7242849606787578E-2 3.2584512424743028E-2 3.7953951889351689E-2 3.2971772920282749E-2 2.8013508410265286E-2 2.3079043569895985E-2 1.8168264160760561E-2 2.3462739134396671E-2 2.8784745377895549E-2 2.3846578600081658E-2 1.8932115022801232E-2 2.4230562020919999E-2 2.9556560943428956E-2 2.4614689450900507E-2 1.9696538941536224E-2 1.4801995554616809E-2 9.9309459759546748E-3 1.5182586895029715E-2 2.0461536346883857E-2 1.5563320972418859E-2 2.0844250241475626E-2 2.6152640342731459E-2 3.1488634072513788E-2 3.685237496969096E-2 4.2244007319533372E-2 3.7241236084399665E-2 3.2262478151194429E-2 3.7630243037580779E-2 3.2649617871000292E-2 3.8019395883929663E-2 3.3036902783686761E-2 2.8078325650324976E-2 3.3424332943706725E-2 2.8463896145576983E-2 2.3527269444078236E-2 1.8614338550746679E-2 2.3911133111210736E-2 2.923547100338908E-2 2.4295140742572885E-2 1.9378524067008573E-2 1.4485507151486887E-2 1.9760831788674604E-2 1.4865979796088835E-2 2.0143282891028624E-2 2.5448027962062136E-2 3.0780357707465011E-2 2.5832611990469045E-2 3.1166941572819518E-2 3.6529009668998302E-2 4.1918960519277126E-2 3.6917749508784459E-2 3.1940544311142238E-2 3.7306635141560296E-2 3.2327563292880779E-2 3.7695666622003854E-2 4.3091684088438331E-2 3.8084844004813823E-2 4.3482885193638854E-2 4.8908996196645793E-2 4.3874233014901787E-2 3.8863636696430337E-2 3.3877091240287482E-2 2.8914481202334086E-2 2.3975691692562862E-2 2.9300365289364194E-2 2.4359723535975153E-2 2.9686394098362268E-2 3.504076 334767392E-2 4.0422975317081944E-2 4.5833174788730835E-2 5.1271507297632413E-2 4.6225404062603781E-2 4.1203522123103298E-2 3.6205745216912444E-2 3.1231957639871188E-2 2.6282044243199687E-2 3.16187108732644E-2 2.6666941061072702E-2 3.2005609154590386E-2 3.7372038322194268E-2 4.2766372921469786E-2 3.7761094331446809E-2 3.2779841078655947E-2 2.7822497841478278E-2 2.2888949851839202E-2 1.7979082892550347E-2 1.3092783294666122E-2 1.8360865767798495E-2 1.3472733612112986E-2 1.8742791826896088E-2 2.404025434439605E-2 2.9365263666986996E-2 2.4424310401385485E-2 1.9507073711458878E-2 1.4613439757643842E-2 1.9889429644383672E-2 2.5192854678534493E-2 3.0523857522863018E-2 3.5882581581982098E-2 4.1269171006208527E-2 4.6683770695440829E-2 4.1659688596102695E-2 4.7076318976802423E-2 5.2521115835481913E-2 4.7469014479471605E-2 4.2441163209970156E-2 4.7861857258661988E-2 4.2832120343820446E-2 3.7826526166170105E-2 3.2844958840572369E-2 2.788730303813769E-2 3.3232317013936141E-2 2.8272801892269328E-2 2.333709244318638E-2 1.8425074399458952E-2 1.3536634042341511E-2 1.8807024539361672E-2 1.3916750821572732E-2 1.918911792584499E-2 2.4488901339059455E-2 1.957135461263193E-2 2.4873125656617701E-2 1.9953734653465949E-2 2.5257494073664066E-2 3.0588833042847208E-2 3.5947894974670103E-2 3.0975345078791738E-2 3.633641687320166E-2 3.1362002072210293E-2 3.6725084482985837E-2 4.2116054922297419E-2 4.7535058407893516E-2 4.2506890127535613E-2 4.792792595619888E-2 5.3377151171171144E-2 4.8320940845549387E-2 4.328900032949079E-2 4.8714103131204167E-2 4.3680275436174254E-2 4.9107412868442557E-2 5.456277141535848E-2 6.0046497826718337E-2 6.5558739615417361E-2 6.0444057665263395E-2 6.59583667651229E-2 7.1501350272301645E-2 7.7073157293717776E-2 8.2673937711645218E-2 7.7477102810629361E-2 8.3079983745244723E-2 7.7881199823267577E-2 8.3486182062348702E-2 8.9120310209072962E-2 8.3892532720069468E-2 7.8689848563013198E-2 8.4299035775540876E-2 8.9937390761573699E-2 8.4705691285918094E-2 9.0346160880604875E-2 8.5112499308378053E-2 7.9903959311697914E-2 8.5519459900118777E-2 9.1164161091599416E-2 8.5926573118359606E-2 8.0714125567391548E-2 7.5526697764668027E-2 8.1119436593044325E-2 7.5930063297397599E-2 8.1524899626544078E-2 8.714882910460231E-2 9.2802003015946433E-2 9.848457343162953E-2 9.3211847479157672E-2 9.889654908604939E-2 0.10461081114129689 0.11035478735923165 0.11612863225349979 0.11077121481868302 0.11654722513574023 0.111187798455088 64 0.10585409702250415 0.11160453832702122 0.10626883654305153 0.10095874612764488 0.10668373160750866 0.11243848701186776 0.10709878227421066 0.10178470811929441 0.10751398860151484 0.10219792145622764 9.6907371433237799E-2 9.1642216050358272E-2 9.7318755573820193E-2 0.1030248131028042 9.7730293999910733E-2 9.2461188588711218E-2 9.8141986769372691E-2 0.10385232510057363 0.10959235719109661 0.11536223744849039 0.11000849870873752 0.11578054290202311 0.11042479629609336 0.10509475727387207 0.1108412500116962 0.11661762451175717 0.12242403615921837 0.12826064114724645 0.1228449900697397 0.11745533411740494 0.11209154851364134 0.11787442456591246 0.12368737157365528 0.12953054590583846 0.13540410474454889 0.12995416504177504 0.13582992669999228 0.14173624231883242 0.136255908355702 0.13080187999559456 0.13668204977157172 0.13122597593266816 0.12579609124819124 0.12039227001019981 0.11501438711415091 0.10966231805600302 0.10433593892933413 0.11007848581176671 0.11585089393798809 0.12165331858646566 0.12748591584311542 0.12207398344706832 0.11668802832652236 0.11132792579055506 0.10599355174676028 0.10068478269837589 9.5401495741423759E-2 9.0143568561865006E-2 8.4910879432767983E-2 7.970330721149077E-2 7.4520731336875645E-2 6.9363031826458643E-2 6.423008927369156E-2 6.9764085737914927E-2 7.5326858983752132E-2 8.0918558650467709E-2 7.5730149568945526E-2 8.1323946346704146E-2 7.6133591404240031E-2 8.1729486079542113E-2 8.7354479407155905E-2 9.3008722700073321E-2 8.7762280831112927E-2 9.3418644691434904E-2 9.9104421643830376E-2 9.3828720419939948E-2 8.8578342561924206E-2 8.3353166517627031E-2 8.8986602983518903E-2 8.375946728919792E-2 8.9395016519101755E-2 9.5059870605001207E-2 0.10075418193214736 9.5470561858872927E-2 9.0212303161950391E-2 8.4979284106772912E-2 7.9771383543060459E-2 7.4588480902053833E-2 6.9430456193724011E-2 6.4297190003994142E-2 5.9188563491974877E-2 6.4696344022133312E-2 7.0232765011048581E-2 6.5095647738995455E-2 7.0634145107238311E-2 7.6201442661796071E-2 8.1797690163637471E-2 8.742303815248853E-2 8.2203407569356512E-2 8.7830865288717197E-2 8.2609277135331283E-2 8.8238845376435115E-2 9.389768737239268E-2 9.9585955346729316E-2 9.4307942761064911E-2 8.9055264635811815E-2 8.3827799365559841E-2 8.9463703922260773E-2 8.4234278143433983E-2 8.9872296389780004E-2 8.4640909367108996E-2 7.9434633002146926E-2 8.5047693093758259E-2 7.9 839464166908236E-2 8.5454629380576241E-2 8.024444715954937E-2 7.5059273813183447E-2 8.0649582037012113E-2 8.6268959863604611E-2 9.1917558454895465E-2 9.7595529758861099E-2 9.2327071216018464E-2 8.708390127418153E-2 8.1865898548065363E-2 8.7491601220515358E-2 8.2271641534656936E-2 7.707673765529055E-2 8.2677536691098119E-2 7.7480684514980913E-2 8.3083584074458816E-2 8.8715618711646016E-2 9.437693992894669E-2 8.9123930617287739E-2 8.389613575032473E-2 7.8693434298723108E-2 8.4302640157076558E-2 7.9097987484322507E-2 7.3918317144397783E-2 7.950269239354868E-2 7.4321079470059725E-2 6.9164338288603355E-2 6.4032349464818061E-2 6.9565317682035221E-2 6.443140415716142E-2 5.9322133417206935E-2 6.483060851097644E-2 7.0367727675233693E-2 7.593363985914503E-2 8.1528494786412775E-2 8.7152442959302245E-2 8.1934111233097573E-2 7.6740827499178765E-2 7.1572471527182602E-2 6.6428923663852002E-2 7.1974354066904223E-2 6.6828877167383061E-2 6.1708098556979563E-2 5.6611899683906008E-2 6.2106281562262389E-2 6.7629234226386226E-2 7.3180906244363575E-2 6.8029637894390538E-2 7.3583392011441484E-2 7.9166025649901162E-2 7.3986028726781505E-2 6.883089578889301E-2 6.3700507489106384E-2 6.923175012804994E-2 7.4791755228715839E-2 6.9632754803617969E-2 6.4498517580560577E-2 7.0033909871979549E-2 6.489774710459395E-2 5.9786237918491913E-2 6.5297126355668089E-2 6.0183700149160746E-2 6.569665538993652E-2 7.1238277997964339E-2 7.6808717043553854E-2 8.2408122372180426E-2 7.7212563384793986E-2 7.2041943080547011E-2 7.7616561184566057E-2 8.3220167302725967E-2 7.8020710499672852E-2 8.362641819427119E-2 8.9261275568881526E-2 9.4925434201839742E-2 0.10061904645968944 0.10634226550128001 0.11209524528188686 0.10675718810453372 0.10144475360163185 9.6157818784343929E-2 9.0896261254179045E-2 9.6568921812700825E-2 0.10227108020612707 9.6980179021137536E-2 9.1714674161835985E-2 8.6474443725859107E-2 8.1259366395974864E-2 7.6069321437274073E-2 8.1664881908747988E-2 8.7289539294673535E-2 8.2070549506058965E-2 7.6876610868429784E-2 8.2476369244945724E-2 8.8105246365019596E-2 8.2882341182467512E-2 8.8513329356616488E-2 9.4173598669270886E-2 8.892156539565832E-2 8.3694741881759072E-2 7.8493007120726599E-2 8.4101170757754584E-2 8.9738496845694904E-2 9.5405137029292542E-2 9.0147192371551998E-2 9.581595777188423E-2 0.10151420075229822 0.10724207459621038 0.10192731263814858 9.6638061537485331E-2 0.10234057945748032 0.10807275047065934 0.11383472877310696 0.11962666936272726 0.11425246134978617 0.10890404953530708 0.10358131009753757 9.828411980906937E-2 0.10399519723207673 9.869602028536284E-2 0.10440923959084691 0.11015216763671942 0.10482343723206311 0.11056851910567 0.10523779021396273 0.11098502672307542 0.10565229859480474 0.10034516756154965 9.5063510757254166E-2 0.10075784101319196 0.10648178178646073 0.10117066923388562 9.588505002156289E-2 9.0624801781459263E-2 9.6296050750722895E-2 9.1033829707119374E-2 8.5796867324525072E-2 8.0585042361367432E-2 7.5398234158032817E-2 8.0990304975654626E-2 8.6611454561528189E-2 9.2261834125248132E-2 9.7941595662699443E-2 0.10365089196014554 0.10938987659833832 0.11515870395664973 0.12095752921722447 0.12678650836915417 0.13264579821267386 0.12720909838125305 0.13307058569283559 0.12763184688150986 0.13349553248529378 0.12805475392936438 0.12264009111050345 0.12847781958427817 0.12306112605027364 0.11767043264523225 0.12348231889498762 0.11808960376429156 0.11272277366622285 0.11850893208928737 0.11314008921525875 0.11892841767917828 0.12474684545111003 0.13059552904745586 0.12516867050802793 0.11976786088958935 0.11439297515731939 0.10904388887656413 0.11481091709872238 0.1206079338676358 0.11522901578507105 0.12102820666715353 0.1268575533418228 0.13271721261920044 0.1386073421248204 0.14452810030386964 0.1390343654224111 0.13356700046838355 0.12812587886613525 0.13399213343623928 0.13988889253010783 0.14581631477126455 0.15177455960807529 0.15776378731803731 0.15220652113891076 0.15819799504883325 0.15263864467259891 0.1586323656248964 7 0.16465725392614594 0.17071347164656192 0.17680118169912418 0.18292054784395972 0.17724252921430872 0.18336419036622331 0.18951768415612769 0.19570317611373955 0.18996380086839348 0.18425197462422527 0.17856756514602901 0.17291044083332796 0.17900957512566129 0.18514042491631488 0.17945175087671661 0.17379038247250844 0.16815618863664028 0.17423060081755093 0.18033659994180229 0.18647435026149983 0.19264401688285981 0.18691932560182201 0.1812221128389333 0.18736446782569582 0.19353876305838957 0.18780977699570922 0.19398638783608702 0.20019511705283488 0.20643613166150976 0.21270959954614965 0.206888593468328 0.21316441415436338 0.21947286910796615 0.21361939933624785 0.20779402621943377 0.20199661489358056 0.19622703114209128 0.19048514139260919 0. 1847708127139247 0.17908391281289782 0.17342431003139591 0.17952611644355931 0.17386439108463025 0.17996848591827042 0.17430463718586275 0.16866797492737051 0.16305836864771917 0.15747568847821003 0.16349456205829682 0.15790978816041701 0.16393091905885138 0.15834405064736878 0.15278399920426144 0.14725063600808097 0.15321633931532319 0.15921306427976289 0.16524097221401779 0.15964781554739038 0.15408150603276294 0.14854191480380563 0.15451433276078563 0.14897266396353381 0.14345759517650891 0.13796899871966173 0.14388643751300401 0.14983464698807181 0.14431544068252911 0.13882272656725303 0.13335637747973017 0.13924983064262486 0.13378143145554033 0.12833928058455379 0.1229232520377479 0.12876245294834421 0.13463201770367572 0.14053210419573503 0.1350575500955955 0.14095984935609263 0.14689284057274432 0.14138775493799516 0.14732297126367278 0.14181582100160717 0.14775326327081562 0.14224404760711562 0.14818371665467267 0.14267243481473013 0.14861433147576686 0.15458712599944091 0.14904510779464353 0.14352969127722925 0.13804074875909844 0.14395856065264589 0.13846755956151324 0.13300291527561803 0.13889453043505129 0.13342783668896296 0.12798738307285595 0.13385291746483485 0.12841042346100351 0.13427815766300077 0.14017640408284859 0.1347035573432509 0.14060401584143589 0.14653515672381157 0.15249713953877553 0.14696515326898929 0.15292937206598811 0.15892460480073134 0.15336176669768786 0.14782563021753892 0.14231606719249479 0.13683295006997076 0.13137615190963481 0.13725930789956498 0.13180046322164696 0.1376858256 3039966 0.13222493366737376 0.12679025398577037 0.13264956330649658 0.12721284540262534 0.12180222374469274 0.12763559530816515 0.13349930040376767 0.13939349676586743 0.14531834294905011 0.1512739983323852 0.14574788314038978 0.15170577213271996 0.15769464214781026 0.15213770786550085 0.14660744686774652 0.15256980559145883 0.1470374705246198 0.1415316906661015 0.14746765545756535 0.14195981071136909 0.13647840361995445 0.14238809131877828 0.13690462848044804 0.13144748626374181 0.12601653832967585 0.12061165894569337 0.11523272298275411 0.12103193314226446 0.12686129919460432 0.13272097795041637 0.13861112703575862 0.14453190489634471 0.13903815175284229 0.14496115014195721 0.13946533662127569 0.14539055637170639 0.15134658726483941 0.157333589 51861676 0.16335172418411359 0.15776763590802978 0.15221035125567117 0.14667974156964392 0.15264247622580607 0.14710979233992227 0.15307476326008995 0.15907075202904242 0.15350721241930287 0.14797037779969013 0.14246011998625163 0.14840091261018018 0.14288858822965134 0.13740272300614897 0.14331721716578105 0.14926246669504328 0.15523863152185768 0.16124587240577148 0.16728435094228167 0.17335422956718172 0.17945567156093123 0.17379428433743871 0.16816007177261905 0.17423450414583685 0.18034052356739538 0.17467488905427175 0.18078319847735402 0.18692327110943641 0.19309527211920563 0.19929936753422561 0.20553572424540367 0.19974915276902561 0.20598784836342454 0.21225898517491437 0.20644014204607486 0.21271363078471461 0.21901974166479521 0.22535 864432145236 0.23173050927192396 0.23813550792013816 0.24457381256132305 0.25104559638664203 0.24504057752398611 0.23906438275187103 0.24550751754218081 0.25198415663340024 0.25849447424789407 0.26503864551398326 0.25896646001551615 0.2655130856075969 0.27209375365275656 0.26598770363522339 0.25991096265777425 0.2664624996635947 0.26038347966520936 0.26693747375946852 0.26085617388542315 0.26741262598962745 0.26132904538487711 0.25527466596702975 0.26180209423005851 0.26836346512005504 0.27495895513867952 0.26883915215401388 0.26274872422367457 0.26931501758963772 0.26322230550520742 0.2571588384387824 0.26369606439866411 0.27026728393353738 0.27687267380999181 0.28351241171380392 0.27735155213757756 0.27122026468731719 0.26511840741681802 0.2716 9702313538568 0.2655928774243359 0.25951803161269904 0.25347234506095795 0.24745567780466526 0.25394244732924953 0.26046294805536174 0.25441272590469599 0.24839154482035353 0.25488318085341954 0.26140857339385737 0.26796789797550558 0.27456133104497837 0.26844343665596249 0.27503934252657358 0.26891915368244601 0.26282834174477032 0.26939504912184331 0.27599590337727697 0.26987112304106597 0.27647445288087957 0.27034737550705135 0.26424970810461756 0.27082380658676164 0.27743209038101302 0.27130041634718416 0.27791117851218972 0.27177720485533108 0.26567267427202546 0.27225417217824011 0.27886989387356698 0.27273131838297382 0.26662220805473558 0.26054242145607276 0.26709724204764451 0.26101517528581586 0.26757245419730213 0.26148810641715503 0.2 5543296350635258 0.26196121491658575 0.25590380108498612 0.24987546283977813 0.25637481524654504 0.26290796428582719 0.25684600605725527 0.25081314522818032 0.24480924213108501 0.25128225019016681 0.25778891789115588 0.25175153108527826 0.24574312373606899 0.25222098797949677 0.24621032723719516 0.2402285176664567 0.24667770595832228 0.24069365296972234 0.23473832343546763 0.24115896271733228 0.24761298932346243 0.24162444697470975 0.24808089409897827 0.24209010580730306 0.24854897435750112 0.24255593928058516 0.23659167077203835 0.23065603075233243 0.23705544211224461 0.23111757599010585 0.23751938738525458 0.23157929432580526 0.2256677137130414 0.23204118582434941 0.23844779999063603 0.232503250550681 0.22658723494803779 0.22069961622028722 0.2 270472542246329 0.23342789994660107 0.23984172502632362 0.23389048474619734 0.24030671526687764 0.24675631018626554 0.25323944299923418 0.25975628810283036 0.26630702080096524 0.26022874710112065 0.26678193658604665 0.27336920265629416 0.26725703048354399 0.26117419673722297 0.26773230256025671 0.26164718750796734 0.26820775288300891 0.27480243319800057 0.26868338151865023 0.27528053510254735 0.2819119938850807 0.27575881631443222 0.26963517399612291 0.27623727690090294 0.28287371074078771 0.28954465403663998 0.28335483969726405 0.29002828486368992 0.28383614909634414 0.27767373558068176 0.28431763900570139 0.278152914338474 0.28479930949303411 0.2786322728074675 0.27249483789799167 0.26638686267608125 0.26030820573523594 0.26686180840505935 0.26 078087172471509 0.26733693225768373 0.26125371498284689 0.25519969715092916 0.26172673557611414 0.26828771460111001 0.2748828107170358 0.28151220133276444 0.27536094276636724 0.26923921024108854 0.2758392541343424 0.26971522571449746 0.27631774488821303 0.28295459716163185 0.27679641509525599 0.28343575645375152 0.29010962238731119 0.28391709619985206 0.27775429413809283 0.28439861646761111 0.27823350310856654 0.27209798229364535 0.26599191197863581 0.25991515080113836 0.25386755807729289 0.26038766937929503 0.25433780856627441 0.26086036517081923 0.25480823541799924 0.24878515588799277 0.25527883869861046 0.24925350027285709 0.25574961847427602 0.26227951649034242 0.26884336997609237 0.26275292180020715 0.26931923699356841 0.275919697025935 0.28 255447945046996 0.2892237627436125 0.2830354886824431 0.27687691833676742 0.2835166783121188 0.29019096503934194 0.28399804840715315 0.27783485777479888 0.27170125045747984 0.26559708445528396 0.27217818929445148 0.26607173398583805 0.25999458966270605 0.25394661563232512 0.26046713803361343 0.26702156715138825 0.26093986362906163 0.26749675091993286 0.27408773402471653 0.2807129902416452 0.2745655678884853 0.28119330884150551 0.27504358095906634 0.28167380758005356 0.28833851137946986 0.28215448652484842 0.27600014498952907 0.28263534574347471 0.28930504954134095 0.28311638530354255 0.28978859050712114 0.28359760527268696 0.29027231282010502 0.29698172884676977 0.2907562165483053 0.29746814887435669 0.30421498324850349 0.29795475132891069 0.3047 0411603582126 0.29844153627884928 0.3051934322674994 0.29892850379261526 0.29269364697441058 0.29941565393867764 0.29317845879977189 0.29990298678553073 0.30666248231681559 0.30039050240169485 0.29414862799016661 0.30087820085571559 0.30764276750016539 0.31444250989116629 0.32127761094260054 0.32814825451950225 0.32177314289780856 0.32864636324087737 0.33555532432973001 0.32914465877294719 0.3227647644108369 0.31641549354166476 0.3100966991726648 0.30380823501663601 0.29754995548855612 0.30429721525709663 0.29803658862386251 0.30478637888470672 0.29852340426606006 0.30527572596824371 0.29901040248359601 0.30576525657651077 0.31255523591070866 0.3062549707783373 0.31304749662638476 0.31987534360884218 0.32673869539560818 0.3336377366116654 0.34057 26528420463 0.34754363063682514 0.34107542120976841 0.34804901340005934 0.35505886826973976 0.34855458570204489 0.35556706954769557 0.34906034761386651 0.3425848579453199 0.33614045062718234 0.32972697646417193 0.3233442869771439 0.31699223439965363 0.32384059401853205 0.3174861591672431 0.31116222560324025 0.31798026917637712 0.32483376657609431 0.33172290216229006 0.33864786125353419 0.34560883013205279 0.33914990774741893 0.33272198819023124 0.33965214252882059 0.34661833366997064 0.34015456566835467 0.33372182375314652 0.32731995899913136 0.33422202278592694 0.32781775707655436 0.33472240941335252 0.32831574184816836 0.33522298370577897 0.34216614322104921 0.34914540716579889 0.35616096328306113 0.3496513906593024 0.34317306398413772 0.350157 56391685526 0.35717838324922302 0.36423571084211903 0.37132973653849821 0.36474735380311341 0.35819656650485832 0.36525918865068374 0.35870594454516036 0.36577121545679536 0.37287322577717075 0.38001216655121217 0.37338810815176626 0.36679584523263764 0.37390318362784747 0.36730844834643372 0.37441845227783532 0.38156542822968009 0.38874956845647457 0.38208357052788355 0.38927040509462874 0.39649461120112095 0.40375638317936691 0.39701835254010587 0.39031266444791335 0.39754229030304256 0.39083408730958791 0.38415808369050186 0.37751412488878744 0.38467719833820935 0.37803074778618595 0.38519650767467417 0.37854756443783577 0.38571601177291259 0.39292173503413186 0.38623571070596796 0.37958177929457926 0.38675560454691116 0.39396673369055524 0.40 121536070574626 0.39448952697435868 0.40174087251462542 0.40902992505170155 0.40226658141145344 0.39553570182067843 0.40279248747014607 0.41008700840499102 0.40331859076464704 0.41061584743662327 0.4179510498432939 0.42532439530247923 0.43273608215805215 0.42585894896369347 0.41901482600866768 0.41220355484382609 0.40542497778057562 0.39867893788722886 0.39196527898537004 0.39920349843609415 0.39248732164360089 0.38580338249971158 0.39300956008871024 0.40025320980117174 0.39353199439412601 0.38684304082103416 0.39405462463330365 0.40130370868139686 0.39457745087972618 0.38788347911550347 0.39510047320690411 0.38840399093551103 0.39562369168837574 0.38892469796827145 0.39614710639770667 0.40340707135097498 0.41070478812200029 0.41804045302023485 0.42541426337594013 0.41857227491173554 0.41176312799215919 0.4191042962577185 0.41229259563568132 0.419636517132987 0.41282226185074866 0.40604071499386496 0.39929171956189435 0.40656803650361639 0.41388219029343531 0.42123437768296124 0.41441245267008298 0.42176739742396752 0.42916058789057221 0.42230061706869737 0.42969658027745483 0.42283403669212305 0.43023277368292212 0.42336765636924412 0.43076916818236421 0.43820916785691266 0.44568785552976875 0.43874855382322586 0.43184256076487437 0.42496971647320292 0.43237955899886371 0.43982793270565801 0.44731503795572758 0.44036792577354 0.44785783898756248 0.455386699750298 0.46295471058899973 0.45593252797817252 0.4489440518438772 0.44198912039502658 0.44948746382108085 0.44252992399473956 0.435 60578035956476 0.42871487261383878 0.43614418995143089 0.44361213973917857 0.43668280146843053 0.42978672402138196 0.43722161498629331 0.4446951673842221 0.4522075822546201 0.44523698585979798 0.43829984832767099 0.44577900753897493 0.43883926830278774 0.44632123249796241 0.45384210290695193 0.46140208184206832 0.46900137266764719 0.46195016607884254 0.45493280528166413 0.46249845586912897 0.47010344783964864 0.47774798576841504 0.47065479543672661 0.47830220037299775 0.47120634981120735 0.4641445593321134 0.47175811104064058 0.47941125321805211 0.48710419173478603 0.47996609161445902 0.48766191529085434 0.48052113809745811 0.47341463663459038 0.48107639274509029 0.4739672260599137 0.48163185563542532 0.47452002272837523 0.46744232661927909 0.475 07302671769946 0.48274340645663161 0.49045367217020619 0.48329949454378918 0.47617965696997899 0.46909399461652312 0.47673328338852916 0.46964496362826424 0.46259066780284863 0.45557023259739493 0.46313919780690149 0.47074752163549749 0.47839540874800224 0.48608306487349195 0.49381069681083423 0.50157851243425067 0.50938672069890889 0.51723553164654335 0.50995280109463992 0.50270502764938563 0.49549204351666853 0.48831368170778844 0.48116977603559108 0.48887185887097639 0.49661399253710559 0.48943024537292734 0.49717528264886668 0.50496059411864103 0.49773678326687154 0.50552501453985932 0.49829849447006791 0.50608964664131251 0.51392131280384756 0.50665449050238909 0.51448909385300157 0.52236443714103742 0.5150570878427605 0.52293538469954304 0. 51562529485298514 0.50835029343769067 0.5161937149635667 0.5240779222813774 0.5167623482544268 0.50948188898280544 0.50223637591568804 0.51004800507044967 0.50279977464611147 0.51061433347427143 0.50336338467359498 0.49614724042716163 0.50392720607738295 0.49670835548821146 0.50449123893675041 0.51231459337922169 0.52017862926479386 0.52808355813697094 0.52074875705791346 0.51344916302403543 0.50618460704151991 0.49895492092772065 0.49175993730726764 0.49951708898126568 0.50731457784396849 0.50007946787031732 0.507879881103243 0.51572085648498001 0.52360260493870214 0.53152533848438344 0.52417401685965825 0.53209972174732867 0.52474564308294136 0.51742686399614324 0.52531748368892339 0.51799595976721657 0.51070957916033399 0.51856526897196797 0.5 1127615568090246 0.504022030133634 0.49680272438899253 0.50458609855581549 0.51240994626830583 0.50515037852621791 0.51297716049455433 0.50571487012418048 0.49848743874758439 0.50627957342907193 0.51411222721090333 0.50684448852029096 0.49961163497539363 0.49241349912751176 0.48524991433169973 0.47812071474290763 0.48580694245957079 0.49353313856036074 0.50129951088087465 0.50910626833745543 0.5018625582494356 0.50967224355233287 0.50242581678328158 0.49521417286272174 0.48803714483298055 0.49577493798611227 0.50355296766364011 0.51137144309549121 0.51923057459958799 0.52713057358750603 0.53507165257016132 0.5430540251635263 0.53564736584274142 0.52827625848669624 0.52094053244595995 0.5136400178902194 0.52151094598324876 0.51420769344252903 0.52 208157344843031 0.52999639763036233 0.52265241492173664 0.5305702074793297 0.53852917255822241 0.54652952425552526 0.53910618253909859 0.53171847286291096 0.53968340892179834 0.5322929285589737 0.54026085178748051 0.53286759969890052 0.54083851121733484 0.54885087147566503 0.5414163872925819 0.54943175250650356 0.54199448009447226 0.55001285139096368 0.55807291821819693 0.5661748973929317 0.55865725788544562 0.55117570304759544 0.54373005967296684 0.55175745598326631 0.54430902019454663 0.53689633689761274 0.54488819784948039 0.55292161647829774 0.56099680888398495 0.55350402420134182 0.54604720488517544 0.53862617830172654 0.53124077264587832 0.53920322466363713 0.53181504918525158 0.52446233694916233 0.51714491773180638 0.52503407130401181 0.51 771390776175252 0.52560602008211377 0.53353917138654094 0.52617818336388544 0.53411430991737774 0.52675056122977426 0.51942215853587137 0.51212893217489919 0.5199920026222089 0.52789596103584446 0.52056206042287245 0.52846898313707147 0.52113233201801346 0.5290422201445073 0.52170281748781355 0.52961567213875038 0.53756967363387198 0.54556503593676831 0.55360197412363954 0.54614468464784593 0.55418463700801479 0.56226639712045667 0.57039018238548311 0.56285230951003284 0.5553506184243846 0.56343844164019163 0.57156832153672088 0.56402479359334468 0.55651747458409662 0.54904619070609284 0.54161076899070348 0.5496271449894552 0.55768520614340056 0.56578516921534638 0.55826940040311257 0.5507897072811776 0.543345916686228 0.53593785628613411 0.54392 473313882217 0.53651389441975583 0.54450376667073863 0.53709014859071913 0.52971211587748357 0.52236949772127161 0.51506212413220953 0.52294044717769705 0.51563033303124417 0.52351161076300667 0.51619875503134427 0.52408298855750735 0.53200822009800652 0.52465458064153614 0.51733623865445666 0.51005302470891523 0.50280477019031244 0.49559130729339884 0.50336838209132462 0.51118589767819955 0.51904406434612627 0.5117526528372649 0.51961376663201886 0.52751575821850549 0.5354588401612419 0.52808863772846792 0.52075381226737116 0.52866173209116174 0.52132415577712421 0.51402179982939389 0.50675449519021276 0.51458961856520191 0.50731958839608882 0.51515765025574867 0.52303647003707865 0.51572589498090071 0.52360766963480154 0.51629435282055436 0.509 01613992701567 0.51686302385463634 0.50958208134013394 0.51743190816310269 0.52532255408555106 0.53325423136679606 0.52589461105623547 0.51857031692316546 0.52646688257116603 0.53440451036053616 0.52703936871080548 0.53497997342810177 0.54296186928992807 0.53555565231733637 0.52818498518621304 0.53613154710918143 0.52875811568305742 0.5367076578846095 0.52933146112676344 0.52199067011335498 0.51468511489681079 0.5225614774942744 0.53047879717724467 0.53843728692256643 0.53105278794533817 0.52370373456320052 0.53162699398292923 0.53959145435164069 0.53220141537075283 0.52484684857697328 0.53277605218957369 0.54074648766095956 0.54875836939679679 0.5568119129176603 0.54933921573565558 0.54190238750012432 0.53450125604012366 0.52713565001113105 0.51 980539889107757 0.52770838696531142 0.53565247057753118 0.54363786342453446 0.55166478031434218 0.54421678936883322 0.55224671667355141 0.54479593243351832 0.53738091195783744 0.54537529270001839 0.55341124422205867 0.54595487024979272 0.53853428687259375 0.54653466516433147 0.55457664542318619 0.54711467752515475 0.53968852707303405 0.53229802214308353 0.5249429916367967 0.51762326527694014 0.52551490625638042 0.53344758376891366 0.54142151120451221 0.5340226879507306 0.5419996059280745 0.53459800781961975 0.54257791746028183 0.55059932263107547 0.54315644588244627 0.55118085940103523 0.5437351912759103 0.55176261427054518 0.54431415372204661 0.55234458732140146 0.54489333330225875 0.5529267786354306 0.54547273009798047 0.53805446099351006 0.530 67179958074107 0.52332457494275353 0.53124586273245589 0.52389588259134001 0.53182014118081522 0.5397856059149555 0.54779249106571348 0.54036308710859804 0.54837297516156291 0.55642451463240317 0.54895367696216768 0.54151869931274921 0.53411940955604797 0.54209683048573964 0.5346947656994081 0.527328230824051 0.51999705531609552 0.52790104000373939 0.52056711501172148 0.51326839285966508 0.52113738850253544 0.51383592903772324 0.52170787586871947 0.52962075682323695 0.53757478475871801 0.53019442579187603 0.52284949254807489 0.51553981498384416 0.50826522387192163 0.51610820303605576 0.50883088366148255 0.50158849541990747 0.50939675559609121 0.50215165116922988 0.50996283975530998 0.50271501812448438 0.49550198603748674 0.50327859636488181 0.511 09564506597938 0.50384238596966258 0.51166236637670504 0.50440638701809681 0.4971852363604099 0.5049705995894842 0.49774674071145464 0.49055755635603959 0.4983084556490911 0.49111657506197548 0.49887038125229788 0.49167580342228678 0.49943251760008289 0.50722956669160357 0.4999948647714838 0.50779483806829573 0.51563537122625092 0.50836032144436483 0.50112019190143187 0.49391481498030498 0.50168317201820267 0.50949192451269742 0.50224636327503647 0.49503558073131626 0.50280976575111924 0.51062437653302517 0.51847962329099695 0.52637571733211019 0.53431287106223735 0.54229129799176112 0.53488829976140062 0.52752083592254584 0.53546394426934318 0.54344835677954384 0.53603980466700207 0.52866681360460044 0.52132921289929834 0.51402683267738158 0.506 75950388053015 0.51459465330070908 0.50732459896486559 0.51516268687948297 0.50788990598246131 0.50065203443374551 0.49344890466846358 0.50121483897273977 0.49400900774567069 0.48683776450849137 0.4797009432388506 0.47259837871130417 0.48025589028060311 0.47315066200725608 0.48081104544969389 0.47370315243153538 0.46662937729986398 0.45958955628882459 0.46717942198152662 0.47480875497583064 0.48247776050170499 0.49018664485631391 0.49793561540956688 0.50572488060969678 0.49849740118277031 0.50628958766892085 0.51412229352479932 0.52199572945112838 0.51469014994976292 0.50741963723000394 0.50018402297129994 0.49298313966103757 0.48581682059066456 0.49354306805773618 0.48637406133105898 0.49410320644998063 0.48693151105902066 0.49466355491652769 0. 50243580540209387 0.51024847159018494 0.51810176364245408 0.52599589281339498 0.51867111252789067 0.5265682023130358 0.51924067494193316 0.51194831970221188 0.50469096776764122 0.51251536080003302 0.52038044067619338 0.52828641896770967 0.53623350834634187 0.52885958750627937 0.53680965736131214 0.54480106757959113 0.53738602245520894 0.54538042977197621 0.53796260370907079 0.54596000924835808 0.53853940120396593 0.54653980609022668 0.55458181308189602 0.56266563850992202 0.57079149983017374 0.57895961562929088 0.57138060947427016 0.57955178864353663 0.58776545794448309 0.58014418374634946 0.57255949166436704 0.56501120610437794 0.5731492643761209 0.58132964055087677 0.57373925827623262 0.58192270241926924 0.59014870047184953 0.59841747371430332 0.59074506984047459 0.58310949350524033 0.59134166287146783 0.58370322288968479 0.57610144741981428 0.56853616047219924 0.56100718690193263 0.56912442427382293 0.56159262703730861 0.5697129086979027 0.57787541582313184 0.57030161382718081 0.57846718221908233 0.58667521156662161 0.59492592266676825 0.58727027823796774 0.59552408368480525 0.58786556808311818 0.58024381335631925 0.57265864305220893 0.58083646799608046 0.58905681762966022 0.5973199130813347 0.58965277749854428 0.59791897194153676 0.60622815059563284 0.61458053697873027 0.62297635577101973 0.61518606926331887 0.6074331761308549 0.59971749688542686 0.60803602786923117 0.61639781521415138 0.62480308385326522 0.63325205988930233 0.62541245000183365 0.63386459474184331 0.64236069063450096 0.65090096622580051 0.64297664158791656 0.65152012012417382 0.64359282354757763 0.63570357799454924 0.64420923660012108 0.63631703226444047 0.64482588083221581 0.63693071660422107 0.62907344916452068 0.62125389660853103 0.62968441687089549 0.63815877583862424 0.64667720147298513 0.63877315090591469 0.64729477129062563 0.65586070410133712 0.66447117976266412 0.65648171809980327 0.6485306058529241 0.65710296500335952 0.66571990042137719 0.67438164390356858 0.68308842845186724 0.69184048827981703 0.70063805881887231 0.70948137672473055 0.70127586611645176 0.71012250062025739 0.71901513762348279 0.72795401633912515 0.73693937722408887 0.74597146198565434 0.73759079896812318 0.74662627112275759 0.75570872773259601 0.74728132583947948 0.73889437547545 0.73054768247316781 0.72224105359729651 0.71397429654002953 0.70574721991663725 0.69755963326103743 0.68941134702138429 0.6813021725556816 0.69004494385297122 0.69883317756100682 0.70766711008432415 0.69947030795591925 0.70830755355729025 0.70010767730021528 0.69194716044917426 0.6838258140790181 0.67574345017143878 0.66769988161061589 0.67637192099499122 0.66832533577421516 0.67700062752024115 0.68572103078334656 0.67762956983558653 0.6695769479003757 0.66156297855045376 0.6702031060389162 0.67888816219031867 0.67082949901180511 0.67951781240666675 0.67145612690711465 0.68014769876703185 0.67208298981295012 0.66405699146184793 0.67271008781744968 0.66468107939592591 0.65669061021482533 0.66530540138794247 0.65731193546128042 0.66592995752567918 0.67459279330481281 0.66655474789694957 0.6585552851070442 0.65059421973853038 0.64267136748378539 0.65121325859470125 0.65979956753939395 0.66843052529059888 0.66042205876920401 0.65245203288711173 0.64452026312925348 0.6530717684975258 0.66166774169371312 0.67030841395052065 0.66229093356355806 0.67093484641808865 0.67962370761946289 0.68835775089908435 0.68025363369476866 0.68899095258998155 0.68088379601754956 0.68962439175684098 0.69841043859397667 0.69025806848872562 0.69904741044486718 0.70788245697918062 0.69968462118568042 0.70852298121584623 0.71740730071816872 0.72633781868190339 0.73531477533904943 0.74433841217081276 0.75340897191410106 0.76252669856805455 0.77169183740060854 0.76318771658108564 0.75472441554149627 0.76384898250231226 0.77302099721132445 0.78224070639682353 0.7736859510061187 0.78290911795135076 0.792180245364698 0.80149958264059462 0.79285238464391972 0.80217521704406836 0.79352477600225679 0.80285110483746869 0.79419741953424872 0.78558527192048433 0.77701446261526597 0.76848479319471275 0.75999606618737814 0.76914804573155271 0.77834761556935694 0.78759502317031771 0.79689051729080362 0.78826544280780775 0.79756442311040843 0.80691175811058269 0.81630769925275781 0.80758942229634445 0.79891299306932195 0.80826734063328254 0.79958765739824278 0.7909496366427311 0.78235307838684598 0.79162131439445771 0.78302153208536418 0.77446302873135431 0.76594560619344376 0.75746906728371521 0.76660790643359067 0.7757942675470455 0.76727045506281955 0.75878755687851807 0.76793325217428654 0.77712650508559289 0.78636756291203813 0.79565667423918085 0.80499408894522473 0.79633011731828751 0.80567103392834283 0.79700381296548684 0.78837819466325243 0.77979397932886885 0.78904890802137917 0.79835196234309058 0.80770339254727475 0.81710345018852082 0.80838135362761587 0.81778493666647956 0.82723741833714537 0.81846667872912704 0.82792270545851876 0.81914867647231793 0.82860824958997426 0.83811701248784232 0.82929405082790053 0.82051343938392662 0.8117749748748837 0.82119620474423316 0.81245446296146073 0.80375468153924556 0.7950966590678572 0.80443116169501017 0.79576989211887406 0.78715019663670338 0.79644337765921436 0.80578488322304254 0.79711711578357192 0.80646212478564672 0.8158557278345322 0.82529817761927204 0.81653674636669948 0.82598273744780659 0.81721802030805701 0.80849537381057823 0.8178995497543935 0.82735262741311644 0.81858133480153339 0.80985214439448594 0.81926337554533735 0.81053091134271971 0.81994567208170199 0.81120993285570986 0.8206282245065597 0.83009549127399396 0.82131103291587881 0.83078185028704166 0.84030191590853454 0.84987148587125905 0.85949081759778978 0.86916016984929856 0.86018820103402183 0.86986117967939891 0.86088584601693774 0.8519535939560563 0.86158375264462794 0.85264815063193367 0.84375543950890042 0.83490541339925772 0.82609786741494129 0.81733259765134947 0.82678272715913659 0.83628199734036435 0.84583066372653448 0.83697067654064705 0.82815321729325198 0.83765961402317712 0.82883884787586593 0.82006042140606161 0.81132413138331239 0.80262977555267234 0.79397715263001944 0.78536606229739525 0.79464996582134195 0.80398214564361314 0.81336285280095999 0.82279233963552523 0.83227085980163018 0.84179866827259886 0.83295803466489038 0.84248941644514797 0.85207036141066284 0.84318042367589152 0.83433315764224725 0.82552835848556438 0.81676582236483353 0.80804534641748238 0.7993667287546784 0.79072976845665588 0.78213426556806387 0.79140136374901804 0.78280263720302279 0.77424518454444824 0.78347125950407959 0.79274531005350091 0.78414013256524395 0.79341766125458335 0.78480925648056132 0.79409026461426047 0.80341953399025479 0.79476312022710149 0.80409588845228264 0.79543622818771165 0.78681813429241054 0.77824140724780699 0.76970584849301749 0.77890831890518131 0.77036955897443637 0.77957548068110372 0.78882927318064566 0.78024289266937852 0.7716977267845655 0.76319357769599949 0.7547302485230587 0.74630754333014804 0.75538834255546505 0.76451636193675365 0.75604668339945724 0.76517812615313452 0.774357052409131 0.78358370908165864 0.77502250727806654 0.78425262431591269 0.79353073796235551 0.78492179042013621 0.77635416582611949 0.76782766583015416 0.77702036969247112 0.78626087561487212 0.79554943216806961 0.80488628921534366 0.81427169791926368 0.80556319376925112 0.79689649043915867 0.80624035218944257 0.7975703984989333 0.80691776457112785 0.81631373694689779 0.82575856837902184 0.83525251293459291 0.82644330087250673 0.81767637302831875 0.8271282901680661 0.81835807437525943 0.80962995561825823 0.81904003138747328 0.81030863923681329 0.80161915776847659 0.79297138581118776 0.80229483701740612 0.79364382179972259 0.78503433145508383 0.77646616666409929 0.76793912906411155 0.77713241253524501 0.78637350108042847 0.77779890827524234 0.7692654735155211 0.76077299924264663 0.76992901883870846 0.77913264973666996 0.77059281301793381 0.77979989564562713 0.77125685614652806 0.7627548232370247 0.77192114831785741 0.78113513828911052 0.7725856896253227 0.78180313521137457 0.79106851151447377 0.80038206777434917 0.809744054526776 0.81915472361031538 0.81042278093698572 0.80173275158848822 0.81110176189674843 0.80240847343964394 0.81178099750153021 0.82120225868853836 0.81246048784683333 0.80376067750516844 0.81314023302819538 0.82256856223994212 0.83204591876359002 0.84157255754116078 0.83273300926496319 0.8422632209131411 0.85184298966188954 0.86147257320813164 0.85253750485673252 0.8621706998819878 0.87185398752137422 0.86286908838127152 0.87255600764085428 0.86356773880417803 0.85462261365791803 0.86426665124893942 0.85531817132294452 0.86496582581382397 0.8560139898499175 0.84710512269863791 0.83823901810968438 0.82941547082275791 0.82063427656280852 0.811895232035307 0.80319813492153758 0.79454278387391408 0.80387440635005869 0.81325455326307927 0.8045509314074164 0.81393459625073517 0.80522771018873152 0.81461489428171308 0.8059047427891608 0.81529544745166471 0.80658202930389677 0.79791043556323804 0.80725956982816705 0.81665731959127363 0.80793736445723541 0.8173386387524133 0.82678879967392604 0.81802021343549125 0.80929371641100079 0.81870204373633815 0.8099722739264037 0.81938412975082109 0.82884492722552561 0.83835492084709862 0.82953081722703259 0.82074906930434288 0.81200947377168209 0.82143192303529511 0.83090336903507889 0.82211503286371057 0.83159003103460205 0.822798398885636 0.81404896657098491 0.80534153153144405 0.79667589218009316 0.80601860681942972 0.79734971750669636 0.80669593603773126 0.81609075490512772 0.8255344268306346 0.81677186158184756 0.82621907526207328 0.81745322370081519 0.82690398046405966 0.836403881162473 0.82758914253289317 0.83709260607406444 0.84664548762564973 0.83778158928504665 0.84733805354932912 0.85694421142778587 0.84803087921293252 0.83916033099271048 0.83033236140394551 0.82154676606920662 0.83101880925276661 0.82222991896835329 0.83170551454698893 0.82291332807716344 0.8323924773831648 0.82359699349172555 0.81484372792296522 0.80613247802893495 0.81552436691468566 0.82496509362264225 0.81620526117325354 0.80748747591962178 0.79881153603520749 0.80816535602259076 0.79948616231368219 0.80884349035771352 0.80016104160399637 0.79152026860429725 0.80083617400103968 0.79219216036583462 0.7835896379960785 0.7750284077336973 0.7665082713765754 0.77569411438773384 0.76717078263867267 0.75868836288200692 0.76783354236899348 0.77702627678931235 0.76849655066072353 0.76000776721755203 0.76915980760708336 0.76066784053056935 0.75221663489602264 0.76132816139748205 0.77048706783674903 0.76198872991113253 0.77115107130667049 0.78036105687746526 0.77181532380445339 0.78102876348823669 0.77247982542349303 0.78169672051569528 0.79096154346237713 0.78236492805375768 0.77380957639909953 0.78303338619637497 0.79230515980459626 0.80162514663558038 0.79297734593172953 0.80230082813057479 0.81167279243685386 0.8210934909575256 0.8123522422009295 0.80365295143836502 0.81303194678584467 0.82245971290913134 0.83193650341625891 0.84146257323402374 0.83262355288250034 0.84215319535748945 0.8517323919733486 0.84284407649187654 0.83399842492471543 0.84353521673432419 0.83468624769399935 0.82587975370506816 0.81711553088728373 0.82656453164789778 0.83606266721246691 0.84561019308197194 0.83675126415517842 0.82793485808723344 0.81916077076841476 0.81042879906872622 0.81984302882388382 0.81110778228552904 0.82052554275341394 0.82999227557573185 0.82120831265296834 0.81246651275223414 0.80376667349102338 0.79510859345826645 0.78649207220966666 0.77791691026306031 0.78716207819642836 0.79645532100305005 0.80579688867226618 0.79712906360663927 0.80647413473739404 0.79780305889065461 0.80715163479688612 0.79847730694986097 0.80782938894600043 0.81723010176851973 0.82667969829771626 0.8179116357458871 0.82736477625176597 0.81859342532575741 0.80986417688419365 0.80117682883514951 0.79253118005674072 0.80185234219303592 0.79320345095050926 0.80252810889545212 0.81190125506170863 0.80320412903741234 0.79454874921803276 0.80388040271396677 0.8132605808080795 0.80455693002020068 0.79589505675610361 0.78727476048367429 0.79656858923818952 0.7879450600098461 0.79724237432189748 0.80658803466837159 0.81598229244864728 0.8072655774448938 0.81666335844760751 0.82611000791153533 0.83560577995267549 0.84515093000842967 0.8547457148444737 0.86439039256166517 0.85544131867736906 0.86508961353449165 0.87478807952487125 0.86578909674315185 0.8754912000462165 0.88524375428645707 0.89504702180874673 0.88595079610406469 0.89575774024380594 0.88665810309063553 0.8776021441958004 0.88736567534561872 0.89717997685741602 0.88807351296850046 0.87901076010625157 0.88878161605880424 0.89860328046231008 0.88948998471609086 0.89931533263661478 0.89019861903995889 0.90002765185896694 0.90990779564863367 0.91983931618600678 0.92982248063017425 0.93985755752945144 0.93054624125331009 0.92127961929529412 0.93127027331562973 0.92200017600371464 0.91277457515889671 0.90359325719813399 0.89445600956358295 0.90430718081331385 0.91420957815354331 0.92416346795994198 0.9341691179933338 0.94422679740689941 0.95433677675341544 0.94495596022499906 0.95506973121816929 0.94568539650832206 0.936346106605082 0.9464151063594286 0.93707231384890322 0.94714508988091772 0.93779879344948935 0.94787534717542687 0.95800429898073935 0.96818592133543935 0.95873862891302908 0.96892406978337697 0.95947323424841668 0.9696624950665087 0.9799047400408547 0.97040119728865859 0.98064728351455988 0.97114017655369 0.9813901054717693 0.97187943296550472 0.98213320601692544 0.99244029868821371 0.98287658525451027 0.97335877764528855 0.96388665551259112 0.9544599995661307 0.94507859156821317 0.93574221432868576 0.9458080738431951 0.93646819508874768 0.94653782970320943 0.95665982641766623 0.94726785925086143 0.9573936521189661 0.96757209910998498 0.9581277530342569 0.96831001735003519 0.95886212926675496 0.94945959104627442 0.94010218500925236 0.95019071637130059 0.94082980093271829 0.9509221158975687 0.96106691090023633 0.95165378972791514 0.942285851537221 0.95238573796521475 0.94301428642298157 0.93368781784815114 0.94374299450096166 0.93441302812735705 0.94447197587361953 0.93513851038942608 0.94520123064345118 0.93586426473636264 0.94593075891299194 0.9560495988593396 0.96622105677340842 0.95678319570089609 0.94739063636153165 0.93804316130699616 0.94812098574579262 0.93877000501421271 0.92946390899014442 0.9 3949712131689345 0.93018753513457231 0.9209226349659263 0.91170220631808974 0.92164305779094402 0.91241917111354742 0.90323955909220244 0.9131364047994821 0.9039533500564445 0.89481437397617358 0.90466740872084994 0.91457167924619864 0.90538173518581688 0.89623590285692489 0.90609632955178099 0.89694706716993244 0.8878417212475167 0.87878008098552862 0.88854973740665355 0.87948469866710166 0.88925801910017066 0.88018958060848984 0.87116467062156899 0.88089472690880122 0.871866432219639 0.88160013766718137 0.8913844583830508 0.90121965756664291 0.91110599978598961 0.92104375098487701 0.91182274098014959 0.90264599182344485 0.91253975098092699 0.9224849576860279 0.93248187946599548 0.92320596644455866 0.93320663747007049 0.94325931198491508 0.95336 426040723676 0.94398811195728194 0.93465696901988693 0.92537061556859146 0.91612883661386224 0.90693141819811562 0.91684746157274599 0.9076465937571967 0.89848989010716207 0.90836203753571954 0.91828552013090547 0.90907774963427701 0.89991417643603233 0.89079458838913927 0.900626720248763 0.89150371199156897 0.90133953129392541 0.91122649685665391 0.92116487464030872 0.93115493198843846 0.94119693763477863 0.93187919233413163 0.94192496413426929 0.95202297394776769 0.9621734934122963 0.95275506064391724 0.96290938695926576 0.9534874219018612 0.94411068227673223 0.93477895100180386 0.94483980154701341 0.93550457049958768 0.94556919426618569 0.93623046213370786 0.92693655591546609 0.91768726044707183 0.92765923420139673 0.93768306221924425 0.928382 18352059187 0.91912594903969302 0.92910540397469954 0.91984569803562088 0.91063043868504989 0.90145941257936157 0.91134700152477444 0.9021725359174555 0.91206383310422634 0.92200656503636846 0.91278093352419387 0.90359958504327764 0.91349830288550282 0.90431351103165225 0.89517280617870032 0.90502770477082972 0.89588357178792966 0.88678333064334747 0.89659460396269308 0.90645689590329925 0.91637047176199649 0.90717189349753879 0.89801746840875052 0.88890698456038852 0.89872930088010272 0.90860269324467935 0.89944140031710473 0.90931849559875388 0.91924695177586768 0.92922703592510247 0.91996674615266194 0.91075090577112916 0.90157930142342768 0.91146751379082969 0.90229246972463373 0.91218439056720202 0.9030059054924795 0.89387147714611559 0.9037 1960882727564 0.91361895079317756 0.92356976933730217 0.91433663444448299 0.9051478185991495 0.89600310906987346 0.88690229414633803 0.89671418607589914 0.90657709984349411 0.91649130076268048 0.9264570555266467 0.91721006166011865 0.90800745336415001 0.91792909212164386 0.90872303247945996 0.89956116192355839 0.90943887996556105 0.91936796214138217 0.91015499592310345 0.90098625194267257 0.9108713804527746 0.92080791163112918 0.91158803365529972 0.92152829143030757 0.93152023854574528 0.94156414378618325 0.9516602773338716 0.94229230800266905 0.93296930492425623 0.94302074530986246 0.9531244531854739 0.9632807003420385 0.97348975998381726 0.98375190673573321 0.99406741665075926 1.0044365672173434 0.99481527169470008 0.98524015839056545 0.9955634 0721419656 0.9859847028595683 0.99631182331443813 1.0066926447956734 1.0171274465486113 1.0074452348051781 1.0178839500261652 1.0081981070660393 0.99855875615212231 1.0089512616841136 1.0193978082448711 1.0298986768477447 1.0201551631988757 1.0104584184155212 1.0008082180071267 0.99120433856069234 1.0015586011212081 1.0119667058470387 1.0224289327174434 1.0127212738403997 1.0030602117259657 0.99344552270968101 0.98387698420067449 0.97435437467651109 0.9846210174248291 0.99494104671543848 0.98536532969120438 0.97583557610868654 0.96635156534336475 0.95691307782971657 0.94751989505613388 0.9576469985104259 0.96782676290268022 0.97805946206977423 0.96856477665183927 0.95911566572391038 0.94971191052843551 0.94035329335789908 0.95044313048336027 0.94108100345704004 0.95117462467501679 0.96132073272332708 0.97151960053348851 0.96205630645092777 0.97225899924447279 0.9627921560480992 0.97299867525954942 0.98325826837089925 0.99357121136642812 0.9840020695518692 0.99431888031353921 0.98474614968803409 0.97521936816953136 0.98549050888401313 0.99581505953021021 0.98623514724446526 0.99656357001013673 0.98698006487408807 0.97744256056269241 0.98772526187761867 0.97818418062060597 0.96868889655362711 0.97892607881570615 0.96942723363739081 0.95997398291593128 0.97016584762709424 0.96070905155848418 0.95129764811100337 0.96144439588118069 0.95202946278095091 0.9621800159874121 0.97238335207054671 0.96291591198060811 0.95349391560310104 0.96365208396423729 0.95422655396120892 0.9643885320418073 0.95495946708800661 0.94557566164598406 0.93623689847008329 0.94630533034212783 0.95642611805990718 0.96659953387381892 0.95715985611122445 0.96733708736300295 0.9578938693436605 0.94849597877081093 0.93914319807271096 0.94922674270268925 0.95936272176474335 0.94995778070027259 0.96009756115991429 0.95068909286634673 0.96083267614925183 0.95142067930373542 0.96156806683611507 0.9521525401153017 0.96230373332390151 0.97250771273718595 0.96303967571604732 0.97324748202977096 0.96377589411602793 0.97398752876543138 0.98425226391501175 0.97472785304821974 0.96524915935358813 0.9558159633886909 0.96598620639831223 0.97620933467158366 0.98648562321187616 0.97695049222045904 0.96746112985780086 0.9580173164344834 0.96819900647994284 0.95875165124883899 0.94934964332284455 0.95948626146812344 0.95008072741307648 0.94072033992149362 0.93140488228987039 0.92213413885487894 0.93212923637692446 0.94217630840608457 0.9328538621257354 0.92357616358753192 0.91434299800231167 0.9051541516119006 0.91506095320028269 0.90586866062492133 0.89672049105392171 0.90658343760740223 0.91649767148296091 0.9072984826598427 0.91721643476967407 0.92718596023047661 0.91793546762137024 0.90872937737678772 0.9186547701391472 0.90944522724247934 0.90027989015171528 0.91016134558050443 0.92009418457752323 0.91087773249155113 0.9208142967005073 0.93080253104335009 0.92153467889434193 0.93152665922459277 0.94157059785256081 0.95166676496139435 0.96181543213919385 0.9523987180649256 0.96255119139886336 0.95313094568014867 0.9437559171408838 0.95386344791001654 0.96402353783914885 0.97423646023591259 0.98450248982913946 0.99482190277625127 1.0051949766706878 0.99557004078266842 0.98599130458691153 0.97645854632489426 0.96697154530253471 0.95753008188508248 0.94813393749203412 0.9582642339669929 0.94886456564395139 0.9589986613853001 0.96918545442450377 0.97942521878751143 0.96992397773733141 0.96046834264419223 0.95105809459949997 0.94169301574542241 0.93237288926984441 0.923097499401349 0.91386663140422253 0.90468007157348218 0.91458440794566442 0.92454024686698211 0.93454785615069058 0.94460750500267432 0.93527338897866152 0.92598407671156391 0.93599919391046416 0.92670639777969388 0.9367252710481484 0.94679624245759886 0.93745162049380237 0.92815185271543199 0.93817824234955238 0.92887498678627445 0.93890513671756315 0.92959839206131889 0.92033631977942454 0.91111870544448315 0.90194533565834956 0.89281599804718947 0.88373048125656295 0.87468857494653141 0.88443695553625346 0.89423602770504207 0.90408605504910855 0.89494644198487272 0.90480016348319414 0.91470512433330686 0.90551453973650697 0.89636806994577167 0.90622918390948981 0.91614157566581933 0.90694409610262339 0.89779076444133077 0.88868136877201231 0.87961569820190655 0.87059354285053736 0.8803206292733603 0.87129509025284801 0.88102582472216295 0.89080715901071827 0.88173128464746675 0.89151628732763366 0.90135217202173745 0.91123920331625063 0.90206525514033253 0.89293534191565893 0.88384925227446365 0.87480677586354627 0.86580770333940116 0.87550990339676615 0.88526255489442951 0.89506592017988074 0.88596960376301737 0.89577664570258531 0.88667691780321278 0.89648763777578977 0.90634937349222411 0.89719889649946127 0.88809234179626384 0.89791042197360449 0.90777955616786743 0.89862221429826161 0.88950882766962991 0.89933427357351214 0.89021746906035926 0.90004659989947333 0.89092637621995574 0.90075919337629973 0.91064314118185674 0.90147205410418385 0.89234498824448383 0.88326173230091021 0.87422207598586588 0.88396803078099251 0.89376466454105374 0.90361224079666735 0.89447490204084334 0.90432617153145589 0.9142286676234197 0.9050403700188272 0.89589617624273687 0.88679587459677167 0.87773925439870704 0.86872610597759325 0.87844348172867681 0.86942695301637918 0.86045370364190044 0.85152352586441937 0.86115144819891443 0.87082943572954896 0.86184945443804706 0.87153107160112508 0.881263033173451 0.87223297061421845 0.88196858206141249 0.87293513286751767 0.88267439555842886 0.87363755845974844 0.8833804737637394 0.89317405222731105 0.88408681677661982 0.87504320005609193 0.86604299269582263 0.85708598633088262 0.84817197359649432 0.85778246785919632 0.8674429366920644 0.87715363996286322 0.86814330249104144 0.85917621463908445 0.86884393095520784 0.87856191939617512 0.8695448221830735 0.86057100703659462 0.85164026620281885 0.84275239292504533 0.85233470536825573 0.84344349878248814 0.83459496998833216 0.84413486383227165 0.83528301648587666 0.84482648817160344 0.83597132102837968 0.82715865868744332 0.81838829712574346 0.82784391627079756 0.81907026547269779 0.82852943085315589 0.8380377838935924 0.82921520253090319 0.83872712158406415 0.82990123140046057 0.83941671780374305 0.83058751755828508 0.8218006974740053 0.83127406110087021 0.82248394560758609 0.83196086212474563 0.84148705860779449 0.83264792072647698 0.84217768991425479 0.85175701390180913 0.86138615037409871 0.87106535835604415 0.88079489821949575 0.89057503169023722 0.90040602185502672 0.89128407295012257 0.9011187501294633 0.9110045676301366 0.90183174570551183 0.91172127078318077 0.92166222139125353 0.93165486494248828 0.9416994702401893 0.93237931278303643 0.94242768520950837 0.95252830917259801 0.94315617328856938 0.95326058538967007 0.94388493457979949 0.93455428689381637 0.94461396918566432 0.95472596182543001 0.94534327720866784 0.95545906225015309 0.94607285875135227 0.95619243761685957 0.94680271391629867 0.93745806088950046 0.92815826219723085 0.93818468516065656 0.92888139867188535 0.93891158194497937 0.92960480635164333 0.92034270328115531 0.9111250583054058 0.90195165802553978 0.91184180664727266 0.92178338404183857 0.91255882379843767 0.92250412968218964 0.91327610985971508 0.92322514563098568 0.91399366493195688 0.90480649534028346 0.91471148911605304 0.92466798885945667 0.93467626240152613 0.94473657896601426 0.95484920917663763 0.94546593297258963 0.95558235582404727 0.94619556051609188 0.93685382182561461 0.92755692348085161 0.93758021948295212 0.92827983442943385 0.9190240912241725 0.92900301649853834 0.93903383218433101 0.92972646978984619 0.93976104743275357 0.93045019440507626 0.9211840334719319 0.91196235011126658 0.90278493083073252 0.91267941247105244 0.92262534541590213 0.9133967437579058 0.90421243938786788 0.91411434407268488 0.90492659522113583 0.91483221351628585 0.92478934102657062 0.93479824559990887 0.92551121402102932 0.91626876019372827 0.92623335774673587 0.93624977120701902 0.94631827001729563 0.95643912502138573 0.94704821722128307 0.93770238577862086 0.94777843818466989 0.95790688606323027 0.96808800187075916 0.97832205948048734 0.98860933418978614 0.97906400938567506 0.96956450214062384 0.97980623755175533 0.99010122998702466 0.9805487440830869 0.99084759755231921 1.0012000050595913 0.99159424503530524 1.0019505351094891 1.0123606778920586 1.0228249534170977 1.0333436431748666 1.023583593687627 1.034106228374803 1.044683580762352 1.0553159353823163 1.0454504188924809 1.0356322568817968 1.0462175446175825 1.0568578758495941 1.0469849580455159 1.0371594302468976 1.0273810649817126 1.0379234465196174 1.0281414139763232 1.018406335189237 1.0289020481322213 1.0191633183011866 1.0296629675563529 1.0199205853120823 1.0102249665025842 1.0206781363283977 1.0311856626373057 1.0417478280830199 1.0523649167890516 1.0425135651884641 1.0327095000755593 1.0229524944751964 1.0132423225017155 1.0035787593537071 0.99396158130880918 1.004330181531615 0.99470939666026315 1.0050818855228969 1.0155083113276162 1.0259889545465199 1.0162642075646966 1.0065861393683861 0.99 695452589941791 0.98736914417510069 0.97782977228306023 0.96833618937610155 0.97857153756085746 0.9888601095561742 0.97931358103030441 0.96981287584135889 0.96035777403732037 0.95094805672194127 0.96109298661689557 0.95167974028113433 0.96182847493059631 0.97202998300023569 0.96256423908183453 0.97276957312506029 0.96330027917405991 0.95387643783402432 0.94449783093242101 0.93516424134394538 0.92587545298549445 0.91663125081116403 0.90743142080727046 0.91735006419546838 0.92732028452928494 0.91806914716354426 0.90886241525715916 0.91878849981649657 0.92876620001554255 0.91950812225546796 0.91029448326864171 0.90112506974895212 0.91101092011164675 0.90183806769511077 0.89270924497017412 0.90255133304401913 0.8934190866454077 0.90326486589596411 0. 89412919453966344 0.90397866635126989 0.91387935541629672 0.90469273451029841 0.91459713672975207 0.90540707047344915 0.91531518723991123 0.90612167434115953 0.89697229030432202 0.90683654621390475 0.89768373079207797 0.88857484888427596 0.87950968960963127 0.870488043099505 0.86150970049262732 0.87118955093518924 0.88091973660005229 0.89070051923037274 0.88162515673806685 0.87259335598572418 0.86360490787699273 0.8546596043191832 0.86430383426164314 0.87399821419980395 0.86500302277164476 0.85605100826234071 0.84714196342268133 0.83827568199825242 0.84783471554464351 0.83896510891002918 0.8485277274763614 0.83965479438447477 0.83082445137142913 0.84034473851856073 0.83151108377367167 0.84103494140929502 0.83219797369053028 0.84172540315372113 0. 83288512121858327 0.82408727263673409 0.8153316537280777 0.80661806179018281 0.79794629509358983 0.80729561582807663 0.81669355303038271 0.80797342397583694 0.81737488578051143 0.80865148632876482 0.79996995919438674 0.79133010339025356 0.80064501992788295 0.81000837403150805 0.8194204175764721 0.82888140374787 0.83839158704735905 0.82956730742953178 0.83908105742816552 0.84864427892679206 0.83977078638794334 0.84933759447716084 0.85895414996844233 0.86862071154827847 0.85965133213284672 0.86932151905993771 0.86034877576845004 0.87002258940244626 0.87974670686733925 0.88952138974304962 0.88045168707228294 0.890230035845059 0.90005923203145355 0.89093894771770255 0.90077183024583474 0.89164812546065475 0.90148469571305023 0.91137241613075837 0.921 31155269463849 0.91208925724170409 0.90291122880694386 0.89377725490867044 0.88468712408510886 0.8756406258895002 0.88539395714412583 0.89519800572127539 0.90505303535102621 0.89590878078134129 0.90576750644140436 0.91567749747489979 0.90648224548702028 0.91639595316355305 0.92636121212000377 0.9171146783018278 0.92708367462899743 0.93710450973706849 0.92780640809033055 0.9185529373314969 0.90934388323230575 0.91927247142511392 0.92925268827652463 0.91999227537279715 0.91077631245100776 0.90160458615124295 0.9114929299992296 0.90231776393523333 0.91220981630769682 0.92215330735249701 0.91292697147720503 0.92287419172888674 0.91364439560858801 0.90445890250966676 0.9143620888027173 0.90517315077646421 0.91508005116050195 0.92503846742653684 0.9350 4866745715498 0.94511092052793244 0.93577438810939828 0.92648267104647308 0.91723555422545 0.92720517910742251 0.91795459424770676 0.90874841219531777 0.89958641981678023 0.89046840500165958 0.90029884070766841 0.89117740627227149 0.90101152878488744 0.91089678873456914 0.90172448414864315 0.9116134514662162 0.90243770689917824 0.9123303829750542 0.92227450096652475 0.93227032837155077 0.94231813407908294 0.93299500703550331 0.92371663100173285 0.93371995748294201 0.94377530126185349 0.93444517981579645 0.94450429475083886 0.93517067413603483 0.94523356164154237 0.95534877616207847 0.96551658979812149 0.95608211016709044 0.94669291603828842 0.95681571920168773 0.94742300374951949 0.93807537333152169 0.92877261153953028 0.9195145030041405 0.910300 83338972068 0.90113138938944992 0.91101727261427534 0.92095456243186979 0.91173398053219668 0.90255765742564198 0.89342538066999877 0.90327119264948297 0.89413549092476541 0.88504364056832641 0.89484586749928186 0.88575060733528521 0.89555651049342888 0.88645783924306043 0.89626742000712456 0.8871653363910903 0.89697859614032405 0.90684288484025388 0.91675846784142334 0.90755802719578438 0.89840174866524447 0.90827343775830394 0.91819645963464724 0.92817108122474767 0.93819757084711664 0.94827619821552189 0.95840723444624287 0.9685909520653635 0.9591417154954498 0.96932925241602641 0.95987647200442949 0.95046906493880812 0.96061150407649021 0.97080668389768809 0.96134681181497905 0.95193234711826702 0.9425630718520992 0.95266439982573026 0.943291 61070656675 0.95339672708224099 0.94402042279224618 0.93468912476284327 0.92540261696398152 0.91616068440255427 0.92612471996144774 0.93614056850524752 0.94620849946147501 0.95632878365867491 0.94693840549711328 0.95706248520569837 0.94766858527671105 0.95779646192015022 0.94839903890293353 0.95853071390522904 0.9687150736175365 0.95926524126417223 0.96945342051874617 0.96000004410025608 0.97019204432957751 0.98043704296009149 0.97093094515388301 0.96147047661714424 0.9520554183293819 0.94268555232140083 0.95278751719347232 0.94341413711094368 0.95351989062392084 0.9636781940551653 0.95425253872370042 0.96441465192506381 0.97462960811507426 0.9848976820772728 0.97537017320330177 0.98564209810395909 0.99596743701409984 0.98638679331643209 0.976852 13670851323 0.9871317678193976 0.97759353533386451 0.98787702171760072 0.99821398223053248 0.98862255511582586 0.99896339240242837 1.0093580020429211 1.0198066636535446 1.0303096583045432 1.0408672685277272 1.031071105638794 1.0213219643317277 1.031832838546253 1.0423983693066936 1.0325948571340215 1.022838401819778 1.0131287774910431 1.0235970471339968 1.0138837813077535 1.0243559769705541 1.0146390682810953 1.0049688007533462 1.0153946385172636 1.0057207442523808 1.0161504921224935 1.0266344746815306 1.0169066292030591 1.027394543674915 1.0176630498652752 1.0079782672259219 1.0184197542154969 1.0289155369374177 1.0394658977294924 1.050071120397686 1.0607314902237541 1.0508399790706799 1.0409959471711407 1.0311991666247193 1.0214494106249208 1.0117464534539211 1.0222075350118818 1.0327230141939436 1.0229659437258127 1.0334853666331871 1.0237246368733479 1.0342480049850895 1.0244836145611611 1.0350109293568792 1.045592986189535 1.0357741398558251 1.0463601653830756 1.057001238243068 1.0471276322995013 1.0373014196644639 1.0478953870467191 1.0585444430593625 1.0692488741632715 1.0593164795672876 1.0494317604653647 1.0600888056197846 1.0502003793528094 1.0608614213254444 1.050969286503082 1.0616343267928983 1.0723548252922215 1.0624075221308189 1.0525079660245908 1.0426559277876728 1.0328511793342918 1.0230934936734872 1.0336135798405897 1.0238522346573546 1.0343762662775733 1.0449550228622169 1.0351392387524783 1.0253705704064662 1.0359024973725801 1.0464891903589177 1.0366660422451948 1.0268900452424177 1.0171609730252542 1.0074786003547329 1.0179174890765776 1.0082314851290102 1.0186742888516811 1.02917139515371 1.0194313724569724 1.0299324155937488 1.0201887399988987 1.010491834046904 1.0008414732434789 0.99123743417191013 0.98167949448788483 0.99198422785922191 0.98242270356549755 0.97290707458838321 0.96343712063035891 0.95401262245133323 0.94463336186356672 0.93529912172662155 0.92600968594233368 0.91676483944981046 0.90756436822045128 0.91748370293519788 0.90827978116110897 0.89912003821153563 0.90899546241023588 0.89983228419066674 0.89071308922655157 0.90054479729052983 0.91042763023644069 0.90125757761130565 0.91114411701488462 0.9210820664233621 0.9310716931687637 0.94111326597324152 0.95120705495630253 0.96135333164207548 0.95193883565019344 0.96208891759557469 0.97229177996707183 0.98254769722290081 0.99285694524846013 1.0032198013637523 0.99360434631720618 0.98403504545488363 0.9943520276912492 1.0047226582352438 0.99509998947571443 1.0054745094209885 1.0159029768699779 1.026385672349702 1.0166590211224236 1.0069790578210358 0.9973455583434947 1.0077317552468812 1.0181719603741652 1.028666454568111 1.0392155201318656 1.0498194408365515 1.0604785019289018 1.0505882051196429 1.0612512637862652 1.0513572577200909 1.0620243154602358 1.0521265987460264 1.0422763910720456 1.0528962283056202 1.0430423264097533 1.0332357232429863 1.0438085490038502 1.0339982679686317 1.0242350762823822 1.0145187 479162265 1.0048490579262288 0.99522578244818294 0.98564869869243155 0.99597407192563248 0.98639339638038948 0.97685870807776354 0.98713837335976806 0.99747149290123893 1.0078583446643257 1.0182992080565803 1.0287943639384745 1.0190561509915699 1.0295552429767261 1.0401089302402053 1.0303164073750524 1.0205708886196523 1.0108721483542777 1.0012199620421773 0.99161410622437485 0.98205435851449785 0.99236104117877333 0.98279770818111523 0.97328027918184579 0.98354133663359167 0.97402033821775036 0.96454504059430501 0.97476067480539563 0.96528182356632963 0.97550128904887479 0.98577389575192909 0.99609992000983927 1.0064796395938904 1.0169133337197787 1.0072321497179235 1.0176697568964568 1.0079849420633535 0.99834661434144945 1.0087380167360251 0.99909607425569225 1.0094913738418221 1.0199407289857998 1.0304444207765262 1.0206982875567987 1.0109989357765259 1.021456130242564 1.0319677021198257 1.0425339341708488 1.0531551106285373 1.063831517203806 1.0539251259212277 1.0646055365760181 1.0753414853662138 1.0861332610901182 1.096981154047787 1.1078854560488356 1.0977676058598012 1.1086759974102725 1.0985543526227031 1.0884812917301141 1.0993413944471109 1.1102579696982362 1.1001287314436845 1.0900481135327547 1.1009163637231252 1.1118411288144858 1.1228227026843212 1.1126331537114362 1.1236188461107357 1.1346616641105118 1.1244152881227811 1.1354622476210197 1.1252120288324385 1.115011011094043 1.1260090683517321 1.1370643155071614 1.1268064067927268 1.13 78658001080493 1.1489827022686114 1.1386675852977222 1.1497886567412707 1.1394696711889125 1.1292002167672055 1.1189800557267229 1.129998752016502 1.1410747455269878 1.1307975867484581 1.1205697583320653 1.1315967210753923 1.1426810240249847 1.1323961551096646 1.1434846151162352 1.1546307351148397 1.1658348149374369 1.1554388078257372 1.1666470896264314 1.1562471835962245 1.1674596689509249 1.1570558625399605 1.1682725530251683 1.1578648447706472 1.1475070935157481 1.1371990594668726 1.1269405039814315 1.138000594602135 1.1491181976940661 1.1602936123220755 1.1715271391061504 1.1611038088384409 1.1507305105560164 1.1404070041053473 1.1515371205266955 1.1412097423481673 1.1523440330083781 1.163536221980022 1.1747866103343183 1.1860955007080571 1.1756022423046586 1.1869153739646432 1.1982873339092595 1.2097184280455879 1.2212089638714252 1.2327592504835567 1.2220420060812356 1.2335966245128582 1.2228753607151965 1.2344343125909156 1.2460533710163886 1.257732848545674 1.2468957308726547 1.2585795886731925 1.2703242025342933 1.2594266463621286 1.2485813984595904 1.2602740217315804 1.2720274466445849 1.2838419893671369 1.2728795478181745 1.2619697259886471 1.2737319685637885 1.2628180551146824 1.274584709001279 1.286412549488086 1.2983018947454243 1.2872700456506463 1.2762911494315232 1.2653649519142518 1.2544912001450634 1.2662145543858179 1.2553367245247657 1.244511108247047 1.2337374549274611 1.2453528896930841 1.2570287247194885 1.2687652740880302 1.2578752007724074 1.2470373998086997 1.2362516202896177 1.2255176125122276 1.2148351279721687 1.2042039193579024 1.2156657797385635 1.2271872417932044 1.216496743032597 1.2058575586660405 1.1952694423844434 1.1847321490609981 1.1960927562361157 1.1855515110061821 1.1969163788634143 1.2083403440335041 1.2198237138224783 1.2091685599961304 1.1985645509081491 1.1880114410637899 1.1993891005573216 1.1888320328746462 1.178325639116848 1.1896529324402558 1.1791425983645425 1.1686827138923928 1.1799598640046334 1.1694960566574113 1.18077743615203 1.1703097044585 1.1815953149216845 1.1711236574100603 1.1824135004285927 1.1719379156265353 1.1832319927877935 1.1945847991502903 1.1840507921143688 1.1954078562333637 1.184869898523 4436 1.1743825230105309 1.1639454869000803 1.1535585485629598 1.1647570530154874 1.1543662191610129 1.1655689235006506 1.176829881902854 1.1663810984697203 1.1559824691970655 1.1456337533449195 1.1567910488623134 1.1464384518277742 1.1575999317772787 1.1472434521047479 1.1369366835346448 1.1480487542890252 1.137738120268438 1.1488543584938342 1.1385398575730639 1.1496602648324439 1.1608384982095727 1.1504664734181667 1.1401442343457595 1.1298715420208998 1.1196481586191993 1.109473847457827 1.1204431114646081 1.1314694156442244 1.1425530566055744 1.1322688019338676 1.1220339116845848 1.1118481489084986 1.1228297592828231 1.1126401764382656 1.1024995035913618 1.0924075059741232 1.1032880250051886 1.114225122735216 1.1252190933734392 1.1362702326589811 1.1260161355422178 1.1370714194470377 1.1481841908281627 1.1378729067121873 1.1489898458270908 1.1386746945671207 1.1497958029788697 1.1609747411543601 1.1506020623968189 1.1402791724973143 1.1514086241943007 1.1410818627981678 1.1308046698567367 1.1205768074414242 1.1103980387657053 1.1213721085672872 1.1324032435318374 1.1434917403982032 1.1546378974482741 1.1442956355405225 1.1554459728453335 1.1666542919041296 1.1562543513029899 1.1674668739297656 1.1570630329349028 1.1682797607061643 1.1578720178547748 1.1690929523476199 1.1586813061763515 1.1483196359067049 1.15949089801342 1.1491253417029554 1.1388095400627813 1.1499313496711081 1.1396116791926869 1.1293415431325617 1.1191207037255255 1.1089489243476431 1.1199154587542512 1.1309390191397735 1.1420199020393005 1.1531584055299051 1.1428232451833615 1.1325376936064813 1.1436268896132353 1.1547737494392245 1.1444308354419164 1.1555818757862144 1.1452350827824405 1.1563903052129092 1.1460396317478874 1.1571990378329766 1.1468444824513782 1.1365396289356116 1.147649635006077 1.1588174131081086 1.1700432636562708 1.1813274886272835 1.1708571166818724 1.1821455736886182 1.1716712749349125 1.1829639655645741 1.1724857385298639 1.1620578069849206 1.1516799295113929 1.1413518658497379 1.1524868955521566 1.1636798274090281 1.1749309625115552 1.1644912938914995 1.1541017356808201 1.1653030647063605 1.1549096099957699 1.1661151399677481 1.1773789386955804 1.188701309176 7975 1.1781955428927486 1.189522159715791 1.2009076749463135 1.2123523948560346 1.2017331033607257 1.1911647844645943 1.2025588413438104 1.2140121473187984 1.2255250104848563 1.214842490434529 1.2263596713847886 1.2379367416759899 1.2495740127327051 1.2612717975989152 1.2730304109464297 1.2848501690833514 1.2967313899625852 1.2857070792907646 1.2975927561030769 1.3095402384348129 1.2984544452903259 1.3104064084058358 1.3224205217295464 1.3112729032252446 1.3001787932897635 1.2891379350819725 1.3010414523443989 1.2899964533731456 1.3019044349306861 1.3138743379923259 1.3027677411699625 1.3147421334240463 1.3036313711836107 1.3156102543137655 1.3044953250930593 1.3164787007835432 1.328524390027618 1.3406327168557617 1.3293976798148539 1.3415105477498912 1.3302712971206918 1.3423887078657195 1.3311452420679641 1.3432671973267176 1.3554521867528169 1.3441460162564032 1.3328941153783722 1.34502516477834 1.3337690439874037 1.3459046430161385 1.3581033471598225 1.3467844510934555 1.3355198857282069 1.347664589133994 1.3363957991061506 1.3485450572615028 1.3607574915592626 1.3730334305153709 1.3616428700488972 1.3739234129731517 1.3862678147206124 1.39867640735716 1.4111495246754173 1.4236875022037299 1.4362906772151893 1.4245964819645565 1.4372043836707724 1.4255058026291527 1.4381184328028245 1.426415464325371 1.4390328247398632 1.4273254671811118 1.4156743049386424 1.4040790682749367 1.4165802794299664 1.4049806940887026 1.3934367867570767 1.3819482901806426 1.3943344212895821 1.4067849602802882 1.4193002420737457 1.4076876009117916 1.3961307004274151 1.4085905800696379 1.3970293452853038 1.3855236044279344 1.3979283271709599 1.4103975544722491 1.422931621755505 1.4355308661886337 1.423840318030928 1.4364442876846892 1.4491137979806497 1.4618491897301493 1.4746508055167462 1.4875189897054337 1.4755788985548475 1.4636961198417842 1.4765073396649617 1.4893851778312199 1.5023299807559427 1.4903187968483143 1.5032684545919257 1.4912527660098842 1.5042072803931359 1.5172291582511805 1.5051464582915748 1.4931217552917753 1.5060859884192928 1.4940567756748799 1.5070258709083895 1.4949921467280292 1.4830161844237346 1.4959278685827382 1.5089066934993687 1.4968639413705 715 1.5098476338656988 1.4978003652231435 1.4858109234700723 1.4738790310374159 1.4620044116884361 1.4501867905123316 1.4629277618229959 1.4757349861844755 1.4638514582507898 1.4520249712511859 1.4402552513891802 1.4285420261825119 1.4411704447186611 1.4294528265840114 1.4177914530164082 1.4303639685720939 1.418698221522948 1.4070884700596378 1.3955344454033516 1.4079912245194492 1.4205127788869505 1.4088943175482931 1.4214205679995446 1.4097977492731468 1.4223286975693674 1.4107015198210342 1.3991301525258932 1.4116056293190282 1.4000299222982968 1.4125100778942481 1.4250551302992984 1.4376654169768548 1.4503412771451347 1.4385796390148382 1.4512602531377157 1.4394942039226546 1.4277846317438256 1.4161312655114551 1.4045338354369998 1.3929920730269023 1.4054356318066423 1.3938895407739702 1.3823988709782551 1.3947873451073423 1.4072402393019008 1.3956854861532517 1.4081430506812489 1.4206653945447916 1.4090462006509763 1.3974827788878517 1.3859748615491898 1.3745221822137537 1.3631244757391277 1.3754127230129711 1.3640107419425087 1.37630359780061 1.3648973405311668 1.3771948067019291 1.3657842716297597 1.3780863498422344 1.3666715353629915 1.3553115119932491 1.3675591318556144 1.3561948480227075 1.3448851127521984 1.3570785153385101 1.3693353236182704 1.3579625140649028 1.3466442939973913 1.3353804013862036 1.3241705754595499 1.3130145566973441 1.3250422323921707 1.3371324520006103 1.3259142162310074 1.3380089701554088 1.3267865270986627 1.3156179517685893 1.3045029856001 1.2934413712692194 1.2824328526871271 1.2714771749942289 1.2832888563041989 1.2723290697939387 1.2614218902589278 1.2731812840882744 1.2622700139246508 1.2514111178578124 1.2406043444920947 1.2298494436385328 1.2414446607454535 1.2306857263738751 1.2422852921510192 1.2539451756702049 1.2431262388269877 1.2547904952688884 1.2665154058442867 1.2556361318962339 1.244809078463132 1.2564820856711405 1.2682157925166306 1.2573283567125508 1.2464931806003303 1.2581749451394524 1.2699174548541778 1.2817210256194196 1.2707687646964465 1.2598690746259034 1.2716203938139583 1.2607166159236511 1.2498651761672175 1.239065823321615 1.2283183073696713 1.2399055625679938 1.2515530714933476 1.2632611474651134 1.2750301054319322 1.2641099609258588 1.2532422331134145 1.2649590927256047 1.2540872890805219 1.2432676700929353 1.2549326619774188 1.2441089851999272 1.2333372620709673 1.2226172432130267 1.2119486804456039 1.2234508135839213 1.2127782496787183 1.2021569140802604 1.191586560892675 1.1810669454003899 1.1705978240624679 1.1818849327475931 1.193230734397881 1.2046355342167501 1.2160996389946774 1.2276233571174497 1.2392069985744607 1.2284588049813032 1.2400467907672064 1.2292945661715238 1.2408868979156158 1.2525395097847771 1.2417273201378101 1.2533843022025271 1.2425680575519547 1.231803730875705 1.243409110276259 1.2326407465469327 1.244250478428977 1.2334780761325179 1.2450921621284072 1.2567666413714753 1.26 85018279066074 1.2576130191326556 1.2467764766408189 1.2584597143193514 1.2476191076906185 1.2368305359737035 1.248462054760767 1.2376694368979151 1.2493053179697844 1.2385086524435294 1.2277638109118003 1.2170705446194234 1.2064286060052503 1.2179020347564777 1.2294351253372118 1.2410281879889653 1.2526815345665083 1.2418686632005889 1.253526380249232 1.2652447174265284 1.2543715427828812 1.2435505593775233 1.2552170222862866 1.2443919805793122 1.2336188990725314 1.2228975283569832 1.2122276202208697 1.2237312038460186 1.2130572940675575 1.2245651919967089 1.2138872790751245 1.2253994929263152 1.2369715702895321 1.2262341067521421 1.2378105241072532 1.2494471388326112 1.2611442639545412 1.2502907714875593 1.239489375784419 1.2511347205384982 1.2628406210852985 1.2519789861040889 1.2411694869707892 1.2304118734333294 1.2197058964408494 1.209051308137933 1.2205383749402503 1.2320851744899399 1.2213711656523882 1.2107085840572567 1.2222042686943548 1.2337597308915655 1.2453752814922021 1.2570512329559618 1.2687878993673332 1.2805855964440434 1.2696387855811118 1.2587445194103224 1.2704899909112561 1.2822965388639949 1.2941644808660877 1.3060941361665916 1.3180858256746579 1.3069590137114195 1.2958856104456045 1.2848653595154653 1.2738980057897908 1.2629832953619999 1.2521209755442624 1.2413107948616497 1.2529656109949308 1.242151376062155 1.2313890494570567 1.2429922725142335 1.2546558323313075 1.2663800426594305 1.2781652188812598 1.2900116780194426 1.2790196219649492 1.2908705239991671 1.2798743454839712 1.2917296920804882 1.2807293895585019 1.2925891823842064 1.3045106461326044 1.316494101492494 1.3053749298053301 1.317362879440318 1.3294131664134081 1.3182319832146239 1.3071044696951937 1.2960303682406566 1.3079697261555081 1.2968914714699618 1.285866392406906 1.2977528976474222 1.309701212715189 1.3217116590213083 1.3337845596482194 1.3459202393583904 1.3346598222094701 1.3234534550628645 1.3123008784785628 1.3243248430466514 1.3131680838000275 1.3020648769977874 1.314035614358176 1.3260685995528387 1.3381641562705138 1.3503226098831207 1.3625442874545133 1.3748295177492769 1.3634303360640803 1.3520858704509724 1.3407958582728075 1.3529679967358264 1.36520343 03188527 1.353850453853322 1.3425519716748262 1.3547332419275353 1.3669778547855587 1.3792861396304437 1.3678655661602175 1.3801784671042507 1.392555395133193 1.404996683187886 1.417502665940463 1.4058986531439488 1.3943503396088577 1.4068009613748238 1.3952483167602248 1.4077036080073784 1.3961466306889427 1.4086065931685257 1.4211313474530023 1.4095099169852277 1.4220393685535511 1.4346339732700297 1.4472940699310342 1.4355470583953651 1.4238564325150671 1.4122219216389946 1.4006432564151274 1.3891201687843346 1.3776523919741699 1.3662396604926936 1.3548817101223287 1.3435782779137413 1.355764884958893 1.3680148623606794 1.356648391021348 1.3689029626546594 1.3812212580604637 1.3697913960217734 1.3584163973208687 1.3470959986137285 1.35930089780652 1.3479762534970487 1.3367059674802628 1.3254897788363573 1.3143274278979429 1.3263619305230123 1.3384590125617324 1.3506189994270534 1.3628422182240745 1.3751289977588397 1.387479668547186 1.3998945628236314 1.3883750689220777 1.4007946192804726 1.3892708051079263 1.4016950132944879 1.4141838273636194 1.4025957449922739 1.391063285416311 1.403496814500476 1.3919600297908739 1.3804786216478777 1.3690523242639681 1.3813713963501408 1.3699408136476601 1.3585650977421513 1.3708296362504107 1.3831579503589131 1.3717187921971901 1.3603345419946433 1.3490049361930692 1.3612197618612734 1.3734981046229522 1.3858402947669917 1.3743882613521099 1.3867350803111411 1.3991461027287593 1.4116216624629492 1.4241620951077567 1.4367677380023172 1.4250712528599059 1.4376816233747776 1.4503575678163267 1.4630994271689719 1.4759075441902509 1.4640231879781376 1.4521958766758423 1.4649472952345568 1.4777650211697768 1.4906493992798597 1.4786942821633162 1.4915834924305655 1.4796238916668987 1.4677216969868976 1.4558766328413606 1.4440884250037218 1.4567976848137416 1.4450050559266354 1.4332690316581873 1.44592203062281 1.4586408251820489 1.4714257574729959 1.4842771714118559 1.4971954127031979 1.4852088747222223 1.4732798721235554 1.4861409274585982 1.4990688602813833 1.4870733297520324 1.5000061110667433 1.4880060817336229 1.5009437133586379 1.4889391835345163 1.5018816672888962 1.5148914519587988 1.5028199729893967 1.4908064371190 477 1.4788505662208764 1.4917405891652251 1.4797802343372322 1.4926750915557858 1.5056370020318761 1.4936099444221229 1.4816406166888965 1.4945451478956788 1.5075167826647364 1.5205558699345931 1.5084572017589069 1.5215011792080535 1.5093979735478547 1.5224468430103038 1.5355635665939578 1.5233928614743069 1.5112805757392302 1.5243392347330746 1.5374657987536868 1.5252859629196691 1.5131645902976545 1.5262330461672025 1.5141071275456 1.5020394133333812 1.4900296241493809 1.5029777781949578 1.515993262641572 1.5039164949808925 1.5169368607547935 1.5048555638231704 1.5178808127550512 1.5057949848538268 1.5188251187750668 1.5067347582049462 1.4947024313655626 1.4827278596950078 1.495638044565422 1.5086153623971623 1.5216601622816279 1.509556193502676 1.497510323773863 1.5104973774574875 1.4984469900456916 1.4864544444934724 1.4745194631599037 1.4626417697367362 1.4754475069393673 1.4635653589060582 1.4763758987723699 1.4892530534459865 1.5021971693239058 1.5152085946043905 1.5031355933502892 1.4911205425022076 1.5040743693232193 1.4920548123504678 1.4800929492511856 1.4681885030947797 1.4563411982799246 1.4691141725109804 1.4572624244829275 1.470040189090239 1.4581839961826057 1.4709665529627554 1.4838155790381617 1.4967314200491604 1.4847471092329245 1.4728203231086066 1.4856789887887714 1.4986045195304731 1.5115972630320318 1.499541596169478 1.4875437965078646 1.4756035862846266 1.4637206890704602 1.476532036653627 1.4894100032442261 1.4774608352286536 1.465569023219556 1.4783899821402979 1.4664937102260245 1.4546545404169393 1.4674187440271078 1.480249321496049 1.4683441247528681 1.4564960729540544 1.4692698525334156 1.4574173572412552 1.47019592749891 1.4583389870469152 1.4465389599090899 1.4592609625006174 1.4720491195056207 1.4849037749270502 1.4978252745566709 1.4858357132387989 1.4987620589476407 1.486768001064692 1.4748315146595812 1.462952323389215 1.4511301522369466 1.4393647275062094 1.4520494240892421 1.4402795868536136 1.4529690407052525 1.4411947893098671 1.4294770543211799 1.417815564460438 1.4303882053956327 1.4187223420097337 1.4312996981881847 1.4439424566187635 1.4322115328269933 1.444859032797694 1.4331237094402649 1.4214447156349515 1.4340362281562533 1.4466932165426662 1.4594160212686882 1.4476108243665986 1.4603384006533053 1.4731321603367027 1.4612611259670865 1.4494470725624442 1.4621841973397691 1.450365713192538 1.4386039577692138 1.4512846983496139 1.4395185317975359 1.4278088428449078 1.4404334488277017 1.453123702761606 1.4658799460159666 1.4540437222750899 1.4668047496309207 1.4796321343290018 1.492526221427513 1.5054873577789363 1.5185158920393871 1.5064270157575979 1.5194604362395374 1.5325616305079834 1.5204053346815449 1.5083073890750733 1.5213505874982638 1.5092481046782722 1.5222961948225993 1.5354121350356769 1.5485962781378628 1.5618489787841798 1.5495521036860156 1.5373142535883226 1.550508287706982 1.5637709308030585 1.577102539 6432345 1.5905034728493797 1.6039740909081965 1.6175147561809196 1.6311258329130607 1.6448076872442088 1.6321126103454366 1.6194784698157787 1.6330997578588211 1.6204608790210986 1.6078826668017974 1.5953648300011487 1.5829070788171431 1.5963381956269926 1.6098391542442534 1.6234103178463237 1.6108179483206615 1.624394201651929 1.6117971094839998 1.6253784544533167 1.6390304224164742 1.6263630763888752 1.6400201643860974 1.627348067597044 1.6147367968725783 1.6021860602475897 1.6157174277608775 1.6293191583852344 1.6166984264249851 1.6303052582423954 1.6439828455852559 1.6577315563822994 1.6449744449116643 1.6587283120252052 1.6459664161274841 1.6597254414913474 1.6735560137871026 1.6607229449209244 1.6745587042345136 1.6617208224541877 1.6489445625064074 1.6627190742314411 1.6499380226751299 1.663717700393041 1.6509318554311543 1.6647167010793966 1.6519260609142155 1.6391968158218271 1.6265286711058824 1.6401866201956334 1.6275137244186944 1.6411767957856718 1.6284991471659005 1.6158823512595042 1.629484939486054 1.6168634117765208 1.6043024673999935 1.5918018155564733 1.6052791849973671 1.5927738449093796 1.5803285304538144 1.5937462388121744 1.607233719253998 1.594718997401579 1.5822643462140511 1.5698694773522237 1.5575341038609332 1.5452579401624007 1.5330407020496213 1.5462125137002793 1.5594528187715211 1.5471674452414179 1.534941041504259 1.5481227349200815 1.5613729731416659 1.5490783828705856 1.5368428066328068 1.5246659611609692 1.5125475645473965 1.5256128118830432 1.5387459985048353 1.5265600177120122 1.539698129804115 1.527507578781055 1.5153755424029058 1.503301739799372 1.4912858914483351 1.5042405780838668 1.4922202233090642 1.5051797684702715 1.4931549055816142 1.4811877620348226 1.4692780607770555 1.4821183066930965 1.4702041388209697 1.4583471589546289 1.4465470925916466 1.4592691374731235 1.4720573369879841 1.4601914617704419 1.4483825427539436 1.4366303065487247 1.4249344810772908 1.4375441403788929 1.4258439285050741 1.4384583169333007 1.426753717012021 1.4151052991703632 1.4276638467260492 1.4160110602617642 1.4285743177751256 1.4169171610498048 1.4053159586767658 1.3937704420751174 1.3822803439531568 1.3946682017417134 1.383173794373353 1 1.3955662981040948 1.4080232428542363 1.3964647312885359 1.384961700578351 1.3973635014213586 1.4098297916287499 1.4223609065452196 1.4107335741938023 1.4232693887796102 1.411637695713468 1.4000618347740432 1.3885415379671278 1.4009619539645572 1.4134469561251732 1.4259968802970242 1.4386120640745688 1.4512928468077568 1.4395266411430794 1.4278169132655925 1.4404415612145738 1.4287274417207438 1.4170695500004844 1.405467616160482 1.4179760477645167 1.4305495232128922 1.4188828855014703 1.431461076506078 1.4441046741039099 1.4568140184092506 1.4450213111208861 1.4577354219387151 1.4459382919134094 1.4586571710313594 1.4714421883207227 1.459579265816783 1.4723690779990304 1.4852253972046254 1.4732963152980432 1.4 614244929846123 1.4742239003481323 1.4623476256264611 1.4751518332797189 1.463271104479976 1.4514474031784719 1.4641949296750001 1.4523667940125602 1.4405954334012998 1.4532865296549868 1.4415107543126426 1.4542066102350688 1.4669684846082913 1.4797967207282547 1.4926916636760419 1.5056536603271575 1.4936265227575869 1.4816571154483502 1.4697451612941981 1.457890384519986 1.4706714145194901 1.4588121917297965 1.4715980151267916 1.4597343446541831 1.447927619799843 1.4361775672248038 1.4244839149021247 1.437091231259616 1.4253931933495698 1.4380052379549877 1.4506828651923538 1.4634264160913544 1.4762362334550296 1.489112661868996 1.502056047710715 1.5150667391588111 1.5281450862024371 1.5160099897886652 1.5039331418376793 1.5169535941752357 1.5048722169231943 1.4928488302819627 1.4808831558966093 1.4937837483072718 1.50675142379847 1.4947190169642375 1.507691555852452 1.4956546363843599 1.5086320404935587 1.5216769271041253 1.5095728778540254 1.5226226568188665 1.535740294634325 1.5489261441664239 1.536691298674425 1.5498820934275321 1.5631414803133556 1.5764698160109853 1.5641027608941327 1.5774360952507824 1.5650644019935784 1.5527520928640093 1.5660264037469025 1.5793697410463867 1.592782463699828 1.5803371078740689 1.5937548608350145 1.6072423861113569 1.6208000465191361 1.6344282067610361 1.6217829513685831 1.6354162227156999 1.6491203870738218 1.6628958130866058 1.6501139131837901 1.637393366400508 1.6247338782417855 1.6121351556262247 1.5995969068792188 1.5871188417261983 1.6005718597031748 1.5880891147765994 1.5756662870256717 1.5633030888479484 1.5509992340214782 1.5642644300383903 1.57759860507459 1.5910021178209783 1.5785653076554378 1.5661881941786917 1.579532372788421 1.5929459411269211 1.6064292600207812 1.6199826921728895 1.6074067752504595 1.5948912227292573 1.6083846570874498 1.6219482573043047 1.609362905669244 1.5968379637220314 1.6103415211333862 1.62391529704328 1.6375596565879054 1.6248993702362835 1.6122998532591493 1.5997608139635053 1.613279570196116 1.6268686239611361 1.6142596545661227 1.6278538047698667 1.6415186445546701 1.6552545415063546 1.6425093197071239 1.6298252749725295 1.6435003664023871 1.6308115646436554 1.6444917847798028 1.6317982242128597 1.6191655927366377 1.6065935978915018 1.5940819486216227 1.6075711747544554 1.595054833115634 1.5825985699166787 1.5702020967810784 1.5578651267165293 1.5711660253754554 1.558824428453653 1.5721303154816124 1.5597840899673008 1.5730949672351309 1.5864750610647538 1.5999247313822909 1.6134443399854792 1.600899807153549 1.5884154880792121 1.6018752486172243 1.5893862474238616 1.5769571934362272 1.5645877989077333 1.5522777774729759 1.5655496219158356 1.578890479949798 1.5923007104455373 1.6057806741398544 1.6193307336453819 1.6329512534603383 1.6203130874437286 1.6077355846239985 1.6212958096640433 1.6087135897776559 1.6222789004445 1.6096919617223664 1.6232623599233231 1.6369033241949245 1.6506 152214807384 1.6378922684176307 1.6252303855292261 1.6126292796786856 1.6000886591362278 1.5876082335723738 1.6010637963869505 1.6145893281281629 1.6020392993531476 1.6155699037097841 1.6030151681719773 1.5905206953647517 1.6039914029806486 1.5914922442463415 1.6049680039164227 IT MAY NOT BE CLEAR TO EVERYONE SO LET ME REPEAT: YOU HAVE TO ANSWER ALL QUESTIONS IN THIS ‘BOOK’ (SESSION 1 TO SESSION 5) IN YOUR EXCEL JOURNAL Your Excel journal should be composed of a text part and an excel file. You should submit at most two documents. The text part should contain a one page answer for each session that explains your work, and makes clear reference to the excel file. The excel file should be (as much as reasonable) self-explanatory. That is, try to include comments that help the reader to follow your steps and understand how you derive your results. You are restricted to one page of text (500 words maximum) per session (5 pages max) and one excel file that should contain 5 sheet (one per session). The last Excel Session will be before the reading break and your journal is due after the reading break. I encourage you to use this forum to post questions about your assignment and to answer others’ questions. You will be graded on the basis of: the clarity of your explanations; the logic of your calculations; the accuracy of your results; and whether your excel file is easy to follow and self-explanatory. Part 1: The goal of this part of your journal is to re-create this Excel sheet, but using the following assumptions: you earn 100K each year, consume 30% of your earnings, and the interest rate is 4%. a. Replicate the Excel sheet and explain what each column mean. b. How do you derive the earliest year you can retire such that your consumption remains constant forever after? What year do you obtain? Part 2: The goal of that part of your journal is to derive a formula that delivers your earliest possible retirement year as a function of your saving rate. Say you earn E each year, you save share alpha of E and consume the rest, and the interest rate is r. c. Assume for now that you always work. How much capital you have in your saving account at the end of the first and second years? Derive the formula that gives your capital at the end of year T. d. How much do you have in your saving account at the end of year 2 if you stop working in year 2? At the end of year 3 if you stop working in year 3 ? At the end of year T if you stop working in T? e. How many years do you have to work before you can stop working and maintain your consumption constant forever after? Plug the values from Part I and check that you obtain the same answer. Part A We want to check the statement on p.141 that “the arithmetic mean is higher than the geometric mean by about half the variance.” 1-Use the Rand() function to generate 400 random rate of return with mean 10.7% and variance 3.2%%. 2-Assume these 400 rates correspond to 400 consecutive years. Compute the arithmetic rate of return, the variance over 400 years, and the geometric rate of return. 3-Resample several times using F9. Would you say that the statement on p.141 holds? Discuss. Part B We want to check the statement ‘Risk grows approximately with the square root of time’ on p. 171. 1-Draw two rates of returns as you did above. Say the first draw is the rate of return over period 1, call it r_01, and the second is the rate of return over period 2, call it r_12. Compute the holding rate over two periods, call it r_02. Repeat this 400 times to obtain 400 draws for each rate of returns (1200 numbers total). 2-Using your three sets of 400 draws, compute the variance of r_01, r_12 and r_02. What should be the relationship between the these variances according to the statement on p.171? Check that this is the case. The purpose of this simulation is to get some intuition for Ivo’s statistical answer to the question of whether it is possible to detect an extra signal of 2bp per day with noise 50bp if one observes 5000 realizations of this signal (See section 12.3 of the textbook and in particular p.289-290). We want to get a sense of what this means using simulations and graphs. You should use the excel sheet supplied. 1-According to Ivo’s N-day statistics, how many days would it take to reach a conclusion about this signal (assuming that you want a T-stat around 2). 2-Check that the function IF(RAND()<0.5,-1,1) draws a random variable that take value +1 and -1 with equal probability. To do so explain what you would expect to see when you draw 1000 independent realizations. Check that this is the case. 3-Explain how the formulas in the excel sheet use this function to draw a signal with 2bp drift and noise 50bp. 4-Compute two 5000-days time series: (a) the realized compounded rate of return (an approximation of a Brownian motion), (b) the compounded rate of return from a 2bp drift alone. Plot these two time series. 5-Using the notion of arithmetic and geometric rate, would you expect the realized return after 5000 days to be on average equal to the compounded rate? If not, what would be a good guess for what you should expect to earn after 1, 2,…5000 days. Add that time series to your chart. 6-Say you draw many samples of 5000 realizations (using the F9 function). According to your answer to question 1, what property would you expect these samples to have? How would you use the chart you produced to check this? 7-Repeat your analysis for a signal with 1bp drift and 100bp noise? Is the difference between the two signals sensible? Note: You’ll have to learn how to draw a ‘scatter XY chart in Excel’. This is a great tool to know to visualize data. You’ll find many online tutorials under that search entry.
Session 5: A DCF approach to Tesla valuation The purpose of this session is to: (a) retrace the main steps taken by A. Damodaran to value Tesla; and (b) replicate the analysis with updated numbers. You should read Chapter 3 from “The Little Book of Valuation” by A. Damodaran to understand the big picture. Your answers should try to make reference to that reading when relevant. Question 2 and 3 refer to sheet ‘valuation output’ in this simplified Excel file. (There are many sheets in this file but you have to look only at the first two. Note also that I have simplified the Excel file so the final valuation is not the same as the ones reported in the paper you read for RN2.) Limit your answers to 100 words per question. 1-Briefly summarize the 4 steps taken in Chapter 3 to value a company. 2-Write a simple (math) formula that summarizes how Damodaran obtains the FCFF in line 13. Your formula should highlight the key inputs and assumptions that go in that formula. Explain. 3-Write a formula that explains how A. Damodaran combines the FCFF with other inputs to obtain the valuation in B25. Explain. The purpose of the next two questions is to update the Tesla valuation using the latest available information following the same methodology as above. You will have to do some research to find the values you need to update the Excel file. 4-Say you update only the ‘base year’ revenue. What valuation do you obtain? Compare the result with the corresponding market valuation. If you had to change just one other input in the Excel file to get a more accurate and current valuation, what would it be? When you make that change, what impact it has on your valuation? 5-How has the Tesla stock performed over the last year? In your opinion, can the valuation model explain this performance? Discuss. Year T Earnings
Incremental
Savings if
work
K(T)=Saving
Account at
beginning of
T
K(T+1)=Saving
Account at end
of T if Work
TildeK(T+1)=Saving
Account at the end of
T if withdraw $5000
at beginning of T and
do not work
Does saving
account decrease if
stop working in T?
TildeK(T+1) 2 10000 5000 5000.0 10250.0 0.0 1 14 10000 5000 88564.9 97993.2 87743.2 1
15 10000 5000 97993.2 107892.8 97642.8 1
16 10000 5000 107892.8 118287.5 108037.5 0
17 10000 5000 118287.5 129201.8 118951.8 0
18 10000 5000 129201.8 140661.9 130411.9 0
19 10000 5000 140661.9 152695.0 142445.0 0
20 10000 5000 152695.0 165329.8 155079.8 0
21 10000 5000 165329.8 178596.3 168346.3 0 r 0.05 NPV of current and future consumption (5K(1+1/r)) 14.7128 >Basis Point Simple Math
bp per day Rate Yearly 9 7 3
1 0
50 7
8 4
8 7 8
3 7
0
0.02 01 3
4 6 0
9
6 9 1 0
2 5 0 3
9 7
0
9 3 7
50 8
8 0.05 9 1
0 71
04 6 0
30 bp per day
4 0.0005 87
0.02 6 509
0.0003 trading days. That’s the number of distinct observations per year.
year
=1.0002^252)
0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 -0.005 0.0002 0.005 0.0002 0.005
Iv
W
ch
or ra
te
Fi
nc
(4
Ed
on
Ju
2 0
17
.
Iv
o
el
, C
po
te
na
e
th
iti
),
ly
17 Iv
ra Fi
20
. o
. I W 1 2
Perfect and Efficient Markets,
and Classical and Behavioral Finance
How Trustworthy are Market Prices ?
This chapter explains the concept of an efficient market, which is not as strict as but 12.1 Market Efficiency
A perfect market sets up stiff competition among many investors. This forces them to use all available information as well as they possibly can. This is called market efficiency: a situation IMPORTANTA price is called efficient if the market has set the price correctly as if it were using all available Warning: Market efficiency is a different concept from mean-variance efficiency ä Mean-variance efficiency, Exhibit 12.1 illustrates an efficient market. Suppose the market considers an expected rate of return of 10% on ABC stock to be a fair rate of return, given ABC’s characteristics. This figure of 277 Iv 278 Perfect and Efficient Markets, and Classical and Behavioral Finance
value tomorrow is really $60 (for an expected rate of return of 20%) or $50 next year (for an Efficient Market
Pricing Model
Today’s Price
The General Case
The financial markets estimate the statis- The financial market determines the ap- The market sets today’s price, so that the ? A Specific Example: ABC
The market estimates ABC’s expected Say the CAPM is the correct pricing model. The price today is $55/1.1 = $50 per Exhibit 12.1: Market Efficiency and Pricing Model. The critical question is If you saw a price of, say, $45.83 today, what The practical use of the “efficient markets” concept begs two questions: the information set? 1. Where does the figure of 10% come from? It has to come from some model that tells you 2. If the market is not perfect and different investors have different information, then exactly What should you conclude if you can determine authoritatively that the expected rate of rate of return is really 20%: wrong; (b) the market was return is really 20%? (This can happen either if you determine that the expected payoff is $60, 1. The CAPM is not the correct model. Instead, the market followed some other pricing model Iv 12.1. Market Efficiency 279
2. The stock market is not efficient.
Can you see why market efficiency is so difficult to prove or reject? If you wish to proclaim a belief in market efficiency, and if you then find empirically that prices are not what your model Short-Term versus Long-Term Market Efficiency Practically useful? Rarely The reason is that no one knows exactly what the correct model of pricing is—the CAPM may Of course, in extreme circumstances, market efficiency can be a useful claim even on such great bets like “+$1 million with 99% probability” and “–$1 with 1% probability.” Expected However, over short horizons (say, a day or so), market efficiency is a surprisingly useful concept. The reason is that over a single day it does not matter as much whether you believe the 2013-01-0 5
IMPORTANT• Over short time intervals (say, days), market efficiency is a very powerful concept. The • Over long time intervals (say, months or years), it is difficult to pin down what the • Prices should move only when there is news about future cash flows or discount rate Iv 280 Perfect and Efficient Markets, and Classical and Behavioral Finance
Relation to Perfect Market Perfect market ⇒ efficient a market is perfect, economic forces drive it instantly toward market efficiency. Put differently, if The converse is not true, however. It is quite possible for an imperfect market—for example, market. one in which there are taxes or different opinions—to be efficient. You could even (crudely) think Another way to understand the difference is to compare assumptions. Of the four perfect- facsimile of “same market assumptions, only one has any overlap with and bearing on the efficient-market concept: Perhaps the most important perfect market assumption driving prices toward efficiency is culprits in keeping prices the absence of transaction costs. Without them, it is easy for you and other investors to trade Here is a practical example of how any market inefficiency would disappear quickly in a markets toward efficiency. perfect market: What would you do if you learned that the market always goes down on rainy Conversely, it is easier to believe that markets are not (or less) efficient if transaction costs efficient even in a overpriced stuff?
are high. But even if the market is not perfect, market inefficiencies should still raise eyebrows. Iv 12.1. Market Efficiency 28 1
still $50. Alas, when you run a few regressions, you learn that the expected future price is not ä Shorting stocks, short are too high. However, this leaves the question of why investors who already own ABC IMPORTANT • If a market is not perfect, self-interested individual behavior should still drive it toward Market Efficiency in Modern Financial Markets You can reasonably assume funds, currencies, and others, seem reasonably close to perfect and thus efficient. They are • The bid-ask spread is often high.
ä Bid-ask spread, • The posted bid-ask spread is only guaranteed for 100 shares—if you want to trade more • Commissions can be high.
• Shorting small stocks can be very costly when compared to the ideal of a perfect world in In a round-trip transaction, you will face the first three issues once when you buy and once when The fact that large-firm stock markets are pretty efficient means that, by and large, you can trust these financial markets to get asset values about right—at least within the limits of ä Great bets, gravy. In an inefficient market, you could not rely on market prices being fair—they could be Iv 282 Perfect and Efficient Markets, and Classical and Behavioral Finance
“Trading Places” and Citrus Futures and money to determine whether prices are fair. The advantage of efficient markets is that if Q 12.1. What does it mean for a market to be efficient?
Q 12.2. As a believer in efficient markets, what would you likely answer when heretics claim Q 12.3. Is market efficiency a more powerful concept over long or short horizons?
Q 12.4. How does an efficient market differ from a perfect market?
Q 12.5. Is it more or less likely for a financial market to be efficient when transaction costs are Q 12.6. Would you expect the market for the dollar-euro exchange rate to be more or less perfect Iv 12.2. Market Efficiency Beliefs and Behavioral Finance 28 3
How to Get Squeezed and Lose Money Even When You Are Right In 1998, I shorted Netscape. I believed that Netscape’s browser was about to be taken to the cleaners by Microsoft’s Internet Later on, I found out that I was not alone. The most reprinted article in the history of Fortune magazine was “Mr. Buffett Not everyone believes there was a bubble. The book’s website (book.ivo-welch.info) has an impromptu email conversation 12.2 Market Efficiency Beliefs and Behavioral Finance
A firm belief in efficient markets is what defines a school of thought known as classical finance, the efficient market hypothesis, or EMH, which holds that all securities are priced efficiently. Almost all financial economists, regardless of camp, believe in basic market efficiency for large markets and liquid securities. No respectable economist believes that it is easy to get Iv 284 Perfect and Efficient Markets, and Classical and Behavioral Finance
The Traditional Classification The traditional classification about the type of the market.
cation, market efficiency comes in three strengths: weak, semistrong, and strong.
Weak market efficiency says that all information in past prices is reflected in today’s stock Semistrong market efficiency says that all public information is reflected in today’s stock prices, Strong market efficiency says that all information, both public and private, is reflected in In this traditional classification, all finance professors nowadays believe that most financial longer believe in perfect markets are not strong-form efficient: Insider trading may be illegal, but it works. However, Market efficiency champions quickly point out that many of these strategies’ returns were strategies seem to have spurious: They disappeared almost as quickly as they were discovered, and they probably were One conceptual question that had vexed academics for a long time was how markets could information must be in be efficient to begin with. After all, if there is no money to be made, why would anyone bother Q 12.7. Which form of market efficiency do momentum trading strategies seem to violate? Iv 12.2. Market Efficiency Beliefs and Behavioral Finance 285
The Fundamentals-Based Classification and Behavioral Finance My preferred taxonomy of belief in whether prevailing market prices reflect underlying values:
A true believer would argue that financial prices always reflect the best net present value A firm believer would argue that financial prices may sometimes deviate from the appropriate A mild believer would also argue that financial prices may sometimes deviate from the appro- A nonbeliever would argue that financial prices regularly deviate from the appropriate value, These classes are progressively weaker along the market efficiency dimension. For example, a Occasionally, there is evidence that refutes even the truest of believers—but this is rare. The most dramatic example occurred in 2000, when the network company 3COM spun off the Where do most finance professors sit in this classification of beliefs? Virtually no academic is a perpetual nonbeliever, and only a very few remain in the “true believer” camp. Instead, most Let me tell you my personal view. I sit right in the middle between the two schools of thought, than they are—that they can predict when stocks are going to go up or down. This is why I Iv 286 Perfect and Efficient Markets, and Classical and Behavioral Finance
But these funds are scarce. Even after decades of academic research that has tried to identify ä Evidence on Fund Performance, One final note: Pundits love to talk about investor psychology. And it is indeed the case that individuals suffer from many cognitive biases. For example, Nobel-prizing winning research Q 12.8. If you believe that market values do not always perfectly reflect underlying fundamental 12.3 The Random Walk and the Signal-to-Noise Ratio
Why is the debate over market efficiency so tough to settle? It is the fact that the signal-to-noise allows our arguments about continue.
ratio in financial returns is low. The signal-to-noise description draws on an analogy from Let me explain. What are typical price change magnitudes? For example, June 17, 2016, was signal-to-noise ratio with a particular day.
a fairly quiet and uneventful day on the financial markets. 10-year Treasuries stood at 1.6%, The Signal You cannot expect a It would amount to over of a company cost $50 today, what do you expect them to cost tomorrow? What is a typical daily Iv 12.3. The Random Walk and the Signal-to-Noise Ratio 287
relevant stock—according to your signal—and end up filthy rich. (The investors on the other So what kind of average daily returns can you expect from the U.S. stock market? Say a 15
basis points. The majority of stocks should allow you to earn expected rates of return of between Great Mathematicians and Gambling: The Origin of the Random Walk Later reinventions and applications of the random-walk concept abound: Jan Ingenhausz (1730–1799), a physician and Fortunately, in 1900, Louis Bachelier introduced the random-walk theory of financial market fluctuations (although Karl Let’s make this into a formula. If your expected rate of return is a small constant m, that is, E r =[E
� P1 – P0]/P0 = m, then your best expectation of the price tomorrow (P1) must be Expected Price Tomorrow = Price Today + Tiny Drift (12.1)
E = P0 + m · P0︸ ︷︷ ︸ Tiny Drift
This is customarily called a random walk with drift. As you just learned, depending on the stock, Note that price behavior very close to a random walk is a necessary consequence of an efficient market, but you cannot conclude that a market is (truly) efficient just because stock Iv 288 Perfect and Efficient Markets, and Classical and Behavioral Finance
day. In this case, stock prices would still follow a random walk, but your signal would allow you A Complication—Transaction Costs the profitability of many no signal can be very accurate. It should not be possible to predict stock price movements ä Transaction costs, exploiting misvaluations, especially short-lived ones that require a lot of trading to exploit. You In an imperfect market with transaction costs, you can view the efficient market hypothesis the EMH in terms of in one of two ways:
1. The EMH should hold if you work with post-transaction cost rates of return. One percent 2. The EMH should hold if reasonably many investors have very low transaction costs, perhaps So the EMH won’t hold perfectly in an imperfect market, but it should be a fairly reasonable Q 12.9. From memory, write down the formula for a random walk.
Q 12.10. What is the typical expected rate of return on a stock on an average trading day?
Q 12.11. What kind of rates of return does a strategy of trading stocks once a day have to offer Iv 12.3. The Random Walk and the Signal-to-Noise Ratio 289
The Noise The daily noise in stock stock prices that you will actually observe:
Price Tomorrow = Price Today + Tiny Drift + Noise
P1 = P0 + m · P0 + ε E (ε) = 0 • The typical day-to-day standard deviation of individual stocks in the market is around June 17, 2016, was on the low side in terms of volatility, but the typical noise movement of 200 IMPORTANTIn the financial market context, “random walk” refers to a process in which the expected value E P1 Tiny Drift ⇔ P1 = P0 + m · P0︸ ︷︷ ︸ + ε0,1︸︷︷︸ where m is a very small positive drift. (Another version of a random walk is E P1 in practice, this version is almost indistinguishable from the one in the formula above.) empirical stock price evidence is highly favorable. Stock prices indeed tend to follow roughly a Q 12.12. What is the typical movement of a stock on an average day?
Q 12.13. If stocks follow a random walk, can the price tomorrow be different from the price Detecting an Interesting Signal in the Noise Detecting a signal in a lot of it to determine whether you are facing a stock with 5 basis points’ signal versus one with, say, 7 Iv 290 Perfect and Efficient Markets, and Classical and Behavioral Finance
How easy is it to detect an extra signal of 2 basis points when hidden in noise of about 200 anything from just 1 day of basis points? Obviously, 1 daily return is not going to do it. If I tell you that your investment pick � /Sdv
� . If To draw reliable conclusions, you need a lot more independent daily observations. Unfortu- returns from the same day nately, you cannot use the returns from many stocks from the same day as independent signals. Fortunately, you can regard returns from different days as independent observations. You deviation, and T-statistic can therefore use sequential days of investment performance to investigate the quality of your p ä How risk and reward grow over times the standard deviation over 1 day. Your expected T-statistic over N days to detect your N-day T-Statistic = Standard Deviation N · E r p � p How many trading days (N) do you need in order to expect a T-statistic of 2 if your 1-day real.
T-statistic is 0.01? You need 2002 = 40, 000 days to have such confidence. This is about 157 IMPORTANT square root of time.
• On an average day, the typical stock may easily move up or down by about 20 to 50 times Iv 12.4. True Arbitrage and Risk(y) Arbitrage 291
Q 12.14. To be a consistent superstar trader, by how many basis points should you be able to Q 12.15. Assume that the typical day-to-day noise (standard deviation) is about 100 basis points. 1. With only 1-day performance, how much extra do you expect to earn per day?
2. How bad is your noise over 1 day?
3. What is your expected T-statistic (the excess mean divided by the standard deviation)?
Recall from your statistics course that a T-statistic of 1.96 gives you good statistical confidence 4. With 252 trading days of performance, how much extra rate of return do you expect to 5. How bad is your noise over 252 days?
6. What is your expected T-statistic now?
7. Work out how many years you would expect to wait before you would obtain reliable 12.4 True Arbitrage and Risk(y) Arbitrage
Measuring investment performance brushes on a closely related topic—what exactly is the so great that you should not be able to find one. It is the desire of traders to exploit any arbitrage The Definition of Arbitrage In a perfect market, the should have the same price. This is true in a perfect market, but even if the market is not perfect, ä Law of One Price, always hold. If it did not hold, you and the other infinitely many potential buyers could find IMPORTANT – that offers positive net cash inflows in at least some scenarios, flow. This means that it is risk-free. Iv 292 Perfect and Efficient Markets, and Classical and Behavioral Finance
An example: $5 for free.
• A risk(y) arbitrage is a business transaction that may not be risk-free but that still offers Arbitrage is an ex-ante concept, not an ex-post concept—beforehand, not after the fact. For defined in terms of (the outlays.
example, it does not mean that a lottery ticket that won was an arbitrage. Ex ante, a lottery ä Ex-ante fair bet, 1. Arbitrage is not the same as “earning money without risk.” After all, Treasuries do just that, 2. Arbitrage is also not the same as “receiving money today without a clear obligation to Now contemplate the difference between the examples of the true arbitrage and the risk(y) bet. Unlike a true arbitrage, possibly lose a little money.
arbitrage in the definition. You can lose $1 with 1% probability in the risky arbitrage, so it is Most of all, unless financial markets are very imperfect, you should expect not to find many arbitrages in competitive describe (sane) markets.
arbitrage opportunities of either type. If you agree with this assessment—basically that the Q 12.16. Is earning money without risk an arbitrage?
Q 12.17. When and why you would prefer a risk(y) arbitrage to a true arbitrage opportunity. Iv 12.4. True Arbitrage and Risk(y) Arbitrage 293
More Hypothetical Arbitrage Examples In a sense, positive-NPV What would a hypothetical arbitrage opportunity look like? For example, if you can buy an Small arbitrages matter only works once for 1 cent, it is unlikely that you can find such an arbitrage opportunity that works Another hypothetical example of arbitrage would involve stock prices that are out of sync on different stock exchanges. If PEP shares are quoted for $51 on the Frankfurt Stock Exchange, But before you conclude that this is an arbitrage, you still have to make sure that you have not forgotten about costs or risks. The arbitrage may be a lot more limited than it seems—or 1. Could the price change in between the time you buy the shares in New York and the time 2. Did you account for the direct and indirect transaction costs? How much commission ä Bid and ask prices, in Frankfurt and get it quickly enough from New York to Frankfurt to make the closing? 3. Could the share prices move when you want to transact a significant amount of shares? 4. Did you account for your fixed cost of setting up your business? If it costs you a million It may be that small arbitrage opportunities occur from time to time, but large financial firms are Q 12.18. Before you dedicate your life to exploiting a seeming arbitrage between financial Iv 294 Perfect and Efficient Markets, and Classical and Behavioral Finance
12.5 Investment Consequences
How does the EMH matter to you if you are an investor? In an efficient market, there should good signal for the future be no obvious signals to outperform the risk-adjusted appropriate expected return to the tune Weak-Form Efficiency and Technical Analysis Could there be “cycles” in prices. So let me start with some trick questions. Look at the various graphs in Exhibit 12.2. Do On the other hand, graphs (c) and (d) could actually be representative. On average, each ups and downs in the market, price in the next month is just a little higher than the previous (i.e., the expected rate of return The Empirical Evidence on Trends
Traders have been trying all sorts of strategies in their efforts to become rich. So how well of return mostly appears to does technical analysis—which tries to find patterns in historical stock prices—typically do? For Iv 12.5. Investment Consequences 295
Pattern (a) Pattern (b)
2011 2013 2015
19
20 21
22
23
Date
S c ri 2011 2013 2015 25
30
35
Date Pattern (c) Pattern (d)
2011 2013 2015 10
15 Exhibit 12.2: Potential Stock Price Patterns. If these patterns were systematic, some of them should make you rich. Which Iv 296 Perfect and Efficient Markets, and Classical and Behavioral Finance
Nasdaq Composite Intel Corp
−3 −2 −1 0 1 2 3
−3
−2
−1
0 Rate of Return Today, in %
R o R rn o o o , % Rate of Return Today, in %
R Exhibit 12.3: The Relation between Lagged and Current Rates of Return. The left panel is the tech-heavy Nasdaq Composite a number of financial websites, such as FINANCE—look up any stock and choose “Charts,” However, over annual horizons, it appears as if stocks tend to continue their pattern just a well over the last year (with well. Are Women Better Investors Than Men? Despite strong evidence to the contrary, many investors still believe that stock prices do not follow random walks, as Odean and Barber, 2001 Iv 12.5. Investment Consequences 297
Investment Manager Performance Evaluation What about celebrity patterns (shoulders, price barriers, faces, etc.) in historical prices and using them to forecast First, recall that the low signal-to-noise ratio means it is difficult to determine why a particular trading strategy has earned high returns:
• Was it because it had a lucky outcome, which will not repeat (random luck)?
• Was it because it took on some risk that your appropriate return model forgot (your fault 2012-12-30
• Or was it because the market was inefficient (you have a good signal, skill, and trading This is not just a problem for academics. In fact, we finance professors are lucky: We can continue But the signal-to-noise ratio problem is not even the only problem that you need to consider when you pick an investment manager. If you believe that the market is inefficient so that your Evidence? Of course, maybe there are some investors who can pick stocks. Unfortunately, they Why would they tell anyone? Enough data? Recall our earlier conclusion that a strategy with great performance requires ä Ascertaining superior Pg.290.
Remarkably, the most common industry standard for evaluating funds is their most recent three years of investment performance. There is no disagreement that most of the 3-year What is Risk? Here is another lesson for the wise (and unwise). Until 2008, I would have sworn that investing in momentum stocks was a strategy that was reasonably well-diversified and ä “Peso” risk., Iv 298 Perfect and Efficient Markets, and Classical and Behavioral Finance
Monkeys on keyboards? There are about 10,000 mutual funds today that invest money on their many years in a row.
ä Mutual funds, investors’ behalf. How many of them are likely to outperform the overall stock market next Who is still alive? What happens to the funds that have underperformed several years in a row? They disappear quietly. (In fact, they don’t even need to appear. The SEC even allows a Why funds’ average good to you as an investor offered today. First, you won’t notice funds that have performed poorly. They have already Who gets the rents from trading ability? Even if the financial markets were inefficient and performance, the fund investor—would profit the even if some fund managers could in fact systematically outperform the market, in a In sum, if you are looking for future performance, past performance may be your best guide. But Obviously, picking the right investment manager is not an easy task. Many mutual funds compensated on the upside. investors’ problem, but the earn fees regardless of whether they make you money or not. Would it be better to have them 2013-06-30 the advice to sell it. This way, I will surely make money from one of you.) My only mistake is Iv 12.5. Investment Consequences 299
The Three Top Investment Books of 1996 Naturally, best-selling books are a great business. However, the stock performance of these three experts was not.
1. From 1996 to 2002, the Motley Fool recommended a number of hypothetical portfolios (now discontinued!). In 1997, 2. Matt Seto stopped publishing his stock-picking performance and decided to pursue a career as a student. 30%, but 9%—significantly lower than the 15% turned in by the S&P 500 stock market index during their investment How disappointing: On average, about one of them should have continued beating the market, one should have done The Empirical Evidence
So what is the empirical evidence? In general, it suggests that fund managers’ luck is far more important than their ability. Whenever academics (or the Wall Street Journal) have searched for But what about persistence? Maybe there are some funds that are better than others? True. outperformed their benchmarks over the last 1-3 years tend to outperform their benchmarks funds: 2013-04-17note—and as the evidence suggests—past performance is no predictor of future performance. Do Fund Managers Know? Nerdnote: There are some high-tech statistical techniques to take into account that researchers have Iv 300 Perfect and Efficient Markets, and Classical and Behavioral Finance
Miserable (T < (–1)) Average or Better (T > 0) Great (T > 1) AUM Before Fees After Fees Before Fees After Fees Before Fees After Fees –$250 million 25.0% 41.0% 44.8% 28.3% 17.4% 8.5% Exhibit 12.4: U.S. Equity Mutual Fund Performance, 1984–2006. This table looks at the historical performance of about Years Relative to Hiring Fired Funds –1.6% +3.1% They fire funds after they have performed poorly, not before they perform poorly. And they There are, of course, other ways to make money: Warren Buffett’s fund, Berkshire Hathaway, that old-fashioned work and provision work better in picking.
for example, runs many businesses (e.g., insurance and aircraft), too. These businesses make ä Business of liquidity provision, himself would of course not attribute his own performance to luck, but to his ability. Still, even In sum, most finance professors nowadays would agree that when one particular investor proof be? earns an unusual amount of money, even over a few years, it is usually more likely due to luck Iv 12.6. A Cynical Perspective 301
IMPORTANTEven in an efficient market, in which no one can pick stocks better than anybody else, with a In the real world, there is little evidence that investors who did well picking stocks in the Q 12.19. If you want to determine whether fund managers have an ability to outperform the Q 12.20. If a firm employs 10,000 analysts, how many of them are likely to issue forecasts Q 12.21. Explain what survivorship bias is and how it manifests itself in the mutual fund context.
12.6 A Cynical Perspective
When fund managers earn great returns, they often become famous. To attract new investors, they then talk more about their performance. The first targets are easiest to find at cocktail Unfortunately, even though genetic algorithms and artificial intelligence are rather sexy high-tech sophisticated ways to pick investment assets, true genetics and intelligence seem to Most funds write monthly communiques to their investors. They are largely collection ex-post on the up often write about the credit they deserve for their brillant insights. They describe Iv 302 Perfect and Efficient Markets, and Classical and Behavioral Finance
We academics are not so different. John Oliver’s May 2016 show on Scientific Studies explains different. it better than I can. I will try it anyway. If you read academic journals, you will find hundreds What about me? Am I not brillant? I placed large short bets on oil in 2013 when it traded above $100/bl. I believed long-term supply and demand could not sustain such a high price. In Asymmetric-Pattern Strategies Not Understanding Profit Choose red, and when black comes up, try again and double up. When you have won, go home The opposite of the usual pattern of hedge funds are strategies that lose money most of the contrarian. time but then gain a lot in a crisis. These are strategies that are very difficult to maintain. Which Iv 12.7. Corporate Consequences 303
12.7 Corporate Consequences
How does the EMH matter to you if you are a manager? Does it matter whether financial markets are perfect, efficient, or neither? Because a perfect market implies an efficient market, you need 1. The market is efficient and perfect.
2. The market is efficient but not perfect.
3. The market is neither efficient nor perfect.
These cases help you organize your thinking about what it takes to create value—which is If the Financial Market is (Close to) Perfect In perfect markets, all that It does not matter how the firm communicates its earnings to investors, what its capital structure Earnings reporting: For example, if you have previously reported your foreign division’s ä Do reported earnings matter?, earnings separately and now you consolidate them into your main earnings, you will indeed Capital structure: For example, say your firm is currently financed with equity only and worth ä Capital structure arbitrage, $100, but if you had a 50-50 debt-equity ratio it would be worth $102. In this case, an Stock splits: In a stock split, each old share becomes multiple new shares. For example, if each ä Stock splits, share trading at $80 were to become two shares, the new shares should trade for $40 each Dividends: The same argument applies to dividends. In a perfect market, a $100 firm that ä Stock dividends, pays $10 in dividends should be worth $90 thereafter—no value is magically created or The lesson is simple: As a manager, you should forget about the smoke and mirrors and instead Iv 304 Perfect and Efficient Markets, and Classical and Behavioral Finance
If the Financial Market is Not Perfect but At Least Efficient An efficient market means you can learn from your own means that you can still obtain valuable market intelligence. Your market price is the aggregate In addition to learning from your own company’s market price, you can also learn from all other market prices. sorts of other market prices. You can find out how good your competitors’ opportunities are, and Let’s consider a specific example of how you can learn from market prices in an efficient (without synergies) is not a over other companies.
market. Put yourselves in the shoes of a smart and successful manager of an aircraft manufacturer. However, in the absence of perfect markets, the efficient market does not mean that you market, it is possible for an should never be able to create value by buying other companies. You can indeed sometimes Iv 12.7. Corporate Consequences 305
outside arbitrageurs cannot accomplish without you. (This violates the infinitely many potential But be careful: Market efficiency means that you cannot create value for your shareholders simply by your personal view that X is undervalued. Yes, you may be smart, but the financial The same argument applies to all sorts of other corporate actions. You may be able to create value by reducing perfect market barriers. For example, you may be able to create value by ä Splits as signals, information to the market.
If the Financial Market is Not Even Efficient What should you do if rational market, as an executive, you may know the firm value better than the market—for ä Strong market efficiency, appropriate market value? The right way to conceptualize your problem is to consider what you If your shares are undervalued, you should recognize that your cost of capital is effectively too high, given the true characteristics of your project. The reason is that you cannot raise ä Separation of financing and Sect. 11.1, Pg.245.
just taking the $500 from the old project. Put differently, the opportunity cost of new . . . and use your cash to own cheap, underpriced shares—for example, from other investors. However, there is
ä Share repurchases, an intrinsic paradox here: As an executive, you are supposed to act on behalf of your Iv 306 Perfect and Efficient Markets, and Classical and Behavioral Finance
If your shares are overvalued, your cost of capital would be very low. You should be tempted sometimes it is better just to take more projects. This is easiest to see if you again consider what you would do if you These are robust insights for CEOs who are not conflicted and wish to act on behalf of their IMPORTANT When managers have superior information: repurchasing the firm’s own shares.
• If the firm is overvalued, CEOs should assume a relatively low cost of capital and consider A good decision rule for managers is to take projects up to the point where the marginal costs (It can become a bit more complex if you see yourself as a representative of both new and ä Overconfidence, that the financial markets do not fully reflect the value of their companies even if they have no Q 12.22. For convenience, assume a zero discount rate. You have no cash on hand and can only 1. Does your second, newer project have a positive or negative NPV?
2. If your investors know both true projects’ costs, but they also (incorrectly) believe that you 3. If you act on behalf of your existing investors, should you take this new project? Iv 12.8. Event Studies 307
Comparison and Summary
Here is a summary of the two conceptual classifications of how markets work:
A summary of the two Efficient versus inefficient markets: If the market is efficient, you can learn from financial Perfect versus imperfect markets: If the market is perfect, you can focus exclusively on your In the real world, financial markets are definitely not 100% perfect. For large firms, they are very close to efficient, but this is not necessarily so for small firms. Still, the economic magnitudes 12.8 Event Studies
The immediacy of price reactions in any efficient market offers a surprisingly useful real-world application: In some cases, market price reactions can allow you to estimate value consequences Capital-Structure-Related and Other Event Study Results Event studies have been to corporate name changes, to analysts’ opinions, to corporate earnings, to stock splits, to • When firms announce increases in dividends, share repurchases, or stock splits (by about Iv 308 Perfect and Efficient Markets, and Classical and Behavioral Finance
• When firms are taken over by other firms (by about 10-30%).
• When firms announce earnings that significantly beat analysts’ expectations.
• When drug firms announce that the FDA has approved one of their drugs.
• When the founding CEO dies (by about 3-4%).
Conversely, firm values decrease on average: • When firms announce new stock sales (by about 1-3%).
• When firms overpay for other firms in acquisitions.
• When firms announce lower-than-expected earnings.
• When firms fend off an acquirer who has made a bid.
• When drug firms announce that the FDA has rejected one of their drugs.
Unfortunately, because we do not know the markets’ probability assessments prior to these Event studies have also informed us whether certain government regulations had a positive benefits? who does not? or negative impact on firms. For example, we know which firms were helped and which were The Effects of Sanctions on South Africa We may all wish we could report success—that sanctions on South Africa’s racist regime had been effective. Unfortunately, Although we can conclude that, despite all its publicity, the embargo was largely ineffective economically, sanctions may Q 12.23. In a perfect market, what kind of response (“unusual” stock price change and “unusual” Q 12.24. What kind of corporate events are greeted as good news by the financial markets? Iv End of Chapter 12 Material 309
Summary This chapter covered the following major points:
• Market efficiency means that the market uses all avail- • In the short run, the appropriate expected rate of • In the long run, it is rarely clear what this “appropri- • Beliefs in efficient markets come in different forms.
– The standard efficient markets classification – A more current efficient markets classification • The overall evidence suggests that it is not easy to separates finance professors into “rationalists” (or • In a perfect and efficient market, investors should – True arbitrage is a riskless bet with no nega- – Risk(y) arbitrage is more like a great bet. An – Both true and risk(y) arbitrage opportunities • Given the millions of investors, many will beat the • Managers can learn valuable information from mar- • Event studies allow you to ascertain the corporate Iv 310 Perfect and Efficient Markets, and Classical and Behavioral Finance
Preview of the Chapter Appendix in the Companion
An online appendix illustrates a specific event study—the value relevance of the elections of Keywords Answers
Q 12.1 The “efficient market” phrase is shorthand for “the mar- Q 12.2 As a believer in market efficiency, you would point out Q 12.3 Market efficiency is a much more powerful concept over Q 12.4 An efficient market is one in which the market uses all Q 12.5 Markets are more likely to be efficient when transaction Q 12.6 The foreign currency market may well be the biggest mar- we would expect arbitrageurs to take advantage of even the smallest Q 12.7 Momentum strategies seem to violate even weak-form Q 12.8 If you believe that market values do not always perfectly Q 12.9 The random-walk formula is on Page 287. It states that Q 12.10 There are about 250 trading days per year. More ac- Q 12.11 A daily trading strategy would have to offer above 20% Iv End of Chapter 12 Material 311
Q 12.12 The typical movement (variation) of a stock is around Q 12.13 Even if the stock price follows a random walk, its actual Q 12.14 If you want to be a superstar trader who outperforms 1.04 – 1 ≈ 1.6basis points per day. points per year of excess performance:
1. With 1 day’s performance, you would expect 200/252 ≈ 0.794 2. The noise was given as 100 basis points per day. p 6. The expected T would be about 200/1, 587 ≈ 0.126. p N ≥ 1.96. The critical N is approximately 250 years. not an arbitrage, because investing in them requires a negative net Q 12.17 If the true arbitrage opportunity can only be done once Q 12.18 Good topics to consider when thinking about how plau- Q 12.19 Yes, it makes sense to look for high-ability managers Q 12.20 If each of the 10,000 analysts has a 50-50 chance Q 12.21 Survivorship bias means that you, as an investor, will Q 12.22 1. This project has a negative NPV, –$200 + $180 = 2. If you do take this second newer project, all your investors 3. The true value of your firm will be ($500+$180) = $680, and Q 12.23 The immediate share price response to the news that Q 12.24 Good news: becoming an acquisition target; the an- End of Chapter Problems
Q 12.25. What kind of evidence would heretics against Q 12.26. Define “efficient market” and explain how it dif- Q 12.27. Peter Lynch, a famous former fund manager for Q 12.28. Evaluate the following statement: It does not mat- Iv 312 Perfect and Efficient Markets, and Classical and Behavioral Finance
Q 12.29. A paper by Frieder and Zittrain looked at a large Q 12.30. What are the three main categories in the tradi- Q 12.31. Comment on the following statement: “An ef- Q 12.32. Describe the fundamentals-based classification of Q 12.33. Does a random walk imply that the expected rate Q 12.34. Define arbitrage. How is it different from a great Q 12.35. Would it make sense for a model of the financial Q 12.36. Assume that the typical day-to-day noise (stan- 1. With only 1 day of performance, how much extra do 2. How bad is your noise over 1 day? 3. What is your expected T-statistic (the excess mean 4. With 252 trading days of performance, how much 5. How bad is your noise over 252 days? 7. Work out how many years you would expect to wait Q 12.37. What kind of costs should you consider when Q 12.38. The typical hedge fund investor evaluates its fund Q 12.39. Why does the average mutual fund in the market Q 12.40. Do you expect fund managers with high ability Q 12.41. If a corporation acquires another firm, it can Q 12.42. Give an example of how the cost of capital for tak- Q 12.43. For convenience, assume a zero discount rate. > aluation output
ase year
2 erminal year
%
.00% 70.00% 70.00% . %
. %
. %
%
2.75% 8.70
8.78
.88
,0 .40
, 8
4.07
,2 .25
,7 . 9
. %
%
%
%
%
%
. 1 0% )
.46
. .16
7.74
0.00% 0.00% 0.00% 0.00% 0.00% 0.00% %
%
.00%
3 $ (21.86) $ (5.21) $ 45.46 $ 169.63 $ 445.34 $ 1,023.93 9.27
.94
.53
. . .52
.72)
7.03)
8)
10.03% 10.03% 10.03% 10.03% 8.00% 8.00% 88
260
07
2
00
656
78
759
90
65
)
)
)
)
$ 3,584.25 8.00% 7
8.74
. %
1.41 1.41 1.41 1.41 1.41 1.41 1.41 1.41 1.41 7
3
9%
2%
%
%
%
%
%
8.00% name
of incorporation
of America
09545
.70 .83
$ 578.74 s to capitalize?
$ 201.89 $ – 0 $ – 0 $ – 0 121.45 stock price =
s: Here is what your company’s numbers look like, relative to industry.
=
0.00% Company 2%
70.00% – % 0% 1.41 1.41 %
10 ROC= 1 %
2.75% 10.03% Yes 0
From last 10K From last 10K %)
Yes 8% 10% V 50% From last 10K Aswath Damodaran: by the sum of cells B5 and B6). Look at the industry averages as well in the worksheet. % of fair value. How much less than 100% you get will depend on whether there are lots of potential buyers for your assets and how much of a hurry you are in to liquidate. It may well be zero for a young growth company with no tangible assets. $ 168.76 3.50 50.00% 0.00% 2.75% 25.01 121.45 168.76 21.2 121 6835
2.75% 21.2 0.00% 2.75% 4290314
7147662
95443592
63409498
.75
.20
11.27% %
4)
Ratio or reinvestment (Input cell B15)
T 5 .98
0 0.00 $ – 0 0 0.00 0.00 0.00 $ – 0 .19
Aswath Damodaran: Inputs s (From footnote to financials)
is next year, ….
Output 7.00% 2 0
Debt outstanding =
$ 233.97 s calculator
19 %
121.45 4 %
$ 168.76 23 5.80% 11.27% %
1.20 7 6 %
2.75% 3 %
%
12 8.43% %
for ERP (if you choose “will input”
0.00% 0.00% 0.00% 5.80% 0.00% 0.00% 0.00% $ 578.74 Region Revenues ERP Weight Weighted ERP 0 %
0.00% %
2 & 56 5.80% %
Direct input %
0.00% 0.0000% 100 2%
07%
/BBB
0.00% 0.0000% 1 0.00% 0.0000% 631 5.80% =
35% 6.85% %
77%
without 168 %
82%
0 Japan 0 6.85% 0.00% 0.0000% 0 Total 100.00% 0 of Convertible =
0 (US Industry Averages)
$ – 0 Automotive 00
00
00
0.0000 $ – 0 0.0000 0 0.0000 $ – 0 0.0000 70 0.0000 $ – 0 0.0000 5 0.0000 $ – 0 0.0000 0.0000 $ – 0 0.0000 $ – 0 0.0000 $ – 0 0.0000 $ – 0 0.0000 $ – 0 0.0000 $ – 0 0.0000 $ – 0 0.0000 Company 89
$ 541.34 $ – 0 Business Revenues EV/Sales Estimated Value Unlevered Beta 2.57% 0.00% 100.00% 83
13
%
10.03% software and services
64
0.0000 $ – 0 0.0000 Aswath Damodaran: 1 $ (216.72) 2.75% Output .00
%
0.00% ≤ to Rating is Spread is D2/D 3 100000 /AAA
9999
2.5 999
/AA
%
9999
0%
2 999
/A+
%
9999
%
1.5 999
/A
9
%
1.2 1.49999 /A-
%
9999
/B
0.9 9999
Baa2/BBB 2.00% 0.75 9999
/BB+
99999
/BB
0.6 9999
Ba2/BB 4.00% 2.49999 Ba1/BB+ 3.00% 0.5 9999
B1/B+ 5.50% Baa2/BBB 2.00% 0.4 9999
B2/B 6.50% A3/A- 1.30% 0.3 9999
B3/B- A2/A 1.00% 0.2 9999
C2/C 8.75% A1/A+ 0.1 0.199999 Ca2/CC Aa2/AA Caa/CCC 100000 Aaa/AAA 0.40% -100000 D2/D 12.00% greater than ≤ to Rating is Spread is C2/C 8.75% A3/A- 1.30% B2/B 6.50% Aaa/AAA 0.40% Ba2/BB 4.00% B2/B 6.50% Ba1/BB+ 3.00% B3/B- 7.25% Baa2/BBB 2.00% Ba1/BB+ 3.00% 9999
A3/A- 1.30% Ba2/BB 4.00% A2/A 1.00% Baa2/BBB 2.00% A1/A+ 0.85% C2/C 8.75% Aa2/AA 0.70% Ca2/CC 9.50% Aswath Damodaran: Unlevered Beta Cost of capital EV/Sales DA
EV/EBIT %
%
%
%
9.00% 66 %
0.98 %
0.94 36 %
%
1.03 %
6.00 3.68 54 %
%
%
1.89 54 %
3.26% %
0.60 %
5.80% 5.77% %
1.11 1.73 %
59.23% 3.26% %
6.79% 1.41 0.81 7.46 1.26 0.00% NA 6.24% %
3.26% NA NA 4.87 4.87 0.98 68 0.00% NA NA 0.89 2.76% NA NA 4.79 4.79 1.32 16.43 35 %
0.84 0.95 %
2.76% 6.24% 0.93 %
1.30 %
3.76% %
0.99 4.56 43 2.98% %
1.05 %
3.76% 20 %
0.96 1.40 2.76% 0.80 18 1.24 1.37 %
2.76% 1.44 )
33 %
1.47 %
2.76% 1.67 19.75 70 %
1.05 %
3.26% 20 %
11.27% 0.99 1.47 %
3.26% %
%
0.90 1.32 5.99 %
1.11 0.98 %
3.76% 11.11 %
%
%
1.39 1.37 9.68% 1.38 8.14 0.86 1.22 8.82% %
3.26% 5.80% 0.84 1.92 10.09 1 1.03 8.00% 4.26% %
0.90 64 %
1.09 1.05 4.26% 33 %
%
%
1.09 4.26% 19.83% 3.42 2.41 1.67 20 0.57 %
%
%
0.54 2.27 7.98 1.49 17 %
0.43 13.21% %
%
0.49 1.79 15 %
5.14% 14.19% 2.26% 0.54 2.26 1.44 64 1.45 10.03% 3.76% 9.18% 1.58 1.49 8.57 2.34 6.39% 1.17 1.22 8.81% 3.76% %
0.59 & Const
30 %
1.40 1.28 9.19% %
2.76% 0.50 7.98 1.89 76 %
%
1.31 3.76% 0.79 2.34 2.38 42 %
1.33 1.11 3.26% 1.34 1.79 7.97 10.37 84 %
0.49 3.76% 4.60% 0.90 1.87 (Div.)
1.34 3.26% %
12.56 %
%
0.77 0.87 3.26% 1.84 1.22 10.10 10 %
8.13% 2.76% 0.39 4.44 0.90 6 %
0.85 1.12 8.26% 2.76% %
6.07% 0.85 1.84 9.73 32 8.48% %
1.47 1.63 %
3.26% %
9.53% 2.00 0.95 8.34 21.64 20 11.68% %
0.98 7.36% 2.76% 10.41% 1.07 3.60 14.37 3.89 23 %
%
1.45 1.80 3.26% 1.12 3.23 22 1.25 1.55 10.73% 3.76% 0.88 2.19 57 %
1.29 3.26% 8.43% 0.82 2.43 10.68 15.66 3.07 27 14.81% 0.88 0.98 7.42% 3.26% 1.23 2.24 11.12 25 1.38 9.76% 3.26% 9.00% 0.34 8.69 136 8.41% 20.19% 0.97 3.26% 1.85 0.99 2.29 28 1.05 1.25 9.00% 2.76% %
0.79 3.16 15.55 32 0.00% NA NA 1.41 1.44 %
2.76% 7.08% NA NA 1.37 1.37 0.72 62 %
NA NA 10.73% 0.90 0.85 6.69% 2.76% 5.80% NA NA .89
1.11 11.68% 8.43% 1.31 1.17 8.56% 8.43% 23.16 31 2.26% 1.21 1.27 9.11% 2.26% 8.57% 15.67 1.31 63 1.11 1.05 7.83% 3.26% %
2.98 1.79 12.22 16.02 94 %
1.18 1.26 2.76% 14.81% 1.55 9.93 12.94 2.76 51 0.35% 3.54% 7.92% 0.60 1.51 %
3.26% 5.00% 0.36 2.64 0.85 87 14.91% 0.82 0.87 3.26% 6.10% 0.92 2.71 46.69 %
1.10 1.07 3.76% %
7.29% 4.21 0.78 3.11 4.57% 0.66 0.84 6.62% 3.76% 5.16% 2.19 0.74 6.02 25 %
1.56 1.63 11.19% 3.26% 9.42% 1.38 1.28 6.90 8.75 1.90 (Div.)
77 %
1.54 %
4.76% 10.03% 0.99 2.18 6.24 2.35 31 11.77% 7.36% %
1.01 1.28 2.76% 0.43 2.89 5.41 1.35 27 0.45% 7.26% 0.46 2.76% 3.31% 1.40 1.03 1.99 14 1.50 1.86 12.56% 3.26% %
1.22 1.57 22 1.05 1.43 10.03% 3.26% %
6.65% 2.34 0.46 4.76 6.94 1.11 12 8.28% 0.72 1.02 %
2.76% 0.56 3.42 3.56 81 26.77% 9.50% 1.45 1.66 3.26% %
0.79 2.00 7.98 1.79 14.61 27 10.50% 9.63% 0.88 1.20 %
2.76% 6.18% 1.56 1.08 7.57 11.20 2.49 32 6.15% 1 1.07 1.37 9.73% 3.26% 1.32 1.18 7.22 1.92 26 1 1.10 1.17 2.76% 7.38% 2.03 0.70 4.39 1.49 %
1.21 1.45 3.76% 8.44% 1.07 1.26 4.06 5.77 1.47 18 1.07 1.17 %
2.76% 0.66 9.57 53 9.50% 4.30% 0.52 0.74 2.26% 1.10 1.70 13.43 6.97% 2.62% 0.58 1.35 4.26% 0.61 1.51 8.92 21.70 0.82 83 1.00 1.03 7.75% 3.76% %
7.09% 0.43 7.17 82 10.50% 7.02% 1.21 1.27 9.12% 3.26% %
7.86% 1.23 1.89 2.57 31 %
0.73 1.30 %
3.26% 0.40 3.12 1.66 12 8.83% 1.94 2.02 2.76% 0.28 4.00 1.12 29 6.27% 0.96 1.17 8.56% 3.76% 1.66 1.32 8.76 3.37 0.01% 1.12 1.43 2.76% 0.09 7.25 8.11 1.29 12 1.15 1.32 9.40% 2.76% 2.99 17.50 51 9.09% 20.31% 1.18 1.45 %
3.26% 7.90% 0.96 1.70 9.89 2.01 11 0.00% NA NA 0.91 0.82 20.74% 2.26% NA NA 28.62 0.82 8.25 65 6.61% 1.08 1.16 8.48% 3.26% 7.72% 1.83 2.46 14.65 6.65 79 8.37% 8.22% %
1.65 1.79 %
3.26% 10.03% 0.87 7.65 10.61 2.76 22.74 42 1.51 1.43 10.05% 2.76% 1.14 9.02 4.94 18.19 19 6.78% 1.10 1.39 9.82% 3.26% %
7.40% 2.17 0.93 13.74 10 5.08% 8.35% 1.04 1.11 8.22% 2.76% 7.53% 2.55 1.31 4.32 38 5.24% 1.14 1.29 3.26% 7.77% 0.61 8.39 2.90 30 8.91% 0.58 0.68 2.76% 4.65% 4.99 0.43 3.18 14.89 27 7.09% 0.66 1.07 2.76% 0.30 3.23 0.93 6.94% 11.71% 1.60 1.49 10.41% 3.26% 1.41 10 11.80% 15.21% 2.01 1.79 40.44% 2.76% 1.21 1.44 8.07 12.22 1.64 17 8.37% 1.37 1.26 9.09% 2.76% 1.42 33 1.27 1.65 2.76% 1.26 0.73 5.63 8.89 0.88 1.37 1.07 3.26% 7.25% 2.29 1.27 76 1.00 1.15 8.43% 3.26% 6.86% 0.90 1.91 5.39 9.47 2.02 23 0.53 0.92 7.08% 2.76% 4.26% 0.72 1.77 5.08 1.77 0.00% NA NA 0.78 0.68 2.76% NA NA 4.08 0.99 11 %
32.82% 0.79 0.86 6.75% 2.76% 2.10 2.30 9.48 10.30 14 9.53% 1.09 1.17 2.76% 2.83 1.37 10.10 34 7.47% 0.87 1.09 8.08% 2.76% 6.17% 0.82 6.19 3.07 16.70 11 4.16% 0.49 4.61% 2.76% 3.36% 0.32 4.36 11.20 2.00 58 6.59% 1.17 1.35 3.26% 0.94 3.51 0.96 1.17 8.53% 3.26% 30.03% 6.56% 1.04 1.64 7.37 9.59 2.11 35.00% 20.00% 25.00% 0.00% 0.00% 25.00% 0.00% 0.00% 10.00% 10.00% 20.00% 0.00% 25.00% 30.00% 20.00% 10.00% 19.00% 25.00% 29.00% 25.00% 30.00% 28.00% 0.00% 10.00% 20.00% 0.00% 35.00% 16.50% 19.00% 20.00% %
25.00% %
0.00% 25.00% 33.33% 0.00% 20.00% 30.00% , Republic of
15.00% 20.00% 12.50% 15.00% 28.80% 12.00% 10.00% 30.00% 25.00% 35.00% 15.00% 30.00% 9.00% 34.00% 25.00% 30.00% 28.00% 12.00% 35.00% 25.00% 30.00% 30.00% 19.00% 25.00% 10.00% 0.00% 20.00% 10.00% 19.00% 18.00% 30.00% 28.00% 0.00% 35.00% 28.00% 17.00% 30.00% 23.00% 25.00% 30.00% 20.00% 30.00% 21.00% 25.00% 0.00% 34.00% 25.00% 20.00% 35.00% 33.00% 28.60% Region 3.25% 4.88% Africa 2.00% 8.80% 3.00% Eastern Europe & Russia 8.05% Caribbean 0.70% 6.85% 1.05% Western Europe 10.00% 15.00% Central and South America Central and South America 7.50% Asia 7.00% 16.30% 10.50% Caribbean B1 4.00% 11.80% 6.00% Asia 6.18% 0.38% Western Europe 9.40% Central and South America B1 4.00% 11.80% 6.00% Middle East Aa3 0.70% 6.85% 1.05% Asia 7.53% 1.73% Asia B3 6.00% 14.80% 9.00% Eastern Europe & Russia B1 4.00% 11.80% 6.00% Asia Ba1 2.40% 9.40% 3.60% Africa B3 6.00% 14.80% 9.00% Central and South America B1 4.00% 11.80% 6.00% Africa A2 1.00% 7.30% 1.50% Eastern Europe & Russia Baa1 1.50% 8.05% 2.25% Caribbean B2 5.00% 13.30% 7.50% Caribbean Ba3 3.25% 10.68% 4.88% Caribbean Aaa 0.00% 5.80% 0.00% North America 6.77% 8.48% 6.96% 1.16% 1.18% 7.58% %
.70
$0.00 $121.45 0.00% NA NA .00
NA NA NA NA Synthetic rating Beta Direct input 1 Direct input Multibusiness(US) Effective tax rate Pre-tax Operating Margin ROIC Sales/Capital EV/Sales 0.98 %
3.86% 9.42% 0.94 0.89 20.80% 5.35% 8.91% 4.86 0.99 12.24% 0.60 16.15% 4.84% 6.35% 6.94% 1.67 0.79 9.50% 1.00 15.05% 1.55 1.55 8.05% 16.30% 5.98% 7.83% 1.49 0.78 16.78% 1.19 27.00% 4.20% 2.50 0.56 7.61% 15.87% 0.31 0.25% %
0.09 0.44 0.00% 0.00% 0.23 3.92 4.05% 7.68% 17.55% 30.71% 21.29% 1.60 2.23 9.19% 0.68 %
0.89 2.91 1.05 2.91% 8.08% 7.25% 0.80 6.52 21.89% 1.03 17.52% 13.12% 1.12 5.90% 0.28 80.60% 5.02% 0.18% 4.13% 0.02% 0.17 6.08 0.81 7.58% 1.71 0.89 0.83 20.08% 4.20% 3.23 1.09 9.79% 15.33% 1.08 2.38 %
0.86 %
6.69% 1.32 1.06 6.76% 16.00% 30.07% 3.43% 7.96% 10.52% 1.78 0.96 7.14% 0.99 16.99% 8.00% 14.69% 1.52 1.08 8.20% 0.94 1.81 14.80% 0.97 13.66% 5.44% 20.43% 4.56 0.90 1.12 7.33% 6.83% 11.68% 27.50% 1.97 1.04 5.02% 0.90 0.21% 48.32% 0.75 32.69% 7.25% 7.89% 0.85 1.70 0.67 6.18% 11.53% 7.62% 0.88 1.46 7.65% NA 2.64 0.97 15.14% 0.96 3.30% 6.86% 7.24% 2.10 1.01 8.43% 1.01 2.78% 6.47% 1.85 0.74 2.24% 208 0.96 12.17% NA 2.32% 2.45 0.49 0.81 59.23% 1.79% 4.52% 6.83% 7.93% 2.28 0.56 8.60% 22.31% 1.69 1.94 3.98% 20.99% 0.86 8.92% 6.76% 2.04 1.31 0.74 13.56% 4.84% 7.78% 1.82 0.71 0.18 16.51% 21.78% 6.43% 0.38% 0.09 0.17 8.01% 3.31% 0.09 11.24 0.69 4.79% 8.05% 12.30% 2.13 1.20 115 0.56 1.06% 2.99% 5.51 0.30 3.43% 0.94 14.93% 4.15% 6.11% 2.63 0.72 3.67% 0.92 14.77% 9.98% 24.36% 1.50 2.55 8.27% 170 0.54 15.05% 4.24% 1.64 1.28 0.78 22.73% 7.95% 12.14% 1.32 2.49 328 0.81 31.97% 2.48% 4.77% 13.81% 0.46 0.96 20.13% 8.16% 14.89% 6.27% 7.84% 1.54 2.33 12.10% %
0.99 31.37% 8.32% 1.57 0.99 9.79% 36.75% 4.16% 6.61% 7.73% 5.94% 1.24 0.99 1.36% 0.84 12.19% 5.73% 11.80% 10.35% 0.95 2.24 10.03% 13.98% 8.68% 2.14 2.09 16.06% 0.98 10.40% 15.35% 3.05 6.26% 0.71 5.89% 7.96% 1.56 0.67 5.98% 34.76% 3.67% 6.60% 7.68% 1.50 0.77 5.07% 4.42% 7.64% 7.35% 7.58% 1.23 0.91 19.51% 1.22 4.72% 4.51% 7.77% 4.29% 24.00% 1.25 4.34 9.16% 448 0.58 5.97% 11.33% 8.11% 3.21% 0.29 10.66% 1.06 32.02% 8.92% 1.83 1.13 15.82% 1.08 27.00% 4.26% 7.44% 12.83% 1.00 1.58 20.44% 0.81 17.48% 4.25% 7.35% 15.21% 2.60 0.72 14.58% 55 1.12 18.11% 7.68% 12.65% 1.69 0.74 14.00% 8.80% 1.05 7.34% 7.14% 8.66% 0.68 2.21 0.70 8.92% 5.03% 8.71% 0.73 2.23 1.12 4.24% 3.28 0.52 0.65 7.51% 7.73% 11.05% 1.74 0.89 9.61% 0.64 1.95% 3.47% 3.98% 1.02 1.06 6.17% 0.88 12.85% 1.13 2.78 18.46% 15.12% 10.49% 5.23% 5.14% 0.64 1.80 1.16 14.66% 4.97% 8.79% 0.58 0.75 15.27% 7.95% 0.26% 1.79 1.18 1.45% 2.99% 61.89% 10.89% 0.07% 0.02 2.02% 4.94% 9.07% 18.00% 11.68% 7.27% 0.60 2.27 3.83% 0.69 4.32% 0.31 3.24 18.54% 0.84 39.24% 12.96% 7.28% 0.36 3.10 0.56 13.51% 8.76% 4.58% 0.18 6.03 10.18% 15.90% 0.86 15.30% 5.97% 11.01% 1.31 1.31 1.93% 8.86% 12.30% 14.39% 15.67% 1.25 0.73 15.30% 6.14% 2.20 1.55 6.48% 0.74 19.42% 2.82% 5.12% 17.68% 12.96% 3.11 0.63 6.02% 15.76% 51 0.68 15.82% 3.91% 7.43% 13.28% 2.72 0.95 0.61 2.60% 3.52% 5.90% 2.06 0.57 16.59% 0.78 2.82% 5.10% 12.28% 3.28 0.65 7.69% 170 0.54 2.15% 4.14% 3.96 0.48 5.93% 1.08 5.00% 4.76% 21.17% 2.83% 5.02% 7.82 2.11 12.55% 1.01 12.16% 20.10% 3.53% 6.62% 13.63% 3.94 0.79 5.00% 12.17% 91 0.84 16.86% 8.10% 15.87% 1.77 0.78 1.20 13.88% 12.19% 8.19% 12.92% 1.30 1.66 5.70% 1.49 22.44% 18.33% 7.82% NA 7.82% 7.97% 1.21 1.52 0.87% 12.94% 0.68 0.35% 5.05% 0.54% 2.97% 0.82 1.24 8.50% 1.87% 7.16% 16.29% 2.12 1.27 8.98% 14.72% 0.86 3.86% 3.97% 1.36 0.75 8.35% 117 0.79 24.24% 4.90% 16.86% 6.29% 0.96 1.87 8.43% 11.64% 1.18 15.23% 9.09% 5.90% 7.46% 9.43% 1.93 1.37 0.63 11.92% 12.33% 0.98 1.56 7.88% 8.79% 18.11% 9.16% 0.59% 0.01 7.27% 16.71% 28.10% 2.44 3.33 6.18% 9.46% 223 0.75 48.75% 8.46% 13.01% 10.37% 1.60 1.14 14.34% 0.55 10.18% 7.81% 1.72 0.79 3.04% 13.65% 61 0.41 7.06% 8.12% 1.00 1.24 8.49% 97 0.53 12.47% 8.81% 0.36 0.64 13.40% 5.74% 8.63% 10.49% 0.77 1.76 8.94% Revenues Revenues (in billions) $ 45 $ 445
2
1
A
B
C
Interest Rate
0
3
Year
D
Discount Factor
(i)
Cash Flow
PV
(ii)
Full Market Value:
$
33
Rent:
$1
9
7
8
37
6
4
30
60
5
$30.
86
1
1.03
0.
97
73
78
64
0.
94
25
59
91
2
1.0609
42
95
90
0.9
15
14
16
Lease Years
Sold
%
3
1.09
27
51
41
65
0.
88
48
70
47
$30.8605
0.
92
58
13
12
4
1.
125
50
81
0.88
84
87
79
0.86
26
44
22
$15.9
36
0.478
10
49
5
1.
159
40
43
62
0.
83
74
56
$8.
53
0.2
55
85
6
1.
19
52
29
374
67
0.8
130
11
7
1.22
98
38
54
309
113
0.7
89
23
E
8
1.2
66
77
34
0.
76
167
32
9
1.
304
18
323
0.74409
39
149
0.0
80
10
1.
343
63
93
391
0.
72
24
21
276
11
1.
384
233
224
127
0.70
137
12
1.42
57
68
379
0.68095
134
13
1.
46
71
35
0.6
61
17
14
1.51
258
249
111
0.64
186
194
15
1.557
96
166
0.62
31
69
392
16
1.6047064391
231
0.6050
164
45
17
1.65
28
0.587
394
18
1.70
243
306
0.570
286
268
19
1.
75
350
0.55
367
20
1.8061
112
347
0.5
375
275
21
1.860
294
0.52
189
250
22
1.916
103
218
0.50669
174
23
1.97
358
0.49
193
363
24
2.03
279
106
337
0.4776055693
25
2.09
377
297
0.46
369
274
26
2.
156
126
0.4501890558
27
2.22
128
0.4
370
28
2.
287
0.424
346
362
29
2.
356
0.4
119
30
2.4
272
247
198
0.3
99
145
31
2.500080
345
399
0.
388
341
32
2.5750
82
0.377026
246
33
2.652
335
238
262
0.
366
34
2.73
190
295
0.
355
339
35
2.8
138
245
383
397
0.34503
242
36
2.898
278
328
324
251
0.
334
293
37
2.985
226
349
0.3
252
152
38
3.0747834782
325
261
0.3
157
354
39
3.1670
269
315
0.3065568408
40
3.26
203
0.2976
280
41
3.
359
0.
288
42
3.4606958935
0.280542936
43
3.5645167703
0.27
237
178
44
3.67145
227
371
0.
264
386
45
3.7815958417
0.
256
365
46
3.8950437
169
0.249258765
47
4.0
118
284
0.24
199
48
4.
132
187
241
0.
234
292
49
4.256
219
0.
228
107
50
4.38
390
281
0.22
146
184
51
4.5
154
319
214
318
0.2
150
52
4.6508858952
215
0.
208
291
53
4.7904
124
0.
202
185
54
4.9341
248
267
0.
196
170
55
5.082
148
0.
191
360
56
5.2346130494
0.1854719
303
57
5.39
165
144
0.
180
352
58
5.55
340
0.1748250827
59
5.7
200
136
0.1697
330
60
5.89
160
104
0.1647894078
61
6.068
351
197
0.1599897
163
62
6.25040
173
0.
155
298
216
63
6.43791
378
329
0.1508056521
64
6.63
105
0.146413
254
65
6.8
299
273
0.
142
66
7.0
348
221
0.1
380
67
7.2459286831
0.
133
68
7.4633065436
398
0.1
300
69
7.687
205
0.1262973594
70
7.9178219
121
0.
122
71
8.1553565695
0.1190473743
72
8.
400
172
0.
115
73
8.6520
177
0.1122
135
74
8.9115783
181
213
0.
108
117
75
9.1789256676
211
0.1057720502
76
9.4542934377
0.
102
109
77
9.7379
222
131
0.099700
301
78 1
0.03
0.0967964095
79
10.3309617053
0.0939770966
80
10.6408905564
0.09
123
81
10.9601172731
239
0.0885824268
82
11.2889
207
0.08600
235
83
11.6275884
151
0.0860023561
0.0834974
331
84
11.9764160675
0.0834974
332
0.0810654691
85
12.3
357
0.078704
338
86
12.705779806
389
0.0764119795
87
13.08695
320
0.074186
387
88
13.47956
179
89
13.8839486501
0.0720256193
90
14.3004671096
0.0699
277
91
14.7294811
229
0.0678910541
92
15.
171
0.06591
364
93
15.6
265
0.06399
382
94
16.095301719
0.062
129
95
16.5781607705
0.0603203
223
96
17.0755055936
0.0585634197
97
17.5877707615
0.056857689
98
18.1154038843
0.055
201
99
18.6588660008
0.053593825
100
19.2186319809
0.05203
283
101
19.7951909403
0.0505173202
102
20.3890466685
0.049045942
103
21.0007180685
0.0476174194
104
21.6
307
396
0.046
230
105
22.2796617989
0.0448839847
106
22.9480516529
0.0435766842
107
23.6364932025
0.0423074604
108
24.3455879985
0.041075
204
109
25.0759556
385
0.0398788391
110
25.8
282
0.0387173
195
111
26.60
308
336
0.0375896306
112
27.401173777
0.036494787
113
28.2
232
0.03543
183
114
29.06990526
0.0343998369
115
29.9420024178
0.0
333
116
30.8402624903
0.032
117
31.7654703651
0.0
314
118
32.7184
344
0.0
305
119
33.6999875103
0.0
296
120
34.7109871356
0.028809
321
121
35.752
316
0.0279702154
122
36.8248862522
0.0
271
123
37.9296328397
0.0
263
124
39.06752
182
0.0
255
125
40.2
395
0.0248511741
126
41.4467339041
0.024127
353
127
42.6901359
212
0.02
342
128
43.9708399988
0.0227423447
129
45.
289
0.0
220
130
46.6486641547
0.02
143
131
48.0481
240
0.0208124671
132
49.4895678018
0.020
206
133
50.9742548358
0.0196177463
134
52.5034824809
0.0190463556
135
54.0785869553
0.0184916074
136
55.700944564
0.0179530169
137
57.37197
290
0.0174301135
138
59.09
313
0.01692
244
139
60.8659
260
0.0164295537
140
62.6919038321
0.015951023
141
64.57
266
0.0154864301
142
66.5098407754
0.015035369
143
68.5051359987
0.0145974457
144
70.5602900787
0.0141722773
145
72.677098781
0.0137594926
146
74.8574117445
0.0133587306
147
77.1031340968
0.0129696414
148
79.4
162
0.01
259
188
149
81.7987149633
0.012
225
150
84.2526764122
0.0118690592
A
Consumption
Year T
Earnings
Incremental Savings if work
K(T)=Saving Account at beginning of T
K(T+1)=Saving Account at end at end of T if Work
TildeK(T+1)=Saving Account at end of T
if withdraw $
70000
Does saving account decrease if stop working in T? TildeK(T+1) 0.3 0.04 1
100000
70000.0
2 100000 70000 70000.0
142800.0
3 100000 70000 142800.0
218512.0
75712.0
4 100000 70000 218512.0
297252.5
154452.5
5 100000 70000 297252.5
379142.6
236
6 100000 70000 379142.6
464308.3
321508.3
7 100000 70000 464308.3
552880.6
410080.6
8 100000 70000 552880.6
644995.8
502195.8
9 100000 70000 644995.8
740795.7
597995.7
10 100000 70000 740795.7
840427.5
697627.5
11 100000 70000 840427.5
944044.6
801244.6
12 100000 70000 944044.6
1051806.4
909006.4
13 100000 70000 1051806.4
1163878.6
10
210
14 100000 70000 1163878.6
1280433.8
11
376
15 100000 70000 1280433.8
1401651.1
1258851.1
16 100000 70000 1401651.1
1527717.2
1384917.2
17 100000 70000 1527717.2
1658825.9
1516025.9
18 100000 70000 1658825.9
1795178.9
1652378.9
19 100000 70000 1795178.9
1936986.1
1794186.1
20 100000 70000 1936986.1
2084465.5
1941665.5
21 100000 70000 2084465.5
2237844.1
209
A1
A2
B1
B2
mean
Variance
SD
Number
Random Rate 1
Arithmetic Rate of Return:
0.1062648258
r_01
r_12
r_02
Relationship Variance
Relationship SD
0.107
0.1788854382
0.0128650798
Variance over 400 years:
0.0342731932
0.1245630465
0.1462773585
0.289061
158
r_01:
0.0
322
0.1796834307
2.5355452159
1.5923395416
2
0.0618276322
Geometric Rate of Return:
0.090283755
0.1820061577
0.1798032382
0.3945346924
r_12:
0.030647233
0.
175
2.6711369279
1.634
361
3
0.1909886181
0.2607343794
0.0284196912
0.2965640611
r_02:
0.0818629558
0.2861170
317
4
0.31842038
A3
-0.11
217
312
-0.2105712421
-0.29912
393
Sqaure Root (2):
1.4142135624
5
-0.213
192
Half of Variance:
0.0171365966
0.1975415055
0.2
373
0.4818074991
6
0.0491
327
P.141 Holds?
0.0159810708
0.095767706
0.1544810882
0.2650430936
7
0.0994614201
0.1823794595
0.1428205481
0.351247542
8
0.0911580267
0.1481002636
0.1586943643
0.3
302
9
0.2744283775
-0.16
310
0.1132522518
-0.0683286107
10
0.2800012322
0.1691673366
0.1878353023
0.3887782
368
11
0.2480456813
0.2784591323
0.2289232368
0.5711281349
12
0.2084834555
-0.2165552419
-0.1880896396
-0.363913084
13
0.1594383682
-0.1100731818
-0.0077371365
-0.1169586671
14
0.0634482076
0.0288598542
0.2119
270
0.2469030966
15
0.0450708338
0.1891123413
0.345908903
0.6004368869
16
0.1719530956
0.1433189595
0.0721980869
0.2258644011
17
0.0030173354
-0.0287350915
0.0427096173
0.012747261
18
0.3070944476
0.3787
153
0.3208170185
0.8210306701
19
0.2627844624
0.1416333773
0.1653820206
0.3304390121
20
0.0016959527
0.4208104289
0.2053868595
0.7126262209
21
0.4778106756
-0.1797399709
0.0573038485
-0.1327359145
22
0.124
176
0.08154223
0.3830804677
0.4958599333
23
-0.2206571868
-0.2476008121
0.1047336277
-0.
168
24
0.0617005223
0.1009341197
-0.1475125479
-0.0614674774
25
0.177
161
0.
311
-0.1521801548
0.1119419235
26
0.1852825062
0.0163475762
-0.0446368137
-0.0290189413
27
-0.0961296264
0.0772711311
0.098846164
0.18375525
28
-0.004286339
-0.0444248019
0.1458023106
0.09490027
29
0.3510215413
-0.0346734279
-0.0380048448
-0.0713605144
30
0.0884022132
0.0144872787
0.3467420706
0.3662526982
31
0.1443219366
0.456862864
0.0078976658
0.46836868
32
0.1035524541
0.3459127289
-0.14
285
0.1536462624
33
0.184500718
0.4063279518
0.4554021603
1.0467727391
34
-0.0482776425
-0.0500754926
0.1199865562
0.0639026777
35
0.2094580012
0.0890446991
0.0919192998
0.1891489
253
36
-0.1373031059
0.0483096644
0.1991709051
0.
257
37
0.0216112662
0.4184325639
0.2371769156
0.7548520243
38
0.3537363575
0.1804831442
0.1623575744
0.
372
39
-0.0759252911
0.0697449048
0.0323273324
0.104
326
40
0.21146
381
-0.046832241
0.0560989212
0.006639442
41
0.0859686421
0.1169592555
0.1399198046
0.2732439763
42
-0.0276600447
-0.361692925
-0.130512543
-0.4450000046
43
-0.1110657798
-0.1830324008
0.3469777848
0.100437207
44
0.1443456991
0.290399088
0.1777293955
0.5197409379
45
0.1563106552
0.1717109462
0.1872496447
0.3911134046
46
-0.0043913638
0.1392994211
0.247926145
0.4217615346
47
0.2941907603
-0.0032904958
0.2423168719
0.2382290335
48
0.1722775807
0.2290907149
0.3716069606
0.6858293798
49
-0.0218603043
-0.0964797804
0.1662837732
0.0537609709
50
-0.0742135374
0.2462806209
0.2713772015
0.5844927681
51
0.1513002884
0.3227659689
0.1789821124
0.5595174162
52
0.4141800549
0.0377642383
0.0652210553
0.1054483171
53
0.2629862613
-0.155912149
0.0807587929
-0.0877446331
54
0.1356450676
0.2129062532
0.2321589302
0.4944932714
55
0.5920735839
0.1849180459
0.3449231945
0.5936237636
56
-0.0282102046
0.085657868
0.0618553624
0.1528116288
57
0.1640638971
0.1899584466
0.3339826326
0.5873839013
58
-0.1072077073
0.1537170002
0.2458294298
0.4373345926
59
0.1042271369
0.0874052412
0.0973983908
0.1933167618
60
0.2987606071
-0.0899935966
0.2367903668
0.1254871534
61
0.158643698
0.0173090823
-0.0564912231
-0.040159952
62
-0.1938439874
-0.0659724593
0.174427847
0.0969479536
63
0.1708572427
-0.1480571419
0.141045914
-0.0278940829
64
0.0461252994
0.00085308
-0.1762997886
-0.1755971065
65
0.2311823934
0.2457957612
0.1953170046
0.4891208576
66
0.1540550698
-0.0529110675
0.2521606638
0.1859075064
67
0.1785817993
0.4212367859
0.3070372665
0.8576094437
68
0.1900722891
0.02199003
0.0680603053
0.0915469835
69
0.0382781567
0.064862169
0.4214742176
0.5136741185
70
-0.0559462195
0.3382556955
0.2007257493
0.6068780727
71
-0.2618841763
0.1309924053
-0.0679168195
0.0541789982
72
0.1705521863
-0.1629513807
-0.016643806
-0.1768830555
73
0.0212033433
0.2107766795
0.2156034661
0.4718243284
74
0.3538891811
0.1183286282
0.3043173247
0.4586554045
75
-0.0012603218
0.1965495066
0.1787623368
0.4104474925
76
-0.0795910626
-0.1081974281
0.0828133994
-0.0343442255
77
-0.0320882581
-0.1479145945
0.2247712862
0.0436097381
78
0.1487729279
0.2302472458
-0.015838846
0.2107615491
79
-0.0567791255
0.2038008095
0.1332108846
0.3641601802
80
0.2977585877
0.1222009423
-0.1005037914
0.009415493
81
0.1023831231
0.141345109
0.2575497753
0.4352982854
82
0.0540190261
-0.2602316262
-0.0983085598
-0.3329571896
83
-0.0814157561
0.1304324153
-0.0526447161
0.0709211217
84
-0.2644683752
-0.0905218418
0.1168676047
0.0157666921
85
-0.1114329549
0.2246713921
0.0632778788
0.302166
86
0.2148839852
0.1011500298
0.0303665101
0.1345881133
87
0.218713379
0.1584938701
0.0747363675
0.2450754937
88
0.2853361052
0.116099263
0.3978702062
0.5601619069
89
0.0917726807
0.262680702
-0.1530918772
0.069374543
90
0.3521620075
0.1052691043
0.5660098742
0.7308623311
91
-0.0777175669
0.0765656895
0.3470985196
0.4502400467
92
0.169712942
0.121163476
0.2414565349
0.391875724
93
0.1019668376
-0.1103421082
0.2184442752
0.0839985652
94
0.0214512166
-0.1791553224
0.1837039766
-0.0283628909
95
0.1415570044
0.1493170249
-0.0633525507
0.0765048598
96
0.2807733951
-0.1620211132
0.1338304639
-0.04987401
97
0.1942438742
0.0749292014
-0.0301318194
0.0425396288
98
0.0457493543
0.3246698877
0.2311021436
0.6308039383
99
0.2828499758
0.5126302689
0.1161551133
0.6883300092
100
0.2116771766
-0.0075164148
0.0832731537
0.0751308233
101
0.0582355458
0.4691304283
0.1136986453
0.6361685677
102
0.0492898119
-0.070270602
0.0468565102
-0.026706727
103
0.0348490452
0.0257991945
0.2371794485
0.2690976817
104
0.0765652469
0.4239747186
0.1146547823
0.5872402299
105
0.1366933042
0.1479504923
0.0637863143
0.2211740232
106
0.0863851313
0.0739972295
-0.0490401699
0.0213282229
107
-0.1521093024
0.1031051081
-0.1956245207
-0.1126893
108
-0.0642145945
0.1730822298
0.0219463126
0.1988270591
109
0.0563353652
0.1481566473
0.1127201015
0.2775769811
110
-0.0494148381
0.1196217587
0.2175905873
0.3632409147
111
0.1015623777
0.298900233
0.2740893123
0.6549149047
112
-0.1319313962
0.3441135406
0.2944401494
0.7398745324
113
-0.3555611351
0.1496908491
-0.1070344811
0.0266342856
114
-0.0354356245
0.3398595815
0.1505595701
0.5415882641
115
0.2481602697
0.1324921724
0.0092433061
0.1429601442
116
0.4468259749
0.3972590496
0.1158140749
0.5590813138
117
-0.0627419775
0.1995992058
0.2279440861
0.4730407505
118
0.1228687525
-0.1531857048
0.3992675796
0.1849197892
119
0.1027024726
0.1735091573
0.101466812
0.2925813903
120
0.3352381444
-0.200728814
0.2483916448
-0.0021965294
121
0.3717317712
-0.0214517174
0.2290640113
0.2026984774
122
0.1590487203
0.0651698583
0.1395100142
0.2137717204
123
0.3073469567
-0.2166468947
0.1246724641
-0.1189843328
124
0.2746859577
0.2760949862
0.1733041125
0.4972474952
125
0.2211339292
0.0827307601
0.2150212503
0.3155408819
126
-0.0777279054
-0.0124189983
0.1346946784
0.1206029071
127
0.0722034763
0.1456261039
0.0340722471
0.1846601596
128
0.1600949269
0.1875835485
0.0657397365
0.265654978
129
-0.3560427555
-0.0404565945
0.0339523265
-0.0078778635
130
0.2208503831
0.0231588822
0.2034080878
0.2312776739
131
0.2707060592
-0.0953577597
-0.0235400175
-0.1166530538
132
0.1215816876
-0.1974151616
-0.1167727765
-0.2911352216
133
-0.0788056223
0.0088767191
-0.0230421409
-0.0143699604
134
0.1927043355
0.2116130581
0.3012511325
0.576612864
135
0.0436699875
0.151185071
-0.0286795757
0.1181695716
136
-0.1428661712
-0.0322198261
-0.2777993712
-0.3010685499
137
-0.1352390425
0.0922202495
0.1381137974
0.2430709358
138
0.1395544728
0.156202341
0.0867053841
0.256451309
139
-0.3771741227
0.0427468098
0.3328019386
0.3897749695
140
0.012241747
-0.1552101095
0.3017768928
0.0997279588
141
0.0026267823
0.2817554803
0.1537037673
0.4787661264
142
0.105773786
0.0420362529
0.1539829359
0.2024920544
143
-0.2217157187
0.0323819152
-0.2137068875
-0.1882452106
144
0.102741417
-0.1936100658
0.1001434402
-0.1128554037
145
0.0646909978
0.3251798931
0.1626227975
0.5406843546
146
-0.1088207101
-0.1777841263
-0.1380018098
-0.2912514049
147
0.23235288
-0.0609614282
0.0285387495
-0.0341624416
148
0.1886606439
0.1003588764
0.3902013653
0.5297204123
149
-0.0963357168
0.0541671293
0.1653593524
0.2284835231
150
0.2039677483
0.058959214
0.2800933
0.3555665948
151
-0.0414071407
0.1910784718
-0.1742406095
-0.016455767
152
0.2203934574
-0.1803542332
0.2439992371
0.0196387087
153
0.0173147442
-0.0326411443
0.005148098
-0.0276610861
154
-0.1011653776
0.0869954506
-0.2043576632
-0.1351403996
155
-0.0745147917
-0.1367566286
0.0941307253
-0.0554989039
156
0.3472064519
-0.1193262922
0.1418632804
0.005608969
157
-0.0975735302
0.1486525559
0.0262356589
0.1787882126
158
-0.0504881533
0.2007161107
-0.0172258431
0.1800327634
159
0.2413231295
0.0031235629
0.3291027205
0.3332542564
160
0.3678955147
0.2728978877
0.2858787659
0.6367923648
161
-0.2514650524
0.2694577745
0.3523735971
0.7167811769
162
0.5148916423
0.2035714525
0.0445749498
0.2572205895
163
0.0830213704
0.4812059706
-0.0250228421
0.4441419875
164
0.5234285168
0.3146293507
0.1348748963
0.491939848
165
0.0409064675
0.3025858973
-0.2213414188
0.0142696866
166
0.2652664076
0.185859217
0.1994928929
0.4224297028
167
0.308319941
0.0819627772
0.1690208134
0.2648370059
168
-0.017332998
-0.0076359432
0.420384965
0.4095389861
169
-0.0117016842
0.1540035085
0.3772912581
0.589398944
170
0.3328846539
-0.1129416
0.269682948
0.1262829243
171
-0.0682695812
0.1585949
0.2918890481
0.4967760625
172
0.4242113461
0.3064793852
0.1244906047
0.4691237938
173
0.2372954521
0.2025727309
-0.1010925954
0.0810015325
174
0.1621948187
0.2236874925
0.3203646731
0.615713736
175
0.2257688014
0.1409373818
-0.0224316248
0.1153443025
176
-0.0820667362
0.3772675414
0.0986971749
0.5131999569
177
0.1967580278
0.1898200908
-0.0112619686
0.1764203743
178
0.0522558179
0.3359913628
0.2001803724
0.6034306113
179
0.2407749514
-0.3900847668
0.2115790538
-0.2610394788
180
0.0992581466
-0.0425072606
0.0417725806
-0.002510318
181
-0.2102012127
0.1032794474
0.034372128
0.1412015098
182
0.4105137748
0.2256066574
0.1404025517
0.3976849594
183
-0.1263080721
0.4715158702
0.1603797165
0.7075171683
184
0.0347440796
-0.2348189141
0.1325416329
-0.1334005635
185
-0.0029283158
0.0126860531
0.2953333636
0.3117660313
186
0.0433330287
0.2251673418
0.2840443382
0.5731691886
187
0.2359478642
0.1647534057
-0.0956584937
0.0533348493
188
0.2316636626
0.1717612939
-0.0838366895
0.0735247062
189
0.044495928
0.083422216
-0.1038295874
-0.0290690657
190
-0.070492704
0.4301938041
0.3262552141
0.8968019898
191
-0.0496206341
0.2300984068
0.3016903542
0.6012072309
192
0.1892347764
-0.0081921303
-0.0102124597
-0.0183209283
193
0.4448474071
0.3856884708
0.0182642253
0.4109969972
194
0.0758411472
0.0885028313
-0.0228187769
0.0636645281
195
0.4468425797
0.0566781227
0.012427116
0.0698095842
196
0.4355867114
-0.0149506414
-0.1773830358
-0.189681687
197
0.3265394033
0.0046676128
0.1918575783
0.197420708
198
0.2526247928
0.1681823715
0.0765389583
0.2575938333
199
-0.0094541989
0.1684221097
0.0667613158
0.2464275072
200
-0.2483369795
0.1997240344
0.035863763
0.2427506529
201
0.320058769
-0.0896839528
0.1619218406
0.057716097
202
-0.0733358093
-0.1227096893
0.3022893925
0.1424858657
203
-0.1290933963
0.200731342
0.0448150241
0.254542146
204
0.2570567467
0.1041669237
0.1656097581
0.2870277408
205
-0.0364949592
-0.1558515123
0.0796897887
-0.0885814976
206
0.1723867637
0.2271543234
0.1251443353
0.3807257356
207
-0.0780318075
-0.234640824
0.1827627524
-0.0947616745
208
-0.0564488417
0.2232617393
-0.0111128715
0.2096677888
209
0.0697467245
0.2785147254
0.4759120355
0.8869752708
210
0.0758902886
0.3490216013
-0.0828057465
0.2373148606
211
0.0138660146
0.4048421176
0.1760722088
0.6521957723
212
0.0920067554
-0.0484322209
0.0687096563
0.0169496741
213
-0.0993672754
0.3139744518
0.1576114105
0.5210718185
214
0.0055606334
0.496865706
0.138729615
0.7045253092
215
0.0033181246
0.2929686268
-0.1732081888
0.0690158728
216
0.248921282
-0.2489494645
0.3249590411
-0.0048
217
0.2249009072
0.1129419744
0.0937202674
0.2172471938
218
0.153227594
0.3625638665
0.5862979839
1.1614323143
219
0.0735268876
0.1269787554
0.1479136531
0.2936743
220
-0.0803501861
0.2900811003
0.1511262616
0.4850462342
221
0.0564173965
-0.0415469991
0.0457151416
0.0022688155
222
0.087907633
0.3443160902
-0.1005042273
0.2092066403
223
0.1147976821
-0.1103993242
-0.114125107
-0.2119250965
224
0.2248424769
0.1580647764
0.0114836573
0.1713635955
225
0.3711342108
0.2522331588
-0.1628803694
0.0482689593
226
-0.0460503703
0.1909983745
0.2771012244
0.5210254823
227
-0.0211720923
-0.0377195024
-0.0644408779
-0.0997297024
228
0.2279238836
-0.158790897
0.1603065792
-0.0239395433
229
0.1249629796
0.2412099827
0.0246692439
0.2718296944
230
0.0898312509
0.3259523566
-0.0843747557
0.2140754505
231
0.1450404676
0.3278513887
-0.017548142
0.304550064
232
0.1175010217
-0.067958318
0.2155254972
0.132920429
233
0.4315386678
-0.1206704108
0.3441792854
0.1819766188
234
0.4496413255
0.4436369788
-0.1313326797
0.2540402659
235
-0.1802001185
-0.1128173655
0.3373763572
0.1864970799
236
0.3527387629
0.2843491847
-0.1626680361
0.0754266252
237
0.2773157958
0.1260283633
-0.1243719385
-0.0140179671
238
0.2106709912
0.1557022406
0.2458775789
0.4398635095
239
0.1429823529
0.0265128323
0.1237822502
0.1535769005
240
0.1967591219
0.2937280625
0.0742641422
0.3898056674
241
-0.0680588936
-0.088129262
0.0003122964
-0.0878444881
242
0.1997899912
0.4364479968
0.0016690966
0.4388455674
243
-0.0309478571
0.4420211842
0.2754924599
0.8392871475
244
-0.1423445465
0.2485328503
0.1264917025
0.4064618961
245
0.4108598983
-0.239739405
0.4346433494
0.0907028064
246
0.3214747597
-0.1813324208
-0.1009034381
-0.2639387943
247
0.1989535839
0.3452082015
0.0861086389
0.4610422488
248
0.0510809327
-0.0508955661
0.1294787898
0.0719933274
249
-0.3923896724
0.2235702909
0.231217564
0.5064812329
250
0.3876192508
0.5074558499
-0.1841737237
0.2298220927
251
-0.2964561797
0.1875999563
0.1842840408
0.4064556751
252
0.1140210546
0.1152407282
0.0639125394
0.1865185952
253
0.4788282304
-0.0677111655
-0.1630678814
-0.2197375306
254
0.0710572853
0.1602739301
-0.0003245945
0.1598973116
255
0.128026271
-0.1348699492
0.1077571338
-0.0416460145
256
-0.057533626
0.0576798677
-0.4474942633
-0.4156258054
257
0.2548864823
0.2141664995
0.5137876829
0.8379902919
258
0.3782519437
0.3342182221
-0.3009241714
-0.0672802909
259
-0.0357191391
0.1393396396
0.025761614
0.1686908676
260
0.0826776151
0.0935182155
0.0302168323
0.126560872
261
0.3713418196
0.1210370615
0.04010753
0.1659990891
262
0.5807697703
-0.2060749728
0.0726396585
-0.14840453
263
0.0610092999
0.2746441665
0.0129957912
0.2912091759
264
0.1108628844
-0.0437696708
0.1068727777
0.0584253206
265
0.0295043524
0.0179964468
0.1158773754
0.1359592032
266
0.2730666985
-0.0660832872
-0.1899049464
-0.2434386905
267
0.2366850396
0.2238591055
0.3039257361
0.5958213851
268
0.0087505072
0.137523063
0.3148191596
0.4956371177
269
0.1993715643
0.0465373505
-0.0080313311
0.0381322626
270
0.0951540522
0.0450135031
0.2948811339
0.3531682698
271
0.1596413387
0.2247158945
0.1878591995
0.4547900421
272
0.1682294279
0.1838289698
0.3416056758
0.5882316651
273
0.204049417
0.1649682633
-0.3677226063
-0.2634169027
274
0.4273184917
0.0999374383
0.2035053061
0.3237805433
275
0.2857165356
0.0536547432
-0.0073664804
0.0458930162
276
0.058202516
0.3429140307
-0.0788782176
0.2369873656
277
0.0972218252
0.2599059334
-0.0998266894
0.1341336952
278
-0.1486645905
0.1978792285
0.1576873397
0.3867696173
279
0.1646143379
-0.0547660958
0.2422747848
0.1742402449
280
0.1496186403
0.1177784972
0.384772615
0.5478690526
281
0.068992549
0.0272771374
0.1484765863
0.17980374
282
-0.2400742302
0.1070289149
-0.1895050226
-0.1027586247
283
0.3800453769
0.0754771536
0.1975915608
0.287982363
284
-0.0387585233
0.0678568287
0.1948916794
0.2759732395
285
0.0087569205
0.1538528064
0.0017373225
0.1558574209
286
0.0504742635
0.2275373848
0.2389425893
0.5208483461
287
0.6201308428
0.390644616
0.1496409456
0.5987419913
288
0.1357725523
0.2444308863
0.2193981885
0.5174567684
289
0.0553466557
0.5918167514
-0.3605025758
0.0179627122
290
-0.0302570807
0.0543724073
0.3198004741
0.391561203
291
-0.1738549454
-0.1266126849
-0.312584898
-0.3996203697
292
0.1150873908
0.2150905658
0.3052170688
0.5859569467
293
-0.0466368789
0.2313906202
0.458321806
0.7957637933
294
0.1823065369
0.0978846725
0.4943609799
0.640636015
295
0.0058623248
-0.2093514293
0.083633698
-0.1432265655
296
0.3101200763
0.0888820683
0.3051483787
0.421152666
297
0.1401071366
0.1480608505
-0.0229291741
0.1217367634
298
0.1416019823
0.4080993259
0.3529798508
0.905130016
299
0.1859391153
0.0001247389
0.1184491546
0.1185886687
300
0.0038656145
0.2033086244
-0.0523318603
0.1403372455
301
-0.2363583149
0.1795766151
-0.0052148552
0.1734252939
302
0.4999618319
0.1560640569
0.1515073426
0.33121625
303
0.1564718697
0.0376668123
0.2011874908
0.2464323946
304
0.0703841649
0.3679462334
0.160578538
0.5876090395
305
0.0040489003
-0.3708536509
0.1871758165
-0.2530926693
306
0.2233162869
0.2140213163
-0.0979892901
0.0950602294
307
0.0656536471
0.3390999457
-0.2397664803
0.0180286649
308
-0.0101138844
-0.1003309007
0.0138650436
-0.0878569494
309
-0.04011343
0.1499558925
0.2293633036
0.413713575
310
0.2847802767
-0.1998146638
0.1073205334
-0.1139383467
311
0.2757419447
0.3303102627
-0.0436610135
0.2722275684
312
0.4578902037
-0.0621374116
-0.0290197953
-0.0893539919
313
-0.0216610627
0.1672956978
-0.2095510805
-0.077312377
314
–
0.0002
0.1419401039
0.2752830955
0.4562969105
315
0.1832265885
0.1024420422
0.0329455964
0.1387626528
316
0.1028505361
0.3909891036
0.3622811482
0.8949182331
317
0.3131645051
0.0550037375
0.3901024645
0.4665632956
318
0.1791106528
-0.015163121
0.4726650861
0.4503348872
319
0.2348381936
0.0756475512
0.2156441271
0.3076046284
320
0.3685359873
0.1896149471
0.0127089014
0.2047336462
321
0.5437556407
0.3105146602
0.1008770868
0.4427155614
322
-0.0777768898
-0.1328901922
0.1358486639
-0.0150944834
323
0.0257841501
0.0931980525
0.0709257319
0.1707339245
324
0.4785573531
0.0398450906
0.02130027
0.0619940717
325
0.0246245735
0.2353133825
0.2747776636
0.5747499076
326
0.345953412
0.1729109014
0.0793577032
0.2659904166
327
0.2503881013
0.2679115342
-0.0497566802
0.2048244654
328
0.2560557225
0.3099933482
-0.0041488492
0.3045583834
329
-0.2303681013
-0.3182308046
0.2033713785
-0.1795784635
330
0.2263720172
0.0338742074
-0.1820907532
-0.1543847257
331
-0.1710847518
-0.0538245076
0.1986626873
0.1341452584
332
0.1928583385
0.3191595556
0.215513238
0.6034559029
333
0.0632420695
0.2371948273
0.0887975848
0.3470547399
334
-0.2636037112
-0.0152533419
0.5636735575
0.5398223101
335
0.025336311
-0.1762782138
0.1599440554
-0.0445288108
336
0.1426909358
0.0045731874
0.2589983352
0.2647559705
337
-0.0225409092
0.0469551817
-0.023982498
0.0218465811
338
-0.0236479373
0.279091852
0.2205541778
0.5612009037
339
0.0497396269
0.1878181463
0.0654883114
0.265606351
340
0.2936736085
0.0322019856
-0.0705819265
-0.040652819
341
0.1242752082
0.1613964854
0.0626093071
0.2341107146
342
0.3206546043
0.0016149671
0.4380379605
0.4403603445
343
-0.030812377
0.0653396877
-0.2428509629
-0.1933790813
344
-0.0676945986
0.2765373268
0.2439868097
0.5879955967
345
0.0396162523
-0.1263599345
0.0463886807
-0.0858329245
346
-0.1534787488
0.3700737712
0.2749321826
0.7467511434
347
-0.1336895504
0.1942153626
0.3042882369
0.5576010497
348
0.2125636155
-0.0721745653
0.0390475177
-0.0359452852
349
0.0033281021
-0.0699126632
0.2536312394
0.1659865408
350
0.1492804458
0.2261295232
0.1819761287
0.4492558271
351
0.1844544761
0.0766322942
0.0387902995
0.1183951834
352
0.0279557331
0.3096766233
0.2134662547
0.5892483869
353
0.1303497009
0.1003517758
0.0542385743
0.1600332874
354
0.354135175
0.4124848615
0.2071575514
0.7050917668
355
0.0358638133
-0.1813695747
0.1279178988
-0.0766520908
356
-0.1748342415
-0.216962987
-0.172939212
-0.3523807909
357
-0.3083015687
0.3292422232
0.331983847
0.77052917
358
0.2603508468
0.0925285131
-0.0478991755
0.0401972982
359
0.2119275462
0.130867511
0.198700845
0.355571841
360
-0.0165830241
0.115107515
-0.2628575593
-0.1780069248
361
0.2678665075
0.3105845555
0.2119282565
0.5883344553
362
0.0495381543
-0.0553083044
-0.0062737638
-0.061235077
363
0.2087288925
0.1443334291
0.3192579687
0.5096709952
364
0.2911125237
0.1283312526
0.1697460534
0.3198610297
365
0.5253746804
-0.18295199
-0.0280994214
-0.2059105663
366
0.0088980068
0.0854211368
0.1655131286
0.2650725851
367
-0.0998487305
0.3211366893
0.0287416383
0.3591083222
368
0.4859812965
-0.05813104
-0.1494523041
-0.1988955262
369
-0.2965203557
0.252236792
0.1255615663
0.409469605
370
0.0467250445
-0.0109803621
-0.3024082093
-0.3100680197
371
0.0047807131
-0.097052618
-0.151967643
-0.2342714034
372
-0.2981787937
0.4282582024
0.2830461914
0.8325212469
373
0.1302985641
-0.0147808735
0.1330527807
0.1163052708
374
0.1064826482
0.487930443
-0.1317898339
0.2918363371
375
0.0113479862
0.31689485
-0.1005561562
0.1844729657
376
-0.1719984427
0.2945493296
0.3864794593
0.7948660545
377
0.2282580013
0.0550504573
-0.0552579662
-0.0032494852
378
0.2637980869
-0.1201708059
0.0262322522
-0.0970909045
379
-0.0076942983
-0.1364228071
0.0568043796
-0.0873678404
380
-0.1394008397
-0.0129343865
0.1869088304
0.1715568929
381
0.16369146
0.0463734143
-0.2609458432
-0.2266733786
382
-0.1083702136
0.0897694386
0.1702569725
0.2753102839
383
0.0279244104
0.1033990381
-0.0755327324
0.0200562938
384
0.1971497967
0.2472593864
0.4253199626
0.777743702
385
0.1461009125
0.0686920911
0.0667947079
0.1400750672
386
0.2510002731
0.2820579648
0.0805421421
0.3853176596
387
-0.2572393639
0.1202026714
0.4327330699
0.6049514123
388
0.3656010587
0.2492897405
-0.0232827315
0.220202863
389
0.3195129442
0.3676350996
0.0335349382
0.4134986582
390
0.162782697
-0.0655575675
-0.2298988091
-0.2803847699
391
0.0879007461
0.3094793378
-0.095934358
0.1838552783
392
0.1646223378
0.3044212492
0.2610143948
0.6448939722
393
-0.1499682822
0.1657516989
-0.0849535103
0.0667169999
394
-0.0771815804
0.0906288711
0.1179904578
0.2193126708
395
0.4123847952
0.0525468107
-0.1412184136
-0.0960921802
396
0.0084047686
0.008421658
0.0854113187
0.0945522816
397
-0.1028484251
0.1931301791
0.117265693
0.3330434163
398
0.4052976824
-0.0448809548
0.3146272865
0.2556255587
399
-0.2404991473
0.4478913505
0.0281590734
0.4886626293
400
0.2095459893
-0.0890408749
-0.1031054803
-0.182965753
2 4 5
Signal
Realized Rate of Return
2bq drift alnoe
-1
-48
-1 52
0.00037504
0.00040004
-1 52
0.0055769902
0.00060012
1 -48
0.0007502207
0.00080024
1 52
0.0059541218
0.0010004001
-1 52
0.0111850832
0.0012006002
1 52
0.0164432457
0.0014008403
-1 -48
0.0115643181
0.0016011204
-1 -48
0.0067088094
0.0018014407
1 -48
0.0018766071
0.002001801
1 52
0.0070863654
0.0022022013
-1 52
0.0123232145
0.0024026418
1 -48
0.0074640631
0.0026031223
-1 52
0.0127028762
0.0028036429
1 52
0.0179689312
0.0030042036
1 -48
0.0130826803
0.0032048045
1 -48
0.0082198835
0.0034054454
1 -48
0.003380428
0.0036061265
1 52
0.0085980062
0.0038068478
1 52
0.0138427159
0.0040076091
1 -48
0.0089762708
0.0042084106
-1 -48
0.0041331847
0.0044092523
1 -48
-0.0006866546
0.0046101342
-1 -48
-0.0054833586
0.0048110562
1 52
-0.0003118721
0.0050120184
-1 52
0.0048865062
0.0052130208
1 52
0.010111916
0.0054140634
1 52
0.015364498
0.0056151462
1 52
0.0206443934
0.0058162693
-1 52
0.0259517442
0.0060174325
1 -48
0.0210271758
0.006218636
-1 52
0.0263365172
0.0064198797
-1 -48
0.0214101019
0.0066211637
1 52
0.0267214344
0.0068224879
-1 -48
0.0217931715
0.0070238524
1 -48
0.0168885643
0.0072252572
1 52
0.0221763848
0.0074267023
-1 -48
0.0172699382
0.0076281876
1 -48
0.0123870425
0.0078297132
-1 52
0.0176514551
0.0080312792
1 -48
0.0127667281
0.0082328854
-1 52
0.0180331151
0.008434532
1 52
0.0233268873
0.0086362189
1 -48
0.0184149182
0.0088379462
-1 52
0.0237106758
0.0090397138
1 -48
0.0187968646
0.0092415217
1 -48
0.0139066396
0.00944337
1 52
0.0191789542
0.0096452587
1 -48
0.0142868952
0.0098471877
1 -48
0.0094183181
0.0100491572
1 -48
0.0045731102
0.010251167
1 52
0.0097968903
0.0104532172
-1 -48
0.0049498653
0.0106553079
1 -48
0.0001261059
0.0108574389
-1 -48
-0.0046744994
0.0110596104
-1 -48
-0.0094520618
0.0112618223
-1 -48
-0.0142066919
0.0114640747
1 -48
-0.0189384998
0.0116663675
-1 -48
-0.023647595
0.0118687008
-1 52
-0.0185705625
0.0120710745
1 -48
-0.0232814238
0.0122734888
1 52
-0.0182024872
0.0124759435
1 52
-0.0130971401
0.0126784386
-1 52
-0.0079652453
0.0128809743
-1 52
-0.0028066645
0.0130835505
-1 52
0.0023787408
0.0132861672
-1 -48
-0.0024326771
0.0134888245
1 52
0.0027546729
0.0136915222
1 -48
-0.0020585495
0.0138942605
1 52
0.003130746
0.0140970394
1 -48
-0.0016842815
0.0142998588
-1 -48
-0.006476197
0.0145027188
1 52
-0.0013098732
0.0147056193
1 -48
-0.0061035858
0.0149085604
1 52
-0.0009353245
0.0151115422
-1 52
0.0042598119
0.0153145645
-1 52
0.0094819629
0.0155176274
-1 52
0.0147312691
0.0157207309
-1 -48
0.009860559
0.015923875
1 -48
0.0050132283
0.0161270598
1 52
0.0102392971
0.0163302852
-1 -48
0.0053901485
0.0165335513
-1 52
0.0106181772
0.016736858
-1 52
0.0158733918
0.0169402054
1 -48
0.0109971995
0.0171435934
-1 -48
0.0061444129
0.0173470221
1 -48
0.0013149197
0.0175504915
1 -48
-0.0034913919
0.0177540016
1 -48
-0.0082746332
0.0179575524
1 -48
-0.013034915
0.0181611439
-1 -48
-0.0177723474
0.0183647762
-1 -48
-0.0224870401
0.0185684491
1 52
-0.0174039727
0.0187721628
-1 52
-0.0122944734
0.0189759172
-1 -48
-0.0170354599
0.0191797124
1 52
-0.0119240443
0.0193835484
-1 52
-0.0067860493
0.0195874251
1 -48
-0.0115534763
0.0197913426
1 -48
-0.0162980196
0.0199953008
1 -48
-0.0210197891
0.0201992999
1 -48
-0.0257188941
0.0204033398
-1 -48
-0.0303954434
0.0206074204
1 -48
-0.0350495453
0.0208115419
-1 52
-0.0300318029
0.0210157042
-1 -48
-0.0346876503
0.0212199074
1 52
-0.029668026
0.0214241513
-1 52
-0.0246222998
0.0216284362
-1 52
-0.0195503357
0.0218327619
-1 -48
-0.0242564941
0.0220371284
1 52
-0.0191826279
0.0222415358
1 52
-0.0140823776
0.0224459841
1 -48
-0.0188147822
0.0226504733
-1 52
-0.013712619
0.0228550034
1 52
-0.0085839246
0.0230595744
-1 -48
-0.0133427218
0.0232641864
1 52
-0.008212104
0.0234688392
1 -48
-0.0129726859
0.023673533
-1 52
-0.0078401438
0.0238782677
1 52
-0.0026809126
0.0240830433
-1 -48
-0.0074680442
0.0242878599
1 -48
-0.0122321976
0.0244927175
-1 52
-0.007095805
0.024697616
1 -48
-0.0118617451
0.0249025556
-1 -48
-0.0166048088
0.0251075361
-1 -48
-0.0213251057
0.0253125576
1 52
-0.0162359962
0.0255176201
-1 52
-0.0111204234
0.0257227236
-1 52
-0.0059782496
0.0259278682
-1 -48
-0.010749554
0.0261330537
-1 -48
-0.0154979562
0.0263382803
-1 52
-0.0103785455
0.026543548
1 -48
-0.0151287285
0.0267488567
-1 52
-0.0100073979
0.0269542065
-1 52
-0.0048594364
0.0271595973
1 52
0.0003152946
0.0273650292
1 -48
-0.0044862189
0.0275705022
-1 52
0.0006904528
0.0277760164
-1 -48
-0.0041128614
0.0279815716
1 -48
-0.0088931196
0.0281871679
1 -48
-0.0136504327
0.0283928053
1 -48
-0.0183849106
0.0285984839
1 -48
-0.023096663
0.0288042036
-1 52
-0.0180167657
0.0290099644
1 52
-0.0129104528
0.0292157664
-1 52
-0.0077775872
0.0294216095
-1 -48
-0.0125402548
0.0296274939
-1 52
-0.0074054641
0.0298334194
-1 52
-0.0022439725
0.0300393861
-1 -48
-0.0070332014
0.0302453939
-1 -48
-0.0117994421
0.030451443
-1 -48
-0.0165428048
0.0306575333
1 -48
-0.0212633993
0.0308636648
-1 -48
-0.025961335
0.0310698375
-1 -48
-0.0306367206
0.0312760515
-1 -48
-0.0352896643
0.0314823067
1 -48
-0.0399202739
0.0316886032
1 -48
-0.0445286566
0.0318949409
-1 52
-0.0395602056
0.0321013199
-1 -48
-0.0441703166
0.0323077401
-1 52
-0.0392000023
0.0325142017
-1 52
-0.0342038423
0.0327207045
-1 -48
-0.0388396638
0.0329272487
1 -48
-0.0434532335
0.0331338341
-1 52
-0.0384791903
0.0333404609
1 52
-0.0334792821
0.033547129
1 52
-0.0284533743
0.0337538384
1 -48
-0.0331167981
0.0339605892
1 52
-0.0280890055
0.0341673813
1 52
-0.0230350683
0.0343742148
1 52
-0.0179548507
0.0345810896
-1 -48
-0.0226686674
0.0347880058
-1 52
-0.0175865445
0.0349949634
-1 52
-0.0124779945
0.0352019624
-1 52
-0.0073428801
0.0354090028
1 -48
-0.0121076342
0.0356160846
1 -48
-0.0168495176
0.0358232078
-1 52
-0.0117371351
0.0360303725
-1 -48
-0.0164807968
0.0362375786
1 52
-0.011366497
0.0364448261
1 -48
-0.0161119378
0.036652115
1 52
-0.0109957199
0.0368594455
1 -48
-0.0157429404
0.0370668173
1 -48
-0.0204673743
0.0372742307
-1 -48
-0.0251691309
0.0374816856
-1 -48
-0.0298483191
0.0376891819
1 52
-0.0248035303
0.0378967197
1 52
-0.0197325087
0.0381042991
-1 -48
-0.0244377926
0.0383119199
-1 -48
-0.0291204912
0.0385195823
1 52
-0.0240719178
0.0387272862
1 -48
-0.0287563726
0.0389350317
1 52
-0.0237059057
0.0391428187
1 -48
-0.0283921174
0.0393506473
-1 52
-0.0233397564
0.0395585174
1 52
-0.0182611231
0.0397664291
1 52
-0.013156081
0.0399743824
-1 52
-0.0080244926
0.0401823773
1 52
-0.0028662199
0.0403904137
1 52
0.0023188757
0.0405984918
-1 -48
-0.0024922549
0.0408066115
1 52
0.0026947854
0.0410147728
1 -48
-0.0021181496
0.0412229758
-1 -48
-0.0069079825
0.0414312204
-1 -48
-0.0116748242
0.0416395066
-1 52
-0.0065355332
0.0418478345
1 52
-0.001369518
0.0420562041
1 -48
-0.0061629443
0.0422646153
-1 52
-0.0009949916
0.0424730683
1 -48
-0.0057902157
0.0426815629
-1 52
-0.0006203248
0.0428900992
-1 -48
-0.0054173472
0.0430986772
1 52
-0.0002455174
0.0433072969
1 52
0.0049532059
0.0435159584
-1 -48
0.0001294305
0.0437246616
1 -48
-0.0046711908
0.0439334065
-1 -48
-0.0094487691
0.0441421932
1 52
-0.0042979027
0.0443510216
-1 52
0.0008797482
0.0445598919
1 -48
-0.0039244746
0.0447688038
-1 52
0.0012551182
0.0449777576
-1 -48
-0.0035509064
0.0451867531
1 -48
-0.008333862
0.0453957905
1 -48
-0.0130938595
0.0456048696
1 52
-0.0079619476
0.0458139906
-1 52
-0.0028033497
0.0460231534
-1 -48
-0.0075898936
0.0462323581
-1 -48
-0.0123534621
0.0464416045
1 -48
-0.0170941655
0.0466508928
-1 -48
-0.0218121135
0.046860223
-1 -48
-0.0265074154
0.0470695951
1 52
-0.0214452539
0.047279009
1 52
-0.0163567693
0.0474884648
-1 52
-0.0112418245
0.0476979625
1 -48
-0.0159878637
0.0479075021
-1 -48
-0.020711122
0.0481170836
-1 -48
-0.0254117086
0.048326707
-1 52
-0.0203438495
0.0485363723
1 52
-0.0152496375
0.0487460796
-1 52
-0.0101289356
0.0489558288
-1 -48
-0.0148803167
0.04916562
-1 52
-0.0097576943
0.0493754531
-1 52
-0.0046084344
0.0495853282
-1 -48
-0.0093863139
0.0497952453
1 -48
-0.0141412596
0.0500052043
1 52
-0.0090147941
0.0502152054
1 52
-0.003861671
0.0504252484
1 -48
-0.008643135
0.0506353334
1 52
-0.0034880793
0.0508454605
1 -48
-0.0082713365
0.0510556296
1 52
-0.0031143475
0.0512658407
-1 52
0.0020694579
0.0514760939
1 52
0.0072802191
0.0516863891
-1 -48
0.002445274
0.0518967264
-1 52
0.0076579895
0.0521071057
-1 52
0.012897811
0.0523175272
-1 52
0.0181648796
0.0525279907
-1 -48
0.0132776882
0.0527384963
-1 52
0.0185467322
0.052949044
1 -48
0.0136577079
0.0531596338
1 52
0.0189287279
0.0533702657
1 52
0.0242271573
0.0535809398
-1 -48
0.019310867
0.0537916559
1 -48
0.0144181748
0.0540024143
1 -48
0.0095489676
0.0542132148
-1 -48
0.0047031325
0.0544240574
1 52
0.0099275888
0.0546349422
1 -48
0.0050799364
0.0548458692
-1 -48
0.0002555527
0.0550568384
-1 -48
-0.004545674
0.0552678497
-1 52
0.0006306885
0.0554789033
-1 -48
-0.0041723388
0.0556899991
1 52
0.0010059651
0.0559011371
1 52
0.0062111961
0.0561123173
1 -48
0.0013813823
0.0563235398
1 -48
-0.0034252483
0.0565348045
1 -48
-0.0082088071
0.0567461115
-1 52
-0.0030514929
0.0569574607
1 52
0.0021326393
0.0571688522
-1 52
0.0073437291
0.0573802859
-1 -48
0.0025084792
0.057591762
1 52
0.0077215233
0.0578032803
-1 -48
0.00288446
0.058014841
-1 52
0.0080994591
0.058226444
-1 -48
0.0032605817
0.0584380893
-1 52
0.0084775368
0.0586497769
1 -48
0.0036368446
0.0588615068
-1 52
0.0088557562
0.0590732791
1 52
0.0141018061
0.0592850938
1 52
0.0193751355
0.0594969508
-1 -48
0.0144821349
0.0597088502
-1 -48
0.0096126206
0.059920792
-1 52
0.0148626062
0.0601327761
-1 -48
0.0099912657
0.0603448027
-1 52
0.0152432203
0.0605568716
-1 52
0.020522485
0.060768983
1 52
0.025829202
0.0609811368
1 52
0.0311635138
0.061193333
1 52
0.0365255641
0.0614055717
1 -48
0.0315502414
0.0616178528
1 -48
0.0265988002
0.0618301764
-1 52
0.031937114
0.0620425424
1 52
0.037303187
0.0622549509
1 -48
0.0323241317
0.0624674019
-1 52
0.0376922172
0.0626798954
1 -48
0.0327112945
0.0628924314
-1 52
0.0380813933
0.0631050099
1 52
0.0434794165
0.0633176309
1 -48
0.0384707153
0.0635302944
-1 52
0.043870763
0.0637430005
1 52
0.049298891
0.0639557491
-1 52
0.0547552452
0.0641685402
-1 52
0.0602399725
0.0643813739
1 -48
0.0551508206
0.0645942502
-1 52
0.0606376049
0.064807169
1 52
0.0661529204
0.0650201305
1 52
0.0716969156
0.0652331345
-1 -48
0.0665527704
0.0654461811
-1 52
0.0720988448
0.0656592704
-1 -48
0.0669527704
0.0658724022
-1 -48
0.0618313971
0.0660855767
-1 -48
0.0567346064
0.0662987938
-1 52
0.0622296263
0.0665120536
1 -48
0.0571309241
0.066725356
-1 52
0.0626280049
0.0669387011
1 52
0.0681536706
0.0671520888
-1 -48
0.0630265329
0.0673655192
-1 52
0.0685542709
0.0675789923
-1 -48
0.0634252104
0.0677925081
-1 -48
0.0583207694
0.0680060666
-1 -48
0.0532408297
0.0682196678
1 52
0.058717682
0.0684333118
-1 -48
0.0536358372
0.0686469984
-1 -48
0.0485783851
0.0688607278
-1 52
0.0540309927
0.0690745
1 -48
0.048971644
0.0692883149
-1 52
0.0544262965
0.0695021725
-1 52
0.0599093133
0.069716073
1 52
0.0654208417
0.0699300162
1 -48
0.0603068216
0.0701440022
1 52
0.0658204171
0.070358031
-1 -48
0.0607044791
0.0705721026
1 -48
0.0556130976
0.070786217
-1 52
0.0611022857
0.0710003743
1 -48
0.0560089948
0.0712145743
-1 -48
0.0509401516
0.0714288172
-1 -48
0.0458956389
0.071643103
-1 52
0.0513342962
0.0718574316
-1 52
0.0568012345
0.0720718031
-1 -48
0.0517285886
0.0722862175
-1 -48
0.0466802914
0.0725006747
1 -48
0.041656226
0.0727151749
1 52
0.0470728383
0.0729297179
-1 -48
0.0420468887
0.0731443038
-1 52
0.0474655325
0.0733589327
-1 -48
0.042437698
0.0735736045
-1 -48
0.037433997
0.0737883192
-1 52
0.0428286538
0.0740030769
-1 52
0.0482513628
0.0742178775
1 -48
0.0432197563
0.0744327211
1 52
0.048644499
0.0746476076
-1 52
0.0540974504
0.0748625371
1 -48
0.0490377826
0.0750775096
1 52
0.0544927791
0.0752925251
-1 -48
0.0494312138
0.0755075836
-1 -48
0.0443939439
0.0757226852
-1 52
0.0498247925
0.0759378297
-1 52
0.0552838814
0.0761530173
1 -48
0.0502185187
0.0763682479
1 52
0.055679655
0.0765835215
1 52
0.0611691892
0.0767988382
1 -48
0.0560755771
0.077014198
-1 52
0.0615671701
0.0772296008
-1 -48
0.0564716477
0.0774450467
-1 52
0.0619653003
0.0776605358
-1 -48
0.0568678668
0.0778760679
-1 -48
0.0517949011
0.0780916431
-1 52
0.0572642346
0.0783072614
-1 -48
0.0521893662
0.0785229229
1 -48
0.0471388573
0.0787386274
-1 -48
0.0421125908
0.0789543752
1 52
0.0475315762
0.079170166
-1 -48
0.0425034247
0.0793860001
1 52
0.0479244425
0.0796018773
-1 -48
0.0428944052
0.0798177976
-1 -48
0.037888512
0.0800337612
-1 -48
0.0329066472
0.080249768
-1 52
0.0382777617
0.0804658179
-1 52
0.0436768061
0.0806819111
1 52
0.0491039255
0.0808980475
-1 52
0.0545592659
0.0811142271
-1 -48
0.0494973814
0.0813304499
1 -48
0.044459794
0.081546716
1 -48
0.039446387
0.0817630253
-1 52
0.0448515082
0.081979378
1 -48
0.0398362209
0.0821957738
-1 -48
0.0348450071
0.082412213
-1 52
0.0402262011
0.0826286954
-1 52
0.0456353774
0.0828452212
1 52
0.0510726813
0.0830617902
-1 52
0.0565382593
0.0832784026
1 -48
0.0514668756
0.0834950582
1 -48
0.0464198346
0.0837117573
1 -48
0.0413970194
0.0839284996
1 -48
0.0363983137
0.0841452853
-1 -48
0.0314236018
0.0843621144
1 -48
0.0264727685
0.0845789868
1 52
0.0318104269
0.0847959026
1 -48
0.0268577369
0.0850128618
-1 52
0.0321973971
0.0852298643
-1 -48
0.0272428496
0.0854469103
1 52
0.0325845124
0.0856639997
1 52
0.0379539519
0.0858811325
1 -48
0.0329717729
0.0860983087
1 -48
0.0280135084
0.0863155284
-1 -48
0.0230790436
0.0865327915
-1 -48
0.0181682642
0.086750098
-1 52
0.0234627391
0.0869674481
-1 52
0.0287847454
0.0871848416
1 -48
0.0238465786
0.0874022785
-1 -48
0.018932115
0.087619759
1 52
0.024230562
0.0878372829
-1 52
0.0295565609
0.0880548504
-1 -48
0.0246146895
0.0882724614
-1 -48
0.0196965389
0.0884901159
1 -48
0.0148019956
0.0887078139
1 -48
0.009930946
0.0889255554
1 52
0.0151825869
0.0891433406
1 52
0.0204615363
0.0893611692
-1 -48
0.015563321
0.0895790415
-1 52
0.0208442502
0.0897969573
1 52
0.0261526403
0.0900149167
-1 52
0.0314886341
0.0902329196
1 52
0.036852375
0.0904509662
-1 52
0.0422440073
0.0906690564
1 -48
0.0372412361
0.0908871902
1 -48
0.0322624782
0.0911053677
1 52
0.037630243
0.0913235887
1 -48
0.0326496179
0.0915418535
-1 52
0.0380193959
0.0917601618
1 -48
0.0330369028
0.0919785139
1 -48
0.0280783257
0.0921969096
1 52
0.0334243329
0.0924153489
1 -48
0.0284638961
0.092633832
1 -48
0.0235272694
0.0928523588
1 -48
0.0186143386
0.0930709292
1 52
0.0239111331
0.0932895434
-1 52
0.029235471
0.0935082013
-1 -48
0.0242951407
0.093726903
-1 -48
0.0193785241
0.0939456484
1 -48
0.0144855072
0.0941644375
-1 52
0.0197608318
0.0943832704
-1 -48
0.0148659798
0.094602147
-1 52
0.0201432829
0.0948210675
1 52
0.025448028
0.0950400317
-1 52
0.0307803577
0.0952590397
1 -48
0.025832612
0.0954780915
1 52
0.0311669416
0.0956971871
1 52
0.0365290097
0.0959163265
-1 52
0.0419189605
0.0961355098
-1 -48
0.0369177495
0.0963547369
1 -48
0.0319405443
0.0965740079
1 52
0.0373066351
0.0967933227
-1 -48
0.0323275633
0.0970126813
1 52
0.0376956666
0.0972320839
-1 52
0.0430916841
0.0974515303
-1 -48
0.038084844
0.0976710206
1 52
0.0434828852
0.0978905548
1 52
0.0489089962
0.0981101329
-1 -48
0.043874233
0.0983297549
-1 -48
0.0388636367
0.0985494209
-1 -48
0.0338770912
0.0987691308
1 -48
0.0289144812
0.0989888846
-1 -48
0.0239756917
0.0992086824
1 52
0.0293003653
0.0994285241
-1 -48
0.0243597235
0.0996484098
-1 52
0.0296863941
0.0998683395
-1 52
0.0350407633
0.1000883132
-1 52
0.0404229753
0.1003083308
1 52
0.0458331748
0.1005283925
1 52
0.0512715073
0.1007484982
-1 -48
0.0462254041
0.1009686479
-1 -48
0.0412035221
0.1011888416
-1 -48
0.0362057452
0.1014090794
-1 -48
0.0312319576
0.1016293612
1 -48
0.0262820442
0.1018496871
1 52
0.0316187109
0.102070057
-1 -48
0.0266669411
0.102290471
1 52
0.0320056092
0.1025109291
-1 52
0.0373720383
0.1027314313
1 52
0.0427663729
0.1029519776
1 -48
0.0377610943
0.103172568
-1 -48
0.0327798411
0.1033932025
-1 -48
0.0278224978
0.1036138811
1 -48
0.0228889499
0.1038346039
-1 -48
0.0179790829
0.1040553708
-1 -48
0.0130927833
0.1042761819
1 52
0.0183608658
0.1044970371
-1 -48
0.0134727336
0.1047179365
-1 52
0.0187427918
0.1049388801
-1 52
0.0240402543
0.1051598679
-1 52
0.0293652637
0.1053808999
-1 -48
0.0244243104
0.105601976
-1 -48
0.0195070737
0.1058230964
-1 -48
0.0146134398
0.1060442611
-1 52
0.0198894296
0.1062654699
1 52
0.0251928547
0.106486723
-1 52
0.0305238575
0.1067080204
-1 52
0.0358825816
0.106929362
-1 52
0.041269171
0.1071507478
1 52
0.0466837707
0.107372178
1 -48
0.0416596886
0.1075936524
-1 52
0.047076319
0.1078151711
-1 52
0.0525211158
0.1080367342
-1 -48
0.0474690145
0.1082583415
1 -48
0.0424411632
0.1084799932
1 52
0.0478618573
0.1087016892
-1 -48
0.0428321203
0.1089234295
-1 -48
0.0378265262
0.1091452142
1 -48
0.0328449588
0.1093670433
-1 -48
0.027887303
0.1095889167
1 52
0.033232317
0.1098108345
1 -48
0.0282728019
0.1100327966
1 -48
0.0233370924
0.1102548032
-1 -48
0.0184250744
0.1104768541
-1 -48
0.013536634
0.1106989495
-1 52
0.0188070245
0.1109210893
1 -48
0.0139167508
0.1111432735
-1 52
0.0191891179
0.1113655022
-1 52
0.0244889013
0.1115877753
-1 -48
0.0195713546
0.1118100928
-1 52
0.0248731257
0.1120324548
-1 -48
0.0199537347
0.1122548613
-1 52
0.0252574941
0.1124773123
1 52
0.030588833
0.1126998078
-1 52
0.035947895
0.1129223477
-1 -48
0.0309753451
0.1131449322
1 52
0.0363364169
0.1133675612
-1 -48
0.0313620021
0.1135902347
-1 52
0.0367250845
0.1138129527
1 52
0.0421160549
0.1140357153
-1 52
0.0475350584
0.1142585225
1 -48
0.0425068901
0.1144813742
-1 52
0.047927926
0.1147042705
-1 52
0.0533771512
0.1149272113
1 -48
0.0483209408
0.1151501968
1 -48
0.0432890003
0.1153732268
-1 52
0.0487141031
0.1155963014
-1 -48
0.0436802754
0.1158194207
-1 52
0.0491074129
0.1160425846
-1 52
0.0545627714
0.1162657931
-1 52
0.0600464978
0.1164890463
1 52
0.0655587396
0.1167123441
1 -48
0.0604440577
0.1169356865
1 52
0.0659583668
0.1171590737
-1 52
0.0715013503
0.1173825055
1 52
0.0770731573
0.117605982
1 52
0.0826739377
0.1178295032
1 -48
0.0774771028
0.1180530691
-1 52
0.0830799837
0.1182766797
1 -48
0.0778811998
0.118500335
1 52
0.0834861821
0.1187240351
-1 52
0.0891203102
0.1189477799
-1 -48
0.0838925327
0.1191715695
1 -48
0.0786898486
0.1193954038
-1 52
0.0842990358
0.1196192829
1 52
0.0899373908
0.1198432067
-1 -48
0.0847056913
0.1200671754
1 52
0.0903461609
0.1202911888
-1 -48
0.0851124993
0.120515247
-1 -48
0.0799039593
0.1207393501
1 52
0.0855194599
0.120963498
-1 52
0.0911641611
0.1211876907
1 -48
0.0859265731
0.1214119282
-1 -48
0.0807141256
0.1216362106
1 -48
0.0755266978
0.1218605378
-1 52
0.0811194366
0.1220849099
1 -48
0.0759300633
0.1223093269
-1 52
0.0815248996
0.1225337888
-1 52
0.0871488291
0.1227582955
-1 52
0.092802003
0.1229828472
1 52
0.0984845734
0.1232074438
1 -48
0.0932118475
0.1234320853
1 52
0.0988965491
0.1236567717
-1 52
0.1046108111
0.123881503
1 52
0.1103547874
0.1241062793
1 52
0.1161286323
0.1243311006
1 -48
0.1107712148
0.1245559668
1 52
0.1165472251
0.124780878
-1 -48
0.1111877985
0.1250058342
-1 -48
0.105854097
0.1252308353
-1 52
0.1116045383
0.1254558815
-1 -48
0.1062688365
0.1256809727
1 -48
0.1009587461
0.1259061089
-1 52
0.1066837316
0.1261312901
1 52
0.112438487
0.1263565164
-1 -48
0.1070987823
0.1265817877
-1 -48
0.1017847081
0.126807104
1 52
0.1075139886
0.1270324654
-1 -48
0.1021979215
0.1272578719
1 -48
0.0969073714
0.1274833235
1 -48
0.0916422161
0.1277088202
1 52
0.0973187556
0.1279343619
-1 52
0.1030248131
0.1281599488
-1 -48
0.097730294
0.1283855808
-1 -48
0.0924611886
0.1286112579
1 52
0.0981419868
0.1288369802
-1 52
0.1038523251
0.1290627476
-1 52
0.1095923572
0.1292885601
1 52
0.1153622374
0.1295144178
1 -48
0.1100084987
0.1297403207
1 52
0.1157805429
0.1299662688
1 -48
0.1104247963
0.130192262
-1 -48
0.1050947573
0.1304183005
1 52
0.11084125
0.1306443841
-1 52
0.1166176245
0.130870513
-1 52
0.1224240362
0.1310966871
-1 52
0.1282606411
0.1313229064
1 -48
0.1228449901
0.131549171
1 -48
0.1174553341
0.1317754809
1 -48
0.1120915485
0.132001836
1 52
0.1178744246
0.1322282363
-1 52
0.1236873716
0.132454682
-1 52
0.1295305459
0.1326811729
1 52
0.1354041047
0.1329077091
1 -48
0.129954165
0.1331342907
-1 52
0.1358299267
0.1333609175
-1 52
0.1417362423
0.1335875897
1 -48
0.1362559084
0.1338143072
-1 -48
0.13080188
0.1340410701
1 52
0.1366820498
0.1342678783
1 -48
0.1312259759
0.1344947319
1 -48
0.1257960912
0.1347216308
-1 -48
0.12039227
0.1349485752
-1 -48
0.1150143871
0.1351755649
-1 -48
0.1096623181
0.1354026
-1 -48
0.1043359389
0.1356296805
1 52
0.1100784858
0.1358568065
-1 52
0.1158508939
0.1360839778
-1 52
0.1216533186
0.1363111946
-1 52
0.1274859158
0.1365384569
1 -48
0.1220739834
0.1367657645
1 -48
0.1166880283
0.1369931177
-1 -48
0.1113279258
0.1372205163
1 -48
0.1059935517
0.1374479604
-1 -48
0.1006847827
0.13767545
-1 -48
0.0954014957
0.1379029851
-1 -48
0.0901435686
0.1381305657
-1 -48
0.0849108794
0.1383581918
1 -48
0.0797033072
0.1385858635
1 -48
0.0745207313
0.1388135806
1 -48
0.0693630318
0.1390413433
1 -48
0.0642300893
0.1392691516
1 52
0.0697640857
0.1394970054
1 52
0.075326859
0.1397249048
-1 52
0.0809185587
0.1399528498
-1 -48
0.0757301496
0.1401808404
1 52
0.0813239463
0.1404088766
1 -48
0.0761335914
0.1406369583
1 52
0.0817294861
0.1408650857
-1 52
0.0873544794
0.1410932587
-1 52
0.0930087227
0.1413214774
-1 -48
0.0877622808
0.1415497417
1 52
0.0934186447
0.1417780516
1 52
0.0991044216
0.1420064073
1 -48
0.0938287204
0.1422348085
1 -48
0.0885783426
0.1424632555
1 -48
0.0833531665
0.1426917481
-1 52
0.088986603
0.1429202865
1 -48
0.0837594673
0.1431488706
1 52
0.0893950165
0.1433775003
1 52
0.0950598706
0.1436061758
1 52
0.1007541819
0.1438348971
1 -48
0.0954705619
0.144063664
-1 -48
0.0902123032
0.1442924768
-1 -48
0.0849792841
0.1445213353
-1 -48
0.0797713835
0.1447502395
-1 -48
0.0745884809
0.1449791896
-1 -48
0.0694304562
0.1452081854
-1 -48
0.06429719
0.1454372271
1 -48
0.0591885635
0.1456663145
1 52
0.064696344
0.1458954478
1 52
0.070232765
0.1461246269
1 -48
0.0650956477
0.1463538518
1 52
0.0706341451
0.1465831226
-1 52
0.0762014427
0.1468124392
-1 52
0.0817976902
0.1470418017
1 52
0.0874230382
0.14727121
1 -48
0.0822034076
0.1475006643
-1 52
0.0878308653
0.1477301644
-1 -48
0.0826092771
0.1479597104
-1 52
0.0882388454
0.1481893024
1 52
0.0938976874
0.1484189402
1 52
0.0995859553
0.148648624
-1 -48
0.0943079428
0.1488783537
-1 -48
0.0890552646
0.1491081294
-1 -48
0.0838277994
0.149337951
1 52
0.0894637039
0.1495678186
-1 -48
0.0842342781
0.1497977322
-1 52
0.0898722964
0.1500276917
1 -48
0.0846409094
0.1502576973
-1 -48
0.079434633
0.1504877488
1 52
0.0850476931
0.1507178464
-1 -48
0.0798394642
0.1509479899
1 52
0.0854546294
0.1511781795
1 -48
0.0802444472
0.1514084152
1 -48
0.0750592738
0.1516386969
1 52
0.080649582
0.1518690246
-1 52
0.0862689599
0.1520993984
-1 52
0.0919175585
0.1523298183
1 52
0.0975955298
0.1525602842
1 -48
0.0923270712
0.1527907963
-1 -48
0.0870839013
0.1530213545
-1 -48
0.0818658985
0.1532519587
1 52
0.0874916012
0.1534826091
1 -48
0.0822716415
0.1537133056
1 -48
0.0770767377
0.1539440483
1 52
0.0826775367
0.1541748371
1 -48
0.0774806845
0.1544056721
1 52
0.0830835841
0.1546365532
-1 52
0.0887156187
0.1548674805
-1 52
0.0943769399
0.155098454
1 -48
0.0891239306
0.1553294737
-1 -48
0.0838961358
0.1555605396
-1 -48
0.0786934343
0.1557916517
1 52
0.0843026402
0.1560228101
1 -48
0.0790979875
0.1562540146
-1 -48
0.0739183171
0.1564852654
1 52
0.0795026924
0.1567165625
-1 -48
0.0743210795
0.1569479058
-1 -48
0.0691643383
0.1571792954
-1 -48
0.0640323495
0.1574107312
1 52
0.0695653177
0.1576422134
-1 -48
0.0644314042
0.1578737418
-1 -48
0.0593221334
0.1581053166
-1 52
0.0648306085
0.1583369376
-1 52
0.0703677277
0.158568605
1 52
0.0759336399
0.1588003187
-1 52
0.0815284948
0.1590320788
-1 52
0.087152443
0.1592638852
-1 -48
0.0819341112
0.159495738
1 -48
0.0767408275
0.1597276371
-1 -48
0.0715724715
0.1599595827
-1 -48
0.0664289237
0.1601915746
1 52
0.0719743541
0.1604236129
-1 -48
0.0668288772
0.1606556976
-1 -48
0.0617080986
0.1608878288
-1 -48
0.0566118997
0.1611200063
1 52
0.0621062816
0.1613522303
1 52
0.0676292342
0.1615845008
1 52
0.0731809062
0.1618168177
-1 -48
0.0680296379
0.162049181
1 52
0.073583392
0.1622815909
-1 52
0.0791660256
0.1625140472
1 -48
0.0739860287
0.16274655
-1 -48
0.0688308958
0.1629790993
1 -48
0.0637005075
0.1632116951
1 52
0.0692317501
0.1634443375
-1 52
0.0747917552
0.1636770263
1 -48
0.0696327548
0.1639097617
1 -48
0.0644985176
0.1641425437
-1 52
0.0700339099
0.1643753722
-1 -48
0.0648977471
0.1646082473
-1 -48
0.0597862379
0.1648411689
1 52
0.0652971264
0.1650741372
1 -48
0.0601837001
0.165307152
-1 52
0.0656966554
0.1655402134
1 52
0.071238278
0.1657733215
-1 52
0.076808717
0.1660064761
-1 52
0.0824081224
0.1662396774
1 -48
0.0772125634
0.1664729254
-1 -48
0.0720419431
0.1667062199
-1 52
0.0776165612
0.1669395612
-1 52
0.0832201673
0.1671729491
-1 -48
0.0780207105
0.1674063837
-1 52
0.0836264182
0.167639865
-1 52
0.0892612756
0.1678733929
1 52
0.0949254342
0.1681069676
1 52
0.1006190465
0.168340589
1 52
0.1063422655
0.1685742571
1 52
0.1120952453
0.168807972
1 -48
0.1067571881
0.1690417336
1 -48
0.1014447536
0.1692755419
-1 -48
0.0961578188
0.169509397
1 -48
0.0908962613
0.1697432989
1 52
0.0965689218
0.1699772476
1 52
0.1022710802
0.170211243
1 -48
0.096980179
0.1704452853
1 -48
0.0917146742
0.1706793743
1 -48
0.0864744437
0.1709135102
-1 -48
0.0812593664
0.1711476929
1 -48
0.0760693214
0.1713819224
-1 52
0.0816648819
0.1716161988
1 52
0.0872895393
0.1718505221
-1 -48
0.0820705495
0.1720848922
1 -48
0.0768766109
0.1723193091
-1 52
0.0824763692
0.172553773
1 52
0.0881052464
0.1727882838
1 -48
0.0828823412
0.1730228414
-1 52
0.0885133294
0.173257446
-1 52
0.0941735987
0.1734920975
1 -48
0.0889215654
0.1737267959
1 -48
0.0836947419
0.1739615412
-1 -48
0.0784930071
0.1741963336
1 52
0.0841011708
0.1744311728
1 52
0.0897384968
0.1746660591
1 52
0.095405137
0.1749009923
1 -48
0.0901471924
0.1751359725
1 52
0.0958159578
0.1753709997
-1 52
0.1015142008
0.1756060739
-1 52
0.1072420746
0.1758411951
-1 -48
0.1019273126
0.1760763633
1 -48
0.0966380615
0.1763115786
-1 52
0.1023405795
0.1765468409
1 52
0.1080727505
0.1767821503
1 52
0.1138347288
0.1770175067
-1 52
0.1196266694
0.1772529102
1 -48
0.1142524613
0.1774883608
1 -48
0.1089040495
0.1777238585
-1 -48
0.1035813101
0.1779594032
1 -48
0.0982841198
0.1781949951
1 52
0.1039951972
0.1784306341
-1 -48
0.0986960203
0.1786663202
1 52
0.1044092396
0.1789020535
1 52
0.1101521676
0.1791378339
-1 -48
0.1048234372
0.1793736615
1 52
0.1105685191
0.1796095362
-1 -48
0.1052377902
0.1798454581
1 52
0.1109850267
0.1800814272
1 -48
0.1056522986
0.1803174435
-1 -48
0.1003451676
0.180553507
-1 -48
0.0950635108
0.1807896177
1 52
0.100757841
0.1810257756
1 52
0.1064817818
0.1812619808
1 -48
0.1011706692
0.1814982332
1 -48
0.09588505
0.1817345328
1 -48
0.0906248018
0.1819708797
1 52
0.0962960508
0.1822072739
1 -48
0.0910338297
0.1824437153
-1 -48
0.0857968673
0.1826802041
1 -48
0.0805850424
0.1829167401
1 -48
0.0753982342
0.1831533235
1 52
0.080990305
0.1833899541
1 52
0.0866114546
0.1836266321
-1 52
0.0922618341
0.1838633575
-1 52
0.0979415957
0.1841001301
-1 52
0.103650892
0.1843369502
1 52
0.1093898766
0.1845738175
-1 52
0.115158704
0.1848107323
-1 52
0.1209575292
0.1850476945
-1 52
0.1267865084
0.185284704
-1 52
0.1326457982
0.1855217609
-1 -48
0.1272090984
0.1857588653
-1 52
0.1330705857
0.1859960171
1 -48
0.1276318469
0.1862332163
-1 52
0.1334955325
0.1864704629
1 -48
0.1280547539
0.186707757
1 -48
0.1226400911
0.1869450986
1 52
0.1284778196
0.1871824876
1 -48
0.1230611261
0.1874199241
1 -48
0.1176704326
0.1876574081
1 52
0.1234823189
0.1878949395
-1 -48
0.1180896038
0.1881325185
1 -48
0.1127227737
0.188370145
1 52
0.1185089321
0.1886078191
-1 -48
0.1131400892
0.1888455406
-1 52
0.1189284177
0.1890833097
1 52
0.1247468455
0.1893211264
1 52
0.130595529
0.1895589906
1 -48
0.1251686705
0.1897969024
1 -48
0.1197678609
0.1900348618
1 -48
0.1143929752
0.1902728688
1 -48
0.1090438889
0.1905109233
-1 52
0.1148109171
0.1907490255
1 52
0.1206079339
0.1909871753
1 -48
0.1152290158
0.1912253728
1 52
0.1210282067
0.1914636178
-1 52
0.1268575533
0.1917019106
-1 52
0.1327172126
0.1919402509
1 52
0.1386073421
0.192178639
1 52
0.1445281003
0.1924170747
-1 -48
0.1390343654
0.1926555581
-1 -48
0.1335670005
0.1928940892
1 -48
0.1281258789
0.1931326681
1 52
0.1339921334
0.1933712946
-1 52
0.1398888925
0.1936099689
-1 52
0.1458163148
0.1938486909
1 52
0.1517745596
0.1940874606
-1 52
0.1577637873
0.1943262781
1 -48
0.1522065211
0.1945651433
-1 52
0.158197995
0.1948040564
1 -48
0.1526386447
0.1950430172
1 52
0.1586323656
0.1952820258
1 52
0.1646572539
0.1955210822
1 52
0.1707134716
0.1957601864
-1 52
0.1768011817
0.1959993384
-1 52
0.1829205478
0.1962385383
-1 -48
0.1772425292
0.196477786
1 52
0.1833641904
0.1967170816
1 52
0.1895176842
0.196956425
-1 52
0.1957031761
0.1971958163
1 -48
0.1899638009
0.1974352554
1 -48
0.1842519746
0.1976747425
1 -48
0.1785675651
0.1979142774
-1 -48
0.1729104408
0.1981538603
-1 52
0.1790095751
0.1983934911
-1 52
0.1851404249
0.1986331698
-1 -48
0.1794517509
0.1988728964
-1 -48
0.1737903825
0.199112671
1 -48
0.1681561886
0.1993524935
1 52
0.1742306008
0.199592364
-1 52
0.1803365999
0.1998322825
-1 52
0.1864743503
0.2000722489
-1 52
0.1926440169
0.2003122634
1 -48
0.1869193256
0.2005523258
-1 -48
0.1812221128
0.2007924363
1 52
0.1873644678
0.2010325948
-1 52
0.1935387631
0.2012728013
-1 -48
0.187809777
0.2015130559
-1 52
0.1939863878
0.2017533585
-1 52
0.2001951171
0.2019937092
1 52
0.2064361317
0.2022341079
1 52
0.2127095995
0.2024745547
-1 -48
0.2068885935
0.2027150496
1 52
0.2131644142
0.2029555926
-1 52
0.2194728691
0.2031961838
-1 -48
0.2136193993
0.203436823
1 -48
0.2077940262
0.2036775104
-1 -48
0.2019966149
0.2039182459
-1 -48
0.1962270311
0.2041590295
1 -48
0.1904851414
0.2043998613
1 -48
0.1847708127
0.2046407413
-1 -48
0.1790839128
0.2048816694
1 -48
0.17342431
0.2051226458
1 52
0.1795261164
0.2053636703
-1 -48
0.1738643911
0.205604743
1 52
0.1799684859
0.205845864
1 -48
0.1743046372
0.2060870332
1 -48
0.1686679749
0.2063282506
1 -48
0.1630583686
0.2065695162
-1 -48
0.1574756885
0.2068108301
1 52
0.1634945621
0.2070521923
-1 -48
0.1579097882
0.2072936027
-1 52
0.1639309191
0.2075350614
1 -48
0.1583440506
0.2077765685
1 -48
0.1527839992
0.2080181238
-1 -48
0.147250636
0.2082597274
1 52
0.1532163393
0.2085013793
1 52
0.1592130643
0.2087430796
1 52
0.1652409722
0.2089848282
-1 -48
0.1596478155
0.2092266252
-1 -48
0.154081506
0.2094684705
-1 -48
0.1485419148
0.2097103642
-1 52
0.1545143328
0.2099523063
1 -48
0.148972664
0.2101942967
-1 -48
0.1434575952
0.2104363356
-1 -48
0.1379689987
0.2106784229
-1 52
0.1438864375
0.2109205586
1 52
0.149834647
0.2111627427
-1 -48
0.1443154407
0.2114049752
-1 -48
0.1388227266
0.2116472562
-1 -48
0.1333563775
0.2118895857
-1 52
0.1392498306
0.2121319636
-1 -48
0.1337814315
0.21237439
-1 -48
0.1283392806
0.2126168649
-1 -48
0.122923252
0.2128593882
1 52
0.1287624529
0.2131019601
-1 52
0.1346320177
0.2133445805
1 52
0.1405321042
0.2135872494
1 -48
0.1350575501
0.2138299669
1 52
0.1409598494
0.2140727329
-1 52
0.1468928406
0.2143155474
1 -48
0.1413877549
0.2145584105
1 52
0.1473229713
0.2148013222
-1 -48
0.141815821
0.2150442825
1 52
0.1477532633
0.2152872913
1 -48
0.1422440476
0.2155303488
-1 52
0.1481837167
0.2157734548
-1 -48
0.1426724348
0.2160166095
-1 52
0.1486143315
0.2162598129
1 52
0.154587126
0.2165030648
1 -48
0.1490451078
0.2167463654
1 -48
0.1435296913
0.2169897147
-1 -48
0.1380407488
0.2172331126
1 52
0.1439585607
0.2174765593
1 -48
0.1384675596
0.2177200546
1 -48
0.1330029153
0.2179635986
-1 52
0.1388945304
0.2182071913
-1 -48
0.1334278367
0.2184508328
1 -48
0.1279873831
0.2186945229
-1 52
0.1338529175
0.2189382618
1 -48
0.1284104235
0.2191820495
1 52
0.1342781577
0.2194258859
-1 52
0.1401764041
0.2196697711
1 -48
0.1347035573
0.219913705
1 52
0.1406040158
0.2201576878
1 52
0.1465351567
0.2204017193
1 52
0.1524971395
0.2206457996
-1 -48
0.1469651533
0.2208899288
-1 52
0.1529293721
0.2211341068
-1 52
0.1589246048
0.2213783336
-48
0.1533617667
0.2216226093
-48
0.1478256302
0.2218669338
-48
0.1423160672
0.2221113072
-48
0.1368329501
0.2223557294
-48
0.1313761519
0.2226002006
52
0.1372593079
0.2228447206
-48
0.1318004632
0.2230892896
52
0.1376858256
0.2233339074
-48
0.1322249337
0.2235785742
-48
0.126790254
0.2238232899
52
0.1326495633
0.2240680546
-48
0.1272128454
0.2243128682
-48
0.1218022237
0.2245577308
52
0.1276355953
0.2248026423
52
0.1334993004
0.2250476028
52
0.1393934968
0.2252926124
52
0.1453183429
0.2255376709
52
0.1512739983
0.2257827784
-48
0.1457478831
0.226027935
52
0.1517057721
0.2262731406
52
0.1576946421
0.2265183952
-48
0.1521377079
0.2267636989
-48
0.1466074469
0.2270090516
52
0.1525698056
0.2272544534
-48
0.1470374705
0.2274999043
-48
0.1415316907
0.2277454043
52
0.1474676555
0.2279909534
-48
0.1419598107
0.2282365516
-48
0.1364784036
0.2284821989
52
0.1423880913
0.2287278953
-48
0.1369046285
0.2289736409
-48
0.1314474863
0.2292194356
-48
0.1260165383
0.2294652795
-48
0.1206116589
0.2297111726
-48
0.115232723
0.2299571148
52
0.1210319331
0.2302031062
52
0.1268612992
0.2304491468
52
0.132720978
0.2306952367
52
0.138611127
0.2309413757
52
0.1445319049
0.231187564
-48
0.1390381518
0.2314338015
52
0.1449611501
0.2316800883
-48
0.1394653366
0.2319264243
52
0.1453905564
0.2321728096
52
0.1513465873
0.2324192441
52
0.1573335895
0.232665728
52
0.1633517242
0.2329122611
-48
0.1577676359
0.2331588436
-48
0.1522103513
0.2334054753
-48
0.1466797416
0.2336521564
52
0.1526424762
0.2338988869
-48
0.1471097923
0.2341456667
52
0.1530747633
0.2343924958
52
0.159070752
0.2346393743
-48
0.1535072124
0.2348863022
-48
0.1479703778
0.2351332794
-48
0.14246012
0.2353803061
52
0.1484009126
0.2356273821
-48
0.1428885882
0.2358745076
-48
0.137402723
0.2361216825
52
0.1433172172
0.2363689069
52
0.1492624667
0.2366161806
52
0.1552386315
0.2368635039
52
0.1612458724
0.2371108766
52
0.1672843509
0.2373582987
52
0.1733542296
0.2376057704
52
0.1794556716
0.2378532916
-48
0.1737942843
0.2381008622
-48
0.1681600718
0.2383484824
52
0.1742345041
0.2385961521
52
0.1803405236
0.2388438713
-48
0.1746748891
0.2390916401
52
0.1807831985
0.2393394584
52
0.1869232711
0.2395873263
52
0.1930952721
0.2398352438
52
0.1992993675
0.2400832108
52
0.2055357242
0.2403312275
-48
0.1997491528
0.2405792937
52
0.2059878484
0.2408274096
52
0.2122589852
0.2410755751
-48
0.206440142
0.2413237902
52
0.2127136308
0.2415720549
52
0.2190197417
0.2418203693
52
0.2253586443
0.2420687334
52
0.2317305093
0.2423171472
52
0.2381355079
0.2425656106
52
0.2445738126
0.2428141237
52
0.2510455964
0.2430626865
-48
0.2450405775
0.2433112991
-48
0.2390643828
0.2435599613
52
0.2455075175
0.2438086733
52
0.2519841566
0.2440574351
52
0.2584944742
0.2443062465
52
0.2650386455
0.2445551078
-48
0.25896646
0.2448040188
52
0.2655130856
0.2450529796
52
0.2720937537
0.2453019902
-48
0.2659877036
0.2455510506
-48
0.2599109627
0.2458001608
52
0.2664624997
0.2460493209
-48
0.2603834797
0.2462985307
52
0.2669374738
0.2465477904
-48
0.2608561739
0.2467971
52
0.267412626
0.2470464594
-48
0.2613290454
0.2472958687
-48
0.255274666
0.2475453279
52
0.2618020942
0.2477948369
52
0.2683634651
0.2480443959
52
0.2749589551
0.2482940048
-48
0.2688391522
0.2485436636
-48
0.2627487242
0.2487933723
52
0.2693150176
0.249043131
-48
0.2632223055
0.2492929396
-48
0.2571588384
0.2495427982
52
0.2636960644
0.2497927068
52
0.2702672839
0.2500426653
52
0.2768726738
0.2502926738
52
0.2835124117
0.2505427324
-48
0.2773515521
0.2507928409
-48
0.2712202647
0.2510429995
-48
0.2651184074
0.2512932081
52
0.2716970231
0.2515434667
-48
0.2655928774
0.2517937754
-48
0.2595180316
0.2520441342
-48
0.2534723451
0.252294543
-48
0.2474556778
0.2525450019
52
0.2539424473
0.2527955109
52
0.2604629481
0.25304607
-48
0.2544127259
0.2532966792
-48
0.2483915448
0.2535473386
52
0.2548831809
0.253798048
52
0.2614085734
0.2540488076
52
0.267967898
0.2542996174
52
0.274561331
0.2545504773
-48
0.2684434367
0.2548013874
52
0.2750393425
0.2550523477
-48
0.2689191537
0.2553033582
-48
0.2628283417
0.2555544188
52
0.2693950491
0.2558055297
52
0.2759959034
0.2560566908
-48
0.269871123
0.2563079022
52
0.2764744529
0.2565591637
-48
0.2703473755
0.2568104756
-48
0.2642497081
0.2570618377
52
0.2708238066
0.25731325
52
0.2774320904
0.2575647127
-48
0.2713004163
0.2578162256
52
0.2779111785
0.2580677889
-48
0.2717772049
0.2583194024
-48
0.2656726743
0.2585710663
52
0.2722541722
0.2588227805
52
0.2788698939
0.2590745451
-48
0.2727313184
0.25932636
-48
0.2666222081
0.2595782253
-48
0.2605424215
0.2598301409
52
0.267097242
0.2600821069
-48
0.2610151753
0.2603341234
52
0.2675724542
0.2605861902
-48
0.2614881064
0.2608383074
-48
0.2554329635
0.2610904751
52
0.2619612149
0.2613426932
-48
0.2559038011
0.2615949617
-48
0.2498754628
0.2618472807
52
0.2563748152
0.2620996502
52
0.2629079643
0.2623520701
-48
0.2568460061
0.2626045405
-48
0.2508131452
0.2628570614
-48
0.2448092421
0.2631096328
52
0.2512822502
0.2633622548
52
0.2577889179
0.2636149272
-48
0.2517515311
0.2638676502
-48
0.2457431237
0.2641204237
52
0.252220988
0.2643732478
-48
0.2462103272
0.2646261225
-48
0.2402285177
0.2648790477
52
0.246677706
0.2651320235
-48
0.240693653
0.2653850499
-48
0.2347383234
0.2656381269
52
0.2411589627
0.2658912545
52
0.2476129893
0.2661444328
-48
0.241624447
0.2663976617
52
0.2480808941
0.2666509412
-48
0.2420901058
0.2669042714
52
0.2485489744
0.2671576523
-48
0.2425559393
0.2674110838
-48
0.2365916708
0.267664566
-48
0.2306560308
0.2679180989
52
0.2370554421
0.2681716825
-48
0.231117576
0.2684253169
52
0.2375193874
0.2686790019
-48
0.2315792943
0.2689327377
-48
0.2256677137
0.2691865243
52
0.2320411858
0.2694403616
52
0.2384478
0.2696942497
-48
0.2325032506
0.2699481885
-48
0.2265872349
0.2702021781
-48
0.2206996162
0.2704562186
52
0.2270472542
0.2707103098
52
0.2334278999
0.2709644519
52
0.239841725
0.2712186448
-48
0.2338904847
0.2714728885
52
0.2403067153
0.2717271831
52
0.2467563102
0.2719815285
52
0.253239443
0.2722359248
52
0.2597562881
0.272490372
52
0.2663070208
0.2727448701
-48
0.2602287471
0.2729994191
52
0.2667819366
0.2732540189
52
0.2733692027
0.2735086697
-48
0.2672570305
0.2737633715
-48
0.2611741967
0.2740181242
52
0.2677323026
0.2742729278
-48
0.2616471875
0.2745277824
52
0.2682077529
0.2747826879
52
0.2748024332
0.2750376445
-48
0.2686833815
0.275292652
52
0.2752805351
0.2755477105
52
0.2819119939
0.2758028201
-48
0.2757588163
0.2760579806
-48
0.269635174
0.2763131922
52
0.2762372769
0.2765684549
52
0.2828737107
0.2768237685
52
0.289544654
0.2770791333
-48
0.2833548397
0.2773345491
52
0.2900282849
0.277590016
-48
0.2838361491
0.277845534
-48
0.2776737356
0.2781011031
52
0.284317639
0.2783567234
-48
0.2781529143
0.2786123947
52
0.2847993095
0.2788681172
-48
0.2786322728
0.2791238908
-48
0.2724948379
0.2793797156
-48
0.2663868627
0.2796355915
-48
0.2603082057
0.2798915187
52
0.2668618084
0.280147497
-48
0.2607808717
0.2804035265
52
0.2673369323
0.2806596072
-48
0.261253715
0.2809157391
-48
0.2551996972
0.2811719222
52
0.2617267356
0.2814281566
52
0.2682877146
0.2816844422
52
0.2748828107
0.2819407791
52
0.2815122013
0.2821971673
-48
0.2753609428
0.2824536067
-48
0.2692392102
0.2827100974
52
0.2758392541
0.2829666395
-48
0.2697152257
0.2832232328
52
0.2763177449
0.2834798774
52
0.2829545972
0.2837365734
-48
0.2767964151
0.2839933207
52
0.2834357565
0.2842501194
52
0.2901096224
0.2845069694
-48
0.2839170962
0.2847638708
-48
0.2777542941
0.2850208236
52
0.2843986165
0.2852778278
-48
0.2782335031
0.2855348833
-48
0.2720979823
0.2857919903
-48
0.265991912
0.2860491487
-48
0.2599151508
0.2863063585
-48
0.2538675581
0.2865636198
52
0.2603876694
0.2868209325
-48
0.2543378086
0.2870782967
52
0.2608603652
0.2873357124
-48
0.2548082354
0.2875931795
-48
0.2487851559
0.2878506981
52
0.2552788387
0.2881082683
-48
0.2492535003
0.2883658899
52
0.2557496185
0.2886235631
52
0.2622795165
0.2888812878
52
0.26884337
0.2891390641
-48
0.2627529218
0.2893968919
52
0.269319237
0.2896547713
52
0.275919697
0.2899127022
52
0.2825544795
0.2901706848
52
0.2892237627
0.2904287189
-48
0.2830354887
0.2906868047
-48
0.2768769183
0.290944942
52
0.2835166783
0.291203131
52
0.290190965
0.2914613716
-48
0.2839980484
0.2917196639
-48
0.2778348578
0.2919780078
-48
0.2717012505
0.2922364034
-48
0.2655970845
0.2924948507
52
0.2721781893
0.2927533497
-48
0.266071734
0.2930119004
-48
0.2599945897
0.2932705027
-48
0.2539466156
0.2935291568
52
0.260467138
0.2937878627
52
0.2670215672
0.2940466202
-48
0.2609398636
0.2943054296
52
0.2674967509
0.2945642907
52
0.274087734
0.2948232035
52
0.2807129902
0.2950821681
-48
0.2745655679
0.2953411846
52
0.2811933088
0.2956002528
-48
0.275043581
0.2958593729
52
0.2816738076
0.2961185447
52
0.2883385114
0.2963777685
-48
0.2821544865
0.296637044
-48
0.276000145
0.2968963714
52
0.2826353457
0.2971557507
52
0.2893050495
0.2974151818
-48
0.2831163853
0.2976746649
52
0.2897885905
0.2979341998
-48
0.2835976053
0.2981937867
52
0.2902723128
0.2984534254
52
0.2969817288
0.2987131161
-48
0.2907562165
0.2989728587
52
0.2974681489
0.2992326533
52
0.3042149832
0.2994924998
-48
0.2979547513
0.2997523983
52
0.304704116
0.3000123488
-48
0.2984415363
0.3002723513
52
0.3051934323
0.3005324057
-48
0.2989285038
0.3007925122
-48
0.292693647
0.3010526707
52
0.2994156539
0.3013128813
-48
0.2931784588
0.3015731438
52
0.2999029868
0.3018334585
52
0.3066624823
0.3020938252
-48
0.3003905024
0.3023542439
-48
0.294148628
0.3026147148
52
0.3008782009
0.3028752377
52
0.3076427675
0.3031358128
52
0.3144425099
0.3033964399
52
0.3212776109
0.3036571192
52
0.3281482545
0.3039178506
-48
0.3217731429
0.3041786342
52
0.3286463632
0.3044394699
52
0.3355553243
0.3047003578
-48
0.3291446588
0.3049612979
-48
0.3227647644
0.3052222902
-48
0.3164154935
0.3054833346
-48
0.3100966992
0.3057444313
-48
0.303808235
0.3060055802
-48
0.2975499555
0.3062667813
52
0.3042972153
0.3065280346
-48
0.2980365886
0.3067893402
52
0.3047863789
0.3070506981
-48
0.2985234043
0.3073121083
52
0.305275726
0.3075735707
-48
0.2990104025
0.3078350854
52
0.3057652566
0.3080966524
52
0.3125552359
0.3083582717
-48
0.3062549708
0.3086199434
52
0.3130474966
0.3088816674
52
0.3198753436
0.3091434437
52
0.3267386954
0.3094052724
52
0.3336377366
0.3096671535
52
0.3405726528
0.3099290869
52
0.3475436306
0.3101910727
-48
0.3410754212
0.3104531109
52
0.3480490134
0.3107152015
52
0.3550588683
0.3109773446
-48
0.3485545857
0.31123954
52
0.3555670695
0.311501788
-48
0.3490603476
0.3117640883
-48
0.3425848579
0.3120264411
-48
0.3361404506
0.3122888464
-48
0.3297269765
0.3125513042
-48
0.323344287
0.3128138145
-48
0.3169922344
0.3130763772
52
0.323840594
0.3133389925
-48
0.3174861592
0.3136016603
-48
0.3111622256
0.3138643806
52
0.3179802692
0.3141271535
52
0.3248337666
0.3143899789
52
0.3317229022
0.3146528569
52
0.3386478613
0.3149157875
52
0.3456088301
0.3151787707
-48
0.3391499077
0.3154418064
-48
0.3327219882
0.3157048948
52
0.3396521425
0.3159680357
52
0.3466183337
0.3162312294
-48
0.3401545657
0.3164944756
-48
0.3337218238
0.3167577745
-48
0.327319959
0.317021126
52
0.3342220228
0.3172845303
-48
0.3278177571
0.3175479872
52
0.3347224094
0.3178114968
-48
0.3283157418
0.3180750591
52
0.3352229837
0.3183386741
52
0.3421661432
0.3186023418
52
0.3491454072
0.3188660623
52
0.3561609633
0.3191298355
-48
0.3496513907
0.3193936615
-48
0.343173064
0.3196575402
52
0.3501575639
0.3199214717
52
0.3571783832
0.320185456
52
0.3642357108
0.3204494931
52
0.3713297365
0.320713583
-48
0.3647473538
0.3209777257
-48
0.3581965665
0.3212419213
52
0.3652591887
0.3215061696
-48
0.3587059445
0.3217704709
52
0.3657712155
0.322034825
52
0.3728732258
0.3222992319
52
0.3800121666
0.3225636918
-48
0.3733881082
0.3228282045
-48
0.3667958452
0.3230927702
52
0.3739031836
0.3233573887
-48
0.3673084483
0.3236220602
52
0.3744184523
0.3238867846
52
0.3815654282
0.324151562
52
0.3887495685
0.3244163923
-48
0.3820835705
0.3246812756
52
0.3892704051
0.3249462118
52
0.3964946112
0.325211201
52
0.4037563832
0.3254762433
-48
0.3970183525
0.3257413385
-48
0.3903126644
0.3260064868
52
0.3975422903
0.3262716881
-48
0.3908340873
0.3265369424
-48
0.3841580837
0.3268022498
-48
0.3775141249
0.3270676103
52
0.3846771983
0.3273330238
-48
0.3780307478
0.3275984904
52
0.3851965077
0.3278640101
-48
0.3785475644
0.3281295829
52
0.3857160118
0.3283952088
52
0.392921735
0.3286608879
-48
0.3862357107
0.32892662
-48
0.3795817793
0.3291924054
52
0.3867556045
0.3294582438
52
0.3939667337
0.3297241355
52
0.4012153607
0.3299900803
-48
0.394489527
0.3302560783
52
0.4017408725
0.3305221296
52
0.4090299251
0.330788234
-48
0.4022665814
0.3310543916
-48
0.3955357018
0.3313206025
52
0.4027924875
0.3315868666
52
0.4100870084
0.331853184
-48
0.4033185908
0.3321195546
52
0.4106158474
0.3323859785
52
0.4179510498
0.3326524557
52
0.4253243953
0.3329189862
52
0.4327360822
0.33318557
-48
0.425858949
0.3334522071
-48
0.419014826
0.3337188976
-48
0.4122035548
0.3339856414
-48
0.4054249778
0.3342524385
-48
0.3986789379
0.334519289
-48
0.391965279
0.3347861928
52
0.3992034984
0.3350531501
-48
0.3924873216
0.3353201607
-48
0.3858033825
0.3355872247
52
0.3930095601
0.3358543422
52
0.4002532098
0.3361215131
-48
0.3935319944
0.3363887374
-48
0.3868430408
0.3366560151
52
0.3940546246
0.3369233463
52
0.4013037087
0.337190731
-48
0.3945774509
0.3374581691
-48
0.3878834791
0.3377256608
52
0.3951004732
0.3379932059
-48
0.3884039909
0.3382608045
52
0.3956236917
0.3385284567
-48
0.388924698
0.3387961624
52
0.3961471064
0.3390639216
52
0.4034070714
0.3393317344
52
0.4107047881
0.3395996007
52
0.418040453
0.3398675207
52
0.4254142634
0.3401354942
-48
0.4185722749
0.3404035213
-48
0.411763128
0.340671602
52
0.4191042963
0.3409397363
-48
0.4122925956
0.3412079242
52
0.4196365171
0.3414761658
-48
0.4128222619
0.3417444611
-48
0.406040715
0.34201281
-48
0.3992917196
0.3422812125
52
0.4065680365
0.3425496688
52
0.4138821903
0.3428181787
52
0.4212343777
0.3430867423
-48
0.4144124527
0.3433553597
52
0.4217673974
0.3436240307
52
0.4291605879
0.3438927556
-48
0.4223006171
0.3441615341
52
0.4296965803
0.3444303664
-48
0.4228340367
0.3446992525
52
0.4302327737
0.3449681923
-48
0.4233676564
0.345237186
52
0.4307691682
0.3455062334
52
0.4382091679
0.3457753347
52
0.4456878555
0.3460444897
-48
0.4387485538
0.3463136986
-48
0.4318425608
0.3465829614
-48
0.4249697165
0.346852278
52
0.432379559
0.3471216484
52
0.4398279327
0.3473910727
52
0.447315038
0.347660551
-48
0.4403679258
0.3479300831
52
0.447857839
0.3481996691
52
0.4553866998
0.348469309
52
0.4629547106
0.3487390029
-48
0.455932528
0.3490087507
-48
0.4489440518
0.3492785524
-48
0.4419891204
0.3495484081
52
0.4494874638
0.3498183178
-48
0.442529924
0.3500882815
-48
0.4356057804
0.3503582991
-48
0.4287148726
0.3506283708
52
0.43614419
0.3508984965
52
0.4436121397
0.3511686762
-48
0.4366828015
0.3514389099
-48
0.429786724
0.3517091977
52
0.437221615
0.3519795395
52
0.4446951674
0.3522499354
52
0.4522075823
0.3525203854
-48
0.4452369859
0.3527908895
-48
0.4382998483
0.3530614477
52
0.4457790075
0.35333206
-48
0.4388392683
0.3536027264
52
0.4463212325
0.3538734469
52
0.4538421029
0.3541442216
52
0.4614020818
0.3544150505
52
0.4690013727
0.3546859335
-48
0.4619501661
0.3549568707
-48
0.4549328053
0.355227862
52
0.4624984559
0.3554989076
52
0.4701034478
0.3557700074
52
0.4777479858
0.3560411614
-48
0.4706547954
0.3563123696
52
0.4783022004
0.3565836321
-48
0.4712063498
0.3568549488
-48
0.4641445593
0.3571263198
52
0.471758111
0.3573977451
52
0.4794112532
0.3576692246
52
0.4871041917
0.3579407585
-48
0.4799660916
0.3582123466
52
0.4876619153
0.3584839891
-48
0.4805211381
0.3587556859
-48
0.4734146366
0.359027437
52
0.4810763927
0.3592992425
-48
0.4739672261
0.3595711024
52
0.4816318556
0.3598430166
-48
0.4745200227
0.3601149852
-48
0.4674423266
0.3603870082
52
0.4750730267
0.3606590856
52
0.4827434065
0.3609312174
52
0.4904536722
0.3612034036
-48
0.4832994945
0.3614756443
-48
0.476179657
0.3617479394
-48
0.4690939946
0.362020289
52
0.4767332834
0.3622926931
-48
0.4696449636
0.3625651516
-48
0.4625906678
0.3628376647
-48
0.4555702326
0.3631102322
52
0.4631391978
0.3633828542
52
0.4707475216
0.3636555308
52
0.4783954087
0.3639282619
52
0.4860830649
0.3642010476
52
0.4938106968
0.3644738878
52
0.5015785124
0.3647467826
52
0.5093867207
0.3650197319
52
0.5172355316
0.3652927359
-48
0.5099528011
0.3655657944
-48
0.5027050276
0.3658389076
-48
0.4954920435
0.3661120754
-48
0.4883136817
0.3663852978
-48
0.481169776
0.3666585748
52
0.4888718589
0.3669319065
52
0.4966139925
0.3672052929
-48
0.4894302454
0.367478734
52
0.4971752826
0.3677522297
52
0.5049605941
0.3680257802
-48
0.4977367833
0.3682993853
52
0.5055250145
0.3685730452
-48
0.4982984945
0.3688467598
52
0.5060896466
0.3691205292
52
0.5139213128
0.3693943533
-48
0.5066544905
0.3696682321
52
0.5144890939
0.3699421658
52
0.5223644371
0.3702161542
-48
0.5150570878
0.3704901975
52
0.5229353847
0.3707642955
-48
0.5156252949
0.3710384484
-48
0.5083502934
0.371312656
52
0.516193715
0.3715869186
52
0.5240779223
0.371861236
-48
0.5167623483
0.3721356082
-48
0.509481889
0.3724100353
-48
0.5022363759
0.3726845173
52
0.5100480051
0.3729590542
-48
0.5027997746
0.373233646
52
0.5106143335
0.3735082928
-48
0.5033633847
0.3737829944
-48
0.4961472404
0.374057751
52
0.5039272061
0.3743325626
-48
0.4967083555
0.3746074291
52
0.5044912389
0.3748823506
52
0.5123145934
0.3751573271
52
0.5201786293
0.3754323585
52
0.5280835581
0.375707445
-48
0.5207487571
0.3759825865
-48
0.513449163
0.376257783
-48
0.506184607
0.3765330346
-48
0.4989549209
0.3768083412
-48
0.4917599373
0.3770837028
52
0.499517089
0.3773591196
52
0.5073145778
0.3776345914
-48
0.5000794679
0.3779101183
52
0.5078798811
0.3781857003
52
0.5157208565
0.3784613375
52
0.5236026049
0.3787370297
52
0.5315253385
0.3790127771
-48
0.5241740169
0.3792885797
52
0.5320997217
0.3795644374
-48
0.5247456431
0.3798403503
-48
0.517426864
0.3801163184
52
0.5253174837
0.3803923416
-48
0.5179959598
0.3806684201
-48
0.5107095792
0.3809445538
52
0.518565269
0.3812207427
-48
0.5112761557
0.3814969869
-48
0.5040220301
0.3817732862
-48
0.4968027244
0.3820496409
52
0.5045860986
0.3823260508
52
0.5124099463
0.382602516
-48
0.5051503785
0.3828790365
52
0.5129771605
0.3831556124
-48
0.5057148701
0.3834322435
-48
0.4984874387
0.3837089299
52
0.5062795734
0.3839856717
52
0.5141122272
0.3842624688
-48
0.5068444885
0.3845393213
-48
0.499611635
0.3848162292
-48
0.4924134991
0.3850931925
-48
0.4852499143
0.3853702111
-48
0.4781207147
0.3856472851
52
0.4858069425
0.3859244146
52
0.4935331386
0.3862015995
52
0.5012995109
0.3864788398
52
0.5091062683
0.3867561356
-48
0.5018625582
0.3870334868
52
0.5096722436
0.3873108935
-48
0.5024258168
0.3875883557
-48
0.4952141729
0.3878658733
-48
0.4880371448
0.3881434465
52
0.495774938
0.3884210752
52
0.5035529677
0.3886987594
52
0.5113714431
0.3889764992
52
0.5192305746
0.3892542945
52
0.5271305736
0.3895321453
52
0.5350716526
0.3898100518
52
0.5430540252
0.3900880138
-48
0.5356473658
0.3903660314
-48
0.5282762585
0.3906441046
-48
0.5209405324
0.3909222334
-48
0.5136400179
0.3912004178
52
0.521510946
0.3914786579
-48
0.5142076934
0.3917569537
52
0.5220815734
0.392035305
52
0.5299963976
0.3923137121
-48
0.5226524149
0.3925921748
52
0.5305702075
0.3928706933
52
0.5385291726
0.3931492674
52
0.5465295243
0.3934278973
-48
0.5391061825
0.3937065829
-48
0.5317184729
0.3939853242
52
0.5396834089
0.3942641212
-48
0.5322929286
0.3945429741
52
0.5402608518
0.3948218827
-48
0.5328675997
0.395100847
52
0.5408385112
0.3953798672
52
0.5488508715
0.3956589432
-48
0.5414163873
0.395938075
52
0.5494317525
0.3962172626
-48
0.5419944801
0.396496506
52
0.5500128514
0.3967758053
52
0.5580729182
0.3970551605
52
0.5661748974
0.3973345715
-48
0.5586572579
0.3976140384
-48
0.551175703
0.3978935612
-48
0.5437300597
0.39817314
52
0.551757456
0.3984527746
-48
0.5443090202
0.3987324651
-48
0.5368963369
0.3990122116
52
0.5448881978
0.3992920141
52
0.5529216165
0.3995718725
52
0.5609968089
0.3998517869
-48
0.5535040242
0.4001317572
-48
0.5460472049
0.4004117836
-48
0.5386261783
0.4006918659
-48
0.5312407726
0.4009720043
52
0.5392032247
0.4012521987
-48
0.5318150492
0.4015324491
-48
0.5244623369
0.4018127556
-48
0.5171449177
0.4020931182
52
0.5250340713
0.4023735368
-48
0.5177139078
0.4026540115
52
0.5256060201
0.4029345423
52
0.5335391714
0.4032151292
-48
0.5261781834
0.4034957722
52
0.5341143099
0.4037764714
-48
0.5267505612
0.4040572267
-48
0.5194221585
0.4043380381
-48
0.5121289322
0.4046189057
52
0.5199920026
0.4048998295
52
0.527895961
0.4051808095
-48
0.5205620604
0.4054618457
52
0.5284689831
0.405742938
-48
0.521132332
0.4060240866
52
0.5290422201
0.4063052914
-48
0.5217028175
0.4065865525
52
0.5296156721
0.4068678698
52
0.5375696736
0.4071492434
52
0.5455650359
0.4074306732
52
0.5536019741
0.4077121594
-48
0.5461446846
0.4079937018
52
0.554184637
0.4082753005
52
0.5622663971
0.4085569556
52
0.5703901824
0.408838667
-48
0.5628523095
0.4091204347
-48
0.5553506184
0.4094022588
52
0.5634384416
0.4096841392
52
0.5715683215
0.4099660761
-48
0.5640247936
0.4102480693
-48
0.5565174746
0.4105301189
-48
0.5490461907
0.4108122249
-48
0.541610769
0.4110943874
52
0.549627145
0.4113766063
52
0.5576852061
0.4116588816
52
0.5657851692
0.4119412133
-48
0.5582694004
0.4122236016
-48
0.5507897073
0.4125060463
-48
0.5433459167
0.4127885475
-48
0.5359378563
0.4130711052
52
0.5439247331
0.4133537195
-48
0.5365138944
0.4136363902
52
0.5445037667
0.4139191175
-48
0.5370901486
0.4142019013
-48
0.5297121159
0.4144847417
-48
0.5223694977
0.4147676386
-48
0.5150621241
0.4150505922
52
0.5229404472
0.4153336023
-48
0.515630333
0.415616669
52
0.5235116108
0.4158997923
-48
0.516198755
0.4161829723
52
0.5240829886
0.4164662089
52
0.5320082201
0.4167495021
-48
0.5246545806
0.417032852
-48
0.5173362387
0.4173162586
-48
0.5100530247
0.4175997218
-48
0.5028047702
0.4178832418
-48
0.4955913073
0.4181668184
52
0.5033683821
0.4184504518
52
0.5111858977
0.4187341419
52
0.5190440643
0.4190178887
-48
0.5117526528
0.4193016923
52
0.5196137666
0.4195855526
52
0.5275157582
0.4198694697
52
0.5354588402
0.4201534436
-48
0.5280886377
0.4204374743
-48
0.5207538123
0.4207215618
52
0.5286617321
0.4210057061
-48
0.5213241558
0.4212899073
-48
0.5140217998
0.4215741653
-48
0.5067544952
0.4218584801
52
0.5145896186
0.4221428518
-48
0.5073195884
0.4224272804
52
0.5151576503
0.4227117658
52
0.52303647
0.4229963082
-48
0.515725895
0.4232809074
52
0.5236076696
0.4235655636
-48
0.5162943528
0.4238502767
-48
0.5090161399
0.4241350468
52
0.5168630239
0.4244198738
-48
0.5095820813
0.4247047578
52
0.5174319082
0.4249896987
52
0.5253225541
0.4252746967
52
0.5332542314
0.4255597516
-48
0.5258946111
0.4258448635
-48
0.5185703169
0.4261300325
52
0.5264668826
0.4264152585
52
0.5344045104
0.4267005416
-48
0.5270393687
0.4269858817
52
0.5349799734
0.4272712789
52
0.5429618693
0.4275567331
-48
0.5355556523
0.4278422445
-48
0.5281849852
0.4281278129
52
0.5361315471
0.4284134385
-48
0.5287581157
0.4286991212
52
0.5367076579
0.428984861
-48
0.5293314611
0.429270658
-48
0.5219906701
0.4295565121
-48
0.5146851149
0.4298424234
52
0.5225614775
0.4301283919
52
0.5304787972
0.4304144176
52
0.5384372869
0.4307005004
-48
0.5310527879
0.4309866405
-48
0.5237037346
0.4312728379
52
0.531626994
0.4315590924
52
0.5395914544
0.4318454043
-48
0.5322014154
0.4321317733
-48
0.5248468486
0.4324181997
52
0.5327760522
0.4327046833
52
0.5407464877
0.4329912243
52
0.5487583694
0.4332778225
52
0.5568119129
0.4335644781
-48
0.5493392157
0.433851191
-48
0.5419023875
0.4341379612
-48
0.534501256
0.4344247888
-48
0.52713565
0.4347116738
-48
0.5198053989
0.4349986161
52
0.527708387
0.4352856158
52
0.5356524706
0.4355726729
52
0.5436378634
0.4358597875
52
0.5516647803
0.4361469594
-48
0.5442167894
0.4364341888
52
0.5522467167
0.4367214757
-48
0.5447959324
0.43700882
-48
0.537380912
0.4372962217
52
0.5453752927
0.437583681
52
0.5534112442
0.4378711977
-48
0.5459548702
0.4381587719
-48
0.5385342869
0.4384464037
52
0.5465346652
0.438734093
52
0.5545766454
0.4390218398
-48
0.5471146775
0.4393096442
-48
0.5396885271
0.4395975061
-48
0.5322980221
0.4398854256
-48
0.5249429916
0.4401734027
-48
0.5176232653
0.4404614374
52
0.5255149063
0.4407495296
52
0.5334475838
0.4410376796
52
0.5414215112
0.4413258871
-48
0.534022688
0.4416141523
52
0.5419996059
0.4419024751
-48
0.5345980078
0.4421908556
52
0.5425779175
0.4424792938
52
0.5505993226
0.4427677896
-48
0.5431564459
0.4430563432
52
0.5511808594
0.4433449544
-48
0.5437351913
0.4436336234
52
0.5517626143
0.4439223502
-48
0.5443141537
0.4442111346
52
0.5523445873
0.4444999769
-48
0.5448933333
0.4447888769
52
0.5529267786
0.4450778346
-48
0.5454727301
0.4453668502
-48
0.538054461
0.4456559236
-48
0.5306717996
0.4459450548
-48
0.5233245749
0.4462342438
52
0.5312458627
0.4465234906
-48
0.5238958826
0.4468127953
52
0.5318201412
0.4471021579
52
0.5397856059
0.4473915783
52
0.5477924911
0.4476810566
-48
0.5403630871
0.4479705928
52
0.5483729752
0.4482601869
52
0.5564245146
0.448549839
-48
0.548953677
0.4488395489
-48
0.5415186993
0.4491293169
-48
0.5341194096
0.4494191427
52
0.5420968305
0.4497090266
-48
0.5346947657
0.4499989684
-48
0.5273282308
0.4502889682
-48
0.5199970553
0.4505790259
52
0.52790104
0.4508691417
-48
0.520567115
0.4511593156
-48
0.5132683929
0.4514495474
52
0.5211373885
0.4517398373
-48
0.513835929
0.4520301853
52
0.5217078759
0.4523205914
52
0.5296207568
0.4526110555
52
0.5375747848
0.4529015777
-48
0.5301944258
0.453192158
-48
0.5228494925
0.4534827964
-48
0.515539815
0.453773493
-48
0.5082652239
0.4540642477
52
0.516108203
0.4543550605
-48
0.5088308837
0.4546459316
-48
0.5015884954
0.4549368607
52
0.5093967556
0.4552278481
-48
0.5021516512
0.4555188937
52
0.5099628398
0.4558099975
-48
0.5027150181
0.4561011595
-48
0.495501986
0.4563923797
52
0.5032785964
0.4566836582
52
0.5110956451
0.4569749949
-48
0.503842386
0.4572663899
52
0.5116623664
0.4575578432
-48
0.504406387
0.4578493547
-48
0.4971852364
0.4581409246
52
0.5049705996
0.4584325528
-48
0.4977467407
0.4587242393
-48
0.4905575564
0.4590159842
52
0.4983084556
0.4593077874
-48
0.4911165751
0.4595996489
52
0.4988703813
0.4598915688
-48
0.4916758034
0.4601835472
52
0.4994325176
0.4604755839
52
0.5072295667
0.460767679
-48
0.4999948648
0.4610598325
52
0.5077948381
0.4613520445
52
0.5156353712
0.4616443149
-48
0.5083603214
0.4619366438
-48
0.5011201919
0.4622290311
-48
0.493914815
0.4625214769
52
0.501683172
0.4628139812
52
0.5094919245
0.463106544
-48
0.5022463633
0.4633991653
-48
0.4950355807
0.4636918451
52
0.5028097658
0.4639845835
52
0.5106243765
0.4642773804
52
0.5184796233
0.4645702359
52
0.5263757173
0.4648631499
52
0.5343128711
0.4651561226
52
0.542291298
0.4654491538
-48
0.5348882998
0.4657422436
-48
0.5275208359
0.4660353921
52
0.5354639443
0.4663285991
52
0.5434483568
0.4666218649
-48
0.5360398047
0.4669151892
-48
0.5286668136
0.4672085723
-48
0.5213292129
0.467502014
-48
0.5140268327
0.4677955144
-48
0.5067595039
0.4680890735
52
0.5145946533
0.4683826913
-48
0.507324599
0.4686763678
52
0.5151626869
0.4689701031
-48
0.507889906
0.4692638971
-48
0.5006520344
0.4695577499
-48
0.4934489047
0.4698516615
52
0.501214839
0.4701456318
-48
0.4940090077
0.4704396609
-48
0.4868377645
0.4707337489
-48
0.4797009432
0.4710278956
-48
0.4725983787
0.4713221012
52
0.4802558903
0.4716163656
-48
0.473150662
0.4719106889
52
0.4808110454
0.472205071
-48
0.4737031524
0.472499512
-48
0.4666293773
0.4727940119
-48
0.4595895563
0.4730885707
52
0.467179422
0.4733831885
52
0.474808755
0.4736778651
52
0.4824777605
0.4739726007
52
0.4901866449
0.4742673952
52
0.4979356154
0.4745622487
52
0.5057248806
0.4748571611
-48
0.4984974012
0.4751521325
52
0.5062895877
0.475447163
52
0.5141222935
0.4757422524
52
0.5219957295
0.4760374009
-48
0.5146901499
0.4763326083
-48
0.5074196372
0.4766278749
-48
0.500184023
0.4769232004
-48
0.4929831397
0.4772185851
-48
0.4858168206
0.4775140288
52
0.4935430681
0.4778095316
-48
0.4863740613
0.4781050935
52
0.4941032064
0.4784007145
-48
0.4869315111
0.4786963947
52
0.4946635549
0.4789921339
52
0.5024358054
0.4792879324
52
0.5102484716
0.47958379
52
0.5181017636
0.4798797067
52
0.5259958928
0.4801756827
-48
0.5186711125
0.4804717178
52
0.5265682023
0.4807678121
-48
0.5192406749
0.4810639657
-48
0.5119483197
0.4813601785
-48
0.5046909678
0.4816564505
52
0.5125153608
0.4819527818
52
0.5203804407
0.4822491724
52
0.528286419
0.4825456222
52
0.5362335083
0.4828421313
-48
0.5288595875
0.4831386998
52
0.5368096574
0.4834353275
52
0.5448010676
0.4837320146
-48
0.5373860225
0.484028761
52
0.5453804298
0.4843255667
-48
0.5379626037
0.4846224318
52
0.5459600092
0.4849193563
-48
0.5385394012
0.4852163402
52
0.5465398061
0.4855133835
52
0.5545818131
0.4858104861
52
0.5626656385
0.4861076482
52
0.5707914998
0.4864048698
52
0.5789596156
0.4867021507
-48
0.5713806095
0.4869994912
52
0.5795517886
0.4872968911
52
0.5877654579
0.4875943504
-48
0.5801441837
0.4878918693
-48
0.5725594917
0.4881894477
-48
0.5650112061
0.4884870856
52
0.5731492644
0.488784783
52
0.5813296406
0.4890825399
-48
0.5737392583
0.4893803565
52
0.5819227024
0.4896782325
52
0.5901487005
0.4899761682
52
0.5984174737
0.4902741634
-48
0.5907450698
0.4905722182
-48
0.5831094935
0.4908703327
52
0.5913416629
0.4911685068
-48
0.5837032229
0.4914667405
-48
0.5761014474
0.4917650338
-48
0.5685361605
0.4920633868
-48
0.5610071869
0.4923617995
52
0.5691244243
0.4926602718
-48
0.561592627
0.4929588039
52
0.5697129087
0.4932573957
52
0.5778754158
0.4935560471
-48
0.5703016138
0.4938547583
52
0.5784671822
0.4941535293
52
0.5866752116
0.49445236
52
0.5949259227
0.4947512505
-48
0.5872702782
0.4950502007
52
0.5955240837
0.4953492108
-48
0.5878655681
0.4956482806
-48
0.5802438134
0.4959474103
-48
0.5726586431
0.4962465997
52
0.580836468
0.4965458491
52
0.5890568176
0.4968451582
52
0.5973199131
0.4971445273
-48
0.5896527775
0.4974439562
52
0.5979189719
0.497743445
52
0.6062281506
0.4980429937
52
0.614580537
0.4983426023
52
0.6229763558
0.4986422708
-48
0.6151860693
0.4989419992
-48
0.6074331761
0.4992417876
-48
0.5997174969
0.499541636
52
0.6080360279
0.4998415443
52
0.6163978152
0.5001415126
52
0.6248030839
0.5004415409
52
0.6332520599
0.5007416292
-48
0.62541245
0.5010417776
52
0.6338645947
0.5013419859
52
0.6423606906
0.5016422543
52
0.6509009662
0.5019425828
-48
0.6429766416
0.5022429713
52
0.6515201201
0.5025434199
-48
0.6435928235
0.5028439286
-48
0.635703578
0.5031444973
52
0.6442092366
0.5034451262
-48
0.6363170323
0.5037458153
52
0.6448258808
0.5040465644
-48
0.6369307166
0.5043473737
-48
0.6290734492
0.5046482432
-48
0.6212538966
0.5049491729
52
0.6296844169
0.5052501627
52
0.6381587758
0.5055512127
52
0.6466772015
0.505852323
-48
0.6387731509
0.5061534934
52
0.6472947713
0.5064547241
52
0.6558607041
0.5067560151
52
0.6644711798
0.5070573663
-48
0.6564817181
0.5073587778
-48
0.6485306059
0.5076602495
52
0.657102965
0.5079617816
52
0.6657199004
0.5082633739
52
0.6743816439
0.5085650266
52
0.6830884285
0.5088667396
52
0.6918404883
0.509168513
52
0.7006380588
0.5094703467
52
0.7094813767
0.5097722407
-48
0.7012758661
0.5100741952
52
0.7101225006
0.51037621
52
0.7190151376
0.5106782853
52
0.7279540163
0.5109804209
52
0.7369393772
0.511282617
52
0.745971462
0.5115848735
-48
0.737590799
0.5118871905
52
0.7466262711
0.5121895679
52
0.7557087277
0.5124920058
-48
0.7472813258
0.5127945042
-48
0.7388943755
0.5130970631
-48
0.7305476825
0.5133996826
-48
0.7222410536
0.5137023625
-48
0.7139742965
0.514005103
-48
0.7057472199
0.514307904
-48
0.6975596333
0.5146107656
-48
0.689411347
0.5149136877
-48
0.6813021726
0.5152166705
52
0.6900449439
0.5155197138
52
0.6988331776
0.5158228177
52
0.7076671101
0.5161259823
-48
0.699470308
0.5164292075
52
0.7083075536
0.5167324933
-48
0.7001076773
0.5170358398
-48
0.6919471604
0.517339247
-48
0.6838258141
0.5176427149
-48
0.6757434502
0.5179462434
-48
0.6676998816
0.5182498326
52
0.676371921
0.5185534826
-48
0.6683253358
0.5188571933
52
0.6770006275
0.5191609647
52
0.6857210308
0.5194647969
-48
0.6776295698
0.5197686899
-48
0.6695769479
0.5200726436
-48
0.6615629786
0.5203766582
52
0.670203106
0.5206807335
52
0.6788881622
0.5209848696
-48
0.670829499
0.5212890666
52
0.6795178124
0.5215933244
-48
0.6714561269
0.5218976431
52
0.6801476988
0.5222020226
-48
0.6720829898
0.522506463
-48
0.6640569915
0.5228109643
52
0.6727100878
0.5231155265
-48
0.6646810794
0.5234201496
-48
0.6566906102
0.5237248337
52
0.6653054014
0.5240295786
-48
0.6573119355
0.5243343845
52
0.6659299575
0.5246392514
52
0.6745927933
0.5249441793
-48
0.6665547479
0.5252491681
-48
0.6585552851
0.5255542179
-48
0.6505942197
0.5258593288
-48
0.6426713675
0.5261645006
52
0.6512132586
0.5264697335
52
0.6597995675
0.5267750275
52
0.6684305253
0.5270803825
-48
0.6604220588
0.5273857986
-48
0.6524520329
0.5276912757
-48
0.6445202631
0.527996814
52
0.6530717685
0.5283024133
52
0.6616677417
0.5286080738
52
0.670308414
0.5289137954
-48
0.6622909336
0.5292195782
52
0.6709348464
0.5295254221
52
0.6796237076
0.5298313272
52
0.6883577509
0.5301372935
-48
0.6802536337
0.5304433209
52
0.6889909526
0.5307494096
-48
0.680883796
0.5310555595
52
0.6896243918
0.5313617706
52
0.6984104386
0.5316680429
-48
0.6902580685
0.5319743765
52
0.6990474104
0.5322807714
52
0.707882457
0.5325872276
-48
0.6996846212
0.532893745
52
0.7085229812
0.5332003238
52
0.7174073007
0.5335069638
52
0.7263378187
0.5338136652
52
0.7353147753
0.534120428
52
0.7443384122
0.534427252
52
0.7534089719
0.5347341375
52
0.7625266986
0.5350410843
52
0.7716918374
0.5353480925
-48
0.7631877166
0.5356551622
-48
0.7547244155
0.5359622932
52
0.7638489825
0.5362694857
52
0.7730209972
0.5365767395
52
0.7822407064
0.5368840549
-48
0.773685951
0.5371914317
52
0.782909118
0.53749887
52
0.7921802454
0.5378063698
52
0.8014995826
0.538113931
-48
0.7928523846
0.5384215538
52
0.802175217
0.5387292381
-48
0.793524776
0.539036984
52
0.8028511048
0.5393447914
-48
0.7941974195
0.5396526603
-48
0.7855852719
0.5399605909
-48
0.7770144626
0.540268583
-48
0.7684847932
0.5405766367
-48
0.7599960662
0.540884752
52
0.7691480457
0.541192929
52
0.7783476156
0.5415011676
52
0.7875950232
0.5418094678
52
0.7968905173
0.5421178297
-48
0.7882654428
0.5424262533
52
0.7975644231
0.5427347385
52
0.8069117581
0.5430432855
52
0.8163076993
0.5433518941
-48
0.8075894223
0.5436605645
-48
0.7989129931
0.5439692966
52
0.8082673406
0.5442780905
-48
0.7995876574
0.5445869461
-48
0.7909496366
0.5448958635
-48
0.7823530784
0.5452048427
52
0.7916213144
0.5455138836
-48
0.7830215321
0.5458229864
-48
0.7744630287
0.546132151
-48
0.7659456062
0.5464413774
-48
0.7574690673
0.5467506657
52
0.7666079064
0.5470600158
52
0.7757942675
0.5473694278
-48
0.7672704551
0.5476789017
-48
0.7587875569
0.5479884375
52
0.7679332522
0.5482980352
52
0.7771265051
0.5486076948
52
0.7863675629
0.5489174163
52
0.7956566742
0.5492271998
52
0.8049940889
0.5495370453
-48
0.7963301173
0.5498469527
52
0.8056710339
0.5501569221
-48
0.797003813
0.5504669534
-48
0.7883781947
0.5507770468
-48
0.7797939793
0.5510872022
52
0.789048908
0.5513974197
52
0.7983519623
0.5517076992
52
0.8077033925
0.5520180407
52
0.8171034502
0.5523284443
-48
0.8083813536
0.55263891
52
0.8177849367
0.5529494378
52
0.8272374183
0.5532600277
-48
0.8184666787
0.5535706797
52
0.8279227055
0.5538813938
-48
0.8191486765
0.5541921701
52
0.8286082496
0.5545030085
52
0.8381170125
0.5548139091
-48
0.8292940508
0.5551248719
-48
0.8205134394
0.5554358969
-48
0.8117749749
0.5557469841
52
0.8211962047
0.5560581335
-48
0.812454463
0.5563693451
-48
0.8037546815
0.556680619
-48
0.7950966591
0.5569919551
52
0.8044311617
0.5573033535
-48
0.7957698921
0.5576148141
-48
0.7871501966
0.5579263371
52
0.7964433777
0.5582379224
52
0.8057848832
0.55854957
-48
0.7971171158
0.5588612799
52
0.8064621248
0.5591730521
52
0.8158557278
0.5594848867
52
0.8252981776
0.5597967837
-48
0.8165367464
0.5601087431
52
0.8259827374
0.5604207648
-48
0.8172180203
0.560732849
-48
0.8084953738
0.5610449955
52
0.8178995498
0.5613572045
52
0.8273526274
0.561669476
-48
0.8185813348
0.5619818099
-48
0.8098521444
0.5622942062
52
0.8192633755
0.5626066651
-48
0.8105309113
0.5629191864
52
0.8199456721
0.5632317703
-48
0.8112099329
0.5635444166
52
0.8206282245
0.5638571255
52
0.8300954913
0.5641698969
-48
0.8213110329
0.5644827309
52
0.8307818503
0.5647956274
52
0.8403019159
0.5651085866
52
0.8498714859
0.5654216083
52
0.8594908176
0.5657346926
52
0.8691601698
0.5660478395
-48
0.860188201
0.5663610491
52
0.8698611797
0.5666743213
-48
0.860885846
0.5669876562
-48
0.851953594
0.5673010537
52
0.8615837526
0.5676145139
-48
0.8526481506
0.5679280368
-48
0.8437554395
0.5682416224
-48
0.8349054134
0.5685552708
-48
0.8260978674
0.5688689818
-48
0.8173325977
0.5691827556
52
0.8267827272
0.5694965922
52
0.8362819973
0.5698104915
52
0.8458306637
0.5701244536
-48
0.8369706765
0.5704384785
-48
0.8281532173
0.5707525662
52
0.837659614
0.5710667167
-48
0.8288388479
0.57138093
-48
0.8200604214
0.5716952062
-48
0.8113241314
0.5720095453
-48
0.8026297756
0.5723239472
-48
0.7939771526
0.5726384119
-48
0.7853660623
0.5729529396
52
0.7946499658
0.5732675302
52
0.8039821456
0.5735821837
52
0.8133628528
0.5738969002
52
0.8227923396
0.5742116795
52
0.8322708598
0.5745265219
52
0.8417986683
0.5748414272
-48
0.8329580347
0.5751563955
52
0.8424894164
0.5754714267
52
0.8520703614
0.575786521
-48
0.8431804237
0.5761016783
-48
0.8343331576
0.5764168987
-48
0.8255283585
0.5767321821
-48
0.8167658224
0.5770475285
-48
0.8080453464
0.577362938
-48
0.7993667288
0.5776784106
-48
0.7907297685
0.5779939463
-48
0.7821342656
0.5783095451
52
0.7914013637
0.578625207
-48
0.7828026372
0.578940932
-48
0.7742451845
0.5792567202
52
0.7834712595
0.5795725715
52
0.7927453101
0.579888486
-48
0.7841401326
0.5802044637
52
0.7934176613
0.5805205046
-48
0.7848092565
0.5808366087
52
0.7940902646
0.5811527761
52
0.803419534
0.5814690066
-48
0.7947631202
0.5817853004
52
0.8040958885
0.5821016575
-48
0.7954362282
0.5824180778
-48
0.7868181343
0.5827345614
-48
0.7782414072
0.5830511083
-48
0.7697058485
0.5833677186
52
0.7789083189
0.5836843921
-48
0.770369559
0.584001129
52
0.7795754807
0.5843179292
52
0.7888292732
0.5846347928
-48
0.7802428927
0.5849517198
-48
0.7716977268
0.5852687101
-48
0.7631935777
0.5855857638
-48
0.7547302485
0.585902881
-48
0.7463075433
0.5862200616
52
0.7553883426
0.5865373056
52
0.7645163619
0.586854613
-48
0.7560466834
0.587171984
52
0.7651781262
0.5874894184
52
0.7743570524
0.5878069162
52
0.7835837091
0.5881244776
-48
0.7750225073
0.5884421025
52
0.7842526243
0.5887597909
52
0.793530738
0.5890775429
-48
0.7849217904
0.5893953584
-48
0.7763541658
0.5897132375
-48
0.7678276658
0.5900311801
52
0.7770203697
0.5903491864
52
0.7862608756
0.5906672562
52
0.7955494322
0.5909853897
52
0.8048862892
0.5913035867
52
0.8142716979
0.5916218474
-48
0.8055631938
0.5919401718
-48
0.7968964904
0.5922585599
52
0.8062403522
0.5925770116
-48
0.7975703985
0.592895527
52
0.8069177646
0.5932141061
52
0.8163137369
0.5935327489
52
0.8257585684
0.5938514554
52
0.8352525129
0.5941702257
-48
0.8264433009
0.5944890598
-48
0.817676373
0.5948079576
52
0.8271282902
0.5951269192
-48
0.8183580744
0.5954459446
-48
0.8096299556
0.5957650338
52
0.8190400314
0.5960841868
-48
0.8103086392
0.5964034036
-48
0.8016191578
0.5967226843
-48
0.7929713858
0.5970420288
52
0.802294837
0.5973614372
-48
0.7936438218
0.5976809095
-48
0.7850343315
0.5980004457
-48
0.7764661667
0.5983200458
-48
0.7679391291
0.5986397098
52
0.7771324125
0.5989594377
52
0.7863735011
0.5992792296
-48
0.7777989083
0.5995990855
-48
0.7692654735
0.5999190053
-48
0.7607729992
0.6002389891
52
0.7699290188
0.6005590369
52
0.7791326497
0.6008791487
-48
0.770592813
0.6011993245
52
0.7797998956
0.6015195644
-48
0.7712568561
0.6018398683
-48
0.7627548232
0.6021602363
52
0.7719211483
0.6024806683
52
0.7811351383
0.6028011645
-48
0.7725856896
0.6031217247
52
0.7818031352
0.603442349
52
0.7910685115
0.6037630375
52
0.8003820678
0.6040837901
52
0.8097440545
0.6044046069
52
0.8191547236
0.6047254878
-48
0.8104227809
0.6050464329
-48
0.8017327516
0.6053674422
52
0.8111017619
0.6056885157
-48
0.8024084734
0.6060096534
52
0.8117809975
0.6063308553
52
0.8212022587
0.6066521215
-48
0.8124604878
0.6069734519
-48
0.8037606775
0.6072948466
52
0.813140233
0.6076163055
52
0.8225685622
0.6079378288
52
0.8320459188
0.6082594164
52
0.8415725575
0.6085810683
-48
0.8327330093
0.6089027845
52
0.8422632209
0.609224565
52
0.8518429897
0.6095464099
52
0.8614725732
0.6098683192
-48
0.8525375049
0.6101902929
52
0.8621706999
0.6105123309
52
0.8718539875
0.6108344334
-48
0.8628690884
0.6111566003
52
0.8725560076
0.6114788316
-48
0.8635677388
0.6118011274
-48
0.8546226137
0.6121234876
52
0.8642666512
0.6124459123
-48
0.8553181713
0.6127684015
52
0.8649658258
0.6130909552
-48
0.8560139898
0.6134135734
-48
0.8471051227
0.6137362561
-48
0.8382390181
0.6140590033
-48
0.8294154708
0.6143818151
-48
0.8206342766
0.6147046915
-48
0.811895232
0.6150276324
-48
0.8031981349
0.615350638
-48
0.7945427839
0.6156737081
52
0.8038744064
0.6159968428
52
0.8132545533
0.6163200422
-48
0.8045509314
0.6166433062
52
0.8139345963
0.6169666349
-48
0.8052277102
0.6172900282
52
0.8146148943
0.6176134862
-48
0.8059047428
0.6179370089
52
0.8152954475
0.6182605963
-48
0.8065820293
0.6185842484
-48
0.7979104356
0.6189079653
52
0.8072595698
0.6192317469
52
0.8166573196
0.6195555932
-48
0.8079373645
0.6198795043
52
0.8173386388
0.6202034802
52
0.8267887997
0.6205275209
-48
0.8180202134
0.6208516264
-48
0.8092937164
0.6211757968
52
0.8187020437
0.6215000319
-48
0.8099722739
0.6218243319
52
0.8193841298
0.6221486968
52
0.8288449272
0.6224731265
52
0.8383549208
0.6227976211
-48
0.8295308172
0.6231221807
-48
0.8207490693
0.6234468051
-48
0.8120094738
0.6237714945
52
0.821431923
0.6240962488
52
0.830903369
0.624421068
-48
0.8221150329
0.6247459522
52
0.831590031
0.6250709014
-48
0.8227983989
0.6253959156
-48
0.8140489666
0.6257209948
-48
0.8053415315
0.626046139
-48
0.7966758922
0.6263713482
52
0.8060186068
0.6266966225
-48
0.7973497175
0.6270219618
52
0.806695936
0.6273473662
52
0.8160907549
0.6276728357
52
0.8255344268
0.6279983702
-48
0.8167718616
0.6283239699
52
0.8262190753
0.6286496347
-48
0.8174532237
0.6289753646
52
0.8269039805
0.6293011597
52
0.8364038812
0.6296270199
-48
0.8275891425
0.6299529453
52
0.8370926061
0.6302789359
52
0.8466454876
0.6306049917
-48
0.8377815893
0.6309311127
52
0.8473380535
0.6312572989
52
0.8569442114
0.6315835504
-48
0.8480308792
0.6319098671
-48
0.839160331
0.6322362491
-48
0.8303323614
0.6325626963
-48
0.8215467661
0.6328892089
52
0.8310188093
0.6332157867
-48
0.822229919
0.6335424299
52
0.8317055145
0.6338691384
-48
0.8229133281
0.6341959122
52
0.8323924774
0.6345227514
-48
0.8235969935
0.6348496559
-48
0.8148437279
0.6351766258
-48
0.806132478
0.6355036612
52
0.8155243669
0.6358307619
52
0.8249650936
0.6361579281
-48
0.8162052612
0.6364851596
-48
0.8074874759
0.6368124567
-48
0.798811536
0.6371398192
52
0.808165356
0.6374672471
-48
0.7994861623
0.6377947406
52
0.8088434904
0.6381222995
-48
0.8001610416
0.638449924
-48
0.7915202686
0.638777614
52
0.800836174
0.6391053695
-48
0.7921921604
0.6394331906
-48
0.783589638
0.6397610772
-48
0.7750284077
0.6400890294
-48
0.7665082714
0.6404170472
52
0.7756941144
0.6407451306
-48
0.7671707826
0.6410732797
-48
0.7586883629
0.6414014943
52
0.7678335424
0.6417297746
52
0.7770262768
0.6420581206
-48
0.7684965507
0.6423865322
-48
0.7600077672
0.6427150095
52
0.7691598076
0.6430435525
-48
0.7606678405
0.6433721612
-48
0.7522166349
0.6437008356
52
0.7613281614
0.6440295758
52
0.7704870678
0.6443583817
-48
0.7619887299
0.6446872534
52
0.7711510713
0.6450161909
52
0.7803610569
0.6453451941
-48
0.7718153238
0.6456742631
52
0.7810287635
0.646003398
-48
0.7724798254
0.6463325987
52
0.7816967205
0.6466618652
52
0.7909615435
0.6469911976
-48
0.7823649281
0.6473205958
-48
0.7738095764
0.6476500599
52
0.7830333862
0.6479795899
52
0.7923051598
0.6483091858
52
0.8016251466
0.6486388477
-48
0.7929773459
0.6489685755
52
0.8023008281
0.6492983692
52
0.8116727924
0.6496282288
52
0.821093491
0.6499581545
-48
0.8123522422
0.6502881461
-48
0.8036529514
0.6506182038
52
0.8130319468
0.6509483274
52
0.8224597129
0.6512785171
52
0.8319365034
0.6516087728
52
0.8414625732
0.6519390945
-48
0.8326235529
0.6522694823
52
0.8421531954
0.6525999362
52
0.851732392
0.6529304562
-48
0.8428440765
0.6532610423
-48
0.8339984249
0.6535916945
52
0.8435352167
0.6539224129
-48
0.8346862477
0.6542531973
-48
0.8258797537
0.654584048
-48
0.8171155309
0.6549149648
52
0.8265645316
0.6552459478
52
0.8360626672
0.655576997
52
0.8456101931
0.6559081124
-48
0.8367512642
0.656239294
-48
0.8279348581
0.6565705419
-48
0.8191607708
0.656901856
-48
0.8104287991
0.6572332363
52
0.8198430288
0.657564683
-48
0.8111077823
0.6578961959
52
0.8205255428
0.6582277752
52
0.8299922756
0.6585594207
-48
0.8212083127
0.6588911326
-48
0.8124665128
0.6592229108
-48
0.8037666735
0.6595547554
-48
0.7951085935
0.6598866664
-48
0.7864920722
0.6602186437
-48
0.7779169103
0.6605506874
52
0.7871620782
0.6608827976
52
0.796455321
0.6612149741
52
0.8057968887
0.6615472171
-48
0.7971290636
0.6618795266
52
0.8064741347
0.6622119025
-48
0.7978030589
0.6625443448
52
0.8071516348
0.6628768537
-48
0.7984773069
0.6632094291
52
0.8078293889
0.663542071
52
0.8172301018
0.6638747794
52
0.8266796983
0.6642075543
-48
0.8179116357
0.6645403958
52
0.8273647763
0.6648733039
-48
0.8185934253
0.6652062786
-48
0.8098641769
0.6655393198
-48
0.8011768288
0.6658724277
-48
0.7925311801
0.6662056022
52
0.8018523422
0.6665388433
-48
0.793203451
0.6668721511
52
0.8025281089
0.6672055255
52
0.8119012551
0.6675389666
-48
0.803204129
0.6678724744
-48
0.7945487492
0.6682060489
52
0.8038804027
0.6685396901
52
0.8132605808
0.668873398
-48
0.80455693
0.6692071727
-48
0.7958950568
0.6695410142
-48
0.7872747605
0.6698749224
52
0.7965685892
0.6702088973
-48
0.78794506
0.6705429391
52
0.7972423743
0.6708770477
52
0.8065880347
0.6712112231
52
0.8159822924
0.6715454654
-48
0.8072655774
0.6718797745
52
0.8166633584
0.6722141504
52
0.8261100079
0.6725485932
52
0.83560578
0.672883103
52
0.84515093
0.6732176796
52
0.8547457148
0.6735523231
52
0.8643903926
0.6738870336
-48
0.8554413187
0.674221811
52
0.8650896135
0.6745566554
52
0.8747880795
0.6748915667
-48
0.8657890967
0.675226545
52
0.8754912
0.6755615903
52
0.8852437543
0.6758967026
52
0.8950470218
0.676231882
-48
0.8859507961
0.6765671283
52
0.8957577402
0.6769024418
-48
0.8866581031
0.6772378223
-48
0.8776021442
0.6775732698
52
0.8873656753
0.6779087845
52
0.8971799769
0.6782443662
-48
0.888073513
0.6785800151
-48
0.8790107601
0.6789157311
52
0.8887816161
0.6792515143
52
0.8986032805
0.6795873646
-48
0.8894899847
0.679923282
52
0.8993153326
0.6802592667
-48
0.890198619
0.6805953185
52
0.9000276519
0.6809314376
52
0.9099077956
0.6812676239
52
0.9198393162
0.6816038774
52
0.9298224806
0.6819401982
52
0.9398575575
0.6822765862
-48
0.9305462413
0.6826130416
-48
0.9212796193
0.6829495642
52
0.9312702733
0.6832861541
-48
0.922000176
0.6836228113
-48
0.9127745752
0.6839595359
-48
0.9035932572
0.6842963278
-48
0.8944560096
0.684633187
52
0.9043071808
0.6849701137
52
0.9142095782
0.6853071077
52
0.924163468
0.6856441691
52
0.934169118
0.685981298
52
0.9442267974
0.6863184942
52
0.9543367768
0.6866557579
-48
0.9449559602
0.6869930891
52
0.9550697312
0.6873304877
-48
0.9456853965
0.6876679538
-48
0.9363461066
0.6880054874
52
0.9464151064
0.6883430885
-48
0.9370723138
0.6886807571
52
0.9471450899
0.6890184932
-48
0.9377987934
0.6893562969
52
0.9478753472
0.6896941682
52
0.958004299
0.690032107
52
0.9681859213
0.6903701134
-48
0.9587386289
0.6907081875
52
0.9689240698
0.6910463291
-48
0.9594732342
0.6913845384
52
0.9696624951
0.6917228153
52
0.97990474
0.6920611598
-48
0.9704011973
0.6923995721
52
0.9806472835
0.692738052
-48
0.9711401766
0.6930765996
52
0.9813901055
0.6934152149
-48
0.971879433
0.693753898
52
0.982133206
0.6940926487
52
0.9924402987
0.6944314673
-48
0.9828765853
0.6947703536
-48
0.9733587776
0.6951093076
-48
0.9638866555
0.6954483295
-48
0.9544599996
0.6957874192
-48
0.9450785916
0.6961265767
-48
0.9357422143
0.696465802
52
0.9458080738
0.6968050951
-48
0.9364681951
0.6971444561
52
0.9465378297
0.697483885
52
0.9566598264
0.6978233818
-48
0.9472678593
0.6981629465
52
0.9573936521
0.6985025791
52
0.9675720991
0.6988422796
-48
0.958127753
0.6991820481
52
0.9683100174
0.6995218845
-48
0.9588621293
0.6998617888
-48
0.949459591
0.7002017612
-48
0.940102185
0.7005418015
52
0.9501907164
0.7008819099
-48
0.9408298009
0.7012220863
52
0.9509221159
0.7015623307
52
0.9610669109
0.7019026432
-48
0.9516537897
0.7022430237
-48
0.9422858515
0.7025834723
52
0.952385738
0.702923989
-48
0.9430142864
0.7032645738
-48
0.9336878178
0.7036052267
52
0.9437429945
0.7039459478
-48
0.9344130281
0.7042867369
52
0.9444719759
0.7046275943
-48
0.9351385104
0.7049685198
52
0.9452012306
0.7053095135
-48
0.9358642647
0.7056505754
52
0.9459307589
0.7059917055
52
0.9560495989
0.7063329039
52
0.9662210568
0.7066741705
-48
0.9567831957
0.7070155053
-48
0.9473906364
0.7073569084
-48
0.9380431613
0.7076983798
52
0.9481209857
0.7080399195
-48
0.938770005
0.7083815274
-48
0.929463909
0.7087232037
52
0.9394971213
0.7090649484
-48
0.9301875351
0.7094067614
-48
0.920922635
0.7097486427
-48
0.9117022063
0.7100905925
52
0.9216430578
0.7104326106
-48
0.9124191711
0.7107746971
-48
0.9032395591
0.711116852
52
0.9131364048
0.7114590754
-48
0.9039533501
0.7118013672
-48
0.894814374
0.7121437275
52
0.9046674087
0.7124861562
52
0.9145716792
0.7128286535
-48
0.9053817352
0.7131712192
-48
0.8962359029
0.7135138534
52
0.9060963296
0.7138565562
-48
0.8969470672
0.7141993275
-48
0.8878417212
0.7145421674
-48
0.878780081
0.7148850758
52
0.8885497374
0.7152280528
-48
0.8794846987
0.7155710984
52
0.8892580191
0.7159142127
-48
0.8801895806
0.7162573955
-48
0.8711646706
0.716600647
52
0.8808947269
0.7169439671
-48
0.8718664322
0.7172873559
52
0.8816001377
0.7176308134
52
0.8913844584
0.7179743395
52
0.9012196576
0.7183179344
52
0.9111059998
0.718661598
52
0.921043751
0.7190053303
-48
0.911822741
0.7193491314
-48
0.9026459918
0.7196930012
52
0.912539751
0.7200369398
52
0.9224849577
0.7203809472
52
0.9324818795
0.7207250234
-48
0.9232059664
0.7210691684
52
0.9332066375
0.7214133822
52
0.943259312
0.7217576649
52
0.9533642604
0.7221020164
-48
0.943988112
0.7224464368
-48
0.934656969
0.7227909261
-48
0.9253706156
0.7231354843
-48
0.9161288366
0.7234801114
-48
0.9069314182
0.7238248074
52
0.9168474616
0.7241695724
-48
0.9076465938
0.7245144063
-48
0.8984898901
0.7248593092
52
0.9083620375
0.7252042811
52
0.9182855201
0.7255493219
-48
0.9090777496
0.7258944318
-48
0.8999141764
0.7262396107
-48
0.8907945884
0.7265848586
52
0.9006267202
0.7269301756
-48
0.891503712
0.7272755616
52
0.9013395313
0.7276210167
52
0.9112264969
0.7279665409
52
0.9211648746
0.7283121342
52
0.931154932
0.7286577966
52
0.9411969376
0.7290035282
-48
0.9318791923
0.7293493289
52
0.9419249641
0.7296951988
52
0.9520229739
0.7300411378
52
0.9621734934
0.730387146
-48
0.9527550606
0.7307332235
52
0.962909387
0.7310793701
-48
0.9534874219
0.731425586
-48
0.9441106823
0.7317718711
-48
0.934778951
0.7321182255
52
0.9448398015
0.7324646491
-48
0.9355045705
0.7328111421
52
0.9455691943
0.7331577043
-48
0.9362304621
0.7335043358
-48
0.9269365559
0.7338510367
-48
0.9176872604
0.7341978069
52
0.9276592342
0.7345446465
52
0.9376830622
0.7348915554
-48
0.9283821835
0.7352385337
-48
0.919125949
0.7355855814
52
0.929105404
0.7359326985
-48
0.919845698
0.7362798851
-48
0.9106304387
0.736627141
-48
0.9014594126
0.7369744665
52
0.9113470015
0.7373218614
-48
0.9021725359
0.7376693257
52
0.9120638331
0.7380168596
52
0.922006565
0.738364463
-48
0.9127809335
0.7387121359
-48
0.903599585
0.7390598783
52
0.9134983029
0.7394076903
-48
0.904313511
0.7397555718
-48
0.8951728062
0.7401035229
52
0.9050277048
0.7404515436
-48
0.8958835718
0.7407996339
-48
0.8867833306
0.7411477939
52
0.896594604
0.7414960234
52
0.9064568959
0.7418443226
52
0.9163704718
0.7421926915
-48
0.9071718935
0.74254113
-48
0.8980174684
0.7428896382
-48
0.8889069846
0.7432382162
52
0.8987293009
0.7435868638
52
0.9086026932
0.7439355812
-48
0.8994414003
0.7442843683
52
0.9093184956
0.7446332252
52
0.9192469518
0.7449821518
52
0.9292270359
0.7453311483
-48
0.9199667462
0.7456802145
-48
0.9107509058
0.7460293505
-48
0.9015793014
0.7463785564
52
0.9114675138
0.7467278321
-48
0.9022924697
0.7470771777
52
0.9121843906
0.7474265931
-48
0.9030059055
0.7477760784
-48
0.8938714771
0.7481256336
52
0.9037196088
0.7484752588
52
0.9136189508
0.7488249538
52
0.9235697693
0.7491747188
-48
0.9143366344
0.7495245538
-48
0.9051478186
0.7498744587
-48
0.8960031091
0.7502244336
-48
0.8869022941
0.7505744784
52
0.8967141861
0.7509245933
52
0.9065770998
0.7512747783
52
0.9164913008
0.7516250332
52
0.9264570555
0.7519753582
-48
0.9172100617
0.7523257533
-48
0.9080074534
0.7526762184
52
0.9179290921
0.7530267537
-48
0.9087230325
0.753377359
-48
0.8995611619
0.7537280345
52
0.90943888
0.7540787801
52
0.9193679621
0.7544295959
-48
0.9101549959
0.7547804818
-48
0.9009862519
0.7551314379
52
0.9108713805
0.7554824642
52
0.9208079116
0.7558335607
-48
0.9115880337
0.7561847274
52
0.9215282914
0.7565359643
52
0.9315202385
0.7568872715
52
0.9415641438
0.757238649
52
0.9516602773
0.7575900967
-48
0.942292308
0.7579416147
-48
0.9329693049
0.7582932031
52
0.9430207453
0.7586448617
52
0.9531244532
0.7589965907
52
0.9632807003
0.75934839
52
0.97348976
0.7597002597
52
0.9837519067
0.7600521997
52
0.9940674167
0.7604042102
52
1.0044365672
0.760756291
-48
0.9948152717
0.7611084423
-48
0.9852401584
0.7614606639
52
0.9955634072
0.7618129561
-48
0.9859847029
0.7621653187
52
0.9963118233
0.7625177517
52
1.0066926448
0.7628702553
52
1.0171274465
0.7632228293
-48
1.0074452348
0.7635754739
52
1.01788395
0.763928189
-48
1.0081981071
0.7642809746
-48
0.9985587562
0.7646338308
52
1.0089512617
0.7649867576
52
1.0193978082
0.7653397549
52
1.0298986768
0.7656928229
-48
1.0201551632
0.7660459615
-48
1.0104584184
0.7663991706
-48
1.000808218
0.7667524505
-48
0.9912043386
0.767105801
52
1.0015586011
0.7674592221
52
1.0119667058
0.767812714
52
1.0224289327
0.7681662765
-48
1.0127212738
0.7685199098
-48
1.0030602117
0.7688736138
-48
0.9934455227
0.7692273885
-48
0.9838769842
0.769581234
-48
0.9743543747
0.7699351502
52
0.9846210174
0.7702891372
52
0.9949410467
0.7706431951
-48
0.9853653297
0.7709973237
-48
0.9758355761
0.7713515232
-48
0.9663515653
0.7717057935
-48
0.9569130778
0.7720601346
-48
0.9475198951
0.7724145467
52
0.9576469985
0.7727690296
52
0.9678267629
0.7731235834
52
0.9780594621
0.7734782081
-48
0.9685647767
0.7738329037
-48
0.9591156657
0.7741876703
-48
0.9497119105
0.7745425078
-48
0.9403532934
0.7748974163
52
0.9504431305
0.7752523958
-48
0.9410810035
0.7756074463
52
0.9511746247
0.7759625678
52
0.9613207327
0.7763177603
52
0.9715196005
0.7766730239
-48
0.9620563065
0.7770283585
52
0.9722589992
0.7773837641
-48
0.962792156
0.7777392409
52
0.9729986753
0.7780947887
52
0.9832582684
0.7784504077
52
0.9935712114
0.7788060978
-48
0.9840020696
0.779161859
52
0.9943188803
0.7795176914
-48
0.9847461497
0.7798735949
-48
0.9752193682
0.7802295696
52
0.9854905089
0.7805856155
52
0.9958150595
0.7809417327
-48
0.9862351472
0.781297921
52
0.99656357
0.7816541806
-48
0.9869800649
0.7820105114
-48
0.9774425606
0.7823669135
52
0.9877252619
0.7827233869
-48
0.9781841806
0.7830799316
-48
0.9686888966
0.7834365476
52
0.9789260788
0.7837932349
-48
0.9694272336
0.7841499935
-48
0.9599739829
0.7845068235
52
0.9701658476
0.7848637249
-48
0.9607090516
0.7852206976
-48
0.9512976481
0.7855777418
52
0.9614443959
0.7859348573
-48
0.9520294628
0.7862920443
52
0.962180016
0.7866493027
52
0.9723833521
0.7870066326
-48
0.962915912
0.7873640339
-48
0.9534939156
0.7877215067
52
0.963652084
0.788079051
-48
0.954226554
0.7884366668
52
0.964388532
0.7887943542
-48
0.9549594671
0.789152113
-48
0.9455756616
0.7895099434
-48
0.9362368985
0.7898678454
52
0.9463053303
0.790225819
52
0.9564261181
0.7905838642
52
0.9665995339
0.7909419809
-48
0.9571598561
0.7913001693
52
0.9673370874
0.7916584294
-48
0.9578938693
0.7920167611
-48
0.9484959788
0.7923751644
-48
0.9391431981
0.7927336394
52
0.9492267427
0.7930921862
52
0.9593627218
0.7934508046
-48
0.9499577807
0.7938094948
52
0.9600975612
0.7941682567
-48
0.9506890929
0.7945270903
52
0.9608326761
0.7948859957
-48
0.9514206793
0.7952449729
52
0.9615680668
0.7956040219
-48
0.9521525401
0.7959631427
52
0.9623037333
0.7963223354
52
0.9725077127
0.7966815998
-48
0.9630396757
0.7970409362
52
0.973247482
0.7974003443
-48
0.9637758941
0.7977598244
52
0.9739875288
0.7981193764
52
0.9842522639
0.7984790002
-48
0.974727853
0.798838696
-48
0.9652491594
0.7991984638
-48
0.9558159634
0.7995583035
52
0.9659862064
0.7999182151
52
0.9762093347
0.8002781988
52
0.9864856232
0.8006382544
-48
0.9769504922
0.8009983821
-48
0.9674611299
0.8013585817
-48
0.9580173164
0.8017188535
52
0.9681990065
0.8020791972
-48
0.9587516512
0.8024396131
-48
0.9493496433
0.802800101
52
0.9594862615
0.803160661
-48
0.9500807274
0.8035212932
-48
0.9407203399
0.8038819974
-48
0.9314048823
0.8042427738
-48
0.9221341389
0.8046036224
52
0.9321292364
0.8049645431
52
0.9421763084
0.805325536
-48
0.9328538621
0.8056866011
-48
0.9235761636
0.8060477384
-48
0.914342998
0.806408948
-48
0.9051541516
0.8067702298
52
0.9150609532
0.8071315838
-48
0.9058686606
0.8074930101
-48
0.8967204911
0.8078545087
52
0.9065834376
0.8082160796
52
0.9164976715
0.8085777228
-48
0.9072984827
0.8089394384
52
0.9172164348
0.8093012263
52
0.9271859602
0.8096630865
-48
0.9179354676
0.8100250191
-48
0.9087293774
0.8103870241
52
0.9186547701
0.8107491015
-48
0.9094452272
0.8111112514
-48
0.9002798902
0.8114734736
52
0.9101613456
0.8118357683
52
0.9200941846
0.8121981355
-48
0.9108777325
0.8125605751
52
0.9208142967
0.8129230872
52
0.930802531
0.8132856718
-48
0.9215346789
0.813648329
52
0.9315266592
0.8140110586
52
0.9415705979
0.8143738608
52
0.951666765
0.8147367356
52
0.9618154321
0.815099683
-48
0.9523987181
0.8154627029
52
0.9625511914
0.8158257954
-48
0.9531309457
0.8161889606
-48
0.9437559171
0.8165521984
52
0.9538634479
0.8169155088
52
0.9640235378
0.8172788919
52
0.9742364602
0.8176423477
52
0.9845024898
0.8180058762
52
0.9948219028
0.8183694774
52
1.0051949767
0.8187331512
-48
0.9955700408
0.8190968979
-48
0.9859913046
0.8194607173
-48
0.9764585463
0.8198246094
-48
0.9669715453
0.8201885743
-48
0.9575300819
0.820552612
-48
0.9481339375
0.8209167226
52
0.958264234
0.8212809059
-48
0.9488645656
0.8216451621
52
0.9589986614
0.8220094911
52
0.9691854544
0.822373893
52
0.9794252188
0.8227383678
-48
0.9699239777
0.8231029155
-48
0.9604683426
0.823467536
-48
0.9510580946
0.8238322296
-48
0.9416930157
0.824196996
-48
0.9323728893
0.8245618354
-48
0.9230974994
0.8249267478
-48
0.9138666314
0.8252917331
-48
0.9046800716
0.8256567915
52
0.9145844079
0.8260219228
52
0.9245402469
0.8263871272
52
0.9345478562
0.8267524046
52
0.944607505
0.8271177551
-48
0.935273389
0.8274831787
-48
0.9259840767
0.8278486753
52
0.9359991939
0.828214245
-48
0.9267063978
0.8285798879
52
0.936725271
0.8289456039
52
0.9467962425
0.829311393
-48
0.9374516205
0.8296772553
-48
0.9281518527
0.8300431907
52
0.9381782423
0.8304091994
-48
0.9288749868
0.8307752812
52
0.9389051367
0.8311414362
-48
0.9295983921
0.8315076645
-48
0.9203363198
0.8318739661
-48
0.9111187054
0.8322403409
-48
0.9019453357
0.8326067889
-48
0.892815998
0.8329733103
-48
0.8837304813
0.8333399049
-48
0.8746885749
0.8337065729
52
0.8844369555
0.8340733142
52
0.8942360277
0.8344401289
52
0.904086055
0.8348070169
-48
0.894946442
0.8351739783
52
0.9048001635
0.8355410131
52
0.9147051243
0.8359081213
-48
0.9055145397
0.836275303
-48
0.8963680699
0.836642558
52
0.9062291839
0.8370098865
52
0.9161415757
0.8373772885
-48
0.9069440961
0.837744764
-48
0.8977907644
0.8381123129
-48
0.8886813688
0.8384799354
-48
0.8796156982
0.8388476314
-48
0.8705935429
0.8392154009
52
0.8803206293
0.839583244
-48
0.8712950903
0.8399511606
52
0.8810258247
0.8403191509
52
0.890807159
0.8406872147
-48
0.8817312846
0.8410553521
52
0.8915162873
0.8414235632
52
0.901352172
0.8417918479
52
0.9112392033
0.8421602063
-48
0.9020652551
0.8425286383
-48
0.8929353419
0.8428971441
-48
0.8838492523
0.8432657235
-48
0.8748067759
0.8436343766
-48
0.8658077033
0.8440031035
52
0.8755099034
0.8443719041
52
0.8852625549
0.8447407785
52
0.8950659202
0.8451097267
-48
0.8859696038
0.8454787486
52
0.8957766457
0.8458478444
-48
0.8866769178
0.8462170139
52
0.8964876378
0.8465862573
52
0.9063493735
0.8469555746
-48
0.8971988965
0.8473249657
-48
0.8880923418
0.8476944307
52
0.897910422
0.8480639696
52
0.9077795562
0.8484335824
-48
0.8986222143
0.8488032691
-48
0.8895088277
0.8491730297
52
0.8993342736
0.8495428643
-48
0.8902174691
0.8499127729
52
0.9000465999
0.8502827555
-48
0.8909263762
0.850652812
52
0.9007591934
0.8510229426
52
0.9106431412
0.8513931472
-48
0.9014720541
0.8517634258
-48
0.8923449882
0.8521337785
-48
0.8832617323
0.8525042052
-48
0.874222076
0.8528747061
52
0.8839680308
0.853245281
52
0.8937646645
0.8536159301
52
0.9036122408
0.8539866533
-48
0.894474902
0.8543574506
52
0.9043261715
0.8547283221
52
0.9142286676
0.8550992677
-48
0.90504037
0.8554702876
-48
0.8958961762
0.8558413817
-48
0.8867958746
0.8562125499
-48
0.8777392544
0.8565837924
-48
0.868726106
0.8569551092
52
0.8784434817
0.8573265002
-48
0.869426953
0.8576979655
-48
0.8604537036
0.8580695051
-48
0.8515235259
0.858441119
52
0.8611514482
0.8588128072
52
0.8708294357
0.8591845698
-48
0.8618494544
0.8595564067
52
0.8715310716
0.859928318
52
0.8812630332
0.8603003037
-48
0.8722329706
0.8606723637
52
0.8819685821
0.8610444982
-48
0.8729351329
0.8614167071
52
0.8826743956
0.8617889904
-48
0.8736375585
0.8621613482
52
0.8833804738
0.8625337805
52
0.8931740522
0.8629062873
-48
0.8840868168
0.8632788685
-48
0.8750432001
0.8636515243
-48
0.8660429927
0.8640242546
-48
0.8570859863
0.8643970594
-48
0.8481719736
0.8647699389
52
0.8577824679
0.8651428928
52
0.8674429367
0.8655159214
52
0.87715364
0.8658890246
-48
0.8681433025
0.8662622024
-48
0.8591762146
0.8666354549
52
0.868843931
0.8670087819
52
0.8785619194
0.8673821837
-48
0.8695448222
0.8677556601
-48
0.860571007
0.8681292113
-48
0.8516402662
0.8685028371
-48
0.8427523929
0.8688765377
52
0.8523347054
0.869250313
-48
0.8434434988
0.8696241631
-48
0.83459497
0.8699980879
52
0.8441348638
0.8703720875
-48
0.8352830165
0.8707461619
52
0.8448264882
0.8711203112
-48
0.835971321
0.8714945352
-48
0.8271586587
0.8718688341
-48
0.8183882971
0.8722432079
52
0.8278439163
0.8726176565
-48
0.8190702655
0.8729921801
52
0.8285294309
0.8733667785
52
0.8380377839
0.8737414519
-48
0.8292152025
0.8741162001
52
0.8387271216
0.8744910234
-48
0.8299012314
0.8748659216
52
0.8394167178
0.8752408948
-48
0.8305875176
0.875615943
-48
0.8218006975
0.8759910661
52
0.8312740611
0.8763662644
-48
0.8224839456
0.8767415376
52
0.8319608621
0.8771168859
52
0.8414870586
0.8774923093
-48
0.8326479207
0.8778678078
52
0.8421776899
0.8782433813
52
0.8517570139
0.87861903
52
0.8613861504
0.8789947538
52
0.8710653584
0.8793705527
52
0.8807948982
0.8797464269
52
0.8905750317
0.8801223761
52
0.9004060219
0.8804984006
-48
0.891284073
0.8808745003
52
0.9011187501
0.8812506752
52
0.9110045676
0.8816269253
-48
0.9018317457
0.8820032507
52
0.9117212708
0.8823796514
52
0.9216622214
0.8827561273
52
0.9316548649
0.8831326785
52
0.9416994702
0.8835093051
-48
0.9323793128
0.8838860069
52
0.9424276852
0.8842627841
52
0.9525283092
0.8846396367
-48
0.9431561733
0.8850165646
52
0.9532605854
0.8853935679
-48
0.9438849346
0.8857706466
-48
0.9345542869
0.8861478008
52
0.9446139692
0.8865250303
52
0.9547259618
0.8869023353
-48
0.9453432772
0.8872797158
52
0.9554590623
0.8876571717
-48
0.9460728588
0.8880347032
52
0.9561924376
0.8884123101
-48
0.9468027139
0.8887899926
-48
0.9374580609
0.8891677506
-48
0.9281582622
0.8895455841
52
0.9381846852
0.8899234932
-48
0.9288813987
0.8903014779
52
0.9389115819
0.8906795382
-48
0.9296048064
0.8910576741
-48
0.9203427033
0.8914358857
-48
0.9111250583
0.8918141729
-48
0.901951658
0.8921925357
52
0.9118418066
0.8925709742
52
0.921783384
0.8929494884
-48
0.9125588238
0.8933280783
52
0.9225041297
0.8937067439
-48
0.9132761099
0.8940854853
52
0.9232251456
0.8944643024
-48
0.9139936649
0.8948431952
-48
0.9048064953
0.8952221639
52
0.9147114891
0.8956012083
52
0.9246679889
0.8959803285
52
0.9346762624
0.8963595246
52
0.944736579
0.8967387965
52
0.9548492092
0.8971181443
-48
0.945465933
0.8974975679
52
0.9555823558
0.8978770674
-48
0.9461955605
0.8982566428
-48
0.9368538218
0.8986362941
-48
0.9275569235
0.8990160214
52
0.9375802195
0.8993958246
-48
0.9282798344
0.8997757038
-48
0.9190240912
0.9001556589
52
0.9290030165
0.90053569
52
0.9390338322
0.9009157972
-48
0.9297264698
0.9012959803
52
0.9397610474
0.9016762395
-48
0.9304501944
0.9020565748
-48
0.9211840335
0.9024369861
-48
0.9119623501
0.9028174735
-48
0.9027849308
0.903198037
52
0.9126794125
0.9035786766
52
0.9226253454
0.9039593923
-48
0.9133967438
0.9043401842
-48
0.9042124394
0.9047210522
52
0.9141143441
0.9051019965
-48
0.9049265952
0.9054830169
52
0.9148322135
0.9058641135
52
0.924789341
0.9062452863
52
0.9347982456
0.9066265353
-48
0.925511214
0.9070078606
-48
0.9162687602
0.9073892622
52
0.9262333577
0.9077707401
52
0.9362497712
0.9081522942
52
0.94631827
0.9085339247
52
0.956439125
0.9089156315
-48
0.9470482172
0.9092974146
-48
0.9377023858
0.9096792741
52
0.9477784382
0.9100612099
52
0.9579068861
0.9104432222
52
0.9680880019
0.9108253108
52
0.9783220595
0.9112074759
52
0.9886093342
0.9115897174
-48
0.9790640094
0.9119720353
-48
0.9695645021
0.9123544297
52
0.9798062376
0.9127369006
52
0.99010123
0.913119448
-48
0.9805487441
0.9135020719
52
0.9908475976
0.9138847723
52
1.0012000051
0.9142675492
-48
0.991594245
0.9146504028
52
1.0019505351
0.9150333328
52
1.0123606779
0.9154163395
52
1.0228249534
0.9157994228
52
1.0333436432
0.9161825827
-48
1.0235835937
0.9165658192
52
1.0341062284
0.9169491323
52
1.0446835808
0.9173325222
52
1.0553159354
0.9177159887
-48
1.0454504189
0.9180995319
-48
1.0356322569
0.9184831518
52
1.0462175446
0.9188668484
52
1.0568578758
0.9192506218
-48
1.046984958
0.9196344719
-48
1.0371594302
0.9200183988
-48
1.027381065
0.9204024025
52
1.0379234465
0.920786483
-48
1.028141414
0.9211706402
-48
1.0184063352
0.9215548744
52
1.0289020481
0.9219391854
-48
1.0191633183
0.9223235732
52
1.0296629676
0.9227080379
-48
1.0199205853
0.9230925795
-48
1.0102249665
0.923477198
52
1.0206781363
0.9238618935
52
1.0311856626
0.9242466658
52
1.0417478281
0.9246315152
52
1.0523649168
0.9250164415
-48
1.0425135652
0.9254014448
-48
1.0327095001
0.9257865251
-48
1.0229524945
0.9261716824
-48
1.0132423225
0.9265569167
-48
1.0035787594
0.9269422281
-48
0.9939615813
0.9273276165
52
1.0043301815
0.9277130821
-48
0.9947093967
0.9280986247
52
1.0050818855
0.9284842444
52
1.0155083113
0.9288699412
52
1.0259889545
0.9292557152
-48
1.0162642076
0.9296415664
-48
1.0065861394
0.9300274947
-48
0.9969545259
0.9304135002
-48
0.9873691442
0.9307995829
-48
0.9778297723
0.9311857428
-48
0.9683361894
0.93157198
52
0.9785715376
0.9319582943
52
0.9888601096
0.932344686
-48
0.979313581
0.9327311549
-48
0.9698128758
0.9331177012
-48
0.960357774
0.9335043247
-48
0.9509480567
0.9338910256
52
0.9610929866
0.9342778038
-48
0.9516797403
0.9346646593
52
0.9618284749
0.9350515923
52
0.972029983
0.9354386026
-48
0.9625642391
0.9358256903
52
0.9727695731
0.9362128555
-48
0.9633002792
0.936600098
-48
0.9538764378
0.936987418
-48
0.9444978309
0.9373748155
-48
0.9351642413
0.9377622905
-48
0.925875453
0.9381498429
-48
0.9166312508
0.9385374729
-48
0.9074314208
0.9389251804
52
0.9173500642
0.9393129654
52
0.9273202845
0.939700828
-48
0.9180691472
0.9400887682
-48
0.9088624153
0.940476786
52
0.9187884998
0.9408648813
52
0.9287662
0.9412530543
-48
0.9195081223
0.9416413049
-48
0.9102944833
0.9420296332
-48
0.9011250697
0.9424180391
52
0.9110109201
0.9428065227
-48
0.9018380677
0.943195084
-48
0.892709245
0.943583723
52
0.902551333
0.9439724398
-48
0.8934190866
0.9443612343
52
0.9032648659
0.9447501065
-48
0.8941291945
0.9451390565
52
0.9039786664
0.9455280843
52
0.9138793554
0.94591719
-48
0.9046927345
0.9463063734
52
0.9145971367
0.9466956347
-48
0.9054070705
0.9470849738
52
0.9153151872
0.9474743908
-48
0.9061216743
0.9478638857
-48
0.8969722903
0.9482534584
52
0.9068365462
0.9486431091
-48
0.8976837308
0.9490328378
-48
0.8885748489
0.9494226443
-48
0.8795096896
0.9498125288
-48
0.8704880431
0.9502024914
-48
0.8615097005
0.9505925319
52
0.8711895509
0.9509826504
52
0.8809197366
0.9513728469
52
0.8907005192
0.9517631215
-48
0.8816251567
0.9521534741
-48
0.872593356
0.9525439048
-48
0.8636049079
0.9529344136
-48
0.8546596043
0.9533250004
52
0.8643038343
0.9537156654
52
0.8739982142
0.9541064086
-48
0.8650030228
0.9544972299
-48
0.8560510083
0.9548881293
-48
0.8471419634
0.9552791069
-48
0.838275682
0.9556701628
52
0.8478347155
0.9560612968
-48
0.8389651089
0.956452509
52
0.8485277275
0.9568437995
-48
0.8396547944
0.9572351683
-48
0.8308244514
0.9576266153
52
0.8403447385
0.9580181407
-48
0.8315110838
0.9584097443
52
0.8410349414
0.9588014262
-48
0.8321979737
0.9591931865
52
0.8417254032
0.9595850252
-48
0.8328851212
0.9599769422
-48
0.8240872726
0.9603689376
-48
0.8153316537
0.9607610113
-48
0.8066180618
0.9611531635
-48
0.7979462951
0.9615453942
52
0.8072956158
0.9619377033
52
0.816693553
0.9623300908
-48
0.807973424
0.9627225568
52
0.8173748858
0.9631151013
-48
0.8086514863
0.9635077243
-48
0.7999699592
0.9639004259
-48
0.7913301034
0.964293206
52
0.8006450199
0.9646860646
52
0.810008374
0.9650790018
52
0.8194204176
0.9654720176
52
0.8288814037
0.965865112
52
0.838391587
0.9662582851
-48
0.8295673074
0.9666515367
52
0.8390810574
0.967044867
52
0.8486442789
0.967438276
-48
0.8397707864
0.9678317636
52
0.8493375945
0.96822533
52
0.85895415
0.9686189751
52
0.8686207115
0.9690126989
-48
0.8596513321
0.9694065014
52
0.8693215191
0.9698003827
-48
0.8603487758
0.9701943428
52
0.8700225894
0.9705883816
52
0.8797467069
0.9709824993
52
0.8895213897
0.9713766958
-48
0.8804516871
0.9717709712
52
0.8902300358
0.9721653254
52
0.900059232
0.9725597584
-48
0.8909389477
0.9729542704
52
0.9007718302
0.9733488612
-48
0.8916481255
0.973743531
52
0.9014846957
0.9741382797
52
0.9113724161
0.9745331074
52
0.9213115527
0.974928014
-48
0.9120892572
0.9753229996
-48
0.9029112288
0.9757180642
-48
0.8937772549
0.9761132078
-48
0.8846871241
0.9765084304
-48
0.8756406259
0.9769037321
52
0.8853939571
0.9772991129
52
0.8951980057
0.9776945727
52
0.9050530354
0.9780901116
-48
0.8959087808
0.9784857296
52
0.9057675064
0.9788814268
52
0.9156774975
0.9792772031
-48
0.9064822455
0.9796730585
52
0.9163959532
0.9800689931
52
0.9263612121
0.9804650069
-48
0.9171146783
0.9808610999
52
0.9270836746
0.9812572721
52
0.9371045097
0.9816535236
-48
0.9278064081
0.9820498543
-48
0.9185529373
0.9824462643
-48
0.9093438832
0.9828427535
52
0.9192724714
0.9832393221
52
0.9292526883
0.9836359699
-48
0.9199922754
0.9840326971
-48
0.9107763125
0.9844295037
-48
0.9016045862
0.9848263896
52
0.91149293
0.9852233548
-48
0.9023177639
0.9856203995
52
0.9122098163
0.9860175236
52
0.9221533074
0.9864147271
-48
0.9129269715
0.98681201
52
0.9228741917
0.9872093724
-48
0.9136443956
0.9876068143
-48
0.9044589025
0.9880043357
52
0.9143620888
0.9884019366
-48
0.9051731508
0.9887996169
52
0.9150800512
0.9891973769
52
0.9250384674
0.9895952163
52
0.9350486675
0.9899931354
52
0.9451109205
0.990391134
-48
0.9357743881
0.9907892122
-48
0.926482671
0.9911873701
-48
0.9172355542
0.9915856076
52
0.9272051791
0.9919839247
-48
0.9179545942
0.9923823215
-48
0.9087484122
0.9927807979
-48
0.8995864198
0.9931793541
-48
0.890468405
0.99357799
52
0.9002988407
0.9939767056
-48
0.8911774063
0.9943755009
52
0.9010115288
0.994774376
52
0.9108967887
0.9951733309
-48
0.9017244841
0.9955723655
52
0.9116134515
0.99597148
-48
0.9024377069
0.9963706743
52
0.912330383
0.9967699484
52
0.922274501
0.9971693024
52
0.9322703284
0.9975687363
52
0.9423181341
0.99796825
-48
0.932995007
0.9983678437
-48
0.923716631
0.9987675173
52
0.9337199575
0.9991672708
52
0.9437753013
0.9995671042
-48
0.9344451798
0.9999670176
52
0.9445042948
1.000367011
-48
0.9351706741
1.0007670844
52
0.9452335616
1.0011672379
52
0.9553487762
1.0015674713
52
0.9655165898
1.0019677848
-48
0.9560821102
1.0023681784
-48
0.946692916
1.002768652
52
0.9568157192
1.0031692057
-48
0.9474230037
1.0035698396
-48
0.9380753733
1.0039705535
-48
0.9287726115
1.0043713476
-48
0.919514503
1.0047722219
-48
0.9103008334
1.0051731764
-48
0.9011313894
1.005574211
52
0.9110172726
1.0059753258
52
0.9209545624
1.0063765209
-48
0.9117339805
1.0067777962
-48
0.9025576574
1.0071791518
-48
0.8934253807
1.0075805876
52
0.9032711926
1.0079821037
-48
0.8941354909
1.0083837001
-48
0.8850436406
1.0087853769
52
0.8948458675
1.0091871339
-48
0.8857506073
1.0095889714
52
0.8955565105
1.0099908892
-48
0.8864578392
1.0103928873
52
0.89626742
1.0107949659
-48
0.8871653364
1.0111971249
52
0.8969785961
1.0115993643
52
0.9068428848
1.0120016842
52
0.9167584678
1.0124040845
-48
0.9075580272
1.0128065654
-48
0.8984017487
1.0132091267
52
0.9082734378
1.0136117685
52
0.9181964596
1.0140144909
52
0.9281710812
1.0144172938
52
0.9381975708
1.0148201772
52
0.9482761982
1.0152231413
52
0.9584072344
1.0156261859
52
0.9685909521
1.0160293111
-48
0.9591417155
1.016432517
52
0.9693292524
1.0168358035
-48
0.959876472
1.0172391706
-48
0.9504690649
1.0176426185
52
0.9606115041
1.018046147
52
0.9708066839
1.0184497562
-48
0.9613468118
1.0188534462
-48
0.9519323471
1.0192572169
-48
0.9425630719
1.0196610683
52
0.9526643998
1.0200650005
-48
0.9432916107
1.0204690135
52
0.9533967271
1.0208731073
-48
0.9440204228
1.021277282
-48
0.9346891248
1.0216815374
-48
0.925402617
1.0220858737
-48
0.9161606844
1.0224902909
52
0.92612472
1.0228947889
52
0.9361405685
1.0232993679
52
0.9462084995
1.0237040278
52
0.9563287837
1.0241087686
-48
0.9469384055
1.0245135903
52
0.9570624852
1.0249184931
-48
0.9476685853
1.0253234768
52
0.9577964619
1.0257285415
-48
0.9483990389
1.0261336872
52
0.9585307139
1.0265389139
52
0.9687150736
1.0269442217
-48
0.9592652413
1.0273496105
52
0.9694534205
1.0277550804
-48
0.9600000441
1.0281606315
52
0.9701920443
1.0285662636
52
0.980437043
1.0289719768
-48
0.9709309452
1.0293777712
-48
0.9614704766
1.0297836468
-48
0.9520554183
1.0301896035
-48
0.9426855523
1.0305956414
52
0.9527875172
1.0310017606
-48
0.9434141371
1.0314079609
52
0.9535198906
1.0318142425
52
0.9636781941
1.0322206054
-48
0.9542525387
1.0326270495
52
0.9644146519
1.0330335749
52
0.9746296081
1.0334401816
52
0.9848976821
1.0338468696
-48
0.9753701732
1.034253639
52
0.9856420981
1.0346604897
52
0.995967437
1.0350674218
-48
0.9863867933
1.0354744353
-48
0.9768521367
1.0358815302
52
0.9871317678
1.0362887065
-48
0.9775935353
1.0366959643
52
0.9878770217
1.0371033035
52
0.9982139822
1.0375107241
-48
0.9886225551
1.0379182263
52
0.9989633924
1.0383258099
52
1.009358002
1.0387334751
52
1.0198066637
1.0391412218
52
1.0303096583
1.03954905
52
1.0408672685
1.0399569598
-48
1.0310711056
1.0403649512
-48
1.0213219643
1.0407730242
52
1.0318328385
1.0411811788
52
1.0423983693
1.041589415
-48
1.0325948571
1.0419977329
-48
1.0228384018
1.0424061325
-48
1.0131287775
1.0428146137
52
1.0235970471
1.0432231766
-48
1.0138837813
1.0436318213
52
1.024355977
1.0440405476
-48
1.0146390683
1.0444493557
-48
1.0049688008
1.0448582456
52
1.0153946385
1.0452672172
-48
1.0057207443
1.0456762707
52
1.0161504921
1.0460854059
52
1.0266344747
1.046494623
-48
1.0169066292
1.046903922
52
1.0273945437
1.0473133027
-48
1.0176630499
1.0477227654
-48
1.0079782672
1.04813231
52
1.0184197542
1.0485419364
52
1.0289155369
1.0489516448
52
1.0394658977
1.0493614351
52
1.0500711204
1.0497713074
52
1.0607314902
1.0501812617
-48
1.0508399791
1.0505912979
-48
1.0409959472
1.0510014162
-48
1.0311991666
1.0514116165
-48
1.0214494106
1.0518218988
-48
1.0117464535
1.0522322632
52
1.022207535
1.0526427096
52
1.0327230142
1.0530532382
-48
1.0229659437
1.0534638488
52
1.0334853666
1.0538745416
-48
1.0237246369
1.0542853165
52
1.034248005
1.0546961736
-48
1.0244836146
1.0551071128
52
1.0350109294
1.0555181342
52
1.0455929862
1.0559292378
-48
1.0357741399
1.0563404237
52
1.0463601654
1.0567516918
52
1.0570012382
1.0571630421
-48
1.0471276323
1.0575744747
-48
1.0373014197
1.0579859896
52
1.047895387
1.0583975868
52
1.0585444431
1.0588092663
52
1.0692488742
1.0592210282
-48
1.0593164796
1.0596328724
-48
1.0494317605
1.060044799
52
1.0600888056
1.0604568079
-48
1.0502003794
1.0608688993
52
1.0608614213
1.0612810731
-48
1.0509692865
1.0616933293
52
1.0616343268
1.0621056679
52
1.0723548253
1.0625180891
-48
1.0624075221
1.0629305927
-48
1.052507966
1.0633431788
-48
1.0426559278
1.0637558475
-48
1.0328511793
1.0641685986
-48
1.0230934937
1.0645814323
52
1.0336135798
1.0649943486
-48
1.0238522347
1.0654073475
52
1.0343762663
1.065820429
52
1.0449550229
1.0662335931
-48
1.0351392388
1.0666468398
-48
1.0253705704
1.0670601691
52
1.0359024974
1.0674735812
52
1.0464891904
1.0678870759
-48
1.0366660422
1.0683006533
-48
1.0268900452
1.0687143134
-48
1.017160973
1.0691280563
-48
1.0074786004
1.0695418819
52
1.0179174891
1.0699557903
-48
1.0082314851
1.0703697814
52
1.0186742889
1.0707838554
52
1.0291713952
1.0711980122
-48
1.0194313725
1.0716122518
52
1.0299324156
1.0720265742
-48
1.02018874
1.0724409795
-48
1.010491834
1.0728554677
-48
1.0008414732
1.0732700388
-48
0.9912374342
1.0736846928
-48
0.9816794945
1.0740994298
52
0.9919842279
1.0745142497
-48
0.9824227036
1.0749291525
-48
0.9729070746
1.0753441383
-48
0.9634371206
1.0757592072
-48
0.9540126225
1.076174359
-48
0.9446333619
1.0765895939
-48
0.9352991217
1.0770049118
-48
0.9260096859
1.0774203128
-48
0.9167648394
1.0778357968
-48
0.9075643682
1.078251364
52
0.9174837029
1.0786670143
-48
0.9082797812
1.0790827477
-48
0.8991200382
1.0794985642
52
0.9089954624
1.0799144639
-48
0.8998322842
1.0803304468
-48
0.8907130892
1.0807465129
52
0.9005447973
1.0811626622
52
0.9104276302
1.0815788948
-48
0.9012575776
1.0819952105
52
0.911144117
1.0824116096
52
0.9210820664
1.0828280919
52
0.9310716932
1.0832446575
52
0.941113266
1.0836613065
52
0.951207055
1.0840780387
52
0.9613533316
1.0844948543
-48
0.9519388357
1.0849117533
52
0.9620889176
1.0853287356
52
0.97229178
1.0857458014
52
0.9825476972
1.0861629506
52
0.9928569452
1.0865801831
52
1.0032198014
1.0869974992
-48
0.9936043463
1.0874148987
-48
0.9840350455
1.0878323817
52
0.9943520277
1.0882499481
52
1.0047226582
1.0886675981
-48
0.9950999895
1.0890853316
52
1.0054745094
1.0895031487
52
1.0159029769
1.0899210493
52
1.0263856723
1.0903390335
-48
1.0166590211
1.0907571014
-48
1.0069790578
1.0911752528
-48
0.9973455583
1.0915934878
52
1.0077317552
1.0920118065
52
1.0181719604
1.0924302089
52
1.0286664546
1.0928486949
52
1.0392155201
1.0932672647
52
1.0498194408
1.0936859181
52
1.0604785019
1.0941046553
-48
1.0505882051
1.0945234762
52
1.0612512638
1.0949423809
-48
1.0513572577
1.0953613694
52
1.0620243155
1.0957804417
-48
1.0521265987
1.0961995978
-48
1.0422763911
1.0966188377
52
1.0528962283
1.0970381615
-48
1.0430423264
1.0974575691
-48
1.0332357232
1.0978770606
52
1.043808549
1.098296636
-48
1.033998268
1.0987162953
-48
1.0242350763
1.0991360386
-48
1.0145187479
1.0995558658
-48
1.0048490579
1.099975777
-48
0.9952257824
1.1003957721
-48
0.9856486987
1.1008158513
52
0.9959740719
1.1012360145
-48
0.9863933964
1.1016562617
-48
0.9768587081
1.1020765929
52
0.9871383734
1.1024970082
52
0.9974714929
1.1029175076
52
1.0078583447
1.1033380911
52
1.0182992081
1.1037587588
52
1.0287943639
1.1041795105
-48
1.019056151
1.1046003464
52
1.029555243
1.1050212665
52
1.0401089302
1.1054422707
-48
1.0303164074
1.1058633592
-48
1.0205708886
1.1062845319
-48
1.0108721484
1.1067057888
-48
1.001219962
1.1071271299
-48
0.9916141062
1.1075485553
-48
0.9820543585
1.1079700651
52
0.9923610412
1.1083916591
-48
0.9827977082
1.1088133374
-48
0.9732802792
1.1092351001
52
0.9835413366
1.1096569471
-48
0.9740203382
1.1100788785
-48
0.9645450406
1.1105008943
52
0.9747606748
1.1109229944
-48
0.9652818236
1.111345179
52
0.975501289
1.1117674481
52
0.9857738958
1.1121898016
52
0.99609992
1.1126122395
52
1.0064796396
1.113034762
52
1.0169133337
1.1134573689
-48
1.0072321497
1.1138800604
52
1.0176697569
1.1143028364
-48
1.0079849421
1.114725697
-48
0.9983466143
1.1151486421
52
1.0087380167
1.1155716718
-48
0.9990960743
1.1159947862
52
1.0094913738
1.1164179851
52
1.019940729
1.1168412687
52
1.0304444208
1.117264637
-48
1.0206982876
1.1176880899
-48
1.0109989358
1.1181116275
52
1.0214561302
1.1185352499
52
1.0319677021
1.1189589569
52
1.0425339342
1.1193827487
52
1.0531551106
1.1198066252
52
1.0638315172
1.1202305866
-48
1.0539251259
1.1206546327
52
1.0646055366
1.1210787636
52
1.0753414854
1.1215029794
52
1.0861332611
1.12192728
52
1.096981154
1.1223516654
52
1.107885456
1.1227761358
-48
1.0977676059
1.123200691
52
1.1086759974
1.1236253311
-48
1.0985543526
1.1240500562
-48
1.0884812917
1.1244748662
52
1.0993413944
1.1248997612
52
1.1102579697
1.1253247411
-48
1.1001287314
1.1257498061
-48
1.0900481135
1.126174956
52
1.1009163637
1.126600191
52
1.1118411288
1.1270255111
52
1.1228227027
1.1274509162
-48
1.1126331537
1.1278764063
52
1.1236188461
1.1283019816
52
1.1346616641
1.128727642
-48
1.1244152881
1.1291533876
52
1.1354622476
1.1295792182
-48
1.1252120288
1.1300051341
-48
1.1150110111
1.1304311351
52
1.1260090684
1.1308572213
52
1.1370643155
1.1312833928
-48
1.1268064068
1.1317096494
52
1.1378658001
1.1321359914
52
1.1489827023
1.1325624186
-48
1.1386675853
1.1329889311
52
1.1497886567
1.1334155288
-48
1.1394696712
1.133842212
-48
1.1292002168
1.1342689804
-48
1.1189800557
1.1346958342
52
1.129998752
1.1351227734
52
1.1410747455
1.1355497979
-48
1.1307975867
1.1359769079
-48
1.1205697583
1.1364041033
52
1.1315967211
1.1368313841
52
1.142681024
1.1372587504
-48
1.1323961551
1.1376862021
52
1.1434846151
1.1381137393
52
1.1546307351
1.1385413621
52
1.1658348149
1.1389690704
-48
1.1554388078
1.1393968642
52
1.1666470896
1.1398247435
-48
1.1562471836
1.1402527085
52
1.167459669
1.140680759
-48
1.1570558625
1.1411088952
52
1.168272553
1.141537117
-48
1.1578648448
1.1419654244
-48
1.1475070935
1.1423938175
-48
1.1371990595
1.1428222962
-48
1.126940504
1.1432508607
52
1.1380005946
1.1436795109
52
1.1491181977
1.1441082468
52
1.1602936123
1.1445370684
52
1.1715271391
1.1449659758
-48
1.1611038088
1.145394969
-48
1.1507305106
1.145824048
-48
1.1404070041
1.1462532128
52
1.1515371205
1.1466824635
-48
1.1412097423
1.1471118
52
1.152344033
1.1475412223
52
1.163536222
1.1479707306
52
1.1747866103
1.1484003247
52
1.1860955007
1.1488300048
-48
1.1756022423
1.1492597708
52
1.186915374
1.1496896227
52
1.1982873339
1.1501195607
52
1.209718428
1.1505495846
52
1.2212089639
1.1509796945
52
1.2327592505
1.1514098904
-48
1.2220420061
1.1518401724
52
1.2335966245
1.1522705404
-48
1.2228753607
1.1527009946
52
1.2344343126
1.1531315348
52
1.246053371
1.1535621611
52
1.2577328485
1.1539928735
-48
1.2468957309
1.1544236721
52
1.2585795887
1.1548545568
52
1.2703242025
1.1552855277
-48
1.2594266464
1.1557165848
-48
1.2485813985
1.1561477281
52
1.2602740217
1.1565789577
52
1.2720274466
1.1570102735
52
1.2838419894
1.1574416755
-48
1.2728795478
1.1578731639
-48
1.261969726
1.1583047385
52
1.2737319686
1.1587363994
-48
1.2628180551
1.1591681467
52
1.274584709
1.1595999804
52
1.2864125495
1.1600319004
52
1.2983018947
1.1604639067
-48
1.2872700457
1.1608959995
-48
1.2762911494
1.1613281787
-48
1.2653649519
1.1617604443
-48
1.2544912001
1.1621927964
52
1.2662145544
1.162625235
-48
1.2553367245
1.16305776
-48
1.2445111082
1.1634903716
-48
1.2337374549
1.1639230697
52
1.2453528897
1.1643558543
52
1.2570287247
1.1647887255
52
1.2687652741
1.1652216832
-48
1.2578752008
1.1656547275
-48
1.2470373998
1.1660878585
-48
1.2362516203
1.1665210761
-48
1.2255176125
1.1669543803
-48
1.214835128
1.1673877711
-48
1.2042039194
1.1678212487
52
1.2156657797
1.1682548129
52
1.2271872418
1.1686884639
-48
1.216496743
1.1691222016
-48
1.2058575587
1.169556026
-48
1.1952694424
1.1699899372
-48
1.1847321491
1.1704239352
52
1.1960927562
1.17085802
-48
1.185551511
1.1712921916
52
1.1969163789
1.1717264501
52
1.208340344
1.1721607954
52
1.2198237138
1.1725952275
-48
1.20916856
1.1730297466
-48
1.1985645509
1.1734643525
-48
1.1880114411
1.1738990454
52
1.1993891006
1.1743338252
-48
1.1888320329
1.174768692
-48
1.1783256391
1.1752036457
52
1.1896529324
1.1756386864
-48
1.1791425984
1.1760738142
-48
1.1686827139
1.1765090289
52
1.179959864
1.1769443307
-48
1.1694960567
1.1773797196
52
1.1807774362
1.1778151955
-48
1.1703097045
1.1782507586
52
1.1815953149
1.1786864087
-48
1.1711236574
1.179122146
52
1.1824135004
1.1795579704
-48
1.1719379156
1.179993882
52
1.1832319928
1.1804298808
52
1.1945847992
1.1808659668
-48
1.1840507921
1.18130214
52
1.1954078562
1.1817384004
-48
1.1848698985
1.1821747481
-48
1.174382523
1.182611183
-48
1.1639454869
1.1830477053
-48
1.1535585486
1.1834843148
52
1.164757053
1.1839210117
-48
1.1543662192
1.1843577959
52
1.1655689235
1.1847946674
52
1.1768298819
1.1852316264
-48
1.1663810985
1.1856686727
-48
1.1559824692
1.1861058064
-48
1.1456337533
1.1865430276
52
1.1567910489
1.1869803362
-48
1.1464384518
1.1874177323
52
1.1575999318
1.1878552158
-48
1.1472434521
1.1882927869
-48
1.1369366835
1.1887304454
52
1.1480487543
1.1891681915
-48
1.1377381203
1.1896060251
52
1.1488543585
1.1900439463
-48
1.1385398576
1.1904819551
52
1.1496602648
1.1909200515
52
1.1608384982
1.1913582355
-48
1.1504664734
1.1917965072
-48
1.1401442343
1.1922348665
-48
1.129871542
1.1926733135
-48
1.1196481586
1.1931118481
-48
1.1094738475
1.1935504705
52
1.1204431115
1.1939891806
52
1.1314694156
1.1944279784
52
1.1425530566
1.194866864
-48
1.1322688019
1.1953058374
-48
1.1220339117
1.1957448986
-48
1.1118481489
1.1961840475
52
1.1228297593
1.1966232843
-48
1.1126401764
1.197062609
-48
1.1024995036
1.1975020215
-48
1.092407506
1.1979415219
52
1.103288025
1.1983811102
52
1.1142251227
1.1988207865
52
1.1252190934
1.1992605506
52
1.1362702327
1.1997004027
-48
1.1260161355
1.2001403428
52
1.1370714194
1.2005803709
52
1.1481841908
1.2010204869
-48
1.1378729067
1.201460691
52
1.1489898458
1.2019009832
-48
1.1386746946
1.2023413634
52
1.149795803
1.2027818317
52
1.1609747412
1.203222388
-48
1.1506020624
1.2036630325
-48
1.1402791725
1.2041037651
52
1.1514086242
1.2045445859
-48
1.1410818628
1.2049854948
-48
1.1308046699
1.2054264919
-48
1.1205768074
1.2058675772
-48
1.1103980388
1.2063087507
52
1.1213721086
1.2067500124
52
1.1324032435
1.2071913624
52
1.1434917404
1.2076328007
52
1.1546378974
1.2080743273
-48
1.1442956355
1.2085159421
52
1.1554459728
1.2089576453
52
1.1666542919
1.2093994369
-48
1.1562543513
1.2098413167
52
1.1674668739
1.210283285
-48
1.1570630329
1.2107253417
52
1.1682797607
1.2111674867
-48
1.1578720179
1.2116097202
52
1.1690929523
1.2120520422
-48
1.1586813062
1.2124944526
-48
1.1483196359
1.2129369515
52
1.159490898
1.2133795389
-48
1.1491253417
1.2138222148
-48
1.1388095401
1.2142649792
52
1.1499313497
1.2147078322
-48
1.1396116792
1.2151507738
-48
1.1293415431
1.2155938039
-48
1.1191207037
1.2160369227
-48
1.1089489243
1.2164801301
52
1.1199154588
1.2169234261
52
1.1309390191
1.2173668108
52
1.142019902
1.2178102841
52
1.1531584055
1.2182538462
-48
1.1428232452
1.218697497
-48
1.1325376936
1.2191412365
52
1.1436268896
1.2195850647
52
1.1547737494
1.2200289817
-48
1.1444308354
1.2204729875
52
1.1555818758
1.2209170821
-48
1.1452350828
1.2213612655
52
1.1563903052
1.2218055378
-48
1.1460396317
1.2222498989
52
1.1571990378
1.2226943489
-48
1.1468444825
1.2231388878
-48
1.1365396289
1.2235835155
52
1.147649635
1.2240282322
52
1.1588174131
1.2244730379
52
1.1700432637
1.2249179325
52
1.1813274886
1.2253629161
-48
1.1708571167
1.2258079887
52
1.1821455737
1.2262531503
-48
1.1716712749
1.2266984009
52
1.1829639656
1.2271437406
-48
1.1724857385
1.2275891693
-48
1.162057807
1.2280346871
-48
1.1516799295
1.2284802941
-48
1.1413518658
1.2289259901
52
1.1524868956
1.2293717753
52
1.1636798274
1.2298176497
52
1.1749309625
1.2302636132
-48
1.1644912939
1.2307096659
-48
1.1541017357
1.2311558079
52
1.1653030647
1.231602039
-48
1.15490961
1.2320483595
52
1.16611514
1.2324947691
52
1.1773789387
1.2329412681
52
1.1887013092
1.2333878563
-48
1.1781955429
1.2338345339
52
1.1895221597
1.2342813008
52
1.2009076749
1.2347281571
52
1.2123523949
1.2351751027
-48
1.2017331034
1.2356221377
-48
1.1911647845
1.2360692621
52
1.2025588413
1.236516476
52
1.2140121473
1.2369637793
52
1.2255250105
1.2374111721
-48
1.2148424904
1.2378586543
52
1.2263596714
1.238306226
52
1.2379367417
1.2387538873
52
1.2495740127
1.239201638
52
1.2612717976
1.2396494784
52
1.2730304109
1.2400974083
52
1.2848501691
1.2405454277
52
1.29673139
1.2409935368
-48
1.2857070793
1.2414417355
52
1.2975927561
1.2418900239
52
1.3095402384
1.2423384019
-48
1.2984544453
1.2427868696
52
1.3104064084
1.2432354269
52
1.3224205217
1.243684074
-48
1.3112729032
1.2441328108
-48
1.3001787933
1.2445816374
-48
1.2891379351
1.2450305537
52
1.3010414523
1.2454795598
-48
1.2899964534
1.2459286558
52
1.3019044349
1.2463778415
52
1.313874338
1.2468271171
-48
1.3027677412
1.2472764825
52
1.3147421334
1.2477259378
-48
1.3036313712
1.248175483
52
1.3156102543
1.2486251181
-48
1.3044953251
1.2490748431
52
1.3164787008
1.2495246581
52
1.32852439
1.249974563
52
1.3406327169
1.2504245579
-48
1.3293976798
1.2508746428
52
1.3415105477
1.2513248177
-48
1.3302712971
1.2517750827
52
1.3423887079
1.2522254377
-48
1.3311452421
1.2526758828
52
1.3432671973
1.253126418
52
1.3554521868
1.2535770433
-48
1.3441460163
1.2540277587
-48
1.3328941154
1.2544785642
52
1.3450251648
1.2549294599
-48
1.333769044
1.2553804458
52
1.345904643
1.2558315219
52
1.3581033472
1.2562826882
-48
1.3467844511
1.2567339448
-48
1.3355198857
1.2571852915
52
1.3476645891
1.2576367286
-48
1.3363957991
1.258088256
52
1.3485450573
1.2585398736
52
1.3607574916
1.2589915816
52
1.3730334305
1.2594433799
-48
1.36164287
1.2598952686
52
1.373923413
1.2603472476
52
1.3862678147
1.2607993171
52
1.3986764074
1.2612514769
52
1.4111495247
1.2617037272
52
1.4236875022
1.262156068
52
1.4362906772
1.2626084992
-48
1.424596482
1.2630610209
52
1.4372043837
1.2635136331
-48
1.4255058026
1.2639663358
52
1.4381184328
1.2644191291
-48
1.4264154643
1.2648720129
52
1.4390328247
1.2653249873
-48
1.4273254672
1.2657780523
-48
1.4156743049
1.2662312079
-48
1.4040790683
1.2666844542
52
1.4165802794
1.2671377911
-48
1.4049806941
1.2675912186
-48
1.3934367868
1.2680447369
-48
1.3819482902
1.2684983458
52
1.3943344213
1.2689520455
52
1.4067849603
1.2694058359
52
1.4193002421
1.2698597171
-48
1.4076876009
1.270313689
-48
1.3961307004
1.2707677517
52
1.4085905801
1.2712219053
-48
1.3970293453
1.2716761497
-48
1.3855236044
1.2721304849
52
1.3979283272
1.272584911
52
1.4103975545
1.273039428
52
1.4229316218
1.2734940359
52
1.4355308662
1.2739487347
-48
1.423840318
1.2744035244
52
1.4364442877
1.2748584051
52
1.449113798
1.2753133768
52
1.4618491897
1.2757684395
52
1.4746508055
1.2762235932
52
1.4875189897
1.2766788379
-48
1.4755788986
1.2771341737
-48
1.4636961198
1.2775896005
52
1.4765073397
1.2780451184
52
1.4893851778
1.2785007274
52
1.5023299808
1.2789564276
-48
1.4903187968
1.2794122189
52
1.5032684546
1.2798681013
-48
1.491252766
1.2803240749
52
1.5042072804
1.2807801397
52
1.5172291583
1.2812362958
-48
1.5051464583
1.281692543
-48
1.4931217553
1.2821488815
52
1.5060859884
1.2826053113
-48
1.4940567757
1.2830618324
52
1.5070258709
1.2835184447
-48
1.4949921467
1.2839751484
-48
1.4830161844
1.2844319435
52
1.4959278686
1.2848888298
52
1.5089066935
1.2853458076
-48
1.4968639414
1.2858028768
52
1.5098476339
1.2862600373
-48
1.4978003652
1.2867172894
-48
1.4858109235
1.2871746328
-48
1.473879031
1.2876320677
-48
1.4620044117
1.2880895942
-48
1.4501867905
1.2885472121
52
1.4629277618
1.2890049215
52
1.4757349862
1.2894627225
-48
1.4638514583
1.289920615
-48
1.4520249713
1.2903785992
-48
1.4402552514
1.2908366749
-48
1.4285420262
1.2912948422
52
1.4411704447
1.2917531012
-48
1.4294528266
1.2922114518
-48
1.417791453
1.2926698941
52
1.4303639686
1.2931284281
-48
1.4186982215
1.2935870538
-48
1.4070884701
1.2940457712
-48
1.3955344454
1.2945045803
52
1.4079912245
1.2949634812
52
1.4205127789
1.2954224739
-48
1.4088943175
1.2958815584
52
1.421420568
1.2963407348
-48
1.4097977493
1.2968000029
52
1.4223286976
1.2972593629
-48
1.4107015198
1.2977188148
-48
1.3991301525
1.2981783585
52
1.4116056293
1.2986379942
-48
1.4000299223
1.2990977218
52
1.4125100779
1.2995575413
52
1.4250551303
1.3000174529
52
1.437665417
1.3004774563
52
1.4503412771
1.3009375518
-48
1.438579639
1.3013977393
52
1.4512602531
1.3018580189
-48
1.4394942039
1.3023183905
-48
1.4277846317
1.3027788542
-48
1.4161312655
1.3032394099
-48
1.4045338354
1.3037000578
-48
1.392992073
1.3041607978
52
1.4054356318
1.30462163
-48
1.3938895408
1.3050825543
-48
1.382398871
1.3055435708
52
1.3947873451
1.3060046796
52
1.4072402393
1.3064658805
-48
1.3956854862
1.3069271737
52
1.4081430507
1.3073885591
52
1.4206653945
1.3078500368
-48
1.4090462007
1.3083116068
-48
1.3974827789
1.3087732691
-48
1.3859748615
1.3092350238
-48
1.3745221822
1.3096968708
-48
1.3631244757
1.3101588102
52
1.375412723
1.3106208419
-48
1.3640107419
1.3110829661
52
1.3763035978
1.3115451827
-48
1.3648973405
1.3120074917
52
1.3771948067
1.3124698932
-48
1.3657842716
1.3129323872
52
1.3780863498
1.3133949737
-48
1.3666715354
1.3138576527
-48
1.355311512
1.3143204242
52
1.3675591319
1.3147832883
-48
1.356194848
1.315246245
-48
1.3448851128
1.3157092942
52
1.3570785153
1.3161724361
52
1.3693353236
1.3166356706
-48
1.3579625141
1.3170989977
-48
1.346644294
1.3175624175
-48
1.3353804014
1.31802593
-48
1.3241705755
1.3184895352
-48
1.3130145567
1.3189532331
52
1.3250422324
1.3194170237
52
1.337132452
1.3198809071
-48
1.3259142162
1.3203448833
52
1.3380089702
1.3208089523
-48
1.3267865271
1.3212731141
-48
1.3156179518
1.3217373687
-48
1.3045029856
1.3222017162
-48
1.2934413713
1.3226661565
-48
1.2824328527
1.3231306897
-48
1.271477175
1.3235953159
52
1.2832888563
1.3240600349
-48
1.2723290698
1.3245248469
-48
1.2614218903
1.3249897519
52
1.2731812841
1.3254547499
-48
1.2622700139
1.3259198408
-48
1.2514111179
1.3263850248
-48
1.2406043445
1.3268503018
-48
1.2298494436
1.3273156718
52
1.2414446607
1.327781135
-48
1.2306857264
1.3282466912
52
1.2422852922
1.3287123405
52
1.2539451757
1.329178083
-48
1.2431262388
1.3296439186
52
1.2547904953
1.3301098474
52
1.2665154058
1.3305758694
-48
1.2556361319
1.3310419846
-48
1.2448090785
1.331508193
52
1.2564820857
1.3319744946
52
1.2682157925
1.3324408895
-48
1.2573283567
1.3329073777
-48
1.2464931806
1.3333739591
52
1.2581749451
1.3338406339
52
1.2699174549
1.3343074021
52
1.2817210256
1.3347742635
-48
1.2707687647
1.3352412184
-48
1.2598690746
1.3357082666
52
1.2716203938
1.3361754083
-48
1.2607166159
1.3366426434
-48
1.2498651762
1.3371099719
-48
1.2390658233
1.3375773939
-48
1.2283183074
1.3380449094
52
1.2399055626
1.3385125184
52
1.2515530715
1.3389802209
52
1.2632611475
1.3394480169
52
1.2750301054
1.3399159065
-48
1.2641099609
1.3403838897
-48
1.2532422331
1.3408519665
52
1.2649590927
1.3413201369
-48
1.2540872891
1.3417884009
-48
1.2432676701
1.3422567586
52
1.254932662
1.3427252099
-48
1.2441089852
1.343193755
-48
1.2333372621
1.3436623937
-48
1.2226172432
1.3441311262
-48
1.2119486804
1.3445999524
52
1.2234508136
1.3450688724
-48
1.2127782497
1.3455378862
-48
1.2021569141
1.3460069938
-48
1.1915865609
1.3464761952
-48
1.1810669454
1.3469454904
-48
1.1705978241
1.3474148795
52
1.1818849327
1.3478843625
52
1.1932307344
1.3483539393
52
1.2046355342
1.3488236101
52
1.216099639
1.3492933749
52
1.2276233571
1.3497632335
52
1.2392069986
1.3502331862
-48
1.228458805
1.3507032328
52
1.2400467908
1.3511733735
-48
1.2292945662
1.3516436081
52
1.2408868979
1.3521139369
52
1.2525395098
1.3525843596
-48
1.2417273201
1.3530548765
52
1.2533843022
1.3535254875
-48
1.2425680576
1.3539961926
-48
1.2318037309
1.3544669918
52
1.2434091103
1.3549378852
-48
1.2326407465
1.3554088728
52
1.2442504784
1.3558799546
-48
1.2334780761
1.3563511306
52
1.2450921621
1.3568224008
52
1.2567666414
1.3572937653
52
1.2685018279
1.357765224
-48
1.2576130191
1.3582367771
-48
1.2467764766
1.3587084244
52
1.2584597143
1.3591801661
-48
1.2476191077
1.3596520021
-48
1.236830536
1.3601239325
52
1.2484620548
1.3605959573
-48
1.2376694369
1.3610680765
52
1.249305318
1.3615402901
-48
1.2385086524
1.3620125982
-48
1.2277638109
1.3624850007
-48
1.2170705446
1.3629574977
-48
1.206428606
1.3634300892
52
1.2179020348
1.3639027752
52
1.2294351253
1.3643755558
52
1.241028188
1.3648484309
52
1.2526815346
1.3653214006
-48
1.2418686632
1.3657944649
52
1.2535263802
1.3662676238
52
1.2652447174
1.3667408773
-48
1.2543715428
1.3672142255
-48
1.2435505594
1.3676876683
52
1.2552170223
1.3681612058
-48
1.2443919806
1.3686348381
-48
1.2336188991
1.369108565
-48
1.2228975284
1.3695823868
-48
1.2122276202
1.3700563032
52
1.2237312038
1.3705303145
-48
1.2130572941
1.3710044206
52
1.224565192
1.3714786214
-48
1.2138872791
1.3719529172
52
1.2253994929
1.3724273078
52
1.2369715703
1.3729017932
-48
1.2262341068
1.3733763736
52
1.2378105241
1.3738510488
52
1.2494471388
1.3743258191
52
1.261144264
1.3748006842
-48
1.2502907715
1.3752756444
-48
1.2394893758
1.3757506995
52
1.2511347205
1.3762258496
52
1.2628406211
1.3767010948
-48
1.2519789861
1.377176435
-48
1.241169487
1.3776518703
-48
1.2304118734
1.3781274007
-48
1.2197058964
1.3786030262
-48
1.2090513081
1.3790787468
52
1.2205383749
1.3795545625
52
1.2320851745
1.3800304734
-48
1.2213711657
1.3805064795
-48
1.2107085841
1.3809825808
52
1.2222042687
1.3814587773
52
1.2337597309
1.3819350691
52
1.2453752815
1.3824114561
52
1.257051233
1.3828879384
52
1.2687878994
1.383364516
52
1.2805855964
1.3838411889
-48
1.2696387856
1.3843179571
-48
1.2587445194
1.3847948207
52
1.2704899909
1.3852717797
52
1.2822965389
1.385748834
52
1.2941644809
1.3862259838
52
1.3060941362
1.386703229
52
1.3180858257
1.3871805696
-48
1.3069590137
1.3876580058
-48
1.2958856104
1.3881355374
-48
1.2848653595
1.3886131645
-48
1.2738980058
1.3890908871
-48
1.2629832954
1.3895687053
-48
1.2521209755
1.390046619
-48
1.2413107949
1.3905246283
52
1.252965611
1.3910027333
-48
1.2421513761
1.3914809338
-48
1.2313890495
1.39195923
52
1.2429922725
1.3924376218
52
1.2546558323
1.3929161094
52
1.2663800427
1.3933946926
52
1.2781652189
1.3938733715
52
1.290011678
1.3943521462
-48
1.279019622
1.3948310166
52
1.290870524
1.3953099828
-48
1.2798743455
1.3957890448
52
1.2917296921
1.3962682026
-48
1.2807293896
1.3967474563
52
1.2925891824
1.3972268058
52
1.3045106461
1.3977062511
52
1.3164941015
1.3981857924
-48
1.3053749298
1.3986654295
52
1.3173628794
1.3991451626
52
1.3294131664
1.3996249917
-48
1.3182319832
1.4001049167
-48
1.3071044697
1.4005849376
-48
1.2960303682
1.4010650546
52
1.3079697262
1.4015452676
-48
1.2968914715
1.4020255767
-48
1.2858663924
1.4025059818
52
1.2977528976
1.402986483
52
1.3097012127
1.4034670803
52
1.321711659
1.4039477737
52
1.3337845596
1.4044285633
52
1.3459202394
1.404909449
-48
1.3346598222
1.4053904309
-48
1.3234534551
1.405871509
-48
1.3123008785
1.4063526833
52
1.324324843
1.4068339538
-48
1.3131680838
1.4073153206
-48
1.302064877
1.4077967837
52
1.3140356144
1.408278343
52
1.3260685996
1.4087599987
52
1.3381641563
1.4092417507
52
1.3503226099
1.409723599
52
1.3625442875
1.4102055437
52
1.3748295177
1.4106875849
-48
1.3634303361
1.4111697224
-48
1.3520858705
1.4116519563
-48
1.3407958583
1.4121342867
52
1.3529679967
1.4126167136
52
1.3652034303
1.4130992369
-48
1.3538504539
1.4135818568
-48
1.3425519717
1.4140645731
52
1.3547332419
1.414547386
52
1.3669778548
1.4150302955
52
1.3792861396
1.4155133016
-48
1.3678655662
1.4159964042
52
1.3801784671
1.4164796035
52
1.3925553951
1.4169628994
52
1.4049966832
1.417446292
52
1.4175026659
1.4179297813
-48
1.4058986531
1.4184133672
-48
1.3943503396
1.4188970499
52
1.4068009614
1.4193808293
-48
1.3952483168
1.4198647055
52
1.407703608
1.4203486784
-48
1.3961466307
1.4208327482
52
1.4086065932
1.4213169147
52
1.4211313475
1.4218011781
-48
1.409509917
1.4222855383
52
1.4220393686
1.4227699954
52
1.4346339733
1.4232545494
52
1.4472940699
1.4237392003
-48
1.4355470584
1.4242239482
-48
1.4238564325
1.424708793
-48
1.4122219216
1.4251937347
-48
1.4006432564
1.4256787735
-48
1.3891201688
1.4261639092
-48
1.377652392
1.426649142
-48
1.3662396605
1.4271344718
-48
1.3548817101
1.4276198987
-48
1.3435782779
1.4281054227
52
1.355764885
1.4285910438
52
1.3680148624
1.429076762
-48
1.356648391
1.4295625774
52
1.3689029627
1.4300484899
52
1.3812212581
1.4305344996
-48
1.369791396
1.4310206065
-48
1.3584163973
1.4315068106
-48
1.3470959986
1.431993112
52
1.3593008978
1.4324795106
-48
1.3479762535
1.4329660065
-48
1.3367059675
1.4334525997
-48
1.3254897788
1.4339392902
-48
1.3143274279
1.4344260781
52
1.3263619305
1.4349129633
52
1.3384590126
1.4353999459
52
1.3506189994
1.4358870259
52
1.3628422182
1.4363742033
52
1.3751289978
1.4368614781
52
1.3874796685
1.4373488504
52
1.3998945628
1.4378363202
-48
1.3883750689
1.4383238874
52
1.4007946193
1.4388115522
-48
1.3892708051
1.4392993145
52
1.4016950133
1.4397871744
52
1.4141838274
1.4402751318
-48
1.402595745
1.4407631869
-48
1.3910632854
1.4412513395
52
1.4034968145
1.4417395898
-48
1.3919600298
1.4422279377
-48
1.3804786216
1.4427163833
-48
1.3690523243
1.4432049265
52
1.3813713964
1.4436935675
-48
1.3699408136
1.4441823062
-48
1.3585650977
1.4446711427
52
1.3708296363
1.4451600769
52
1.3831579504
1.4456491089
-48
1.3717187922
1.4461382388
-48
1.360334542
1.4466274664
-48
1.3490049362
1.4471167919
52
1.3612197619
1.4476062153
52
1.3734981046
1.4480957365
52
1.3858402948
1.4485853557
-48
1.3743882614
1.4490750727
52
1.3867350803
1.4495648877
52
1.3991461027
1.4500548007
52
1.4116216625
1.4505448117
52
1.4241620951
1.4510349206
52
1.436767738
1.4515251276
-48
1.4250712529
1.4520154327
52
1.4376816234
1.4525058357
52
1.4503575678
1.4529963369
52
1.4630994272
1.4534869362
52
1.4759075442
1.4539776336
-48
1.464023188
1.4544684291
-48
1.4521958767
1.4549593228
52
1.4649472952
1.4554503146
52
1.4777650212
1.4559414047
52
1.4906493993
1.456432593
-48
1.4786942822
1.4569238795
52
1.4915834924
1.4574152643
-48
1.4796238917
1.4579067473
-48
1.467721697
1.4583983287
-48
1.4558766328
1.4588900083
-48
1.444088425
1.4593817863
52
1.4567976848
1.4598736627
-48
1.4450050559
1.4603656374
-48
1.4332690317
1.4608577106
52
1.4459220306
1.4613498821
52
1.4586408252
1.4618421521
52
1.4714257575
1.4623345205
52
1.4842771714
1.4628269874
52
1.4971954127
1.4633195528
-48
1.4852088747
1.4638122167
-48
1.4732798721
1.4643049792
52
1.4861409275
1.4647978402
52
1.4990688603
1.4652907997
-48
1.4870733298
1.4657838579
52
1.5000061111
1.4662770147
-48
1.4880060817
1.4667702701
52
1.5009437134
1.4672636241
-48
1.4889391835
1.4677570768
52
1.5018816673
1.4682506283
52
1.514891452
1.4687442784
-48
1.502819973
1.4692380272
-48
1.4908064371
1.4697318748
-48
1.4788505662
1.4702258212
52
1.4917405892
1.4707198664
-48
1.4797802343
1.4712140104
52
1.4926750916
1.4717082532
52
1.505637002
1.4722025948
-48
1.4936099444
1.4726970353
-48
1.4816406167
1.4731915747
52
1.4945451479
1.4736862131
52
1.5075167827
1.4741809503
52
1.5205558699
1.4746757865
-48
1.5084572018
1.4751707216
52
1.5215011792
1.4756657558
-48
1.5093979735
1.4761608889
52
1.522446843
1.4766561211
52
1.5355635666
1.4771514523
-48
1.5233928615
1.4776468826
-48
1.5112805757
1.478142412
52
1.5243392347
1.4786380405
52
1.5374657988
1.4791337681
-48
1.5252859629
1.4796295949
-48
1.5131645903
1.4801255208
52
1.5262330462
1.4806215459
-48
1.5141071275
1.4811176702
-48
1.5020394133
1.4816138937
-48
1.4900296241
1.4821102165
52
1.5029777782
1.4826066385
52
1.5159932626
1.4831031599
-48
1.503916495
1.4835997805
52
1.5169368608
1.4840965005
-48
1.5048555638
1.4845933198
52
1.5178808128
1.4850902384
-48
1.5057949849
1.4855872565
52
1.5188251188
1.4860843739
-48
1.5067347582
1.4865815908
-48
1.4947024314
1.4870789071
-48
1.4827278597
1.4875763229
52
1.4956380446
1.4880738382
52
1.5086153624
1.4885714529
52
1.5216601623
1.4890691672
-48
1.5095561935
1.489566981
-48
1.4975103238
1.4900648944
52
1.5104973775
1.4905629074
-48
1.49844699
1.49106102
-48
1.4864544445
1.4915592322
-48
1.4745194632
1.4920575441
-48
1.4626417697
1.4925559556
52
1.4754475069
1.4930544668
-48
1.4635653589
1.4935530776
52
1.4763758988
1.4940517883
52
1.4892530534
1.4945505986
52
1.5021971693
1.4950495087
52
1.5152085946
1.4955485186
-48
1.5031355934
1.4960476283
-48
1.4911205425
1.4965468379
52
1.5040743693
1.4970461472
-48
1.4920548124
1.4975455565
-48
1.4800929493
1.4980450656
-48
1.4681885031
1.4985446746
-48
1.4563411983
1.4990443835
52
1.4691141725
1.4995441924
-48
1.4572624245
1.5000441012
52
1.4700401891
1.5005441101
-48
1.4581839962
1.5010442189
52
1.470966553
1.5015444277
52
1.483815579
1.5020447366
52
1.49673142
1.5025451456
-48
1.4847471092
1.5030456546
-48
1.4728203231
1.5035462637
52
1.4856789888
1.504046973
52
1.4986045195
1.5045477824
52
1.511597263
1.5050486919
-48
1.4995415962
1.5055497017
-48
1.4875437965
1.5060508116
-48
1.4756035863
1.5065520218
-48
1.4637206891
1.5070533322
52
1.4765320367
1.5075547428
52
1.4894100032
1.5080562538
-48
1.4774608352
1.508557865
-48
1.4655690232
1.5090595766
52
1.4783899821
1.5095613885
-48
1.4664937102
1.5100633008
-48
1.4546545404
1.5105653135
52
1.467418744
1.5110674265
52
1.4802493215
1.51156964
-48
1.4683441248
1.5120719539
-48
1.456496073
1.5125743683
52
1.4692698525
1.5130768832
-48
1.4574173572
1.5135794986
52
1.4701959275
1.5140822145
-48
1.458338987
1.5145850309
-48
1.4465389599
1.5150879479
52
1.4592609625
1.5155909655
52
1.4720491195
1.5160940837
52
1.4849037749
1.5165973025
52
1.4978252746
1.517100622
-48
1.4858357132
1.5176040421
52
1.4987620589
1.5181075629
-48
1.4867680011
1.5186111844
-48
1.4748315147
1.5191149067
-48
1.4629523234
1.5196187297
-48
1.4511301522
1.5201226534
-48
1.4393647275
1.5206266779
52
1.4520494241
1.5211308033
-48
1.4402795869
1.5216350294
52
1.4529690407
1.5221393564
-48
1.4411947893
1.5226437843
-48
1.4294770543
1.5231483131
-48
1.4178155645
1.5236529427
52
1.4303882054
1.5241576733
-48
1.418722342
1.5246625048
52
1.4312996982
1.5251674373
52
1.4439424566
1.5256724708
-48
1.4322115328
1.5261776053
52
1.4448590328
1.5266828409
-48
1.4331237094
1.5271881774
-48
1.4214447156
1.5276936151
52
1.4340362282
1.5281991538
52
1.4466932165
1.5287047936
52
1.4594160213
1.5292105346
-48
1.4476108244
1.5297163767
52
1.4603384007
1.5302223199
52
1.4731321603
1.5307283644
-48
1.461261126
1.5312345101
-48
1.4494470726
1.531740757
52
1.4621841973
1.5322471051
-48
1.4503657132
1.5327535546
-48
1.4386039578
1.5332601053
52
1.4512846983
1.5337667573
-48
1.4395185318
1.5342735106
-48
1.4278088428
1.5347803653
52
1.4404334488
1.5352873214
52
1.4531237028
1.5357943789
52
1.465879946
1.5363015378
-48
1.4540437223
1.5368087981
52
1.4668047496
1.5373161598
52
1.4796321343
1.5378236231
52
1.4925262214
1.5383311878
52
1.5054873578
1.538838854
52
1.518515892
1.5393466218
-48
1.5064270158
1.5398544911
52
1.5194604362
1.540362462
52
1.5325616305
1.5408705345
-48
1.5204053347
1.5413787086
-48
1.5083073891
1.5418869844
52
1.5213505875
1.5423953618
-48
1.5092481047
1.5429038408
52
1.5222961948
1.5434124216
52
1.535412135
1.5439211041
52
1.5485962781
1.5444298883
52
1.5618489788
1.5449387743
-48
1.5495521037
1.545447762
-48
1.5373142536
1.5459568516
52
1.5505082877
1.546466043
52
1.5637709308
1.5469753362
52
1.5771025396
1.5474847312
52
1.5905034728
1.5479942282
52
1.6039740909
1.548503827
52
1.6175147562
1.5490135278
52
1.6311258329
1.5495233305
52
1.6448076872
1.5500332352
-48
1.6321126103
1.5505432418
-48
1.6194784698
1.5510533505
52
1.6330997579
1.5515635611
-48
1.620460879
1.5520738738
-48
1.6078826668
1.5525842886
-48
1.59536483
1.5530948055
-48
1.5829070788
1.5536054244
52
1.5963381956
1.5541161455
52
1.6098391542
1.5546269687
52
1.6234103178
1.5551378941
-48
1.6108179483
1.5556489217
52
1.6243942017
1.5561600515
-48
1.6117971095
1.5566712835
52
1.6253784545
1.5571826178
52
1.6390304224
1.5576940543
-48
1.6263630764
1.5582055931
52
1.6400201644
1.5587172342
-48
1.6273480676
1.5592289777
-48
1.6147367969
1.5597408235
-48
1.6021860602
1.5602527716
52
1.6157174278
1.5607648222
52
1.6293191584
1.5612769751
-48
1.6166984264
1.5617892305
52
1.6303052582
1.5623015884
52
1.6439828456
1.5628140487
52
1.6577315564
1.5633266115
-48
1.6449744449
1.5638392768
52
1.658728312
1.5643520447
-48
1.6459664161
1.5648649151
52
1.6597254415
1.5653778881
52
1.6735560138
1.5658909637
-48
1.6607229449
1.5664041419
52
1.6745587042
1.5669174227
-48
1.6617208225
1.5674308062
-48
1.6489445625
1.5679442923
52
1.6627190742
1.5684578812
-48
1.6499380227
1.5689715728
52
1.6637177004
1.5694853671
-48
1.6509318554
1.5699992642
52
1.6647167011
1.570513264
-48
1.6519260609
1.5710273667
-48
1.6391968158
1.5715415721
-48
1.6265286711
1.5720558804
52
1.6401866202
1.5725702916
-48
1.6275137244
1.5730848057
52
1.6411767958
1.5735994226
-48
1.6284991472
1.5741141425
-48
1.6158823513
1.5746289654
52
1.6294849395
1.5751438911
-48
1.6168634118
1.5756589199
-48
1.6043024674
1.5761740517
-48
1.5918018156
1.5766892865
52
1.605279185
1.5772046244
-48
1.5927738449
1.5777200653
-48
1.5803285305
1.5782356093
52
1.5937462388
1.5787512564
52
1.6072337193
1.5792670067
-48
1.5947189974
1.5797828601
-48
1.5822643462
1.5802988167
-48
1.5698694774
1.5808148764
-48
1.5575341039
1.5813310394
-48
1.5452579402
1.5818473056
-48
1.533040702
1.5823636751
52
1.5462125137
1.5828801478
52
1.5594528188
1.5833967238
-48
1.5471674452
1.5839134032
-48
1.5349410415
1.5844301859
52
1.5481227349
1.5849470719
52
1.5613729731
1.5854640613
-48
1.5490783829
1.5859811541
-48
1.5368428066
1.5864983504
-48
1.5246659612
1.58701565
-48
1.5125475645
1.5875330532
52
1.5256128119
1.5880505598
52
1.5387459985
1.5885681699
-48
1.5265600177
1.5890858835
52
1.5396981298
1.5896037007
-48
1.5275075788
1.5901216214
-48
1.5153755424
1.5906396458
-48
1.5033017398
1.5911577737
-48
1.4912858914
1.5916760052
52
1.5042405781
1.5921943404
-48
1.4922202233
1.5927127793
52
1.5051797685
1.5932313219
-48
1.4931549056
1.5937499681
-48
1.481187762
1.5942687181
-48
1.4692780608
1.5947875719
52
1.4821183067
1.5953065294
-48
1.4702041388
1.5958255907
-48
1.458347159
1.5963447558
-48
1.4465470926
1.5968640248
52
1.4592691375
1.5973833976
52
1.472057337
1.5979028742
-48
1.4601914618
1.5984224548
-48
1.4483825428
1.5989421393
-48
1.4366303065
1.5994619277
-48
1.4249344811
1.5999818201
52
1.4375441404
1.6005018165
-48
1.4258439285
1.6010219168
52
1.4384583169
1.6015421212
-48
1.426753717
1.6020624296
-48
1.4151052992
1.6025828421
52
1.4276638467
1.6031033587
-48
1.4160110603
1.6036239794
52
1.4285743178
1.6041447042
-48
1.416917161
1.6046655331
-48
1.4053159587
1.6051864662
-48
1.3937704421
1.6057075035
-48
1.382280344
1.606228645
52
1.3946682017
1.6067498907
-48
1.3831737944
1.6072712407
52
1.3955662981
1.607792695
52
1.4080232429
1.6083142535
-48
1.3964647313
1.6088359164
-48
1.3849617006
1.6093576835
52
1.3973635014
1.6098795551
52
1.4098297916
1.610401531
52
1.4223609065
1.6109236113
-48
1.4107335742
1.611445796
52
1.4232693888
1.6119680852
-48
1.4116376957
1.6124904788
-48
1.4000618348
1.6130129769
-48
1.388541538
1.6135355795
52
1.400961954
1.6140582866
52
1.4134469561
1.6145810983
52
1.4259968803
1.6151040145
52
1.4386120641
1.6156270353
52
1.4512928468
1.6161501607
-48
1.4395266411
1.6166733907
-48
1.4278169133
1.6171967254
52
1.4404415612
1.6177201647
-48
1.4287274417
1.6182437088
-48
1.41706955
1.6187673575
-48
1.4054676162
1.619291111
52
1.4179760478
1.6198149692
52
1.4305495232
1.6203389322
-48
1.4188828855
1.620863
52
1.4314610765
1.6213871726
52
1.4441046741
1.62191145
52
1.4568140184
1.6224358323
-48
1.4450213111
1.6229603195
52
1.4577354219
1.6234849115
-48
1.4459382919
1.6240096085
52
1.458657171
1.6245344105
52
1.4714421883
1.6250593173
-48
1.4595792658
1.6255843292
52
1.472369078
1.6261094461
52
1.4852253972
1.626634668
-48
1.4732963153
1.6271599949
-48
1.461424493
1.6276854269
52
1.4742239003
1.628210964
-48
1.4623476256
1.6287366062
52
1.4751518333
1.6292623535
-48
1.4632711045
1.629788206
-48
1.4514474032
1.6303141636
52
1.4641949297
1.6308402264
-48
1.452366794
1.6313663945
-48
1.4405954334
1.6318926678
52
1.4532865297
1.6324190463
-48
1.4415107543
1.6329455301
52
1.4542066102
1.6334721192
52
1.4669684846
1.6339988136
52
1.4797967207
1.6345256134
52
1.4926916637
1.6350525185
52
1.5056536603
1.635579529
-48
1.4936265228
1.6361066449
-48
1.4816571154
1.6366338662
-48
1.4697451613
1.637161193
-48
1.4578903845
1.6376886253
52
1.4706714145
1.638216163
-48
1.4588121917
1.6387438062
52
1.4715980151
1.639271555
-48
1.4597343447
1.6397994093
-48
1.4479276198
1.6403273692
-48
1.4361775672
1.6408554346
-48
1.4244839149
1.6413836057
52
1.4370912313
1.6419118825
-48
1.4253931933
1.6424402648
52
1.438005238
1.6429687529
52
1.4506828652
1.6434973466
52
1.4634264161
1.6440260461
52
1.4762362335
1.6445548513
52
1.4891126619
1.6450837623
52
1.5020560477
1.645612779
52
1.5150667392
1.6461419016
52
1.5281450862
1.64667113
-48
1.5160099898
1.6472004642
-48
1.5039331418
1.6477299043
52
1.5169535942
1.6482594503
-48
1.5048722169
1.6487891022
-48
1.4928488303
1.64931886
-48
1.4808831559
1.6498487238
52
1.4937837483
1.6503786935
52
1.5067514238
1.6509087692
-48
1.494719017
1.651438951
52
1.5076915559
1.6519692388
-48
1.4956546364
1.6524996326
52
1.5086320405
1.6530301326
52
1.5216769271
1.6535607386
-48
1.5095728779
1.6540914507
52
1.5226226568
1.654622269
52
1.5357402946
1.6551531935
52
1.5489261442
1.6556842241
-48
1.5366912987
1.656215361
52
1.5498820934
1.656746604
52
1.5631414803
1.6572779533
52
1.576469816
1.6578094089
-48
1.5641027609
1.6583409708
52
1.5774360953
1.658872639
-48
1.565064402
1.6594044135
-48
1.5527520929
1.6599362944
52
1.5660264037
1.6604682817
52
1.579369741
1.6610003753
52
1.5927824637
1.6615325754
-48
1.5803371079
1.6620648819
52
1.5937548608
1.6625972949
52
1.6072423861
1.6631298144
52
1.6208000465
1.6636624403
52
1.6344282068
1.6641951728
-48
1.6217829514
1.6647280119
52
1.6354162227
1.6652609575
52
1.6491203871
1.6657940096
52
1.6628958131
1.6663271684
-48
1.6501139132
1.6668604339
-48
1.6373933664
1.667393806
-48
1.6247338782
1.6679272847
-48
1.6121351556
1.6684608702
-48
1.5995969069
1.6689945624
-48
1.5871188417
1.6695283613
52
1.6005718597
1.6700622669
-48
1.5880891148
1.6705962794
-48
1.575666287
1.6711303987
-48
1.5633030888
1.6716646247
-48
1.550999234
1.6721989577
52
1.56426443
1.6727333975
52
1.5775986051
1.6732679441
52
1.5910021178
1.6738025977
-48
1.5785653077
1.6743373582
-48
1.5661881942
1.6748722257
52
1.5795323728
1.6754072002
52
1.5929459411
1.6759422816
52
1.60642926
1.6764774701
52
1.6199826922
1.6770127655
-48
1.6074067753
1.6775481681
-48
1.5948912227
1.6780836777
52
1.6083846571
1.6786192945
52
1.6219482573
1.6791550183
-48
1.6093629057
1.6796908493
-48
1.5968379637
1.6802267875
52
1.6103415211
1.6807628329
52
1.623915297
1.6812989854
52
1.6375596566
1.6818352452
-48
1.6248993702
1.6823716123
-48
1.6122998533
1.6829080866
-48
1.599760814
1.6834446682
52
1.6132795702
1.6839813571
52
1.626868624
1.6845181534
-48
1.6142596546
1.685055057
52
1.6278538048
1.6855920681
52
1.6415186446
1.6861291865
52
1.6552545415
1.6866664123
-48
1.6425093197
1.6872037456
-48
1.629825275
1.6877411863
52
1.6435003664
1.6882787346
-48
1.6308115646
1.6888163903
52
1.6444917848
1.6893541536
-48
1.6317982242
1.6898920244
-48
1.6191655927
1.6904300028
-48
1.6065935979
1.6909680888
-48
1.5940819486
1.6915062825
52
1.6075711748
1.6920445837
-48
1.5950548331
1.6925829926
-48
1.5825985699
1.6931215092
-48
1.5702020968
1.6936601335
-48
1.5578651267
1.6941988656
52
1.5711660254
1.6947377053
-48
1.5588244285
1.6952766529
52
1.5721303155
1.6958157082
-48
1.55978409
1.6963548713
52
1.5730949672
1.6968941423
52
1.5864750611
1.6974335211
52
1.5999247314
1.6979730079
52
1.61344434
1.6985126025
-48
1.6008998072
1.699052305
-48
1.5884154881
1.6995921154
52
1.6018752486
1.7001320339
-48
1.5893862474
1.7006720603
-48
1.5769571934
1.7012121947
-48
1.5645877989
1.7017524371
-48
1.5522777775
1.7022927876
52
1.5655496219
1.7028332462
52
1.5788904799
1.7033738128
52
1.5923007104
1.7039144876
52
1.6057806741
1.7044552705
52
1.6193307336
1.7049961615
52
1.6329512535
1.7055371608
-48
1.6203130874
1.7060782682
-48
1.6077355846
1.7066194838
52
1.6212958097
1.7071608077
-48
1.6087135898
1.7077022399
52
1.6222789004
1.7082437803
-48
1.6096919617
1.7087854291
52
1.6232623599
1.7093271862
52
1.6369033242
1.7098690516
52
1.6506152215
1.7104110254
-48
1.6378922684
1.7109531076
-48
1.6252303855
1.7114952983
-48
1.6126292797
1.7120375973
-48
1.6000886591
1.7125800048
-48
1.5876082336
1.7131225208
52
1.6010637964
1.7136651453
52
1.6145893281
1.7142078784
-48
1.6020392994
1.71475072
52
1.6155699037
1.7152936701
-48
1.6030151682
1.7158367288
-48
1.5905206954
1.7163798962
52
1.603991403
1.7169231722
-48
1.5914922442
1.7174665568
52
1.6049680039
1.7180100501
Excel Journal Format due Monday February 24th
Session 2: Extreme Early Retirement
Session 3: Arithmetic and Geometric Rates of Return
5. Session 4: Signal-to-noise ratio
3 10000 5000 10250.0 15762.5 5512.5 1
4 10000 5000 15762.5 21550.6 11300.6 1
5 10000 5000 21550.6 27628.2 17378.2 1
6 10000 5000 27628.2 34009.6 23759.6 1
7 10000 5000 34009.6 40710.0 30460.0 1
8 10000 5000 40710.0 47745.5 37495.5 1
9 10000 5000 47745.5 55132.8 44882.8 1
10 10000 5000 55132.8 62889.5 52639.5 1
11 10000 5000 62889.5 71033.9 60783.9 1
12 10000 5000 71033.9 79585.6 69335.6 1
13 10000 5000 79585.6 88564.9 78314.9 1
s 0.6
T 10.87572
105000
2
MEAN (DRIFT)
STANDARD DEVIATION (VARIATIONS AROUND THE DRIFT)
bp per day
Rate
Yearly
1
0.0001
0.02
5
51
8
9
12
50
0.005
0.0
7
3
25
39
2
0.0002
0.05
6
86
38
91
10
0.01
0.
15
87
4
78
3
0.0003
0.07
85
18
47
150
0.015
0.
23
11
61
4
0.0004
0.10
60
31
16
20
0.3
17
49
57
5
0.0005
0.
13
24
45
250
0.025
0.39
68
26
67
6
0.0006
0.1
63
76
53
89
30
0.03
0.47
62
35
36
7
0.0007
0.
19
28
41
153
350
0.035
0.
55
56
77
75
8
0.0008
0.
22
32
59
71
40
0.04
0.6
34
80
14
9
0.0009
0.25
44
96
450
0.045
0.71
43
52
54
10
0.001
0.28
64
340
444
500
0.
79
37
253
33
11
0.0011
0.31
92
29
233
550
0.055
0.8
73
97
93
27
12
0.0012
0.35
285
70
600
0.06
0.
95
247
72
13
0.0013
0.
387
338
122
65
0.065
1.031
84
113
Assume drift of 5bp per day and noise
200
YEAR
DAY
Arithmetic
0.13
42
46
509
Noise
0.1
58
74
507
Geometric
0.1
21
464
Note: we assume here only
252
Stock prices, however, should be compounded over the entire year, that is,
365
Drift Noise
Enter values for the drift and the noise in green cells
For example 2bp per day is about 5.17% year (1.0
517
Noise (standard dev.) should be about 20-50 times larger than drift
Day
drift bp/day
noise bp/day
1 0.005
2 0.0002
-0.005
3 0.0002 -0.005
4 0.0002 0.005
5 0.0002 0.005
6 0.0002 0.005
7 0.0002 0.005
8 0.0002 -0.005
9 0.0002 -0.005
10 0.0002 -0.005
11 0.0002 0.005
12 0.0002 0.005
13 0.0002 0.005
14 0.0002 -0.005
15 0.0002 0.005
16 0.0002 0.005
17 0.0002 0.005
18 0.0002 -0.005
19 0.0002 0.005
20 0.0002 -0.005
21 0.0002 0.005
22 0.0002 -0.005
23 0.0002 0.005
24 0.0002 0.005
25 0.0002 -0.005
26 0.0002 -0.005
27 0.0002 0.005
28 0.0002 -0.005
29 0.0002 0.005
30 0.0002 0.005
31 0.0002 0.005
32 0.0002 0.005
33 0.0002 0.005
34 0.0002 0.005
35 0.0002 0.005
36 0.0002 -0.005
37 0.0002 -0.005
38 0.0002 0.005
39 0.0002 0.005
40 0.0002 0.005
41 0.0002 -0.005
42 0.0002 0.005
43 0.0002 0.005
44 0.0002 -0.005
45 0.0002 -0.005
46 0.0002 -0.005
47 0.0002 0.005
48
49 0.0002 0.005
50 0.0002 0.005
51 0.0002 0.005
52 0.0002 -0.005
53 0.0002 0.005
54 0.0002 -0.005
55 0.0002 0.005
56 0.0002 -0.005
57 0.0002 -0.005
58 0.0002 -0.005
59 0.0002 0.005
60 0.0002 -0.005
61 0.0002 0.005
62 0.0002 -0.005
63 0.0002 -0.005
64 0.0002 -0.005
65 0.0002 0.005
66
67 0.0002 -0.005
68 0.0002 0.005
69
70 0.0002 -0.005
71 0.0002 0.005
72 0.0002 0.005
73 0.0002 -0.005
74 0.0002 0.005
75 0.0002 -0.005
76 0.0002 -0.005
77 0.0002 0.005
78 0.0002 0.005
79 0.0002 0.005
80 0.0002 0.005
81
82
83
84 0.0002 0.005
85 0.0002 -0.005
86 0.0002 -0.005
87 0.0002 -0.005
88
89 0.0002 0.005
90
91 0.0002 0.005
92 0.0002 -0.005
93 0.0002 -0.005
94
95 0.0002 -0.005
96 0.0002 0.005
97 0.0002 -0.005
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113 0.0002 0.005
114
115
116
117
118
119
120
121
122 0.0002 -0.005
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150 0.0002 -0.005
151
152
153 0.0002 -0.005
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200 0.0002 -0.005
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233 0.0002 0.005
234
235
236
237
238
239
240
241
242
243
244
245
246
247 0.0002 0.005
248
249
250 0.0002 -0.005
251
252 0.0002 -0.005
253 0.0002 -0.005
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285 0.0002 0.005
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338 0.0002 -0.005
339
340 0.0002 -0.005
341
342
343
344
345
346
347
348
349
350 0.0002 -0.005
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365 0.0002 -0.005
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387 0.0002 -0.005
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444 0.0002 -0.005
445
446
447
448
449
450 0.0002 -0.005
451
452
453
454
455
456
457
458
459
460
461
462
463
464 0.0002 -0.005
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500 0.0002 0.005
501
502
503
504
505
506
507 0.0002 -0.005
508
509 0.0002 0.005
510
511
512
513
514
515
516
517 0.0002 0.005
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550 0.0002 -0.005
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600 0.0002 -0.005
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
3071
3072
3073
3074
3075
3076
3077
3078
3079
3080
3081
3082
3083
3084
3085
3086
3087
3088
3089
3090
3091
3092
3093
3094
3095
3096
3097
3098
3099
3100
3101
3102
3103
3104
3105
3106
3107
3108
3109
3110
3111
3112
3113
3114
3115
3116
3117
3118
3119
3120
3121
3122
3123
3124
3125
3126
3127
3128
3129
3130
3131
3132
3133
3134
3135
3136
3137
3138
3139
3140
3141
3142
3143
3144
3145
3146
3147
3148
3149
3150
3151
3152
3153
3154
3155
3156
3157
3158
3159
3160
3161
3162
3163
3164
3165
3166
3167
3168
3169
3170
3171
3172
3173
3174
3175
3176
3177
3178
3179
3180
3181
3182
3183
3184
3185
3186
3187
3188
3189
3190
3191
3192
3193
3194
3195
3196
3197
3198
3199
3200
3201
3202
3203
3204
3205
3206
3207
3208
3209
3210
3211
3212
3213
3214
3215
3216
3217
3218
3219
3220
3221
3222
3223
3224
3225
3226
3227
3228
3229
3230
3231
3232
3233
3234
3235
3236
3237
3238
3239
3240
3241
3242
3243
3244
3245
3246
3247
3248
3249
3250
3251
3252
3253
3254
3255
3256
3257
3258
3259
3260
3261
3262
3263
3264
3265
3266
3267
3268
3269
3270
3271
3272
3273
3274
3275
3276
3277
3278
3279
3280
3281
3282
3283
3284
3285
3286
3287
3288
3289
3290
3291
3292
3293
3294
3295
3296
3297
3298
3299
3300
3301
3302
3303
3304
3305
3306
3307
3308
3309
3310
3311
3312
3313
3314
3315
3316
3317
3318
3319
3320
3321
3322
3323
3324
3325
3326
3327
3328
3329
3330
3331
3332
3333
3334
3335
3336
3337
3338
3339
3340
3341
3342
3343
3344
3345
3346
3347
3348
3349
3350
3351
3352
3353
3354
3355
3356
3357
3358
3359
3360
3361
3362
3363
3364
3365
3366
3367
3368
3369
3370
3371
3372
3373
3374
3375
3376
3377
3378
3379
3380
3381
3382
3383
3384
3385
3386
3387
3388
3389
3390
3391
3392
3393
3394
3395
3396
3397
3398
3399
3400
3401
3402
3403
3404
3405
3406
3407
3408
3409
3410
3411
3412
3413
3414
3415
3416
3417
3418
3419
3420
3421
3422
3423
3424
3425
3426
3427
3428
3429
3430
3431
3432
3433
3434
3435
3436
3437
3438
3439
3440
3441
3442
3443
3444
3445
3446
3447
3448
3449
3450
3451
3452
3453
3454
3455
3456
3457
3458
3459
3460
3461
3462
3463
3464
3465
3466
3467
3468
3469
3470
3471
3472
3473
3474
3475
3476
3477
3478
3479
3480
3481
3482
3483
3484
3485
3486
3487
3488
3489
3490
3491
3492
3493
3494
3495
3496
3497
3498
3499
3500
3501
3502
3503
3504
3505
3506
3507
3508
3509
3510
3511
3512
3513
3514
3515
3516
3517
3518
3519
3520
3521
3522
3523
3524
3525
3526
3527
3528
3529
3530
3531
3532
3533
3534
3535
3536
3537
3538
3539
3540
3541
3542
3543
3544
3545
3546
3547
3548
3549
3550
3551
3552
3553
3554
3555
3556
3557
3558
3559
3560
3561
3562
3563
3564
3565
3566
3567
3568
3569
3570
3571
3572
3573
3574
3575
3576
3577
3578
3579
3580
3581
3582
3583
3584
3585
3586
3587
3588
3589
3590
3591
3592
3593
3594
3595
3596
3597
3598
3599
3600
3601
3602
3603
3604
3605
3606
3607
3608
3609
3610
3611
3612
3613
3614
3615
3616
3617
3618
3619
3620
3621
3622
3623
3624
3625
3626
3627
3628
3629
3630
3631
3632
3633
3634
3635
3636
3637
3638
3639
3640
3641
3642
3643
3644
3645
3646
3647
3648
3649
3650
3651
3652
3653
3654
3655
3656
3657
3658
3659
3660
3661
3662
3663
3664
3665
3666
3667
3668
3669
3670
3671
3672
3673
3674
3675
3676
3677
3678
3679
3680
3681
3682
3683
3684
3685
3686
3687
3688
3689
3690
3691
3692
3693
3694
3695
3696
3697
3698
3699
3700
3701
3702
3703
3704
3705
3706
3707
3708
3709
3710
3711
3712
3713
3714
3715
3716
3717
3718
3719
3720
3721
3722
3723
3724
3725
3726
3727
3728
3729
3730
3731
3732
3733
3734
3735
3736
3737
3738
3739
3740
3741
3742
3743
3744
3745
3746
3747
3748
3749
3750
3751
3752
3753
3754
3755
3756
3757
3758
3759
3760
3761
3762
3763
3764
3765
3766
3767
3768
3769
3770
3771
3772
3773
3774
3775
3776
3777
3778
3779
3780
3781
3782
3783
3784
3785
3786
3787
3788
3789
3790
3791
3792
3793
3794
3795
3796
3797
3798
3799
3800
3801
3802
3803
3804
3805
3806
3807
3808
3809
3810
3811
3812
3813
3814
3815
3816
3817
3818
3819
3820
3821
3822
3823
3824
3825
3826
3827
3828
3829
3830
3831
3832
3833
3834
3835
3836
3837
3838
3839
3840
3841
3842
3843
3844
3845
3846
3847
3848
3849
3850
3851
3852
3853
3854
3855
3856
3857
3858
3859
3860
3861
3862
3863
3864
3865
3866
3867
3868
3869
3870
3871
3872
3873
3874
3875
3876
3877
3878
3879
3880
3881
3882
3883
3884
3885
3886
3887
3888
3889
3890
3891
3892
3893
3894
3895
3896
3897
3898
3899
3900
3901
3902
3903
3904
3905
3906
3907
3908
3909
3910
3911
3912
3913
3914
3915
3916
3917
3918
3919
3920
3921
3922
3923
3924
3925
3926
3927
3928
3929
3930
3931
3932
3933
3934
3935
3936
3937
3938
3939
3940
3941
3942
3943
3944
3945
3946
3947
3948
3949
3950
3951
3952
3953
3954
3955
3956
3957
3958
3959
3960
3961
3962
3963
3964
3965
3966
3967
3968
3969
3970
3971
3972
3973
3974
3975
3976
3977
3978
3979
3980
3981
3982
3983
3984
3985
3986
3987
3988
3989
3990
3991
3992
3993
3994
3995
3996
3997
3998
3999
4000
4001
4002
4003
4004
4005
4006
4007
4008
4009
4010
4011
4012
4013
4014
4015
4016
4017
4018
4019
4020
4021
4022
4023
4024
4025
4026
4027
4028
4029
4030
4031
4032
4033
4034
4035
4036
4037
4038
4039
4040
4041
4042
4043
4044
4045
4046
4047
4048
4049
4050
4051
4052
4053
4054
4055
4056
4057
4058
4059
4060
4061
4062
4063
4064
4065
4066
4067
4068
4069
4070
4071
4072
4073
4074
4075
4076
4077
4078
4079
4080
4081
4082
4083
4084
4085
4086
4087
4088
4089
4090
4091
4092
4093
4094
4095
4096
4097
4098
4099
4100
4101
4102
4103
4104
4105
4106
4107
4108
4109
4110
4111
4112
4113
4114
4115
4116
4117
4118
4119
4120
4121
4122
4123
4124
4125
4126
4127
4128
4129
4130
4131
4132
4133
4134
4135
4136
4137
4138
4139
4140
4141
4142
4143
4144
4145
4146
4147
4148
4149
4150
4151
4152
4153
4154
4155
4156
4157
4158
4159
4160
4161
4162
4163
4164
4165
4166
4167
4168
4169
4170
4171
4172
4173
4174
4175
4176
4177
4178
4179
4180
4181
4182
4183
4184
4185
4186
4187
4188
4189
4190
4191
4192
4193
4194
4195
4196
4197
4198
4199
4200
4201
4202
4203
4204
4205
4206
4207
4208
4209
4210
4211
4212
4213
4214
4215
4216
4217
4218
4219
4220
4221
4222
4223
4224
4225
4226
4227
4228
4229
4230
4231
4232
4233
4234
4235
4236
4237
4238
4239
4240
4241
4242
4243
4244
4245
4246
4247
4248
4249
4250
4251
4252
4253
4254
4255
4256
4257
4258
4259
4260
4261
4262
4263
4264
4265
4266
4267
4268
4269
4270
4271
4272
4273
4274
4275
4276
4277
4278
4279
4280
4281
4282
4283
4284
4285
4286
4287
4288
4289
4290
4291
4292
4293
4294
4295
4296
4297
4298
4299
4300
4301
4302
4303
4304
4305
4306
4307
4308
4309
4310
4311
4312
4313
4314
4315
4316
4317
4318
4319
4320
4321
4322
4323
4324
4325
4326
4327
4328
4329
4330
4331
4332
4333
4334
4335
4336
4337
4338
4339
4340
4341
4342
4343
4344
4345
4346
4347
4348
4349
4350
4351
4352
4353
4354
4355
4356
4357
4358
4359
4360
4361
4362
4363
4364
4365
4366
4367
4368
4369
4370
4371
4372
4373
4374
4375
4376
4377
4378
4379
4380
4381
4382
4383
4384
4385
4386
4387
4388
4389
4390
4391
4392
4393
4394
4395
4396
4397
4398
4399
4400
4401
4402
4403
4404
4405
4406
4407
4408
4409
4410
4411
4412
4413
4414
4415
4416
4417
4418
4419
4420
4421
4422
4423
4424
4425
4426
4427
4428
4429
4430
4431
4432
4433
4434
4435
4436
4437
4438
4439
4440
4441
4442
4443
4444
4445
4446
4447
4448
4449
4450
4451
4452
4453
4454
4455
4456
4457
4458
4459
4460
4461
4462
4463
4464
4465
4466
4467
4468
4469
4470
4471
4472
4473
4474
4475
4476
4477
4478
4479
4480
4481
4482
4483
4484
4485
4486
4487
4488
4489
4490
4491
4492
4493
4494
4495
4496
4497
4498
4499
4500
4501
4502
4503
4504
4505
4506
4507
4508
4509
4510
4511
4512
4513
4514
4515
4516
4517
4518
4519
4520
4521
4522
4523
4524
4525
4526
4527
4528
4529
4530
4531
4532
4533
4534
4535
4536
4537
4538
4539
4540
4541
4542
4543
4544
4545
4546
4547
4548
4549
4550
4551
4552
4553
4554
4555
4556
4557
4558
4559
4560
4561
4562
4563
4564
4565
4566
4567
4568
4569
4570
4571
4572
4573
4574
4575
4576
4577
4578
4579
4580
4581
4582
4583
4584
4585
4586
4587
4588
4589
4590
4591
4592
4593
4594
4595
4596
4597
4598
4599
4600
4601
4602
4603
4604
4605
4606
4607
4608
4609
4610
4611
4612
4613
4614
4615
4616
4617
4618
4619
4620
4621
4622
4623
4624
4625
4626
4627
4628
4629
4630
4631
4632
4633
4634
4635
4636
4637
4638
4639
4640
4641
4642
4643
4644
4645
4646
4647
4648
4649
4650
4651
4652
4653
4654
4655
4656
4657
4658
4659
4660
4661
4662
4663
4664
4665
4666
4667
4668
4669
4670
4671
4672
4673
4674
4675
4676
4677
4678
4679
4680
4681
4682
4683
4684
4685
4686
4687
4688
4689
4690
4691
4692
4693
4694
4695
4696
4697
4698
4699
4700
4701
4702
4703
4704
4705
4706
4707
4708
4709
4710
4711
4712
4713
4714
4715
4716
4717
4718
4719
4720
4721
4722
4723
4724
4725
4726
4727
4728
4729
4730
4731
4732
4733
4734
4735
4736
4737
4738
4739
4740
4741
4742
4743
4744
4745
4746
4747
4748
4749
4750
4751
4752
4753
4754
4755
4756
4757
4758
4759
4760
4761
4762
4763
4764
4765
4766
4767
4768
4769
4770
4771
4772
4773
4774
4775
4776
4777
4778
4779
4780
4781
4782
4783
4784
4785
4786
4787
4788
4789
4790
4791
4792
4793
4794
4795
4796
4797
4798
4799
4800
4801
4802
4803
4804
4805
4806
4807
4808
4809
4810
4811
4812
4813
4814
4815
4816
4817
4818
4819
4820
4821
4822
4823
4824
4825
4826
4827
4828
4829
4830
4831
4832
4833
4834
4835
4836
4837
4838
4839
4840
4841
4842
4843
4844
4845
4846
4847
4848
4849
4850
4851
4852
4853
4854
4855
4856
4857
4858
4859
4860
4861
4862
4863
4864
4865
4866
4867
4868
4869
4870
4871
4872
4873
4874
4875
4876
4877
4878
4879
4880
4881
4882
4883
4884
4885
4886
4887
4888
4889
4890
4891
4892
4893
4894
4895
4896
4897
4898
4899
4900
4901
4902
4903
4904
4905
4906
4907
4908
4909
4910
4911
4912
4913
4914
4915
4916
4917
4918
4919
4920
4921
4922
4923
4924
4925
4926
4927
4928
4929
4930
4931
4932
4933
4934
4935
4936
4937
4938
4939
4940
4941
4942
4943
4944
4945
4946
4947
4948
4949
4950
4951
4952
4953
4954
4955
4956
4957
4958
4959
4960
4961
4962
4963
4964
4965
4966
4967
4968
4969
4970
4971
4972
4973
4974
4975
4976
4977
4978
4979
4980
4981
4982
4983
4984
4985
4986
4987
4988
4989
4990
4991
4992
4993
4994
4995
4996
4997
4998
4999
5000
5001
5002
5003
5004
5005
5006
5007
5008
5009
5010
5011
5012
5013
5014
5015
5016
5017
5018
5019
5020
5021
5022
5023
5024
5025
5026
5027
5028
5029
5030
5031
5032
5033
5034
5035
5036
5037
5038
5039
5040
5041
5042
5043
5044
5045
5046
5047
5048
5049
5050
5051
5052
5053
5054
5055
5056
5057
5058
5059
5060
5061
5062
5063
5064
5065
5066
5067
5068
5069
5070
5071
5072
5073
5074
5075
5076
5077
5078
5079
5080
5081
5082
5083
5084
5085
5086
5087
5088
5089
5090
5091
5092
5093
5094
5095
5096
5097
5098
5099
5100
5101
5102
5103
5104
5105
5106
5107
5108
5109
5110
5111
5112
5113
5114
5115
5116
5117
5118
5119
5120
5121
5122
5123
5124
5125
5126
5127
5128
5129
5130
5131
5132
5133
5134
5135
5136
5137
5138
5139
5140
5141
5142
5143
5144
5145
5146
5147
5148
5149
5150
5151
5152
5153
5154
5155
5156
5157
5158
5159
5160
5161
5162
5163
5164
5165
5166
5167
5168
5169
5170
5171
5172
5173
5174
5175
5176
5177
5178
5179
5180
5181
5182
5183
5184
5185
5186
5187
5188
5189
5190
5191
5192
5193
5194
5195
5196
5197
5198
5199
5200
5201
5202
5203
5204
5205
o
el
, C
po
na
e
th
iti
),
ly
W
ch
or
ra
Fi
nc
(4
Ed
on
Ju
20
.
o
W
el
ch
, C
or
po
te
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
17
Iv
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
vo
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
closely linked to that of a perfect market. A market is said to be efficient if it does not
ignore available information. To illuminate perfect and efficient markets, this chapter
also explains arbitrage, an essential concept of finance, without which no study of
finance would be complete. We then discuss the consequences of the concepts: What
do efficient and/or perfect markets mean for predicting stock performance? How
should you interpret the success of famous investors? And how can you use the
concept of efficient markets to run an event study to help assess the valuation impact
of big corporate events?
Market efficiency means the
market uses all available
information in setting the
price.
in which prices reflect all available information. In a fully efficient market, you should not be
able to use any available information to predict future returns better than the market can.
information. (PS: It is not necessary that any investor has all the information.)
(the efficient frontier), which was used in the context of portfolio optimization.
Economists love “efficiency” and thus use the term in many contexts.
Sect. 8.2, Pg.171.
An example: ABC’s price
today is based on the best
estimate of future
characteristics, obtained
from a model like the CAPM.
10% could come, for instance, from the CAPM. Market efficiency then pins down the relationship
between the best estimate of the price next year and the price today. In our example, if the
market expects ABC to trade for $55 next year, it should set the price today at $50. The market
would not be efficient if it had set today’s price at $49 or $51. You can turn this around, too.
You should not be able to locate information that tells you today when/if/that the true expected
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
expected rate of return of 0%). If you could find information telling you authoritatively that
a better estimate of next year’s price is $60 (or $50), then ABC’s stock would be mispriced. A
market that has overlooked your information would not be efficient.
tical distribution of future cash flows, in-
cluding their expected cash flow values,
covariances, liquidity, and anything else
possibly of interest.
propriate expected rate of return, given all
value-relevant characteristics.
expected rate of return is as the model
states.
?
?
?
value next year to be $55 per share. It
also estimates all other interesting charac-
teristics, such as cash flows, market-betas,
covariances, liquidity, etc.
Then the financial market looks at ABC’s
market beta, the risk-free rate, and the
expected rate of return on the market, and
sets ABC’s expected rate of return. Say
this CAPM expected rate of return is 10%.
share.
would you conclude has gone wrong? Is it the market or the model?
What is the model? What is
what rate of return ABC should have to offer given its characteristics, such as risk, liquidity,
and so on. The CAPM is such a model (though only a modestly successful one). Without a
good model of what you should expect the rate of return to be, market efficiency is too
vague a concept to be meaningful.
what information set are we talking about? If you are ABC’s CEO, then you may have more
information than the public. You may know whether the SEC will open an investigation
against you and whether you have the next new hit drink in the lab right now. You could
know whether $50 today is too high or too low. Put differently, the market may be efficient
with respect to publicly available information, but it need not be efficient with respect to
insider information.
If you find the expected
(a) Your 10% model could be
not efficient.
not $55, or if the expected payoff is $55, but today’s price is $45.83.) You could now draw one
of two conclusions:
and wanted to set the expected rate of return for ABC at 20% in the first place.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Is market efficiency so
difficult to disprove that it
becomes a “faith”?
predicted, you would simply proclaim that it was your model for the appropriate expected returns
in your financial market that was wrong, not that the market was inefficient. It was your fault,
not the market’s. You just have to go back and search more—possibly forever—until you find the
right pricing model.
Over long horizons (say, 1 year or longer), market efficiency is extremely difficult to disprove.
over very long horizons,
where efficiency is often
more a matter of faith.
often be a reasonable model, but it is not infallible and its estimates are rarely accurate in
practice. We are not sure whether a stock like ABC should earn 10%, 20%, or 30% a year. This
renders market efficiency a concept that in practice often evades empirical testing. It is also why
market efficiency is sometimes (unfairly) disparaged as being more religion than science. Based
on the existing long-run evidence, some reasonable analysts conclude that financial markets
are generally efficient (and our [CAPM] pricing model is wrong); and other reasonable analysts
conclude that financial markets are generally not efficient.
Okay, let me qualify this for
long horizons.long horizons. We know that no reasonable model of financial markets should give investors
returns this high would be way out of line with any reasonable pricing model. Even expected
rates of return of 100% per year would surely be unreasonable for (most) stocks. Of course, few
people doubt that the stock market is, to such a first approximation, efficient—we all know that
you just can’t earn that much. But there is a large gray zone where it is difficult to distinguish
between model error and market inefficiency. Because no one knows for sure what the correct
model of expected stock returns is, no one can tell you affirmatively whether the stock market
set the price of ABC stock so as to offer investors an expected rate of return on ABC of, say, 10%
a year or 12% a year.
Practically useful?
Definitely yes over short
horizons.
expected rate of return on ABC is 0%, 10%, or 20% per annum. Even on the high end of 20% per
annum, the expected rate of return is still only about 5 basis points per day. Roughly speaking,
regardless of whether you believe in the CAPM or not, you should expect day-to-day returns
to be just a tiny bit above 0%. You should attribute most daily price movements to random
fluctuations, presumably caused by unpredictable news of changes in the economic environment.
However, if you can predict day-to-day stock movements (and you have thousands of days of
historical stock returns to work with), then chances are that you would not blame the pricing
model. Instead, you would probably conclude that the market is not efficient. Dilbert on Predictability of Noise:
expected rate of return should be tiny. If it is different, the market is probably inefficient.
appropriate expected rate of return is. This makes it difficult to disentangle errors in the
pricing model from market inefficiency.
changes, where news is defined as the unanticipated component of new information that
is arriving. Such news can be firm-specific or market-wide.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Although the efficient market concept is different from the perfect market concept, the two are
market. intimately linked—in fact, so much so that they are often casually confused. The reason is that if
a market were perfect but inefficient, everyone would want to earn great returns and trade the
same way. It would be too easy to become rich. Market prices would instantly adjust to prevent
this. Therefore, if a market is perfect, it is inevitably also efficient.
Efficient market 6⇒ perfect
of market efficiency as the result of the trades of many investors with many different information
sets (opinions). The market price is the outcome at which investors no longer wish to trade
further. Appropriately weighted, one half believes the market price is too low; the other half
believes it is too high. Of course, efficiency should be contemplated market by market. It is
probable that some financial markets are efficient while others are not. The closer a market is to
being perfect, the more likely it is to being efficient.
Efficient market is a weak
information.”
the one regarding “same information set and opinions.” And even the information requirements
are weaker. It is not necessary that all investors have the same information and opinion (as in
the perfect-market setting), just that the market price is the same “as if” the market itself had
access to all the information at once. So, a market can be efficient even when investors know
different bits and pieces of information and/or to have different opinions, just as long as the
market-price is the same that it would be if they were all sharing their information and opinions.
Transaction costs are often
from their efficient levels.
on any information that the market has not yet incorporated in the stock price—and thereby
earn an unusually good expected rate of return. However, the no-free-lunch axiom applies here,
too. High transaction costs would make it more likely that you could expect to find violations of
efficient markets. But if it is very expensive to trade and if the market is therefore not efficient and
does not respond to news immediately, it would also be very difficult for you to take advantage
of such inefficiencies.
Investor competition pushes
days and up on sunny ones? It is unlikely that the average investor requires extra return to hold
stocks on sunny days—and, even if the average investor does, it is enough for you if you are not
among them. You would never buy stocks when the weather forecast predicts that rain is coming.
Instead, you would only buy stocks when the weather forecast predicts that the sun will shine.
Investors like yourself—and there are of course many such investors in perfect markets—would
rapidly bid up the prices before the sun shone, so that the prices would no longer systematically
go up on sunny days. The end result is that if markets are efficient, then you should not be
able to earn abnormally good sunny-day returns—at least not this easily. In a reasonable world,
to earn higher expected rates of return, you must be willing to take on something that other
investors are reluctant to take on—such as higher portfolio risk. Today’s weather alone should
not do it. (Interestingly, academics do disagree on whether the weather in New York City has a
small influence on stock returns. Some papers claim it does, so that the market is inefficient.
Others dispute this, claiming the historical correlation is spurious and disappears if the statistical
tests are done correctly. All agree that the weather influence is small, however.)
Prices should be generally
nonperfect financial market.
Who would be willing to hold
For example, let’s say that the appropriate rate of return on ABC was still 10% and the price was
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
really $55 but $51. (The true expected rate of return would thus not be 10%, but 2%.) In a
perfect market, some investors may want to short some ABC and use the shorting proceeds to
buy another stock. This may not be possible if the market is imperfect and the costs of going
Sect. 7.2, Pg.155.
shares would not want to sell them ASAP. They would not incur the shorting transaction costs
and would avoid the then lower-than-appropriate rate of return. (Maybe they are asleep?! Or
maybe even the non-short related plain selling transaction costs are too high?!) Such “economic
self-interested behavior” adds to the “third-party investor pressure” in driving markets toward
efficient pricing, even in a market that is imperfect.
• If a market is perfect, market forces should drive it strongly and quickly toward efficiency.
efficiency. But this force is much weaker, and third-party traders may not be able to aid in
the process.
In the United States, the financial markets for Treasuries, large corporate stocks, index mutual
that markets are efficient
for large corporate stocks.
definitely very competitive. There are millions of buyers and sellers, thousands of tax-exempt
investors, and modest transaction costs, and it seems unlikely that some investors have real inside
information. It is difficult to believe that you or I could outsmart the prices in such markets. After
all, thousands of other traders are likely equally as smart. They would flock to good bargains
and avoid bad bargains along with us. Of course, the smaller the firm, the less perfect and the
less efficient the market in its stock is likely to be. Many small stocks on the NASDAQ exchange
trade only rarely, and they can have large transaction costs:
Sect. 11.3, Pg.252.
shares, the price is likely to move against you.
which you have full access to the proceeds (e.g., to earn interest).
you sell. Thus, it is unlikely that small stocks will immediately and fully reflect all information
appropriately. The historical prices you see posted may be “stale” and may not even reflect the
price that would have applied if you had wanted to trade. Market efficiency is never white or
black, but always a shade of gray—just as it is for perfect markets. Large, liquid S&P 100 stocks
are pretty close to efficient; small NASDAQ stocks may not be.
The advantage of an
efficient market: Prices can
be trusted.
the typical transaction costs—and to get it right immediately. As an investor, would you not
rather face an inefficient market? If it were inefficient, you might be able to find some good
bets (opportunities that earn unusually high expected rates of return). But it would not all be
Sect. 12.4, Pg.291.
inappropriately too high or too low. You would never really know whether you are overpaying or
underpaying. Investing would be a very messy business. You might have to spend a lot of time
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
The 1983 hit comedy Trading Places, starring Dan Akroyd and Eddie Murphy, centers around the trading of orange juice
frozen concentrate futures contracts. (A future is a contract that specifies terms to buy or sell a commodity in the
future—in this case, oranges.) If it is going to rain or if there is a frost, oranges will be scarcer and the futures price will rise.
You can learn more about futures contracts at the website of the Chicago Mercantile Exchange at http://www.cme.com.
In a 1984 paper in the American Economic Review, Richard Roll found that these citrus futures contracts predict whether
the U.S. Weather Service’s forecast for central Florida temperatures is too high or too low. It is a great example of how
financial markets help aggregate information better than the best nonfinancial institution. This should not surprise you.
After all, there is a lot of money at stake!
you hold a portfolio of many large and liquid stocks, you do not have to spend a lot of time and
money to perform due diligence in order to determine whether stocks are fairly priced. All you
need to do is to make sure you are appropriately diversified to meet your risk-reward preference.
And you can probably accomplish this goal by buying just a few large index-mimicking mutual
funds.
that they can reject market efficiency because they have found assets that pay too much for their
risk?
low?
and efficient than the NYSE?
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Even in cases where it is probable that the market mispriced stocks, such as technology stocks during the famous “Internet
bubble” at the turn of the millennium, it was almost impossible for an individual investor to take advantage of the market
inefficiency. Believe me, I know.
Explorer. I was right on my prediction—but in February 1999, AOL paid a lot of money to acquire Netscape. Not satisfied
with one mistake, I proceeded to my next mistake. I believed Yahoo (YHOO) was worth less than what it was trading for. I
speculated that it would go down. After I had lost more than three times my original investment, I realized that I had to
either close my bet or risk going bankrupt. Consequently, I terminated my bet. Yes, I would have been right in the end
and made a lot of money if I had held on longer, but I simply could not afford the risk (and mental anguish) any longer. I
learned from this episode—after 15 years as a financial economist—that even if the stock market is irrational and even if it
overvalues a stock by three times, it can also be irrational enough to overvalue it by yet another three times.
on the Stock Market,” from November 22, 1999, in which famed financier Warren Buffett warned about the overvaluations
of tech stocks and Internet stocks. Like me, Buffett had suffered from years of poor performance (and from yet another
quarter of misery to follow), as Internet stocks reached ever higher.
between myself and Eugene Fama (perhaps the most famous finance professor alive and a strong defender of market
efficiency). This will give you an authentic impression of the ongoing dialogue among finance professors.
Classical versus behavioral
finance.an outgrowth of the school of rational economics. This belief is that the evidence supports
In contrast, another school of thought, often dubbed behavioral finance, posits that markets
sometimes do not use all available information. Depending on how strong a believer in classical
finance versus behavioral finance you are, you may believe that there are no especially good
trading opportunities, few trading opportunities, or plenty of trading opportunities. Both camps
agree, however, that market perfection plays a crucial role in determining whether a particular
market is efficient or not.
Many large financial markets
in the United States are
probably close to efficient.
very rich trading on easily available information. Instead, the disagreement is, loosely, about
whether stock markets are “99% efficient” or “97% efficient.” Classical finance believes in the
former, behavioral finance in the latter. Of course, you can trade millions of dollars in large-firm
stocks or market indexes relatively easily and at low transaction costs. Thus, it does not require
huge efficiency violations for behavioral finance economists to be right and for classical finance
economists to be wrong. Exploiting just the tiny—say, 100% – 97% = 3%—violations from
market efficiency could make you a star investor. (This is also not coincidentally why so many
fund managers publicly proclaim their faith in behavioral finance.) However, don’t take me too
literally here—the 99% versus 97% is an analogy, and there is really a spectrum of beliefs in
market efficiency among economists and fund managers. Now, although you should realize that
any classification scheme really identifies just segments on a continuous line, you can still try to
classify financial economists and investors by their faiths in efficiency. Let’s look at some such
classifications.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
The traditional definition of market efficiency focuses on information. In the traditional classifi-
of market efficiency is
information needed to beat
prices so that technical analysis (trading based solely on historical price patterns) cannot
be used to beat the market. Put differently, the market is the best technical analyst.
so that neither fundamental trading (based on underlying firm fundamentals, such as
cash flows or discount rates) nor technical analysis can be used to beat the market. Put
differently, the market is both the best technical and fundamental analyst.
today’s stock prices, so that nothing—not even private insider information—can be used
to beat the market. Put differently, the market is the best analyst and cannot be beat.
Many finance professors no
efficiency.
arguments rage on as to which markets are semistrong-form efficient or even weak-form efficient,
and even for large and liquid financial markets (such as large firms traded on the NYSE or
NASDAQ, or some options on the CBOE). Finance professors regularly publish claims that some
new rule would have outperformed reasonable average rates of return historically, often by large
margins. Prominently among them are some particular forms of momentum strategies (buying
stocks that have gone up and selling stocks that have gone down over the last year) and value
strategies (buying boring old-economy stocks, selling glamorous high-growth new-economy
stocks). These strategies would have offered “excess returns” as high as 1-2% per month.
Why do many trading
worked historically?
never real to begin with. Also, many of these trading strategies would have required such high
transaction costs that they would not have been profitable in the real world. That is, even if
prices had not incorporated all information, thus leaving the market inefficient, they may have
been well within the bounds of transaction costs. Yet some trading strategies, such as momentum
or value, do seem to have produced large historical excess returns even after transaction costs.
One good question is whether they will continue to work. (Personally, I am not claiming that
they will or will not work in the future.) A second good question raised by EMH proponents is
what part of these strategy returns was appropriate compensation for risk (not captured by the
CAPM) and thus not excessive to begin with.
The returns to collecting
“balance” with their costs.
collecting information on firms? And if no one bothers to collect information on them, how can
the market incorporate all information and thus be efficient? Eventually, a resolution to this
puzzle was offered by Grossman and Stiglitz. They argued that markets can never be 100%
efficient—they can only be, say, “99%” efficient. In equilibrium, good information collectors
should earn just about enough trading profits to break even on their costs of information collecting.
On the margin, the expected costs of learning and trading on more information are exactly equal
to the expected trading profits. The informed investors earn this money trading against noise
traders, who do not collect information and who may trade for idiosyncratic reasons (e.g., to
pay for tuition).
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
I prefer an alternative classification of market efficiency, which divides economists based on their
market efficiency is based
on how much prices deviate
from value.
estimate of all future cash flows. This means that stock prices should change correctly if
and only if news about fundamentals (cash flows or discount rates) appears.
best estimate of future cash flows. However, transaction costs make it practically impossible
for investors to find unusually good bets.
priate best estimate of future cash flows. However, unlike a firm believer, a mild believer
would argue that there are occasions when it is possible to exploit this misvaluation. This
would result in the occasional unusually good bet. Usually, the profitabilities of such bets
should remain within economically reasonable magnitudes—a couple of percentage points
a year on the high side. Mild believers thus think that smart fund managers can offer
investors slightly better bets, but nothing more. There are no guarantees.
and to an extent that allows investors to obtain great bets fairly routinely.
firm believer need not be a true believer. Firm belief can be the right club to join if financial price
changes are indeed unpredictable, but not because of news about fundamentals. There could be
unrelated noise in stock price changes, especially in the short run. A mild believer need not be
a firm believer: Transaction costs may be low enough to permit great trading strategies based
on efficient markets violations. A nonbeliever need not be a mild believer: Financial markets
may just beg to be exploited. This classification is related to but not the same as the earlier
classification. For example, it is possible that markets do not reflect all fundamental information,
yet stock returns are unpredictable.
There is even some really
weird but dramatic evidence
against market efficiency.
PDA company Palm. Widely reported in the press at the time, 3COM retained 95% of Palm’s
stock—and announced that each shareholder of 3COM would soon receive 1.525 shares of Palm.
After the IPO, Palm closed at $95.06 per share. Therefore, 3COM should have been worth at least
1.525 ·$95.06 ≈ $145. Instead, 3COM shares closed at $81.81. (It was impossible to exploit this
discrepancy, because it was impossible to find Palm shares to short. Palm shares later enjoyed an
almost uninterrupted fall in price, down to less than $2 per share by 2003.)
This evidence as a whole
suggests that the financial
markets are usually
somewhere between mildly
and firmly efficient.
finance professors are somewhere between the “mild believer” camp (the center of behavioral
finance) and the “firm believer” camp (the center of classical finance). The debates between the
two more extreme sides of these camps—the more “classical rational economists” and the more
“behavioral economists”—are intellectually exciting. After all, bringing new evidence to bear on
these disagreements is the process by which we learn more.
Buyer beware: Here is my
own opinion.somewhere in the firm-to-mild camp. In my view, most investors believe that they are smarter
believe that trading in the stock market seems so (inexplicably) active. Some pundits like to call
this “investor psychology.” However, I also believe that ordinary individual investors are unlikely
to be able to find rate-of-return patterns in the stock market that earn high excess returns. A
very few sophisticated funds may be able to earn systematically a few basis points extra per year.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
better-performing funds, we have usually found that only about half of all funds outperform the
market and half underperform the market—even before fund transaction costs.
Sect. 12.5, Pg.299.
Behavioral Finance
has argued that investors are “loss-averse,” which induces them to make mistakes. It is very
plausible that loss aversion influences their stock trading patterns. But it is not so plausible
that loss aversion necessarily influences stock prices. There are two problems. The first is that
different investors would have started out at different investment levels. They would thus suffer
from loss aversion relative to different starting points. This means that, in the aggregate, prices
would not necessarily behave as if investors are loss-averse. The second is that, if prices were
badly set because of investor loss aversion (or most other behavioral mistakes), a few smart
investors would try to take advantage of this behavioral bias. They would quickly drive prices
back to where they would look like random walks.
values, but that trading costs nevertheless prevent you from exploiting this profitably (in large
scale), where would you classify yourself?
The low signal-to-noise ratio
market efficiency to
physics—the signal (the appropriate expected price change) is small compared to the noise (the
day-to-day price volatility that clouds our senses).
Let me illustrate the
stock’s rate of return on a
up 5 basis points; 13-week T-bills traded at 0.3% (unchanged); and just about half of all stocks
advanced and half declined. The S&P 500 dropped from 2078.0 to 2071.2, about 30 bp. The
Dow-Jones had 12 gainers and 18 losers. On this day, the volume leaders (not the biggest price
movers) were Wester Gas (down 5.8%), Greif B (+3.7%), Synchrony (–5%), Alon (+1%), and
Linked in (60%). Intel Corp increased from $31.69 to $31.76, up 0.2%. What can you learn
from this magnitude? Read on.
Let’s first put your statistical and financial expertise to good use: In a perfect market, if the shares
real-world trading signal to
be as strong as 1% per day:
1,000% per year.
rate of return on a stock? Could you expect a reasonable model of market prices to predict
that 1 day’s stock price movement could be something on the order of ±1%? Think about it:
If the expected rate of return on a stock were the same as the typical up or down movement
of 1% per day, the rate of return on this stock over the 252 trading days in one year would be
more than 1,000%. The $50 stock would be worth over $600 by next year. Who would want to
sell such a stock? Who would not want to bid a lot more than $50 for it right now? The same
argument applies to a price decline of 1% per day. An investment strategy of holding onto such
stocks would transform $50 into less than $5 by next year. Who would ever want to hold onto
such stocks? The same logic would also apply to a signal that tells you on some days that one
particular stock is expected to go up by 1% and on other days that some other particular stock is
expected to go down by 1%. Each day, you would earn 1% by either going long or short in the
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
side would end up poor.)
reasonable range of rates of return is between 0% and 40% per year. For 252 trading days,
absent complications, this gives you daily rates of return of between 0 basis points and about
5 and 10 basis points a day. One basis point of signal per day is 3% per year. Thus, when you
test for market efficiency with a reasonable model of stock pricing, about 5 to 10 basis points per
day is what you would expect to find for most stocks. If your signal allows you to earn 1 bp extra
per day, then your strategy will be better by about 3% per year.
In the 1700s, it was not beneath mathematicians to study how to gamble in order to gamble better. Jacob Bernoulli
(1654–1705) and Abraham DeMoivre (1667–1754) studied the random walk of a gambler’s stake in fair games.
plant physiologist, placed charcoal powder on an alcohol film and observed that the grains moved randomly. The botanist
Robert Brown (1773–1858) reported erratic dancing of small particles in fluids at rest. Albert Einstein (1879–1955)
considered such fluids to be composed of discrete molecules, whose many collisions with a “Brownian particle” caused
the particle to jump in random directions—a random walk. Einstein’s analysis not only explained Brownian motion,
which has itself become a building block of high-tech finance nowadays, but also bolstered the case for the existence of
atoms, which was not yet universally accepted. The first recorded use of the phrase “random walk” was by Lord Raleigh
(1842–1919) in 1899. (Raleigh made a connection between diffusive heat flow and random scattering and showed that a
one-dimensional random walk could provide an approximate solution to a parabolic differential equation.) The name is
believed to have originated with the description of a drunk who stands on a ladder. The drunk can walk up or down and
does so in a random fashion—just like stocks.
Pearson (1857–1936) introduced the term “random walk” only later, in 1905), finding that bond prices could diffuse in the
same manner as heat. Unfortunately, this has only pointed out the obvious: It is not easy for an investor to outperform the
market. The first rigorous and published investigation of the random-walk hypothesis was done by Alfred Cowles, an eclectic
investor and economist at Yale in the 1930s and 1940s. Mostly Michael F. Schlesinger, Office of Naval Research, Scienceweek.com, 2001.
Over short intervals, the
stock price should follow a
mostly unpredictable
random walk with practically
no drift.
�
�
�
roughly the price today (P0).
�
P1
�
this tiny drift m may be around 5 to 10 basis points for most stocks. You should not be able to
predict better than this drift, because this is your expected rate of return in an efficient perfect
market.
Don’t wag the tail: Market
efficiency ⇒ random walk.
Random walk 6⇒ market
efficiency.
prices follow roughly a random walk. For example, a market would be inefficient if you could
find advance knowledge based on some other external signal—say, whether the sun is shining on
a particular day—that would tell you whether the stock price will go up or down the following
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
to outperform the EMH. The random walk only states that the known lagged price can’t be this
signal.
The important point of perfect markets (and market efficiency) is that, given today’s information,Transaction costs destroy
high turnover strategies.
accurately enough to earn, say, 1% on a given day. Of course, in the real world, financial markets
are not perfect and there are financial transaction costs that would also prevent you from really
Sect. 11.3, Pg.250.
would have to pay money to your broker to buy the shares, and again to sell them. (This is why
financial markets are not exactly perfectly competitive, only approximately perfectly competitive.)
Even small transaction costs can render trading strategies with very high turnover unprofitable.
Even if the bid-ask spread is only 10 basis points, if incurred 252 trading days a year, you would
only be left with (1 – 0.1%)252 = 0.999252 ≈ 78% of your original investment. For a daily trading
strategy in which you have to pay the bid-ask spread every day, you need to have a signal that
allows you to earn at least 23% per year before you break even—and few signals are that good.
It may be best to think of
after-transaction costs.
per day is still unreasonably large, because typical round-trip transaction costs should not
exceed 10 to 30 basis points, depending on the stock and the size of the trade. A daily rate
of return of 0.7% is still way too large.
because they already had specific trading desires. For example, a signal may tell some
investors to buy a stock today and sell it tomorrow. They would have to pay transaction
costs to take advantage of it. But investors who were considering selling the stock anyway
may need to wait only another day to take advantage of the soon-to-be misvaluation and
then sell. Such investors really incur no additional transaction costs. However, if they are
all asleep at the switch, it may be impossible for others to take advantage of their failures.
description of reality—at least it is one that you can use to compute back-of-the-envelope
magnitudes, and it is a hypothesis that can be tested.
so that you can earn a positive rate of return? Assume typical real-world trading transaction
costs are about 10 basis points.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
To put more emphasis on the noise, we can write our random walk with drift in terms of the
returns is much larger than
the daily signal.
What do we know about reasonably typical standard deviations for the price noise of U.S. stocks?
There is no particular theoretical reason why the day-to-day standard deviation of a particular
stock could not be 10%, 50%, or even 100%. So it is best for us simply to rely on the empirical
data. Historical averages suggest the following:
2-3% per day—of course depending on the firm. For well-diversified portfolios, like stock
market indexes, the standard deviation is usually lower—perhaps 1-2% per day.
to 300 basis points for individual stocks was clearly much higher than the 5 to 10 basis points
that you would expect them to earn.
tomorrow is (almost) the same as the value today. Technically,
�
�
= P0 + m · P0︸ ︷︷ ︸
Tiny Drift
Noise
�
�
= P0 +m;
Naturally, actual values tomorrow will likely be different from their values today. The
random walk, at least in the short run. This means that you cannot get rich trading based on
past prices.
today?
You now know that the tiny drift is typically around 5 to 10 basis points per day, and the noise is
noise is difficult.typically about 100 to 300 basis points per day for U.S. stocks and stock portfolios. How easy is
basis points’ signal? Why 7 basis points? Because it is what you should be earning extra every
day if you have a signal that allows you to earn an extra 5% per year in expected performance,
above and beyond what your model of risk-adjusted returns says you should be earning. (A
performance of 5% per year in risk-adjusted returns would be stellar for just about any fund.) Put
differently, to determine whether your signal is real or illusory, you must be able to distinguish
between an appropriate 5 basis points and an excessive 7 basis points for the average daily rate
of return.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
You cannot conclude
return
happened to earn 50 basis points today, you could not reliably conclude that it was your signal.
In fact, if anything, you should believe it was primarily noise. Recall from your statistics course
that the T-statistic is defined as the mean divided by the standard deviation, E
r
�
r
�
your strategy performs as expected, your 1-day T-statistic would be only 2bp/200bp = 0.01. To
have good statistical confidence, you would want a T-statistic of around 2. Your expected 0.01 is
a long way off.
You cannot consider multiple
as independent observations.
First, your signal may apply only to some particular stocks and not to all stocks. Second, all
stocks tend to move together on a given day and are therefore not independent observations.
(If all 100 oil stocks go up, and your signal suggested holding oil stocks, you do not have 100
independent observations confirming your signal’s ability to predict.)
You can use consecutive days
as independent observations.
Here is how mean, standard
accumulate over time.
signal. How many daily returns would you need to expect to be able to reliably detect a signal
of an extra 2 basis points hidden in noise of 200 basis points? Let’s ignore compounding and
pretend that rates of return over time are just the simple sum of daily rates of return. In this
case, your expected rate of return over N days is N times the expected rate of return over 1 day.
Recall from Section 8.2 that the standard deviation of your rate of return over N days is
N
time,
Sect. 8.2, Pg.170.
superior excess rate of return is therefore
Excess Mean
=
�
�
N · Sdv
r
� =
N · 1-day T-Statistic
Only diversified strategies
that perform well for many
decades give us the chance
to learn whether they are
years worth of data. This is if your strategy performs as expected—if the world is not changing
and your signal’s forecasting ability is not deteriorating. If your signal is not about individual
stocks but about large diversified portfolios, then the noise is lower than 200 basis points. If it is,
say, noise of 100 basis points per day, which may be the case for highly diversified portfolios,
then you “only” need about 1002 = 10, 000 days (39 years) of data. There are many signals for
such diversified trading strategies, which can therefore be examined with real-world data. (I
already described some of these, principally momentum and book/market value, although it
is not perfectly clear whether their high historical average returns were due to risk or market
inefficiencies.) Still, with the world and the signal always changing (after all, there may be more
and more investors trying to profit from historical signals), the historical evidence alone may not
always be entirely convincing.
• The quality of your inference about a strategy’s performance increases roughly with the
as much as it offers in expected rate of return. Therefore, it takes at least many decades,
if not centuries, of data to reliably conclude whether a signal-based strategy of picking
individual stocks is real or illusory.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
outperform the risk-adjusted financial market per typical day?
Assume that you have the kind of stock-picking ability that earns you an extra 200 basis points
per annum. Assume no transaction costs. Ignore compounding and assume that your rate of
return is the sum of returns over trading days. Assume there are 252 trading days per year.
above the 95% level. In Section 8.2, you learned that the standard deviation grows with the
square root of time.
earn per annum?
statistical evidence that you have a positive ability to pick stocks.
Do you understand
arbitrage?financial concept of arbitrage? Intuitively, an arbitrage is a great investment opportunity, perhaps
opportunity as soon as it appears that makes financial markets efficient. It is a matter of basic
financial literacy for you to understand what arbitrage is.
First recall that the law of one price states that two identical items at the same time and location
market will be efficient and
the law of one price will
hold.
it can be (and in fact usually is) still true. For example, even if all investors disagree about the
future, even if there are taxes, even if there are transaction costs, and even if there is only one
market maker, it should be, and usually still is, the case that one share of Intel Corp costs the
same as another. But in a perfect market, the law of one price does not just usually hold; it must
Sect. 1.1, Pg.2.
arbitrage opportunities. The arbitrage concept is so important that you should understand it
exactly, not just intuitively.
• A true arbitrage is a business transaction
– and under no circumstance—either today or in the future—has a negative net cash
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
an excessive expected rate of return given its (risk and other) characteristics. A good way
to think of a risk(y) arbitrage is as a great bet. Admittedly, the term “risk(y) arbitrage”
is an oxymoron. However, Wall Street uses the term “risk arbitrage” for a particular type
of trading (most often in the context of M&A transactions) that is similar to the sense in
which we shall be using it. Thus, we shall commit the same sin.
An example: A chance to win $1,000,000 with 99% probability and to lose $1 with 1%
probability.
Arbitrage is the “perpetual
motion” of economics. It is
possibility of) negative cash
ticket is not an arbitrage. Please also pay close attention to what the “no-negative-cash-flow”
condition means in the definition of arbitrage:
Sect. 6.1, Pg.106.
and they are not arbitrage. The reason is that you have to lay out cash to buy Treasuries.
This is a negative net cash flow today.
repay”: If you are willing to accept risk, you can often receive cash today. For example,
insurance companies take money in exchange for the possibility that they may have to pay
up in the future.
“Risk(y)” arbitrage ≈ great
a risk(y) arbitrage could
“just” a great bet and not a true arbitrage. One difference is conceptual: Every investor would
want to take a true arbitrage opportunity, but an infinitely risk-averse investor would not take a
risk(y) arbitrage. This does not mean that, given an either-or choice, a less risk-averse investor
would necessarily prefer the small, true arbitrage opportunity. In our example, would you prefer
the $5 true arbitrage, if it cannot be repeated, to the risk(y) arbitrage with an expected payout
of close to $1 million? (If you could scale the true arbitrage opportunity to take it infinitely
many times, the true arbitrage opportunity would dominate.) Of course, this example of risk(y)
arbitrage is extreme. More realistically, bets are never this great—“very good” is rare enough.
And because there is still risk, you may not want to scale up good but risk(y) arbitrage bets in the
same way you would always want to scale up true arbitrage bets as much as possible. Eventually,
with enough investment in the risk(y) bet, your risk aversion would kick in and stop you from
taking more of it.
There should be few
financial markets. Only this
fact allows us to study and
world is sane and that money does not grow on trees—you can draw some surprisingly strong
conclusions about how financial markets work. If you disagree, why are you still in this class? If
you are right, you should be among the richest people in the world and there is little that this
book can teach you.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Of course, it is difficult to find real-world examples of arbitrage. Arbitrage is principally a concept.
projects under certainty are
arbitrage.
item for $1, borrow at an interest rate of 9% (all costs, including your time), and sell the item
tomorrow for $1.10 for sure, you earn 1 cent for certain today without any possible negative net
cash flows in the future. If you ever stumble upon such an opportunity, please take it—it is a
positive-NPV project! More than this, it is a true arbitrage because you cannot lose money in
any scenario; it is riskless. Yet it is obviously not a very important arbitrage by itself. Searching
for 1-cent arbitrage opportunities in financial markets is potentially more lucrative, because
they often allow transactions to be scaled up. If you could repeat this 1-cent arbitrage 1 billion
if they are scalable.times, then you could earn $10 million. Unfortunately, although you may find an arbitrage that
for 1 billion items. After all, you are not the only one searching in the financial markets! True
arbitrage opportunities are difficult or outright impossible to find in the real world, especially in
very competitive financial markets.
Arbitrage could conceivably
occur between different
financial markets.
and for $50 on the New York Stock Exchange, you could theoretically buy one share in New York
for $50 and sell it in Frankfurt for $51. You then pocket $1 today. If you can do this with 20,000
PEP shares worth $1 million, you earn $20,000 without effort or risk.
But be skeptical. There are
many complications to take
into account.
may not even be present at all. Consider the following issues:
you sell the shares in Frankfurt (even if it is only 3 seconds)? If such execution-timing risk
exists, this is not pure arbitrage because there is a chance of a negative net cash flow. The
real-world evidence suggests that price discrepancies between markets often disappear
within a few seconds.
do you have to pay? Is $51 the Frankfurt bid price at which you can sell shares in a
market, and $50 the NYSE ask price at which you can buy shares? Can you sell the share
Pg.252.
Have you accounted for the value of your own time watching the screen for opportunities?
Only the first 100 shares may be available for $50 for a net profit of $100. The next 900
shares may cost $50.50—perhaps still worthwhile, but less profitable. And buying the
remaining 19,000 shares may cost you $51 or more.
dollars to get offices and computers in order to “arbitrage” a few thousand dollars, it is
obviously not a real arbitrage. So you must account for how expensive it is to set up your
operations.
constantly running automated computer trading programs that search for even tiny arbitrage
opportunities in order to exploit them as soon as they appear—and thereby make them disappear.
markets, what questions should you ask?
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Is the past rate of return a
rate of return?
of, say, 10 basis points a day above transaction costs. For sure, it should not be possible for you
or anyone else to earn arbitrage returns. Let’s consider two examples—technical analysis and
investment fund management.
The main point of the traditional classification of market efficiency, specifically the “weak” version,
the market? is the claim that you should not become rich by trading a strategy that relies only on historical
they show what stock market patterns could look like? Perhaps. Does it make sense to think that
all these patterns can predict the future? Absolutely not! Graphs (a) and (b) display a strong
regular cycling pattern. If they indicated future returns, you should quickly become a wealthy
technical analyst. You would buy the stock only when it has “bottomed out”—a pattern that
you can reasonably detect if you see a multimonth period of losses followed by about a quarter
of stable returns. It need not be the kind of regular cycles in the figure: Any good predictable
patterns (such as “every time the price hits $22, it drops by $2”) would allow you to get rich.
Now, if you look hard enough, can you find some stocks in the real world that have historically
behaved like these graphs? Yes—because with over 10,000 stocks currently trading, by pure
chance, maybe one or two could show a pattern that would look remarkably similar to a cycle
pattern. But, despite assurances from some stock analysts that you could have made money if
you had just trusted their cycle patterns and that you should trust them henceforth, the patterns
would not represent the future—they would just be historical coincidence.
Cycles are not reasonably
likely—although there are
too.
on stocks is positive), but the important aspect of (c) and (d) is that there is a lot of noise, up
or down. Noise is by definition unpredictable, and stock prices must largely be unpredictable,
or you could outsmart the stock market. Incidentally, one of these graphs is a real stock price
that I picked at random, while the other is a simulated random walk. Can you detect which
one? I cannot! The real-world price series looks just like a simulation of patternless day-to-day
random-walk changes. In fact, if you ever look at graphical representations of stock prices, most
will look like graphs (c) and (d) and not like graphs (a) and (b). (Solution: Graph (d) was an
actual stock price series of Intel.)
Predicting with past rates
fail.
example, according to one version, stocks that rise one day are more likely to fall back the next
day. Exhibit 12.3 shows tomorrow’s rate of return on the tech-heavy Nasdaq market index and
on Intel Corp as a function of today’s rate of return (from 2000 to 2016). The graphs show no
pattern that would allow you to get rich quickly. There is definitely not much juice in trying to
predict how a stock will perform tomorrow, given how it performed today. (Although difficult
to spot here, there is a small day-to-day reversal in this data—a tiny negative slope. This is
caused by the bid-ask bounce: If a stock’s closing price is a [higher] ask price, on average it will
fall back the next day when it will close with either a bid or an ask price with roughly equal
probability. If the stock’s closing price is a [lower] bid price, on average it will gain the next day.
This is a data illusion and not exploitable.) Similar conclusions apply if you extend your use of
historical price information beyond yesterday. You can even try out your own technical analysis at
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
to
k
P
c
e
20
S
to
c
k
P
ri
c
e
5
20
25
30
Date
S
to
c
k
P
ri
c
e
2011 2013 2015
15
20
25
30
35
Date
S
to
c
k
P
ri
c
e
ones? And which is the real series?
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
1
2
3
a
te
f
e
tu
T
m
rr
w
in
−3 −2 −1 0 1 2 3
−3
−2
−1
0
1
2
3
a
te
o
f
R
e
tu
rn
T
o
m
o
rr
o
w
,
in
%
Market Index (IXIC). The right panel is Intel Corp. Both plots graph the rate of return against itself one day earlier from
2010 to 2016. Obviously, there is no obvious pattern.
then “Technical Analysis”; it is fun, but unfortunately fairly useless.
Momentum: Firms that did
1-month lag) continue to do
little bit. This is the “momentum” effect mentioned earlier. It should be covered in more detail in
an investments course. (Of course, as you already know from Section 12.1, it is very difficult to
determine whether an extra few percent is an appropriate rate of return to compensate investors
for some risk, or whether it is a market inefficiency.)
Analyzing 35,000 households from 1991 to 1997, Terry Odean and Brad Barber found that men trade 45% more than
women. Apparently, men are overconfident in their trading prowess. (Men also have a higher propensity to suffer from
compulsive gambling and other mental disorders.) On average, the men’s investment rates of return were lower than
women’s by a little less than 1% per year. Much, but not all, of women’s better returns could be attributed to the higher
transaction costs that men incurred for transactions that did not gain them higher returns.
evidenced by the plethora of financial talk shows and investment newsletters. It would perhaps be better for the general
public to watch more sports and cooking shows and fewer investment shows—especially for males like myself!
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
What about all the televised stock analysts who explain which stocks are undervalued and which
investors?stocks are overvalued? And what about the aforementioned technical analysis, the art of seeing
future prices? And what about famous investors such as Warren Buffett, George Soros, and many
others? Should you trust them?
What could you conclude
from their stellar past
performances? There are
three possibilities.
in measuring performance)? Dilbert on Hard Work, Luck, and Success:
ability)?
to write papers that argue one side or the other. The real conundrum is faced by every investor
in the real world every day: How do you distinguish between a good and a bad signal—between
skill and luck—when it comes to investing or to selecting a fund manager?
Here are possible objections
to believing in their magical
investment abilities (and in
inefficient markets).
fund manager can make you money, consider the following:
would not want anyone to learn how they do it. In fact, they may want to do so secretly
and privately, never eager to appear on anyone’s radar screen. This can make it difficult to
find investors with superior ability and thus impossible to confirm their abilities.
many decades before you can realistically conclude that it has worked. (This is assuming
that the world is not changing.) Few strategies have such long track records.
performance,
The industry standard of
three years’ performance is
not driven by the need to
get solid statistical
inference.
performance of funds is noise. This means that many investors (and especially investors in
hedge funds) shift their holdings often based on noise. Why? Either they do not understand
how long it takes to determine reliably whether a strategy works (possible), or they do
not care too much about reliability (more likely). If they believe that there are many
other strategies that also have a close to 50-50 probability of success, then eliminating one
strategy that had 3 bad years and therefore only a 49-51 probability of success may not be
a costly choice.
Is Momentum Risk?
yet outperformed the overall stock market. On average, it had delivered abnormal returns
to the tune of about 5-10% per year. Stocks that have gone up over the last year and which
are therefore momentum purchase candidates did not seem to be particularly risky. More
importantly, momentum stock portfolios appeared well-diversified—a fact that should have
moderated their ups and downs. Yet, after many decades of superior performance, in 2009,
this momentum strategy suddenly lost 83 percent of its investment! (One plausible reason
is that too many hedge funds were trying to chase momentum returns, and they all had to
unload at the same time.) Which other seemingly great investment strategies are exposed
to some risk factors that have just not shown themselves yet?
Pg.201.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Pure chance means that
some investors succeed
Sect. 7.2, Pg.157.
year (at least before they collect fees) if none of them has any superior investing ability?
About 5,000. How many of these outperform the year thereafter? About 2,500. Even if
there is absolutely no ability, pure randomness means that about 10 funds outperform
the market every year for 10 years in a row. With enough candidates, some funds will
inevitably produce consistently positive long-run track records.
Good past performers grow.
fund family to “incubate” funds privately for the purpose of obtaining track records. Start
1,024 of these funds, and after 10 years, you should expect to be able to go public with at
least 1 of them that has outperformed 10 years in a row!) What happens to the funds that
have outperformed several years in a row? They proudly announce their performances,
advertise, boast, and collect more investments from outside investors. Their managers are
supported by larger “research teams,” appear better dressed and more “professional,” and
fly in executive jets. They are the ones that are most visible. Indeed, if you made money
10 years in a row in the stock market, would you not yourself believe that you have the
ability to pick stocks?
Now put yourself in the shoes of an investor looking at the universe of mutual funds
historical performance looks
today.
disappeared. Second, you will notice that the larger funds seem to have done better. On
average, it will seem that currently available funds indeed can make you money—even if
in the real world there is absolutely no ability. This phenomenon is called survivorship
bias, because it means that you cannot consider the historical performance of existing
funds to be a fair projection of their future performance.
If there was superior fund
manager—not the
most.
reasonable market, these fund managers would charge appropriately high fees to capture
all the advantages that they provide to investors. After all, it is the fund manager who
would have the scarce skill (picking stocks) and not the typical investor. Investors with
money would compete to place money with such managers and accept higher and higher
fund fees. In the end, it would be highly unlikely that uninformed investors could earn
excess returns by investing in some manager’s actively trading fund.
always remember that recent past performance is still a very poor guide.
Many hedge funds are
This does not solve
alternative is no better.
participate in the upside (as is the case for hedge funds)? Maybe, but consider this: I give
you stock tips, and I ask for money only if you make money. In fact, I only want 10% of your
winnings. “You have nothing to lose.” I only get something if I help you make money. Sounds
like a deal? Now, if I pick a stock randomly, I have a 50-50 chance of making money. If you gain,
I get something. If you lose, I pay nothing. In effect, I am arbitraging you! Remember, next time
someone gives you a great stock tip, regard it with some skepticism: It probably has a 50-50
chance of being right. (Maybe I should give you the advice to buy a stock, and your neighborDilbert on Management Books:
that I have told you my plan.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
The three best-selling investment books of spring 1996 were David and Tom Gardner’s Motley Fool Investment Guide, based
on a popular investment website; Matt Seto’s The Whiz Kid of Wall Street’s Investment Guide (Matt Seto was 17 years of age
at the time); and the Beardstown Ladies’ Common-Sense Investment Guide, authored by septuagenarians whose first book
mixed cooking recipes with investment advice. All touted “common-sense methods” to beat the market, earning 30% per
year or more. Not a week went by without dozens of prominent radio and TV shows featuring their advice. Why does
anyone need a Ph.D in finance? It is difficult to argue with performance!
they launched a real-money portfolio, called DRIP. From July 28, 1997, to July 31, 2002, it lost about 10%, while
the S&P 500 lost 2.5% and NASDAQ lost 15%. One should not judge a fund by just 5 years of performance (and
certainly not without risk adjustment), but it does appear that the Motley Fool has not exactly found the Holy Grail of
investment opportunities.
3. The Beardstown Ladies, five books richer, were found to have miscalculated their returns: Their returns were not
period.
about the same as the market, and one should have underperformed it. Time Magazine, March 1998.
You must realize that even
top investors seem to have
at most mild predictive
abilities.
better performance among analysts or professional fund managers who have outperformed in
the past, they have found little or no exceptional forward-looking performance. Exhibit 12.4
shows a typical result in the literature: There were more funds that performed miserably than
what we would have expected by pure chance. Fewer than half of the funds could beat the zero
benchmark. And many fewer funds than expected by random chance did great.
Are there some persistently
good performers at least?But the empirical evidence is again disappointing. Only about 54% of mutual funds that have
over the following 1-3 years. This is better than 50%, but not by much. And if you subtract fund
fees, the average performance drops significantly below 50%. As fund prospectuses so aptly Dilbert on past performance + hedge
There is a whole industry full of fund managers whose job it is to allocate assets to the actual
investing funds. Chances are that your corporate pension fund will be managed by some. (So
is mine. So is the UCLA endowment.) They of course all swear that they are immune to this,
because they know which funds are better than others. Beside the occasional Madoff misstep,
could they really tell? Goyal and Gupta (JF, 2008) look at 3,400 retirement plan sponsors from
1994 to 2003 and find that they were not particularly prophetic:
searched, individually and collectively, for anomalies. This is beyond our scope.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
what to expect → Should be <16% Should be >50% Should be >16%
< $5 million 22.4% 37.8% 48.2% 32.1% 21.2% 10.2%
> $1 billion 29.8% 45.0% 41.5% 28.3% 15.6% 7.9%
1,308 mutual funds, with an average of $650 million assets under management (AUM). You don’t need to be too concerned
about the details, but the T mentioned in the first row is similar to the T-statistic of the alpha that was mentioned in
Chapter 10. A negative alpha and a negative T means underperformance. For example, the second line tells you that if
monkeys had done the investing, you would have expected about 16% of the mutual funds to have a T as lousy as –1. In
real life, 22.4% of mutual funds with less than $5 million AUM managed to perform as lousy before fees, 37.8% after fees.
As a group, only the best small funds with AUM outperformed the random benchmark (21.2% had good performance,
instead of the expected 16%), but fees negated this group advantage. Source: Fama-French, JF 2010.
–2 to 0 0 to +2
Hired Funds 7.6% +2.3%
hire funds after they have performed well, not before they perform well. So why do these
managers pretend that they can do a good job managing your money? Well, how much would
you pay for a plan sponsor who admitted that it could not pick funds better than either you or a
monkey?
For the most part, it seems
insurance (or liquidity)
earning returns than stock
money. But it is money earned the old-fashioned way—through hard work, liquidity provision,
and risk-taking. Writing insurance is risky business, and it deserves extra return. Warren Buffett
Sect. 11.3, Pg.253.
he acknowledges that the efficient markets hypothesis is the most natural benchmark. He is
on record as stating that “the professors who taught efficient market theory said that someone
throwing darts at the stock tables could select stock portfolios having prospects just as good as
ones selected by the brightest, most hard-working securities analyst. Observing correctly that
the market was frequently efficient, they went on to conclude incorrectly that it was always
efficient.” Even Buffett is still a mild believer!
Where should the burden of
than to ability. The burden of proof is with the side that is claiming superior signals and investing
ability—and a number of former finance professors have taken up the challenge and started their
own funds. On the client side, if I were you, I would be very cautious investing my money with
anyone who charges high fees.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
very large number of investors, many will beat the market. A small number of investors will beat
the market again and again.
past are better at picking stocks in the future when compared to investors who did poorly.
stock market, given that many of them are likely to beat the market, does it make sense to look
for these high-ability managers among the better historical performers?
that beat the market 10 years in a row if none of them has any special ability and there are no
transaction costs?
Buy Low, Sell High.
parties and hedge fund conferences. Thereafter, it is usually admiring students in universities.
A few lucky investors even go on to write books. Please read some of them. They all seem so
sensible. All you need to do is to buy low and to sell high. Having sat through many presentations
and having read many books, I can confidentally state that about half emphasize the “buy low”
while the other half emphasize the “sell high.” When I am in a good mood, I can fake admiration
for their brillant investment insights. When I am in a bad or cynical mood, I offer ambiguous
praise that amuses only myself. (These are our university donors, after all.)
Rat Selection
have been somewhat neglected. Fortunately, Michael Marcovici has remedied this with his “I
Trained Rats to Trade, and Win, on Wall Street” true laboratory experiments. Sure enough, a
number of them outperformed. Unfortunately, their ability to present their superior ability to
potential investors (and thus generate higher fees) is limited by their lacking eloquence.
Grandiose Claims and Dumb
Excuses.rationalizations and platitudes. Read some with an open mind. There are some patterns. Funds
competitive advantages, signals, edges, exciting and smart strategies, sentiment reading abilities,
contrarian acumen, etc. Funds on the down often write that nobody could have known; that
Buffett did it, too; unprecedented market turmoil; irrational herd sentiments; unpredictability;
temporary profit-taking; dollar averaging; the market failing to understand fundamentals;
deteriorating data and decision making of others; fat-tail risk; dislocations; short-sellers; the
Chinese, Russians, Saudis, Jews, or Arabs; the Fed doing too little or not enough, and so on. Yet,
the simple fact is that neither is on target. Not the ups and not the downs. Most performance in
financial markets is luck. In 2016, about a thousand hedge funds closed shop, usually because of
poor performance. There are a lot of one-hit wonders among them (and, of course, about half as
many two-hit wonders, and about a quarter as many four-hit wonders).
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Academics are not so
of papers showing how to beat the market. Just like fund managers, academics do not get
rewarded for writing papers that opine “the markets are fairly priced.” They get rewarded for
writing papers that find that factor X had amazing returns. It’s even better when the factor can
be claimed to be behavioral—hedge funds and investors (our consulting clients) love irrational
behavior stories. The problem is that even if each individual economist is (or were) scrupulously
honest, as a collective, with thousands of us mining the data, we will find many factors that
seem statistically significant, yet are entirely spurious. Most of the time, hedge funds try to
replicate and further test the academic factors right after the first public posting. When they
hold up, many academically oriented hedge funds start trying to exploit past patterns. They all
slowly pile up into the factor as they backtest the factor, itself contributing to some further good
performance. Virtually every academic equity fund is playing “value” and “momentum” in some
strategy or another. And then, one day, they realize that they may have overreached and then all
seem to want to withdraw roughly at the same time. This seems to have happened to so-called
momentum strategies in 2009.
Intellectual Humility, please.
2014, the oil price dropped below $50/bl, and made my oil bets my best bets ever. I had talked
about this in 2013 to my colleagues, who are now admiring my foresight. It is easy to rationalize
how smart and prescient I was. But it’s really all non-sense. I don’t like to bet on horses, I like to
bet on financials. I placed a bet, pure and simple. Ex-ante, someone on the other side believed
the opposite. I happened to win. In financial markets, it is easy to place bets and someone ends
up winning. In this case, it was me. Does this make me a brillant investor? Or just a lucky one?
But funds can wittingly or unwittingly seem even better than random gamblers. It is not difficult
Sources to show good historic performance. You can even do it on a roulette table. Just double up.
and record today’s investment performance as a gain. With a lot of money, it is likely that you
will have years of good performance without losses. Many funds unwittingly follow strategies
with such payoffs. They make a little money most of the time until they have dramatically large
losses. The 2008 Great Recession showed exactly this pattern for many strategies. Many investors
(banks in particular) who had made small amounts of money for a long time suddenly lost it all.
Writing options or making markets are other strategies that follow this pattern: modest returns
most of the time, followed by a sudden large disaster. I don’t think they even knew this and
tried to deceive their investors. They just stumbled onto the “has made nice little money for a
long time” investment strategy and followed it. My advice: be very skeptical about claims that
someone expects to beat liquid financial markets.
It is difficult to be a
investor wants to earn negative rates of return for years on end, while their peers are doing
well? The bears on real estate in the first half of 2000 went out of business long before the Great
Recession of 2007-8. Only a few very lucky investors managed to maintain their shorts—and,
just as there are books by and about successful investors, there are movies about these lucky
unicorns, too (in this case, The Big Short). Yes, in theory, you can offer a fund with a negative
market-beta strategy with negative expected rates of return, because it provides great insurance.
In practice, your investors will drift away when the market goes up, and withdraw their gains
when the market goes down to cover their losses elsewhere. It’s tough to bet against the market.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
When creating value for
your firm, there are three
different market scenarios
to consider.
to think about three different cases:
the most important question if you are the CFO. Can you add value by changing your capital
structure? Can you create value by splitting your shares, so that every share becomes two shares?
Can you create value by paying out dividends next year rather than this year? Can you create
value by changing how you present your earnings to investors? Can you create value by taking
over other companies when they are priced too low if you do not have any unique knowledge or
anything unique to add?
If the financial market is perfect, the answers to these questions are simple—they are always no.
counts are the firm’s
underlying projects.
is, how many shares it has, how it pays out its dividends, and so on. In fact, you already know
that the firm is worth the value of its underlying projects’ present values. Everything else is
irrelevant.
You cannot fool your
investors by how you report
your earnings.
Sect. 14.1, Pg.355.
increase the firm’s reported earnings. However, it will not create anything intrinsically
valuable. Such a change should not add or subtract firm value. Your firm owned the
subsidiaries’ cash flows before and after its reporting change. Your investors can add or
subtract the subsidiaries’ numbers themselves, whether you include or exclude them in
your overall report.
There must be no value to
changing capital structure.
Sect. 17.2, Pg.451.
arbitrageur could buy your firm, issue $51 in debt and $51 in equity, and pocket $2. With
legions of entrepreneurs competing to do this, your firm value would instantly adjust to
$102. Thus, a $100 price for your firm would be absurd.
Stock splits must be
irrelevant, too.
Sect. 20.2, Pg.558.
in a perfect market. Nothing fundamental about your underlying projects would have
changed. Splitting by itself cannot add value. If this were not the case—for example, if
shares would be worth $41 each after the split—arbitrageurs would buy the old shares for
$80, and sell them an instant later for the equivalent of 2 ·$41 = $82, pocketing $2.
Still trying to fool investors,
this time with dividends?
Fugeddaboutit.
Sect. 20.2, Pg.558.
destroyed. Keeping the money for another year in the marginal zero-NPV investment (e.g.,
Treasuries) is as good as paying it out. Investors in a perfect market can borrow against
this extra future money and use it today.
focus exclusively on finding and executing projects with positive net present values.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
If markets are not perfect but efficient, the implications are not as profound. However, it
“the price is right.” Thus,
market price.
assessment of many investors who have put their money where their mouths are. The market
price aggregates a whole lot of information that you as a corporate manager may not learn as
easily yourself. For instance, if your stock price seems very high relative to current fundamentals,
it probably means that the market sees great opportunities ahead for your firm and expects that
you will take them. Thus, you should consider growing the business. Naturally, a high firm
value allows you to raise more funds from the financial markets at favorable rates. On the other
hand, if the stock price is very low, it probably means that the financial market anticipates your
business to go down or expects you to waste the remaining money. In this case, you should
think carefully about whether you should reinvest investors’ money into the business or into
repurchasing the (relatively cheap) stock.
You can also learn from
whether you should get into the fray. Commodity price information can also be very helpful. If
the price of oil in the forward market is $100/barrel, it probably does not make sense for you to
plan ahead based on an oil price of $70/ barrel. The financial market price for oil forwards is
very large and efficient. It makes no sense for you to plan your business around much lower
or higher oil prices in 6 months, simply because if you really knew this better, you could get
rich easily without needing any of your current businesses—just start trading oil futures. This
may sound obvious, but it is sometimes easy to overlook the obvious in the heat of battle. For
instance, a large conglomerate oil company in the 1990s planned to explore for more oil, based
on a working assumption of doubling oil prices within two years. This company could just have
purchased oil in the market instead of drilling. Why explore for oil if you can buy oil cheaper in
the market? If you are a farmer planting, the futures exchanges provide you with forward prices
for corn and wheat, and you can use this free price information to help you decide which crop to
plant.
Personal opinion alone
good argument for taking
Every morning, you read the newspaper, and every morning you think that company X should
really be worth a lot more. It makes no sense to you that X has annual earnings of $10/share but
its shares are trading at only $50/share. X just seems undervalued. Should you go out and buy it?
If the market is perfect, the answer is no. You would have no competitive advantage in owning
X. The hordes of arbitrageurs could have accomplished it in an instant, and less expensively than
you ever could. On the other hand, owning X would not do any harm, either. But let’s take away
the perfect market assumption and leave only the efficient market one. This means that both
your aircraft company’s price and the price of X are correct. Buying X because you think that X is
undervalued is likely to be wrong. After all, our working assumption is that the financial markets
have used all available information to find the best possible price.
However, in an imperfect
acquisition to add value. . .
create value. The trick is that you must be able to do something that investors cannot do for
themselves, because the market is imperfect. Most likely, this would be related to your business’s
real operations. For example, if X is a supersonic aircraft parts supplier, you may have better
information about the supplier’s product. You may know that you will reward it with a huge
contract soon. Or, by owning the patents of this supplier, you may make it more difficult for
other aircraft companies to compete with you. Or you may find cost savings by cutting out the
middleman in purchasing these parts, or improving X’s products through your own intellectual
capital, or by increasing the scale of operations. All of these can add value to the firm—value that
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
buyers assumption of a perfect market.)
. . . as long as you have more
than just an opinion that the
market got prices wrong.
markets are just as smart and presumably could recognize just as well whether X is undervalued—
in fact, chances are that the target was rightly valued to begin with and it was you who got the
target value wrong. For example, if X manufactures diapers, it is highly unlikely that you would
create value for your shareholders, even if the firm is trading for only 5 times earnings and this
makes no sense to you.
In an imperfect market, you
can also create value with
financial transactions that
reduce market
imperfections.
reducing the costs with which investors can trade your shares (e.g., by listing on an exchange).
Or you may be able to reduce the mistrust that your investors have in your creditworthiness by
hiring a good auditor or by reporting your earnings in a transparent fashion. Indeed, there is
evidence that many corporate activities can create value by reducing the perfect market frictions,
even in very efficient financial markets. For example, when firms split their shares 2-to-1, it is
not necessarily the case that the two post-split shares are worth exactly half of the pre-split share
of, say, $80. Instead, they tend to be worth a little more, say, around $40.20. The likely reason is
that managers signal their confidence in the future by splitting shares today. This brings more
Sect. 20.4, Pg.570.
Loosely speaking, financial markets tend to be reasonably, but not always perfectly, efficient.
markets are not efficient?Perfect market efficiency is almost surely not a good description of reality. Even in a perfectly
example, you may know that your company is about to sign a large contract, but this information
cannot yet be disclosed. What should you do if you know that the stock price is not equal to the
Sect. 12.2, Pg.284.
would do if you were the sole owner of the firm. You would really care about firm value. (As its
executive, you should want to maximize this value on behalf of the owners.)
If you are undervalued,
sometimes it is better to
pass up positive-NPV
projects. . .
risky capital at fair prices—especially equity capital. The CAPM clearly is no longer the
right model for the cost of capital.
For example, assume you know that your current projects will return $500 tomorrow. Also
assume that you have no cash and that you can only raise financing through equity. Now
assume you come across a new project that costs $100 and will return a terrific $200
tomorrow. The problem is that your investors do not believe that the firm will return $700,
falsely believing that the combined firm will only be worth, say, $200. Thus, to raise $100,
you would have to sell 50% of your firm, and keep only 50% of the true $700 return, for a
true $350 share of it. You would therefore be better off passing up this new project and
investing,
capital to fund this project is way too high for you.
You would definitely not want to raise cash at these “high” prices. Instead, you would
repurchase your own shares.want to do the opposite. The best use of corporate cash may now be to repurchase your
Sect. 20.2, Pg.558.
shareholders. Therefore, repurchasing underpriced shares from them at bargain prices
would not be what would make the selling shareholders better off. (It would, however,
make your remaining shareholders better off.)
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
If you are overvalued,
to issue more shares.
were the primary owner of this overpriced firm. You would want to sell more equity shares
at higher prices and pay the money out in dividends to existing shareholders. (Alternatively,
you can just invest in Treasury securities.) Here the paradox is, of course, that just one
instant later, as CEO, you are now the representative of these new shareholders to whom
you have just sold overpriced shares. They will not be happy campers. (Many researchers
believe that this is exactly what happened when AOL purchased Time-Warner at the height
of the Internet craze in the late 1990s. AOL used its overpriced shares to buy Time-Warner’s
real assets.)
existing shareholders.
• If the firm is undervalued, CEOs should assume a relatively high cost of capital and consider
issuing more of the firm’s own shares.
and benefits of projects are the same as what they could obtain from repurchasing or issuing the
firm’s own shares.
old shareholders, though.) But be careful: Most executives are notorious for always believing
Sect. 13.7, Pg.339.
inside information—as an executive, you should be wary of your own perceptions and biases!
raise financing for new projects by issuing more equity. You know that your existing project will
truly return $500 next year. Everyone knows that your second, newer project costs $200, but
only you know that it will return only $180 next year. This newer project is the only one that
investors think is in line with your current expertise—you cannot raise funds and deposit them
elsewhere (or any new investors would smell a rat).
have the magic touch and any of your expertise projects will earn a rate of return of 100%,
what fraction of the firm would you have to sell to raise $200 to start the new project?
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
market concepts and their
consequences.
market prices, because they accurately incorporate the information of financial market
participants. This means that you cannot create value by buying other companies just
because you think that these companies are worth more than they are trading for.
If the market is inefficient, you may be able to identify underpriced firms that you can
take over, or even create value by working on how information about your own company
comes to the market.
projects’ net present values. You can forget about most financial choices, such as what
your capital structure should be, how you should report earnings, and so on.
If the market is imperfect, you can create value, often by reducing the market imperfections
themselves. For example, you could signal what you know about your company’s prospects
by reporting earnings sooner. On occasion, this can even become a dilemma: For example,
what should you do if you know that a project has a positive NPV but the financial market
does not believe you? If you take it, your stock price may go down. Now you have to think
about the lesser of two evils—passing up on the project, or passing up on a higher stock
price.
Don’t be too dogmatic:
Nothing is perfectly
perfect, or perfectly
imperfect.
of deviations should be fairly modest. As a real-world manager of a publicly traded corporation,
it is generally better for you to focus on underlying value creation than on actions that investors
can accomplish for themselves without you. It makes sense for you to believe that market prices
are almost always informative, but not to believe too slavishly that they are also always fully
efficient—you may have better information than the market. Use it wisely when you have it.
Market reactions should be
immediate and reflect all
value changes.
more easily than traditional NPV techniques, using a technique called an event study. An event
study is an empirical analysis of the effect of a set of events on the price of assets. The idea of
an event study is that if the public market is valuing projects appropriately, and if the value of
an unexpected event or action is $1 million, then the stock price should increase by $1 million
at the instant the event becomes publicly known. You can therefore (often) back out cash flow
value changes from stock price changes. The details of how to conduct such a study are in the
appendix.
Researchers have run event studies on all sorts of interesting events, ranging from new legislation,
used on many different
events. In finance, they
often tell us whether
corporate actions are good
news.
corporate dividends, to corporate debt and equity issuance and retirement, to deaths of the
founder, and so on. Here are some of the more important findings. (You will see some more
evidence obtained from event studies again in later chapters, especially in the chapters on capital
structure and payout policies.) On the day of the announcement, firm values increase on average:
0.1-1%; if you are interested, there is a longer explanation in Chapter 20).
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Bad news…
announcements (some of the effects would have already been anticipated and thus already
incorporated in the stock price), these value estimates are conservative lower bounds.
Government Regulation—who
hurt when the telecommunications, trucking, and airline markets were deregulated—or how the
Treasury’s rescue program of 2008 (“TARP”) helped some banks, but not others.
South Africa’s apartheid regime (1948–1994) rightly deserved to be overthrown. To accelerate its demise, the U.S. Congress
imposed banking and tax-related sanctions on firms doing business with South Africa’s apartheid regime.
the event study evidence clearly shows that sanctions played no economic role. Upon the announcement of new sanctions
or corporate divestments, neither prices of targeted U.S. companies nor of South African financial securities moved. One
explanation is that there were too many loopholes and non-U.S. firms that were willing and able to evade the embargo.
still be appropriate on moral grounds regardless of their economic effectiveness. Whether to boycott socially objectionable
behavior is a decision that policymakers should make, not economists. The role of the financial economist is only to
inform policymakers of the ultimate effectiveness of their actions. Even this one failed on the economic effectiveness
benchmark. Teoh, Welch, and Wazzan, Journal of Business, 1999.
rate of return) would you expect when your company announces that it has struck oil and plans
to pay a special dividend next month? What reaction do you expect over this month? What
reaction do you expect on the day that it pays the dividends?
What events are greeted as bad news?
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
able information in setting prices to offer “appropri-
ate rates of return.”
return on stocks must be small. Therefore, market ef-
ficiency prescribes that stocks roughly follow random
walks.
ate rate of return” should be. Because noise makes it
difficult to measure the average rate of return accu-
rately, it is also difficult to test either models like the
CAPM or long-run market efficiency.
emphasizes what information it would take to
beat the market: weak form (past stock price
patterns are not enough to beat the market),
semistrong form (other historical firm informa-
tion is not enough to beat the market), and
strong form (inside information is not enough
to beat the market).
emphasizes the rationality of the stock market:
true believer (stock prices always reflect under-
lying project NPVs), firm believer (small devia-
tions between price and value, but difficult to
take advantage of), mild believer (small devia-
tions between price and value, and somewhat
possible to take advantage of), or nonbeliever
(arbitrage opportunities abound).
become rich—a belief shared by most finance profes-
sors. The relative strength of their beliefs in market
efficiency—the extent to which professors believe
that market prices always reflect underlying value—
“classical” economists) and “behavioralists.”
not find arbitrage opportunities:
tive net cash flows under any circumstances.
Everyone would like to take all true arbitrage
opportunities. When and if they appear, they
are likely to be very small.
infinitely risk-averse investor would not want
to take it, because there is a chance that risk(y)
arbitrage will lose money.
should be very rare in the real world. An in-
vestor who is not too risk-averse may or may
not prefer taking one large, great bet to taking
one tiny, true arbitrage.
stock market by chance, and some investors will beat
the stock market many years in a row. Market ef-
ficiency does not mean that there are not some in-
vestors who will beat the stock market 10 years in a
row ex post; rather, it means that any one particular
investor is unlikely to beat the stock market ex ante
10 years in a row.
ket prices, both from their own share prices and from
other prices. To improve corporate firm value, man-
agers must create fundamental value—they must un-
dertake positive-NPV projects. Simple activities such
as purchasing a random firm to lower risk or splitting
shares will not add value.
value impact of sharp events, such as election results,
legislative action (FDA rulings), or corporate events
(dividend increases).
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
2006 for the overall market, health care stocks, and oil stocks. It explains the limitations of event
studies—specifically, how it is important to take out the expected events and focus only on the
unexpected, i.e., the real news.
Behavioral finance, 283. Bid-ask bounce, 294. Brownian motion, 287. Classical finance, 283. Due diligence, 282.
EMH, 283. Efficient market hypothesis, 283. Efficient, 277. Event study, 307. Fundamental trading, 284. Futures
contract, 282. Great bet, 292. Market efficiency, 277. Noise trader, 284. Noise, 286. Random walk, 287.
Rational economics, 283. Risk(y) arbitrage, 292. Semistrong market efficiency, 284. Signal, 286. Signal-to-noise
ratio, 286. Spurious, 284. Strong market efficiency, 284. Survivorship bias, 298. Technical analysis, 284. True
arbitrage, 291. Volatility, 286. Weak market efficiency, 284.
ket uses all available information in the setting of its price.” There
are further nuances about what “available” means, which creates
different classifications of market efficiency.
that the heretics are wrong in how they measure the risk-reward
trade-off (the model for what expected rates of return should be).
Your second line of defense would be to ask the provocative question
of why the heretics are not yet rich. (Of course, you would have to
claim it was by pure chance if the heretic that you are talking to is
rich.)
short horizons, because the expected rate of return over a short
horizon (say, a day) is very small (a few basis points) in virtually all
reasonable models of market pricing.
available information. In a perfect market, market pressures by
arbitrageurs will make market efficiency come true, so a perfect
market should be efficient. However, an efficient market need not
be perfect. For example, stocks could be priced fairly even when
there are taxes.
costs are low, because this makes it easier for smart investors to
compete away any unusual opportunities.
ket in the world, with the dollar and the euro being the world’s
two main currencies. With so many smart investors trading on the
exact same instrument, and with incredibly low transaction costs,
inefficiency. Thus, it would seem likely that the foreign exchange
market is much more efficient—and much closer to perfection than,
say, U.S. stock markets.
market efficiency—unless you believe that their returns are just
normal because they reflect some sort of normal compensation for
risk.
reflect underlying fundamental values, but that trading costs never-
theless prevent you from exploiting this profitably (in large scale),
then you should classify yourself as a firm believer in market effi-
ciency.
the expected price tomorrow is the price today plus a drift. The drift
can be a small constant or a very small fraction of the price today.
curately, it is 252 on average. If a stock has an expected rate of
return of 20% per year—which is definitely on the high side for most
firms—the daily rate of return would be 1.21/252 – 1 ≈ 7.24 basis
points. If you computed the non-compounding 0.20/252 ≈ 7.84
basis points, or even used 365 calendar days instead of 252 trading
days, you would still get a reasonably similar answer—the average
daily rate of return is very small.
per annum in order to overcome typical transaction costs. The
calculation in the text came to about 23% per annum.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
plus or minus 2% to 3% a day. The average rate of return on a day
is much lower. Thus, the signal-to-noise ratio is very low.
price can definitely—and most likely will be—different from today’s.
Only the expected price is the same as the price today.
by, say, about 4% per year, you would have to earn an extra
252
p
Q 12.15 With 100 basis points per day of noise and 200 basis
basis points per day.
3. The expected T-statistic is about 0.794/100 ≈ 0.00794.
4. Over 252 days, the performance was given as 200 basis points.
5. The noise would be 100 ·
252 ≈ 1, 587 basis points.
7. You need to solve (0.79 · N)/(100 ·
N) ≥ 1.96, or 0.0079 ·p
Q 12.16 No! Treasuries earn money without risk, but they are
cash flow upfront.
and gains $10, it is probably worse than a risk(y) arbitrage that
loses 1 cent with 1% probability, and gains $1,000,000 with 99%
probability.
sible an arbitrage is include: time and execution risk, direct and
indirect transaction costs, price impact of trades, and fixed costs.
among historical high performers. However, many high-ability man-
agers will have underperformed historically, and many low-ability
managers will have outperformed historically.
to beat the market in any given year, then the answer is that
10, 000/210 ≈ 10 analysts beat the market 10 years in a row.
only see the funds that were ex post successful. Most unsuccessful
funds do not show up in the historical statistics of funds in existence
today. Existing funds will therefore have had positive performances
in the past.
–$20, at the zero interest rate. (A positive interest rate would
make it even more negative.)
would believe that your firm would be worth ($500 + $200) ·
(1 + 100%) = $1,400. To raise $200 in funding, you would
therefore have to sell $200/$1,400 ≈ 14.286% of your firm.
the 14.3% stake is worth only $97.14. Put differently, your old
investors have just sold a $180 project for $97.14, giving them
a net profit of $82.86. You can also compute this directly:
Your old investors will therefore own (1 – 14.286%) ·$680 ≈
$582.86. This is $82.86 more than the $500 that they would
own if you did not take the new project. You should take it if
you are acting on behalf of the existing investors.
you have struck oil would be positive. Over the following month,
you would not expect any unusual upward or downward drift: It
should be about zero. Finally, when your firm pays out the special
dividend, the rate of return should be zero on average, too, because
the market would have known that the dividend would be paid. Of
course, its share price will have to drop by the amount of the divi-
dend paid to keep the return around zero. Chapter 20 explains how
this may not be the case in the presence of market imperfections,
especially personal income taxes on dividend payouts.
nouncement of new dividends, share repurchases, and stock splits;
earnings significantly higher than analysts’ projections; FDA ap-
provals; and CEO deaths. Bad news: Acquiring other firms at too
high a price; the issuance of new equity stock; earnings significantly
lower than analysts’ projections; declining an acquirer’s bid; and
FDA rejections.
market efficiency ideally want to muster? If they fail to
find this kind of evidence, does it mean that you should
conclude that markets are efficient?
fers from a perfect market.
Fidelity, suggested that it is wise to invest in stocks based on
“local knowledge”—you invest in the stock of your local su-
permarket if you notice that it does better than expected. In
an efficient stock market, is this a wise recommendation?
ter what portfolio you are holding in a perfect and efficient
stock market.
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
Iv
o
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
. I
vo
W
el
ch
, C
or
po
ra
te
Fi
na
nc
e
(4
th
Ed
iti
on
),
Ju
ly
20
17
.
sample of spam email touting a particular stock. Such dis-
tributions increased the trading volume and resulted in a
4–5% gain over the 2 days following the spam release. Is
this evidence against market efficiency?
tional market efficiency classification? Give an example of
what each excludes.
ficient market seems like an impossible concept. In an
efficient market, no one can earn excess returns. Therefore,
no one collects information. Therefore, prices do not con-
tain information, and collecting information should earn
excess returns.”
the strength of belief in market efficiency. Explain how one
individual can be at one level but not in the level above or
below.
of return on a stock is zero?
bet? Is one always better than the other?
world to assume that there is no arbitrage? Would it make
sense for a model of the financial world to assume that
there are no great bets?
dard deviation) is about 100 basis points. Assume that you
have the kind of stock-picking ability that earns you an
extra 400 basis points per annum. Assume no transaction
costs. Ignore compounding and assume that your rate of
return is the sum of returns over trading days. Assume
there are 252 trading days per year.
you expect to earn per day?
divided by the standard deviation)?
extra do you expect to earn per annum?
6. What is your expected T-statistic now?
before you would obtain statistically significant evi-
dence to prove that you have a positive ability to pick
stocks.
evaluating whether an opportunity is an arbitrage?
based on the most recent three years of performance. What
do you think of this practice?
today appear to have been a great performer? Does this
evidence suggest that these funds will be good performers
in the future, at least on average?
to prefer compensation that is more performance based?
How good an “insurance” is this for fund investors?
lower the firm’s uncertainty. This should lower its cost of
capital. This should create value. Is this correct?
ing a project can be too high if the market has undervalued
your firm.
You know that your current projects cost $400 today and
will truly return $500 next year—but your investors believe
they will return only $400. In addition, you have no cash
on hand and can only raise financing for new projects by
issuing more equity. A new project costs $200 and will
return $220 next year. Your investors mistakenly believe
that your firm will earn an internal rate of return of 0%,
either with or without this new project. Acting on behalf of
your existing investors, should you take this project? Does
it have a positive NPV?
2
V
B
1
3
4
5
6
7
8
9
1
0
T
Revenue growth rate
7
0.00
7
0.00%
70
56
55
43
10
29
65
16.
20
2.75%
Revenues
$ 1,
32
$ 2,
25
$ 3,
83
9.93
$ 6,5
27
$
11
97
$
18
86
5.5
$ 29,
53
$
42
63
$
54
94
31
$ 63,67
0.9
$ 65,42
1.94
$ 67,
22
1.04
EBIT (Operating) margin
-1
64
-0.
23
1.1
8%
2.60
4.01%
5.43%
6.
84
8.
26
9.67%
1
1.09
12
50%
2.5
EBIT (Operating income)
$ (2
1.86
$ (5.21)
$ 45
$ 169.63
$ 445
34
$ 1,023.93
$ 2,02
0.72
$ 3,
48
9.47
$ 5,2
99
$ 7,05
8.25
$ 8,
17
$ 8,40
2.63
Tax rate
7.00%
1
4.00
2
1.00
2
8.00%
35
5.00%
EBIT(1-t)
$ 1,
87
$ 3,00
0.94
$ 4,186.
33
$ 5,0
81
$ 5,3
15
$ 5,46
1.71
– Reinvestment
$ 659.64
$ 1,
121
38
$ 1,906.35
$ 3,24
0.
79
$ 5,509.35
$ 7,5
66
30
$ 9,027.79
$ 8,887.27
$ 6,2
95
$ 1,24
1.81
$ 1,87
7.46
FCFF
$ (664.84)
$ (1,075.92)
$ (1,7
36
$ (2,795.45)
$ (4,485.42)
$ (5,
68
$ (6,026.85)
$ (4,700.94)
$ (1,21
3.5
$ 4,073.72
$ 3,
58
4.25
Cost of capital
10.03%
9.63%
9.22%
8.81%
8.41%
Cumulated discount factor
0.90
0.8
0.75
0.6
82
0.
62
0.5
0.
51
0.4
0.43
0.40
PV(FCFF)
$ (604.23)
$ (888.67)
$ (1,30
3.68
$ (1,907.10)
$ (2,78
1.02
$ (3,2
16.43
$ (3,120.90)
$ (2,237.
14
$ (532.75)
$ 1,655.85
Terminal cash flow
Terminal cost of capital
Terminal value
$ 68,27
1.37
PV(Terminal value)
$ 27,75
0.3
PV (CF over next 10 years)
$ (14,936.06)
Sum of PV
$ 12,814.31
–
Debt
$
57
+ Cash
$ 20
1.89
Value of equity in common stock
$ 12,437.46
Number of shares
12
1.45
Estimated value /share
$ 10
2.41
Price
$
168
76
Price as % of value
16
4.79
Implied variables
After year 10
Sales to capital ratio
1.41
Invested capital
$ 1,698
$ 2,358
$ 3,479
$ 5,385
$ 8,626
$ 14,
136
$ 21,702
$ 30,730
$ 39,
61
$ 45,
91
$ 47,154
ROIC
–
1.2
–
0.2
1.31
3.15%
5.16%
7.24%
8.66%
9.
77
1
0.57
1
1.07
1
1.27
Input sheet
Date of valuation
Aug-09
Important: Before you run this spreadsheet, go into preferences in Excel and check under Calculation options
Company
Tesla
There should be a check against the iteration box. If there is not, you will get circular reasoning errors.
Numbers from your base year below ( in consistent units)
This year
Last year
Country
United States
–
0.1
631
Industry (US)
Automotive
Industry (Global)
Auto & Truck
Revenues $ 1,3
28
$ 413.26
Operating income or EBIT
$ (216.72)
$ (394.28)
Don’t adjust operating income for leases or R&D, if you plan to use the spreadsheet option to do so. (see below)
Interest expense
$
19
$ (0.25)
Book value of equity
$ 629.43
$ 124.70
Book value of debt
$ 45
2.34
Do you have
R&D expense
Yes
If you want to capitalize R&D, you have to input the numbers into the R&D worksheet.
Do you have operating lease commitments?
No
If you have operating leases, please enter your lease commitments in the lease worksheet below and I will convert to debt
Cash and cross holdings
$ 746.06
Non-operating assets
$ – 0
Minority interests
Number of shares outstanding =
Current
$ 16
8.76
Computed number
Effective tax rate
If you are not working in US dollars, you should add the inflation differential to the industry averages.
Marginal tax rate =
35.00%
Industry (US data)
Industry (Global data)
The value drivers below:
Revenue growth in the most recent year =
22
1.5
42.
35%
78.00%
Compounded annual revenue growth rate over next 5 years =
Target Porsche revenues
Pre-tax operating margin in the most recent year =
1.64
5.80%
5.98%
Target pre-tax operating margin (EBIT as % of sales in year 10) =
12.5
95th percentile: Auto industry
Sales to capital ratio in most recent year =
1.32
1.49
Sales to capital ratio (for computing reinvestment) =
Average for US
Return on invested capital in most recent year=
12
8.22%
5.77
7.83%
Market numbers
Year
1.34
Standard deviation in stock prices =
59.23%
Riskfree rate
Cost of capital =
6.79%
Initial cost of capital =
See cost of capital worksheet
Other inputs
Treated it as 60% auto, 40% technology company for the moment
Do you have employee options outstanding?
Number of options outstanding =
25.01
From last 10K
Average strike price =
$
21.2
Average maturity =
3.50
Standard deviation on stock price =
50.00%
Used 80th percentile of US stock standard deviatons
Default assumptions.
In stable growth, I will assume that your firm will have a cost of capital similar to that of typical mature companies (riskfree rate +
4.5
Do you want to override this assumption =
Mature companies generally see their risk levels approach the average
If yes, enter the cost of capital after year 10 =
Though some sectors, even in stable growth, may have higher risk.
I will assume that your firm will earn a return on capital equal to its cost of capital after year 10. I am assuming that whatever competitive advantages you have today will fade over time.
Do you want to override this assumption = No
Mature companies find it difficult to generate returns that exceed the cost of capital
If yes, enter the return on capital you expect after year 10
12%
But there are significant exceptions among companies with long-lasting competitive advantages.
I will assume that your firm has no chance of failure over the foreseeable future.
Do you want to override this assumption = Yes
Many young, growth companies fail, especially if they have trouble raising cash. Many distressed companies fail, because they have trouble making debt payments.
If yes, enter the probability of failure =
Tough to estimate but a key input.
What do you want to tie your proceeds in failure to?
B: Book value of capital, V= Estimated fair value for the company
Enter the distress proceeds as percentage of book or fair value
This can be zero, if the assets will be worth nothing if the firm fails.
I will assume that your effective tax rate will adjust to your marginal tax rate by your terminal year. If you override this assumption, I will leave the tax rate at your effective tax rate.
Do you want to override this assumption = No
I will assume that you have no losses carried forward from prior years ( NOL) coming into the valuation. If you have a money losing company, you may want to override tis.
Do you want to override this assumption = Yes
Check the financial statements.
If yes, enter the NOL that you are carrying over into year 1
$1,070.00
Enter the revenues from the most recent period (you can either use annual or the trailing 12 months). If your company had no revenues, enter a very small positive number. (You need a base for your growth rate)
Aswath Damodaran:
Enter the operating income or EBIT from the most recent time period, even if that number is negative. If you have operating leases, enter the adjusted operating income (see the operating lease worksheet for the amount you have to adjust operating income by).
Aswath Damodaran:
Enter the book value of equity (total) from the end of the most recent time period (i.e. the most recent balance sheet). This book equity will include everything – paid in capital, retained earnings etc. and may even be negative for companies that have been losing money for a while.
Aswath Damodaran:
Enter the book value of interest bearing debt (short and long term) at your company from the most recent balance sheet. (Do not include accounts payable, supplier credit or other non-interest bearing liabilities.)
Aswath Damodaran:
Enter the cash balance from the most recent balance sheet. This should include marketable securities.
Aswath Damodaran:
Enter the most recent update you have on the number of shares. If you have different classes of shares, aggregate them all and enter one number. Count restricted stock units (RSUs) as shares but don’t count shares underlying employee options.
Aswath Damodaran:
Enter the most recent stock price (how about today’s?) in here.
Aswath Damodaran:
Enter your effective (not marginal) tax rate for your firm. You will find this in your company’s annual report. If you cannot, you can compute it as follows, from the income statement:
Effective tax rate = Taxes paid/ Taxable income
If your effective tax rate varies across years, you can use an average.
Aswath Damodaran:
I don’t have a crystal ball but you should look at
a. Revenue growth in your company in recent years
b. Your company’s revenues, relative to the overall market size and larger players in the sector.
Suggestion: Check your revenues in year 10 against the overall market and see what market share are you giving your company. Check your company’s revenues against other companies in the sector.
Note that this number can be negative for a declining firm.
Aswath Damodaran:
You should start by looking at your company’s current pre-tax operating margin but also look at the average for your industry. (You can check my estimates of industry averages in the last worksheet on this spreadsheet.)
Aswath Damodaran:
You are probably wondering what this is but it is how I compute how much you are going to reinvest to keep your business growing in future years. The higher you set this number, the more efficiently you are growing and the higher the value of your growth. Again, look at your company’s current number (divide cell
B3
Aswath Damodaran:
This should be today’s long term riskfree rate. If you are working with a currency where the government has default risk, clean up the government bond rate to make it riskfree (by subtracting the default spread for the government).
Aswath Damodaran:
Enter the current cost of capital for your firm. If you don’t know what it is, you can use the worksheet to compute it.
Aswath Damodaran:
Check your company’s annual report or 10K. If it does have options outstanding, enter the total number here (vested and non vested, in the money and out…)
Aswath Damodaran:
Enter the weighted average strike price of your options. (Should be in your 10K or annual report.)
Aswath Damodaran:
The weighted average maturity of your options should be reported in your financial statements.
Aswath Damodaran:
If you have a standard deviation for your stock, enter that number. If not, use the industry average standard deviation from the worksheet.
Aswath Damodaran:
Mature companies tend to have costs of capital closer to the market average. While the riskfree rate + 4.5% is a close approximation of the average, you can use a slightly higher number (riskfree rate + 6%) for mature companies in riskier businesses and a slightly lower number (risfree rate + 4%) for safer companies.
Aswath Damodaran:
The default assumption is that competitive advantages will fade to zero over time. While this is a good assumption for many firms (about 7 in 10), there are some firms with sustainable competitive advantages (brand name, for instance), where the excess returns may continue beyond year 10. If your firm is one of those, you can enter a return on capital higher than your cost of capital in the cell below. Just don’t get carried away. At the maximum, the excess return should not exceed 5% for a mature firm.
Aswath Damodaran:
This is a really difficult business to generate excess returns in, especially for mature companies. So, I will assume that the excess returns will converge to zero in year 10.
Aswath Damodaran:
Companies at either end of the life cycle – young, growth and old, declining firms have a significant likelihood of failure. While we tend to ignore this in conventional DCF, it is worth thinking about whether you want to estimate a probability of failure. It is not easy to do but it can be done by looking at either history (with young, growth companies) or the debt market (with distressed companies).
Aswath Damodaran
While the company is doing well right now and has little debt, it is still a money losing company that is one big shock (legal, financial, macro) from disaster. I have attached a 10% probability that this will happen and an estimate that the business will have to be sold at a substantial discount (50%) on fair value in that event.
Aswath Damodaran:
If the firm fail and has to liquidate its assets, you need to specify what the liquidation proceeds will be tied to. For young growth companies, I would tie it to value and with distressed firms (especially ones with significant assets in place), I would use book value.
Aswath Damodaran:
You will generally not get 100
Aswath Damodaran:
Companies generally pay less than the marginal tax rate on their income. Some of that is due to tax deferral and others to quirks in the tax law. Over time, the conservative assumption is to require the tax rate to move towards the marginal tax rate. However, if you believe that your firm’s tax benefits are permanent, you can override this assumption.
Aswath Damodaran:
If your company has been losing money for a while, there will be accumulated losses from prior periods. Check your financial statements.
Aswath Damodaran:
This is the NOL from prior years carried forward into this year.
Aswath Damodaran:
This is a statutory tax rate. I use the tax rate of the country the company is domiciled in. See worksheet embedded in this spreadshseet for country tax rates.
Aswath Damodaran:
If you are using trailing 12-month data, it is best if the last year is the 12-month period just prior to the one that you are using. Thus, if you are looking at June 2011-June 2012, your trailing 12 month for the income statement numbers will be June 2010-June 2011 and your balance sheet numbers should be as of June 2011.
Aswath Damodaran:
Enter the market value of those non-cash assets whose earnings are (and will never) show up as part of operating income. The most common non-operating assets are minority holdings in other companies (which are not consoldiated). You can find the book value of these holdings on the balance sheet, but see if you can convert to market value. (I apply a price to book ratio, based on the sector that the company is in to the book value).
Aswath Damodaran:
Enter the “market” value of minority interests. This is a uniquely accounting item and will be on the liability side of your company’s balance sheet. It reflects the requirement that if you own more than 50% of another company or have effective control of it, you have to consolidate that company’s statements with yours. Thus, you count 100% of that subsidiaries assets, revenues and operating income with your company, even if you own only 60%. The minority interest reflects the book value of the 40% of the equity in the subsidiary that does not belong to you. Again, it is best if you can convert the book value to a market value by applying the price to book ratio for the sector in which the subsidiary operates
Aswath Damodaran:
If you are in multiple businesses, you can construct your own weighted averages using the industry average table from this spreadsheet and your company’s business breakdown.
Aswath Damodaran:
Assuming that the cyclical nature of this business will result in a higher cost of capital.Option value
Valuing Options or Warrants
Enter the current stock price =
Enter the strike price on the option =
$ 2
1.20
Enter the expiration of the option =
Enter the standard deviation in stock prices =
(volatility)
Enter the annualized dividend yield on stock =
Enter the treasury bond rate =
Enter the number of warrants (options) outstanding =
Enter the number of shares outstanding =
Do not input any numbers below this line
VALUING WARRANTS WHEN THERE IS DILUTION
Stock Price=
# Warrants issued=
25.008
Strike Price=
# Shares outstanding=
Adjusted S =
164.831
356
T.Bond rate=
Adjusted K =
Variance=
0.2500
Expiration (in years) =
3.495
Annualized dividend yield=
Div. Adj. interest rate=
d1 =
2.76
N (d1) =
0.99
d2 =
1.82
N (d2) =
0.96
Value per option =
$
145
Value of all options outstanding =
$3,644.97
Diagnostics
VALUATION DIAGNOSTICS
Invested capital at start of valuation
$ 1,69
8.11
Invested capital at end of valuation
$ 47,154.31
Change in invested capital over 10 years
$ 45,
456
Change in EBIT*(1–t) (after-tax operating income) over 10 years
$ 8,199.60
Marginal ROIC over 10 years
18.04%
ROIC at end of valuation
Average WACC over the 10 years (compounded)
9.42%
Your calculated value as a percent of current price
6
0.68
Inputs
If calculated value is negative or looks too low
If calculated value looks too high
Revenue growth rate (input cell B3)
Increase revenue growth rate
Decrease revenue growth rate
Last period EBIT as % of revenue (Input cell
B1
Increase the target pre-tax operating margin
Decrease the target pre-tax operating margin
Sales to
Capital
Decrease the sales/capital ratio
Increase the sales/capital ratio
Return on capital in perpetuity (B30 & B31)
Increase relative to your cost of capital
If higher than your cost of capital, lower towards your cost of capital
R& D converter
R & D Converter
This spreadsheet converts R&D expenses from operating to capital expenses. It makes the appropriate adjustments to operating income, net
income, the book value of assets and the book value of equity.
Inputs
Over how many years do you want to amortize R&D expenses
! If in doubt, use the lookup table below
Enter the current year’s R&D expense =
$
310.06
The maximum allowed is ten years
Enter R& D expenses for past years: the number of years that you will need to enter will be determined by the amortization period
Do not input numbers in the first column (Year). It will get automatically updated based on the input above.
Year
R& D Expenses
-1
273.98
! Year -1 is the year prior to the current year
-2
208
! Year -2 is the two years prior to the current year
-3
93.00
-4
-5
0
0
0
0
Output
Year
R&D Expense
Unamortized portion
Amortization this year
Current 310.06 1.00 310.06
-1 273.98
0.80
219.18
$ 54.80
-2 208.98
0.60
12
5.39
$ 4
1.80
-3 93.00 0.40
37.20
$ 18.60
-4 0.00
0.20
-5 0.00 0.00 0.00 $ – 0
0 0.00 0.00 0.00 $ – 0
0 0.00 0.00 0.00 $ – 0
0 0.00 0.00 0.00 $ – 0
0 0.00 0.00 0.00 $ – 0
Value of Research Asset =
$69
1.83
$
115
Amortization of asset for current year =
$115.19
Adjustment to Operating Income =
$19
4.87
! A positive number indicates an increase in operating income (add to reported EBIT)
Tax Effect of R&D Expensing
$68
By expensing R&D rather than capitalizing it, the firm gets a tax benefit. This is the dollar value of that tax benefit.Operating lease converter
Operating Lease Converter
The yellow cells are input cells. Please enter them.
Operating lease expense in current year =
$ 380.00
Operating Lease
Commitment
Year Commitment
!
Year 1
1
$5
6.00
2
$47.00
3
$39.00
4
$35.00
5
$31.00
6 and beyond
$93.00
Pre-tax Cost of Debt =
! If you do not have a cost of debt, use the synthetic rating estimator
Number of years embedded in yr 6 estimate =
! I use the average lease expense over the first five years
to estimate the number of years of expenses in yr 6
Converting Operating Leases into debt
Year Commitment
Present Value
1
$ 56.00
$ 52.34
2
$ 47.00
$ 4
1.05
3
$ 39.00
$ 3
1.84
4
$ 35.00
$ 26.70
5
$ 31.00
$ 2
2.10
6 and beyond
$ 4
6.5
$ 59.94
! Commitment beyond year 6 converted into an annuity for ten years
Debt Value of leases =
$ 233.97
Restated Financials
Depreciation on Operating Lease Asset =
$ 3
3.42
! I use straight line depreciation
Adjustment to Operating Earnings =
$346.58
! Add this amount to pre-tax operating income
Adjustment to
Total
! Add this amount to debt
Cost of capital worksheet
Estimation of Current Cost of Capital
Your inputs
Operating
Region
ERP
Inputs Computed number Country Revenues ERP
Weight
Weighted ERP
Equity
Argentina
14.80%
9.31%
1.38
Number of Shares outstanding =
Bolivia
10.68
1.96%
0.21%
Current Market Price per share =
Brazil
130
8.43%
63.73%
5.37%
Canada
0.65
Approach for estimating beta
Multibusiness(US)
If direct input, enter levered beta (or regression beta)
Chile
6.85%
3.43%
0.24%
Unlevered beta =
1.26
Ecuador
16.30%
2.94%
0.48
Riskfree Rate =
Paraguay
11.80%
1.47
0.17
What approach do you want to use to input ERP?
Country of incorporation
Peru
5.88%
0.50
Direct input
5.75%
Equity Risk Premium used in cost of equity =
Total
204
100.00%
9.00%
Debt
Operating Regions ERP calculator
Book Value of Straight Debt =
Interest Expense on Debt =
$ 19.83
Africa
1
0.09
0.0000
Average Maturity =
Australia
New Zealand
4.21
0.2444%
Approach for estimating pre-tax cost of debt
Caribbean
1
2.57
If direct input, input the pre-tax cost of debt
7.000%
Central and South America
9.18%
7.5
0.69
If actual rating, input the rating
Baa2
Eastern Europe &
Russia
8.48%
If synethetic rating, input the type of company
Middle East
6.96%
Pre-tax Cost of Debt = 7.00%
North America
47.48%
2.7538%
Tax Rate
Western Europe
374
2
8.14
1.92
Asia
Japan
7.58%
1
2.64
0.95
Book Value of Convertible Debt =
Interest Expense on Convertible =
1329
6.5748%
Maturity of Convertible Bond =
Market Value
Multi
Business
Business Revenues
EV/Sales
Estimated Value
Unlevered
Beta
Debt value of operating leases =
$ 60.00
0.81
$ 48.60
1.11
Computers/Peripherals
$ 40.00
1.3800
$ 55.20
1.39
Preferred Stock
Number of Preferred Shares =
Current Market Price per Share=
Annual Dividend per Share =
0.0000 $ – 0 0.0000
Output 0.0000 $ – 0 0.0000
Estimating Market Value of Straight Debt =
$ 541.34
Estimated Value of Straight Debt in Convertible =
Value of Debt in Operating leases =
Estimated Value of Equity in Convertible =
Levered Beta for equity =
1.28
$ 100.00
$ 103.80
1.25
Equity Debt Preferred Stock Capital
Multi Business (Global Industry Averages)
Market Value
$ 20,495.90
$ 21,037.24
Weight in Cost of Capital
9
7.43%
Advertising
$ 84.00
0.93
$ 78.82
0.98
Cost of Component
1
0.18
4.55%
7.14%
Internet
$ 16.00
4.3369
$ 69.39
1.21
0.0000 $ – 0 0.0000
0.0000 $ – 0 0.0000
0.0000 $ – 0 0.0000
0.0000 $ – 0 0.0000
0.0000 $ – 0 0.0000
0.0000 $ – 0 0.0000
0.0000 $ – 0 0.0000
0.0000 $ – 0 0.0000
0.0000 $ – 0 0.0000 Company $ 100.00
$ 148.21
1.0914
Use a sector average beta, if need be.
Aswath Damodaran:
If your company has risk exposure in emergiing markets, incorporate that risk premiums here. See worksheet on country risk premiums.
Aswath Damodaran:
Interest expense (gross) from most recent financial statement.
Aswath Damodaran:
Generally found in footnotes to financial statements.
Aswath Damodaran:
Current, long term cost of borrowing money. If you have a rating use it, if not use a synthetic rating. See the worksheet attached.
Aswath Damodaran:
If you pick operating regions or countries, please input the revenues by country or region in the table to the right.
Aswath Damodaran:
1: Large market cap (>$5 billion) and safe.
2: Small market cap (<$5 billion) or risky.
If company has volatile earnings or is in risky business, use 2, even if large market cap.
Synthetic rating
Inputs for synthetic rating estimation
Please read the special cases worksheet (see below) before you use this spreadsheet.
Before you use this spreadsheet, make sure that the iteration box (under calculation options in excel) is checked.
Enter the type of firm =
Enter current Earnings before interest and taxes (EBIT) =
(Add back only long term interest expense for financial firms)
Enter current interest expenses =
$19.83
(Use only long term interest expense for financial firms)
Enter long term risk free rate =
Interest coverage ratio =
–
100000
Estimated Bond Rating =
D2/D
Note: If you get REF! All over the place, set the operating lease commitment question in cell F5
Estimated Company Default Spread =
1
2.00
to No, and then reset it to Yes. It should work.
Estimated County Default Spread (if any) =
Estimated Cost of Debt =
14.75%
If you want to update the spreads listed below, please visit http://www.bondsonline.com
For large manufacturing firms
Ratings and Default spreads (reordered from highest to lowest)
If interest coverage ratio is
If long term interest coverage ratio is
>
≤ to
Rating is
Spread is
greater than
-100000
0.199999
1
2.00%
Aaa
0.40%
0.2
0.64
Caa/CCC
1
0.50%
2.99
Aa2
0.70
0.65
0.79
Ca2/CC
9.5
2.49
A1
0.85
0.8
1.24
C2/C
8.75
1.99
A2
1.00%
1.25
1.49999
B3/B-
7.25
A3
1.30
1.5
1.74
B2
6.50%
1.19
1.75
1.999999
B1/B+
5.50%
0.89
Ba1
3.00%
2
2.24
Ba2
4.00%
0.74
2.25
0.59
2.5
2.999999
0.49
3
4.249999
0.39
7.25%
4.25
5.499999
0.29
5.5
6.499999
0.85%
9.50%
6.5
8.499999
0.70%
0.05
0.099999
10.50%
8.50
0.049999
For smaller and riskier firms
If interest coverage ratio is
-100000 0.499999 D2/D 12.00% Rating is Spread is
0.5 0.799999 Caa/CCC 10.50% A1/A+ 0.85%
0.8 1.249999 Ca2/CC 9.50% A2/A 1.00%
1.25
1.499999
1.5 1.999999 B3/B- 7.25% Aa2/AA 0.70%
2
2.499999
2.5 2.999999 B1/B+ 5.50% B1/B+ 5.50%
3
3.499999
3.5
3.9999999
4
4.499999
4.5
5.99
6
7.499999
7.5
9.499999
9.5
12.499999
12.5 100000 Aaa/AAA 0.40% Caa/CCC 10.50%
D2/D 12.00%
If your most recent year’s operating income is unusually low or high, you can use the average operating income from the last few years.
Aswath Damodaran:
Enter the interest expense from the most recent income statement.
Aswath Damodaran:
I use a 10 year government bond rate.Industry Averages(US)
Industry Name
Number of firms
Annual Average Revenue growth – Last 5 years
Pre-tax Operating Margin
After-tax ROC
Average effective tax rate
Equity (Levered) Beta
Cost of equity
Std deviation in stock prices
Pre-tax cost of debt
Market Debt/Capital
Sales/Capital
EV/EBIT
Price/Book
Trailing PE
Advertising 32
8.67%
1
1.77
11.49%
1
6.02
1.44
1.68
1
1.51
9
7.40%
4.76
29.00%
1.40
1.22
7.77
10.40
2.04
31.25
Aerospace/Defense
12.56
10.24%
1
9.40%
20.08%
0.92
7.45%
44.98%
2.76%
2
1.03
6.23%
2.71
7.42
9.15
3.11
15.79
Air Transport
1
3.21%
8.38%
1
7.97
2
1.35
0.82
7.73%
6
4.94
3.26%
37.14%
5.59%
2.74
0.78
9.32
14.60
Apparel
7.69%
10.37
1
3.86%
1
8.57
1.29
1.36
9.68%
7
4.88%
3.76%
1
2.11
8.78%
1.52
1
1.73
14.68
3.38
21.64
Auto Parts
20.10%
6.72%
1
7.65
18.77%
1.66
1.76
11.94%
57.43%
1
9.59
9.98%
3.40
6.40
8.92
2.27
15.39
Automotive 12
4
2.35
1
6.24
1
1.79
5
0.84
13.95
15.84
Bank
416
NA
1
6.39%
0.45
0.77
5
0.34
5
6.18%
3.83%
16.58
Bank (Midwest)
20.99%
0.76
6.95%
36.37%
33.27%
5.19%
Beverage
2.62%
20.74%
1
4.56
1
8.82%
7.26%
4
7.17
18.22%
3.23
12.74
15.58
4.54
19.92
Biotechnology
214
20.93%
18.54%
1
4.57%
2.98
1.23
8.89
79.99%
13.73%
7.98
5.70
2
2.46
30.77
31.24
Building Materials
1.28%
4.30%
9.48
1.57
1
0.87
7
9.76%
39.48%
7.47%
0.88
1.54
14.45
35.82
1.67
29.27
Cable TV
9.08%
1
9.19%
1
0.52
21.23%
9.90%
4
0.45%
39.80%
6.62%
2.37
7.08
12.35
4.09
2
2.28
Chemical (Basic)
18.73%
1
4.84%
1
7.75%
21.89%
9.73
39.24%
19.83%
8.13%
1.56
7.44
9.69
2.77
31.77
Chemical (
Diversified
1
5.70%
1
5.02%
1
8.12%
19.75
1.55
1
0.75%
4
9.02
14.30%
9.45%
1.63
8.53
11.11
3.18
Chemical (Specialty)
25.40%
1
1.16
1
2.48%
1
5.35%
1.18
8.59%
6
2.90
17.03%
7.46%
1.58
1.70
1
0.86
15.23
3.60
1
7.57
Coal
7.08%
14.19%
10.10
1
0.28
56.54%
4
0.61
6.90
9.34
1.33
29.76
Computer Software
191
14.81%
29.99%
4
3.31%
1
2.43
7.42%
6
8.39
6.15%
7.10%
1.87
3.33
9.70
3.94
77.29
Computers/Peripherals 81
3.89
1
6.94
34.66%
1
0.01
81.83%
4.26%
8.84%
9.05%
2.66
6.92
3.57
46.69
Diversified Co.
113
1
7.36%
14.91%
9.21%
17.18%
6
0.46
44.04%
12.87
2.38
1
6.19
Drug
223
20.19%
2
5.24%
6.94%
5.14%
1.08
80.68%
1
2.89
7.30%
3.05
8.93
12.10
3.04
28.46
E-Commerce
15.67
8.24%
5.46%
10.52%
7.86%
80.60%
6.31%
7.53%
1.17
5.07
3
2.19
61.51
5.15
237.12
Educational Services
10.29%
1
8.69
4
2.33
2
1.72
0.91
7.01%
83.08%
6.13%
0.54
2.91
13.29
Electric Util. (Central)
4.05%
17.55%
6.47%
30.12%
0.36
5.08
1
7.29%
2.26
45.95%
3.37
12.94
15.66
Electric Utility (East)
1.50
20.51%
6.69%
33.49%
0.30
4.24%
2.26%
4
0.44
3.07
2.78
8.96
13.54
17.08
Electric Utility (West)
2.83
16.44%
6.17%
2
9.09%
0.38
0.58
44.87%
3.44%
7.87
13.74
16.05
Electrical Equipment
9.11%
13.77%
15.98%
16.15%
1.43
67.79%
10.94%
10.80
22.95
Electronics
123
3.54%
1
4.60%
11.31%
74.24%
1
8.34
7.61%
3.03
6.63
9.28
1.90
15.11
Engineering
8.58%
4.83%
1
3.16
25.00%
4
6.03
11.68%
8.31%
3.96
10.42
4
4.34
Entertainment
1
0.73
1
9.12%
1
0.41
12.56%
1.60
1
1.05%
70.99%
25.30%
8.83%
9.53
12.22
27.83
Entertainment Tech
6.07%
17.30%
19.51%
1
1.01
8.20%
5
3.25%
1
0.35%
7.56%
1.97
20.13
Environmental
20.11%
14.65
8.90%
7.60%
0.66
5.62%
79.24%
30.11%
8.44
12.78
2.29
16.99
Financial Svcs.
256
5.86%
61.83%
7.33%
16.23%
0.56
9.53%
55.15%
67.15%
4.44
0.15
8.15
13.19
1.98
22.15
Food Processing
119
14.61
9.73%
1
3.56
21.63%
6.83%
52.26%
19.03%
5.90%
12.53
2.93
24.85
Foreign Electronics
-4.59%
3.41%
5.44%
2
3.12
1.12
1.10
31.24%
31.37%
6.10%
2.30
11.52
31.52
Funeral Services
8.91%
14.37
8.28%
28.66%
2
6.75%
3
3.10
12.80
2.09
17.80
Furn/Home Furnishings
2.78%
1
4.06
16.69%
11.20
55.60%
1
8.07
11.22
2.18
Healthcare Information
20.68%
16.53%
2
0.31
0.97
44.41%
6.77%
21.77
54.59
Heavy Truck & Equip
27.10%
11.12
15.21%
22.74
12.22%
55.26%
32.11%
8.92%
1.85
7.96
10.05
1
6.08
Homebuilding
11.34%
9.44%
7.68%
7.12%
66.75%
33.14%
7.92%
2
1.15
23.16
2.54
49.55
Hotel/Gaming
14.27%
15.55
10.21%
17.52%
1.65
11.33%
55.66%
30.91%
35.36
Household Products
13.01%
1
6.56%
24.66%
50.86%
15.33%
6.58%
13.50
3.75
18.49
Human Resources
16.17%
3.05%
12.19%
2
6.61%
1.46
51.64%
9.75%
6.81
1
1.06
2.21
3
0.55
Industrial Services
7.90%
9.95%
0.83
7.38%
57.24%
26.77%
5.92%
8.87
12.52
34.78
Information Services
8.56%
20.35%
12.71%
18.33%
48.75%
2
2.15%
7.37
10.89
3.90
31.49
Insurance (Life)
21.09%
10.11%
4
2.20
35.84%
20.40
Insurance (Prop/Cas.)
2.17
2
8.57%
17.68%
291.86
295
1
6.65
Internet
194
13.12%
21.54%
9
7.81%
4.76%
2.24%
2.40
4.15
31.64
5.25
18
1.13
Investment Companies
42.77%
2
6.90%
5.87%
24.10%
7.02%
0.26
4.89
18.19
64.45
IT Services
6.33%
11.19%
21.77%
1
6.27%
5
6.11%
5.41
7.51%
4.36
39.49
Machinery
17.69%
1
1.95%
13.43
22.73%
9.07%
4
5.07%
7.97%
1.53
21.30
Maritime
12.18%
1
0.53
62.52%
64.44%
10.36
21.66
22.57
Med Supp Invasive
7.09%
21.19%
1
2.60%
6.78%
55.49%
1
4.15%
10.16
12.81
2.82
Med Supp Non-Invasive
143
8.96%
6.43%
19.94%
10.61
7.94%
67.73%
1
1.42
9.78
12.07
35.61
Medical Services
118
10.05%
14.44%
1
7.72%
7
4.16%
33.44%
7.32
2.03
29.94
Metal Fabricating
1
9.43%
14.66%
1
4.39
2
3.30%
6
0.59%
19.09%
63.26
Metals & Mining
21.71%
3
4.97%
25.19%
11.24
1.62
1
1.14
93.05%
1
3.36%
5.27
36.66
Natural Gas (Div.)
28.13%
2
2.02
9.16%
44.57%
29.12%
6.97%
10.26
53.21
Natural Gas Utility
7.04%
2
8.80%
0.32
4.40%
2
8.44%
3
9.82%
9.89
14.20
23.01
Newspaper
–
6.65%
12.30%
10.99%
1
8.35%
54.39%
28.21%
9.57
8.72
12.77
2.70
115.92
Office Equip/Supplies
12.17%
6.59%
10.89%
22.66%
51.92%
4
1.91
21.17
Oil/Gas Distribution
19.29%
7.62%
1
8.11%
7.65%
3
5.63
34.81%
5.56%
12.02
17.73
37.30
Oilfield Svcs/Equip.
16.51%
18.20%
11.39%
59.58%
21.70
9.34%
1
2.13
Packaging & Container
11.11%
23.09%
8.72%
3
6.52
3
5.97%
1
7.22
Paper/Forest Products
10.40%
1.16%
11.43%
52.28%
3
0.07%
7.39%
11.38
29.45
Petroleum (Integrated)
2
4.94%
11.99%
4.65%
30.34%
8.55%
47.25%
16.99%
5.81
11.29
Petroleum (Producing)
176
32.94%
21.76%
1
4.99
11.71%
10.18%
71.26%
21.95%
24.25
Pharmacy Services
1
6.76%
5.48%
11.53%
23.18%
8.53%
4
2.23
15.88%
7.44%
3.34
11.98
2.58
19.67
Pipeline MLPs
20.21%
8.99%
6.05%
24.88%
30.73%
4.61%
18.87
2.96
130.50
Power
101
8.17%
6.19%
9.61%
84.63%
62.04%
5.23%
30
4.86
Precious Metals
28.17%
39.11%
11.91%
11.13%
7
7.77%
1
2.01
3.64
9.30
1.61
24.60
Precision Instrument
5.78%
1
4.13%
60.11%
17.50
14.89
26.86
23.56
Property Management
1
4.32
13.68%
4.72%
16.50%
9.30%
5
0.63
52.96%
5.41%
15.96
22.79
44.26
Public/Private Equity
–
8.37%
38.25%
19.17%
13.48%
42.00%
2
2.32%
10.84%
10.30
10.45
8.65
Publishing
10.07%
11.20%
22.69%
65.72%
2
6.55%
6.88%
13.14
14.22
R.E.I.T.
127
161.63%
1
4.58%
0.04%
10.04%
34.76%
27.01%
7.78%
13.11
16.85
Railroad
44.26%
2
8.08%
12.37%
2
8.60%
3
5.73%
19.00%
7.93%
0.67
3.32
9.13
11.81
Recreation
5.39%
11.54%
1
0.14
52.30%
27.41%
14.69
24.73
Reinsurance
3.58%
6.49%
15.90%
5.67%
28.62
Restaurant
16.78%
21.41%
19.23%
50.92%
11.62%
11.50
19.52
Retail (Hardlines)
14.89%
2
2.55
1
2.14
63.49%
20.64%
2.61
Retail (Softlines)
9.79%
9.37%
30.03%
25.57%
42.54%
5.29%
9.60%
5.17
1
2.12
Retail Automotive
22.30%
9.57%
32.69%
6
4.20%
3
0.71
11.03
3.46
15.97
Retail Building Supply
13.54%
25.56%
31.82%
10.49%
12.23
15.74
25.76
Retail Store
1
6.35%
12.85%
24.83%
9.26%
63.15%
20.37%
3.61
11.67
20.34
Retail/Wholesale Food
3.34%
11.26%
3
1.18%
5.69%
2
9.93%
25.84%
8.27
12.98
Securities Brokerage
1.86%
3
2.82%
30.41%
7.95%
40.56%
72.57%
3.38%
8.79
9.85
20.01
Semiconductor
142
2
0.38%
22.88%
53.65%
9.14%
9.64%
2.16
6.98
10.58
2.72
50.55
Semiconductor Equip
-5.75%
11.35%
12.16%
1
4.52%
10.63%
25.21
Shoe
13.34%
17.66%
19.89%
47.32%
1.90%
8.94%
3.24
14.09
16.98
3.66
13.75
Steel
2
6.86%
8.19%
7.59%
24.24%
11.32%
45.66%
35.98%
7.84%
23.48
Telecom. Equipment
105
1.06%
1
4.90%
26.25%
14.01%
7.96%
64.86%
1
1.75%
6.74
8.51
2.08
24.80
Telecom. Services
19.34%
20.13%
13.66%
16.22%
64.04%
2
4.14%
18.25
Telecom. Utility
0.46%
14.69%
7.49%
26.94%
43.85%
51.98%
12.05
16.70
Thrift
170
15.84%
5.68%
4
1.73%
16.32%
5.03%
4.08
29.69
Tobacco
1
3.51
22.35%
31.97%
36.44%
15.87%
5.94%
11.46
19.42
Toiletries/Cosmetics
11.07%
21.44%
27.33%
8.52%
40.10%
17.10%
7.35%
12.39
6.04
20.39
Trucking
1
5.05%
11.97%
25.94%
4
8.32%
29.74%
2.44
10.96
Water Utility
26.21%
5.89%
3
1.45%
0.33
37.24%
42.26%
16.62
20.46
Wireless Networking
1
5.93%
12.27%
10.06%
9.62%
6
2.91%
20.43%
8.05%
2.68
10.48
16.83
29.68
Total Market
6177
12.24%
17.13%
12.88%
14.93%
59.15%
33.45
Country tax rates
Country Tax Rate
Afghanistan
20.00%
Albania
10.00%
Angola
Argentina 35.00%
Armenia
Aruba
28.00%
Australia
30.00%
Austria
Bahamas
Bahrain
Bangladesh
2
7.50%
Barbados
Belarus
18.00%
Belgium
33.99%
Bermuda
Bolivia 25.00%
Bonaire
Bosnia and Herzegovina
Botswana
22.00%
Brazil
34.00%
Bulgaria
Cambodia
Canada
2
6.00%
Cayman Islands
Chile
1
8.50%
China
Colombia
33.00%
Costa Rica
Croatia
Curacao
27.50%
Cyprus
Czech Republic
Denmark
Dominican Republic
Ecuador
23.00%
Egypt
Estonia
21.00%
El Salvador
Fiji
Finland
24.50%
France
33.33%
Georgia
Germany
29.48%
Gibraltar
Greece
Guatemala
31.00%
Guernsey
Honduras
Hong Kong
Hungary
Iceland
India
3
2.45
Indonesia
Ireland
1
2.50
Isle of Man
Israel
Italy
31.40%
Jamaica
Japan
3
8.01%
Jersey
Jordan
14.00%
Kazakhstan
Kenya
Korea
24.20%
Kuwait
15.00%
Latvia
Libya
Liechtenstein
Lithuania
Luxembourg
Macau
Macedonia
Malawi
Malaysia
Malta
Mauritius
Mexico
Montenegro
Mozambique
32.00%
Namibia
Netherlands
New Zealand 28.00%
Nigeria
Norway
Oman
Pakistan
Panama
Papua New Guinea
Paraguay 10.00%
Peru 30.00%
Philippines
Poland
Portugal
Qatar
Romania
16.00%
Russia 20.00%
Saba
Samoa
27.00%
Saudi Arabia
Serbia
Singapore
17.00%
Slovak Republic
Slovenia
South Africa
34.55%
Spain
Sri Lanka
St Eustatius
St Maarten
34.50%
Sudan
Sweden
26.30%
Switzerland
21.17%
Syria
Taiwan
Tanzania
Thailand
Trinidad and Tobago
Tunisia
Turkey
Uganda
Ukraine
United Arab Emirates
55.00%
United Kingdom
24.00%
United States
40.00%
Uruguay
Vanuatu
Venezuela
Vietnam
Yemen
Zambia
Zimbabwe
25.75%
Africa average
29.02%
North America average
Asia average
22.89%
Europe average
20.50%
Latin America average
28.30%
Oceania average
EU average
22.60%
OECD average
25.25%
Global average
24.43%
Country equity risk premiums
Country
Long-Term Rating
Adj. Default Spread
Total Risk Premium
Country Risk Premium
Albania B1 4.00% 11.80% 6.00%
Eastern Europe & Russia
Angola
Ba3
10.68%
Argentina B3 6.00% 14.80% 9.00% Central and South America
Armenia Ba2 2.75% 9.93% 4.13% Eastern Europe & Russia
Australia Aaa 0.00% 5.80% 0.00%
Australia & New Zealand
Austria Aaa 0.00% 5.80% 0.00% Western Europe
Azerbaijan
Baa3
Bahamas
Baa1
1.50%
2.25%
Bahrain Baa1 1.50% 8.05% 2.25% Middle East
Bangladesh Ba3 3.25% 10.68% 4.88% Asia
Barbados Baa3 2.00% 8.80% 3.00% Caribbean
Belarus B3 6.00% 14.80% 9.00% Eastern Europe & Russia
Belgium
Aa3
Belize
Caa3
20.80%
Bermuda Aa2 0.50% 6.55% 0.75% Caribbean
Bolivia Ba3 3.25% 10.68% 4.88% Central and South America
Bosnia and Herzegovina B3 6.00% 14.80% 9.00% Eastern Europe & Russia
Botswana A2 1.00% 7.30% 1.50% Africa
Brazil Baa2 1.75% 8.43%
2.63%
Bulgaria Baa2 1.75% 8.43% 2.63% Eastern Europe & Russia
Cambodia B2 5.00%
13.30%
Canada Aaa 0.00% 5.80% 0.00% North America
Cayman Islands Aa3 0.70% 6.85% 1.05% Caribbean
Chile Aa3 0.70% 6.85% 1.05% Central and South America
China Aa3 0.70% 6.85% 1.05% Asia
Colombia Baa3 2.00% 8.80% 3.00% Central and South America
Costa Rica Baa3 2.00% 8.80% 3.00% Central and South America
Croatia Baa3 2.00% 8.80% 3.00% Eastern Europe & Russia
Cuba
Caa1
Cyprus B3 6.00% 14.80% 9.00% Western Europe
Czech Republic A1 0.85% 7.08% 1.28% Eastern Europe & Russia
Denmark Aaa 0.00% 5.80% 0.00% Western Europe
Dominican Republic B1 4.00% 11.80% 6.00% Caribbean
Ecuador Caa1 7.00% 16.30% 10.50% Central and South America
Egypt B2 5.00% 13.30% 7.50% Africa
El Salvador Ba3 3.25% 10.68% 4.88% Central and South America
Estonia A1 0.85% 7.08% 1.28% Eastern Europe & Russia
Fiji Islands
Finland Aaa 0.00% 5.80% 0.00% Western Europe
France
Aa1
0.25%
Georgia Ba3 3.25% 10.68% 4.88% Eastern Europe & Russia
Germany Aaa 0.00% 5.80% 0.00% Western Europe
Greece Caa1 7.00% 16.30% 10.50% Western Europe
Guatemala Ba1
2.40%
3.60%
Honduras B2 5.00% 13.30% 7.50% Central and South America
Hong Kong Aa1 0.25% 6.18% 0.38% Asia
Hungary Ba1 2.40% 9.40% 3.60% Eastern Europe & Russia
Iceland Baa3 2.00% 8.80% 3.00% Western Europe
India Baa3 2.00% 8.80% 3.00% Asia
Indonesia Baa3 2.00% 8.80% 3.00% Asia
Ireland Ba1 2.40% 9.40% 3.60% Western Europe
Isle of Man Aaa 0.00% 5.80% 0.00%
Financial Center
Israel A1 0.85% 7.08% 1.28% Middle East
Italy Baa2 1.75% 8.43% 2.63% Western Europe
Jamaica B3 6.00% 14.80% 9.00% Caribbean
Japan Aa3 0.70% 6.85% 1.05% Asia
Jordan Ba2 2.75% 9.93% 4.13% Middle East
Kazakhstan Baa2 1.75% 8.43% 2.63% Eastern Europe & Russia
Kenya B1 4.00% 11.80% 6.00% Africa
Korea Aa3 0.70% 6.85% 1.05% Asia
Kuwait Aa2 0.50% 6.55% 0.75% Middle East
Latvia Baa3 2.00% 8.80% 3.00% Eastern Europe & Russia
Lebanon
Lithuania Baa1 1.50% 8.05% 2.25% Eastern Europe & Russia
Luxembourg Aaa 0.00% 5.80% 0.00% Western Europe
Macao
Malaysia A3
1.15%
Malta A3 1.15% 7.53% 1.73% Western Europe
Mauritius Baa1 1.50% 8.05% 2.25% Africa
Mexico Baa1 1.50% 8.05% 2.25% Central and South America
Moldova
Mongolia
Montenegro Ba3 3.25% 10.68% 4.88% Eastern Europe & Russia
Morocco
Namibia Baa3 2.00% 8.80% 3.00% Africa
Netherlands Aaa 0.00% 5.80% 0.00% Western Europe
New Zealand Aaa 0.00% 5.80% 0.00% Australia & New Zealand
Nicaragua
Nigeria Ba3 3.25% 10.68% 4.88% Africa
Norway Aaa 0.00% 5.80% 0.00% Western Europe
Oman A1 0.85% 7.08% 1.28% Middle East
Pakistan Caa1 7.00% 16.30% 10.50% Asia
Panama Baa2 1.75% 8.43% 2.63% Central and South America
Papua New Guinea B1 4.00% 11.80% 6.00% Asia
Paraguay B1 4.00% 11.80% 6.00% Central and South America
Peru Baa2 1.75% 8.43% 2.63% Central and South America
Philippines Ba1 2.40% 9.40% 3.60% Asia
Poland A2 1.00% 7.30% 1.50% Eastern Europe & Russia
Portugal Ba3 3.25% 10.68% 4.88% Western Europe
Qatar Aa2 0.50% 6.55% 0.75% Middle East
Romania Baa3 2.00% 8.80% 3.00% Eastern Europe & Russia
Russia Baa1 1.50% 8.05% 2.25% Eastern Europe & Russia
Saudi Arabia Aa3 0.70% 6.85% 1.05% Middle East
Senegal
Singapore Aaa 0.00% 5.80% 0.00% Asia
Slovakia
Slovenia Baa2 1.75% 8.43% 2.63% Western Europe
South Africa Baa1 1.50% 8.05% 2.25% Africa
Spain Baa3 2.00% 8.80% 3.00% Western Europe
Sri Lanka B1 4.00% 11.80% 6.00% Asia
St. Maarten
St. Vincent & the Grenadines
Suriname
Sweden Aaa 0.00% 5.80% 0.00% Western Europe
Switzerland Aaa 0.00% 5.80% 0.00% Western Europe
Taiwan Aa3 0.70% 6.85% 1.05% Asia
Thailand Baa1 1.50% 8.05% 2.25% Asia
Trinidad and Tobago Baa1 1.50% 8.05% 2.25% Caribbean
Tunisia Baa3 2.00% 8.80% 3.00% Africa
Turkey Ba1 2.40% 9.40% 3.60% Western Europe
Ukraine B3 6.00% 14.80% 9.00% Eastern Europe & Russia
United Arab Emirates Aa2 0.50% 6.55% 0.75% Middle East
United Kingdom Aaa 0.00% 5.80% 0.00% Western Europe
United States of America
Uruguay Baa3 2.00% 8.80% 3.00% Central and South America
Venezuela B1 4.00% 11.80% 6.00% Central and South America
Vietnam B2 5.00% 13.30% 7.50% Asia
Zambia B1 4.00% 11.80% 6.00% Africa
Row Labels
Default Spread (Weighted average)
Total ERP (Weighted Average)
Country Risk Premium (Weighted Average)
Africa
2.86%
10.09%
4.29%
Australia & New Zealand 0.00% 5.80% 0.00%
Caribbean 4.52%
12.57%
Central and South America 2.26% 9.18% 3.38%
Eastern Europe & Russia
1.79%
2.68%
Middle East
0.77%
North America 0.00% 5.80% 0.00%
Western Europe 0.70% 6.85% 1.05%
Asia without Japan
1.78
Japan 0.70% 6.85% 1.05%
Traiing 12 month
Last 10K
First X months: Last year
First X months: Current year
Trailing 12 month
Revenues
$413.26
$41.30
$956.74
$1,
328
R&D expense
$273.98
$107.17
$143.25
$310.06
Operating income or EBIT
-$394.28
-$194.94
-$17.38
-$216.72
Interest expenses
$0.25
$2
0.23
$0.15
-$19.83
Book value of equity
$124.70
$629.43
Book value of debt
$452.34
$578.74
Do you have operating lease commitments?
Cash and cross holdings
$201.89
$746.06
Non-operating assets
$0.00
Minority interests $0.00 $0.00
Number of shares outstanding =
$121.45
Current stock price =
Effective tax rate = 0.00%
22.31%
Marginal tax rate =
Lease commitments
Year 1
$142.00
Year 2
$128.00
Year 3
$
117
Year 4
$110.00
Year 5
$102.00
Beyond year 5
$252.00
Answer keys
Yes/No
Book or Market Value
ERP choices
Cost of debt
Yes B
Will input
No V Country of incorporation Synthetic rating 2
Single Business(US)
Operating countries
Actual rating
Single Business(Global)
Operating regions
Multibusiness(Global)
Global industry averages
Industry Name Number of firms
Unlevered beta corrected for cash
Market D/E Ratio
Market Debt to Capital
Dividend Payout
Net Margin
ROE
Revenue Growth rate: Last 5 years
Expected Earnings growth: Next 5 years
Advertising
255
32.29%
24.41%
1
3.92
34.69%
8.10%
42.52%
4.53
6.82%
21.10%
Aerospace/Defense
210
26.27%
13.31%
33.18%
16.43%
35.50%
5.45%
Air Transport
160
100.92%
50.23%
51.21%
1.66%
21.78%
Apparel
1166
17.84%
15.14%
13.42%
37.80%
6.48%
11.70%
12.92%
14.17%
Auto & Truck 130 0.77
9
3.91%
48.43%
12.66%
5.81%
18.61%
7.89%
Auto Parts
624
37.00%
16.55%
12.54%
6.60%
13.90%
14.33%
Bank
568
367.12%
78.59%
18.93%
3
2.02%
20.42%
8.97%
0.02
11.36
9.33%
15.27%
Banks (Regional)
944
142.34%
58.74%
18.85%
15.95%
1
8.68%
7.17%
Beverage 99 0.74
21.29%
12.82%
10.12%
1
4.77%
18.97%
14.06%
Beverage (Alcoholic)
209
24.36%
19.59%
18.60%
33.05%
1
1.69
18.89%
1
7.27%
1
4.32%
9.46%
17.42%
Biotechnology
666
13.07%
11.56%
34.78%
1
7.16%
11.45%
18.82%
Broadcasting
144
40.12%
2
8.63%
31.74%
8.49%
15.89%
15.03%
2.06
6.87%
Brokerage & Investment Banking
525
4
15.35%
1
1.36%
36.87%
5.54%
16.91%
Building Materials
420
44.77%
30.93%
16.08%
36.75%
2.46%
6.14%
5.13%
1.84%
19.07%
Business & Consumer Services
709
25.13%
18.11%
40.69%
7.85%
12.28%
19.57%
7.64%
15.23%
Cable TV 65 0.76
56.80%
36.22%
1
4.42%
15.91%
18.41%
26.04%
11.67%
5.51
Chemical (Basic)
760
40.13%
28.64%
13.56%
5
7.82
3.79%
8.03%
7.99%
Chemical (Diversified) 86 1.11
4
2.99%
20.09%
43.49%
9.84%
15.67%
Chemical (Specialty)
693
20.55%
17.05%
30.49%
12.65%
15.64%
1.48
10.95%
1
5.12%
Coal & Related Energy
322
25.95%
20.60%
6.36%
55.14%
15.68%
10.92%
15.36%
15.30%
Computer Services
938
15.82%
17.31%
21.36%
8.16%
28.10%
9.20%
14.72%
Computer Software
1068
14.49%
22.50%
16.62%
40.08%
3.22
1
0.54%
19.64%
Computers/Peripherals
371
16.06%
13.83%
12.32%
16.88%
9.96%
1
7.06%
32.20%
3.28
Construction
466
48.57%
14.87%
50.95%
5.17%
10.85%
10.75%
1
8.76%
Diversified
365
79.08%
44.16%
13.26%
25.92%
9.25%
1
3.98%
Educational Services 145 1.10
2
0.26%
16.84%
14.29%
-1.40%
11.08%
-2.57%
21.01%
20.40%
Electrical Equipment
847
29.89%
23.01%
13.88%
50.70%
11.05%
20.52%
Electronics
1188
31.80%
24.12%
12.33%
30.54%
4.48%
6.20%
1
8.27%
Electronics (Consumer & Office)
57.73%
36.60%
-5.21%
–
13.51%
3.57%
-1.34%
16.82%
Engineering
1141
8
3.04%
45.37%
17.02%
15.76%
Entertainment 356 0.97
2
8.71%
8.79%
28.43%
7.88%
16.46%
10.39%
21.13%
Environmental & Waste Services
307
40.91%
29.03%
11.25%
62.60%
2.97%
13.28%
12.01%
1
4.79%
Farming/Agriculture
331
42.90%
30.02%
28.83%
3.84%
10.86%
17.26%
22.13%
Financial Svcs.
520
656.46%
86.78%
17.11%
14.39%
11.59
10.60%
16.59%
Financial Svcs. (Non-bank & Insurance)
149
679.35%
87.17%
1
3.67%
13.70%
6.42%
0.22%
13.81%
21.86%
Food Processing
1223
27.68%
21.68%
15.80%
43.33%
13.63%
10.36%
20.44%
Food Wholesalers
70.98%
41.51%
18.45%
54.16%
10.56%
13.98%
11.57%
Furn/Home Furnishings
323
26.97%
21.24%
30.24%
12.02%
13.60%
25.07%
Healthcare Equipment
448
17.33%
8.87%
37.02%
18.21%
13.27%
15.75%
Healthcare Facilities
80.65%
44.65%
16.54%
10.37%
26.49%
14.16%
17.71%
1
5.74%
Healthcare Products
155
19.42%
1
6.26%
13.49%
12.03%
14.31%
14.20%
18.06%
Healthcare Services
24.23%
1
7.34%
16.77%
3
0.87%
7.19
13.17%
16.52%
Heathcare Information and Technology
266
16.76%
12.10%
16.39%
2
1.93
Heavy Construction
334
60.13%
37.55%
1
7.82%
4.74%
15.66%
11.92%
10.97%
Homebuilding 155 1.00
58.09%
19.22%
1
4.51%
10.35%
Hotel/Gaming
618
30.37%
23.29%
36.52%
8.02%
14.85%
Household Products 456 0.82
1
4.25%
12.47%
43.82%
14.34%
16.86%
22.08%
11.76%
Information Services
171
12.13%
10.81%
16.19%
31.17%
22.04%
42.97%
2.36
14.57%
Insurance (General)
220
57.51%
36.51%
13.65%
21.45%
11.52%
10.66%
15.55%
Insurance (Life) 117 0.94
61.35%
38.02%
1
7.28%
8.95%
12.51%
Insurance (Prop/Cas.) 220 0.65
39.18%
28.15%
11.96%
3
1.87%
8.42%
Internet software and services
715
18.74%
21.16%
19.32%
23.77%
Investment Co.
95.78%
48.92%
3
8.86%
14.53%
3.62
8.47%
Machinery
1249
25.23%
20.15%
17.48%
5.32%
10.87%
1
2.83%
3.89%
Metals & Mining
1700
21.26%
45.90%
15.44%
10.76%
10.67%
Office Equipment & Services
162
32.17%
24.34%
41.76%
12.40%
2.53%
Oil/Gas (Integrated)
22.11%
25.53%
27.55%
10.78%
16.80%
Oil/Gas (Production and Exploration)
1219
30.67%
2
3.47%
6.41%
44.13%
17.88%
21.47%
18.55%
Oil/Gas Distribution
198
61.85%
38.21%
115.27%
10.38%
11.00%
16.37%
17.40%
Oilfield Svcs/Equip.
570
36.67%
26.83%
14.22%
26.59%
2.36%
11.21%
11.01%
15.38%
26.79%
Packaging & Container
399
63.06%
38.67%
17.17%
43.18%
2.80%
16.01%
Paper/Forest Products
318
91.95%
47.90%
11.75%
80.79%
5.18%
13.86%
Pharma & Drugs
823
14.74%
12.53%
44.83%
12.55%
21.12%
13.76%
1
8.46%
13.72%
Power
719
0.47
105.84%
51.42%
93.77%
3.62%
1
3.97%
11.64%
Precious Metals
1237
12.78%
3.52%
61.89%
6.98%
18.63%
3.02
40.88%
18.47%
Publshing & Newspapers
401
39.77%
28.46%
1731.52%
0.16%
10.44%
-4.05%
R.E.I.T. 48 0.14
560.60%
84.86%
55.74%
2.67%
47.03
Railroad 56 0.46
65.38%
39.53%
21.56%
24.67%
17.27%
Real Estate
415
77.09%
4
3.53%
12.96%
22.44%
13.08%
15.39%
8.51%
5.65%
Real Estate (Development)
611
64.59%
17.32%
32.51%
19.74%
24.18%
12.44%
19.95%
Real Estate (Operations & Services)
439
85.84%
46.19%
22.36%
22.99%
29.36%
Recreation
292
31.84%
24.15%
28.25%
9.65%
10.47%
16.35%
Reinsurance 35 0.86
42.79%
29.97%
11.47%
24.17%
6.02%
Restaurant
298
0.62
23.26%
18.87%
20.90%
40.98%
11.37%
19.63%
1
8.98%
15.53%
Retail (Automotive)
138
51.60%
34.04%
16.71%
Retail (Building Supply)
18.80%
23.15%
38.17%
12.75%
5.10%
13.61%
Retail (Distributors)
842
97.73%
49.42%
19.16%
30.47%
11.51%
6.29%
Retail (General)
226
32.07%
24.28%
22.21%
35.74%
13.35%
15.61%
Retail (Grocery and Food)
38.11%
27.59%
23.43%
39.98%
12.11%
12.94%
13.19%
Retail (Internet)
108
11.10%
14.07%
44.11%
31.94%
Retail (Special Lines)
536
13.85%
31.63%
18.53%
Rubber& Tires
51.66%
34.06%
16.29%
4.71%
11.74%
10.45%
35.67%
Semiconductor
564
38.44%
7.21%
11.30%
10.20%
17.73%
Semiconductor Equip
264
-1.37%
-1.66%
Shipbuilding & Marine
351
90.71%
47.56%
11.28%
497.14%
Shoe 95 1.06 7.42% 6.90% 16.82%
18.13%
9.81%
18.16%
Steel
725
81.02%
44.76%
12.68%
411.43%
0.33%
0.72%
17.15%
Telecom (Wireless)
31.99%
14.76%
111.38%
12.46%
Telecom. Equipment
550
13.22%
46.05%
11.82%
3.55%
18.69%
Telecom. Services
325
65.54%
39.59%
103.40%
5.58%
14.71%
9.01%
Thrift 295 0.02
5432.46%
98.19%
39.07%
-12.11%
-0.00%
112.28
8.29%
Tobacco 48 0.49
15.48%
13.40%
19.70%
63.68%
44.22%
47.52%
Tranportation
32.77%
19.61%
42.98%
5.01%
11.17%
Trucking
185
77.55%
43.68%
21.99%
21.81%
2.95%
6.16%
Utility (General)
107.15%
51.73%
23.56%
91.00%
3.71%
10.48%
5.63%
Utility (Water)
63.18%
38.72%
14.78%
54.81%
16.28%
27.53%
4.03
17.20%
12.97%
Grand Total
40943
98.96%
49.74%
37.49%
5.11%
16.07%
test
Base
-21.857
1
-5.20642
2
45.464902
3
169.6272206
4
445.33898326
5
1023.92987555
6
2020.7215372481
7
3489.4661025356
8
5299.1581119516
9
7058.2476163242
10
8177.7425279911
Pre-tax operating income
Pre-tax Operating Income
1328.696
2258.7832
3839.93144
6527.883448
11097.4018616
18865.58316472
29534.0704443692
42263.2548058923
54794.3098558393
63670.9880524853
65421.9402239286Summary sheet
Year Revenues Pre-tax operating income
Base
$ 1,329
$ (22)
1
$ 2,259
$ (5)
2
$ 3,840
3
$ 6,528
$ 170
4
$ 11,097
5
$ 18,866
$ 1,024
6
$ 29,534
$ 2,021
7
$ 42,263
$ 3,489
8
$ 54,794
$ 5,299
9
$ 63,671
$ 7,058
10
$ 65,422
$ 8,178
We provide professional writing services to help you score straight A’s by submitting custom written assignments that mirror your guidelines.
Get result-oriented writing and never worry about grades anymore. We follow the highest quality standards to make sure that you get perfect assignments.
Our writers have experience in dealing with papers of every educational level. You can surely rely on the expertise of our qualified professionals.
Your deadline is our threshold for success and we take it very seriously. We make sure you receive your papers before your predefined time.
Someone from our customer support team is always here to respond to your questions. So, hit us up if you have got any ambiguity or concern.
Sit back and relax while we help you out with writing your papers. We have an ultimate policy for keeping your personal and order-related details a secret.
We assure you that your document will be thoroughly checked for plagiarism and grammatical errors as we use highly authentic and licit sources.
Still reluctant about placing an order? Our 100% Moneyback Guarantee backs you up on rare occasions where you aren’t satisfied with the writing.
You don’t have to wait for an update for hours; you can track the progress of your order any time you want. We share the status after each step.
Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types.
Although you can leverage our expertise for any writing task, we have a knack for creating flawless papers for the following document types.
From brainstorming your paper's outline to perfecting its grammar, we perform every step carefully to make your paper worthy of A grade.
Hire your preferred writer anytime. Simply specify if you want your preferred expert to write your paper and we’ll make that happen.
Get an elaborate and authentic grammar check report with your work to have the grammar goodness sealed in your document.
You can purchase this feature if you want our writers to sum up your paper in the form of a concise and well-articulated summary.
You don’t have to worry about plagiarism anymore. Get a plagiarism report to certify the uniqueness of your work.
Join us for the best experience while seeking writing assistance in your college life. A good grade is all you need to boost up your academic excellence and we are all about it.
We create perfect papers according to the guidelines.
We seamlessly edit out errors from your papers.
We thoroughly read your final draft to identify errors.
Work with ultimate peace of mind because we ensure that your academic work is our responsibility and your grades are a top concern for us!
Dedication. Quality. Commitment. Punctuality
Here is what we have achieved so far. These numbers are evidence that we go the extra mile to make your college journey successful.
We have the most intuitive and minimalistic process so that you can easily place an order. Just follow a few steps to unlock success.
We understand your guidelines first before delivering any writing service. You can discuss your writing needs and we will have them evaluated by our dedicated team.
We write your papers in a standardized way. We complete your work in such a way that it turns out to be a perfect description of your guidelines.
We promise you excellent grades and academic excellence that you always longed for. Our writers stay in touch with you via email.