Finance work

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.

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(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

>2

>

1 A B C Interest Rate

: 0

.0

3

Year D

iscount Rate Discount Factor (i) Cash Flow PV (ii)

PV

Full Market Value: $

33

.33 Rent: $1

0 1 1 0.

9 7

0

8

7

37

8

6

4

30

.8

60 5 $30.

86

0 1

1.03 0.

97

08

73 78 64 0.

94 25

9

59

0

91

D
2

1.0609

0.9

42

5

95 90

91

0.9

15 14 16

594 Lease Years Sold % 3

1.09

27

27

0.91

51 41 65

94

0.

88

8

48 70 47

9

88

$30.8605 0.

92 58 13

6

12

1 4

1.

125 50

8

81 0.88

84 87

04

79 0.86

26

0878

44 22 $15.9

36

9 0.478

10

7

49

91 5

1.

159

27

40

7

43

0.8

62

6087844

0.

83 74

842

56

7

10

$8.

53

02 0.2

55

9060

85

1 6

1.

19

40

52 29

65

0.8

374

8425

67 0.8

130

915

11

3 7

1.22

98

7

38

6

54

0.81

309

15

113 0.7

89

409

23

43 E 8

1.2

66 77

00814

0.7894092

34

3

0.

76

64

167 32

3

Lease Years % Interest Rate:
9

1.

304

773

18

38

0.7664167

323 0.74409

39 149

88 0.97

0.0

4

0651

80

13 10

1.

343

91

63

7

93

0.74409

391

49

0.

72 24 21 276

6 11

1.

384 233

8707

0.7

224

2

127

66

0.70

137

98802 12

1.42

57

6088

68

0.701

379

8802

0.68095

134 13

1.

46

8533

71 35

0.68095134

0.6

61

1

17

8058 14

1.51

258

97

249

0.66

111

78058

0.64

186 194

74 15

1.557

96

74

166

0.6418619474

0.62

31

6

69 392 16

1.6047064391

0.6

231

669392

0.6050

164 45

8 17

1.65

28

476323

0.6050164458

0.587

394

6076 18

1.70

243 306

12

0.5873946076

0.570

286

0

268 19

1.

75 350

60531

0.5702860268

0.55

367

57542 20 1.8061

112 347

0.5536757542

0.5

375

49

275

9 21

1.860

294

5717

0.5375492759

0.52

189 250

09 22

1.916

103

4089

0.5

218

925009

0.50669

174

84 23

1.97

358

65111

0.5066917484

0.49

193

37

363 24

2.03

279

4

106

5

0.4919

337

363

0.4776055693 25

2.09

377

79

297

0.4776055693

0.46

369

47

274 26

2.

156

59

126

75

0.4636947274

0.4501890558 27

2.22

128

90056

0.4501890558

0.4

370

767532 28

2.

287

9276757

0.4370767532

0.424

346 362

3 29

2.

356

565506

0.4243463623

0.4

119

867595 30

2.4

272

6

247

12

0.41

198

67595

0.3 99

987

145

2 31

2.500080

345

3

0.

399

9871452

0.

388

3370

341 32

2.5750

82

7557

0.3883370341

0.377026

246

7 33

2.652

335 238

4

0.3770

262

467

0.

366

0448997 34

2.73

190

5

295

5

0.3660448997

0.

355

38

339

78 35

2.8

138

6

245

44

0.355

383 397

8

0.34503

242

51 36

2.898

278 328

0.3450

324 251 0.

334

98

293

69 37

2.985

226

6778

0.3

349

829369

0.3

252

26

152

4 38

3.0747834782

0.

325

2

261

524

0.3

157

5

354

6 39

3.1670

269

825

0.

315

753546

0.3065568408 40

3.26

203

7792

0.3065568408

0.2976

280

008 41

3.

359

8989258

0.2976280008

0.

288

959224 42

3.4606958935

0.288959224

0.280542936 43

3.5645167703

0.280542936

0.27

237 178

25 44

3.67145

227

34

0.272

371

7825

0.

264

4

386

238 45

3.7815958417

0.2644386238

0.

256

7

365

279 46

3.8950437

169

0.2567365279

0.249258765 47

4.0

118

950

284

0.249258765

0.24

199

88009 48

4.

132

25

187

93

0.

241

9988009

0.

234

950

292

2 49

4.256

219

4356

0.2349502922

0.

228 107

0798 50

4.38

390

60187

0.2

281

070798

0.22

146

3

184

3 51

4.5

154

2

319

93

0.2

214

6

318

43

0.2

150

128003 52

4.6508858952

0.

215

0128003

0.

208

750

291

5 53

4.7904

124

721

0.2087502915

0.

202

670

185

9 54

4.9341

248

463

0.20

267

01859

0.

196

767

170

8 55

5.082

148

5917

0.1967671708

0.

191

0

360

882 56

5.2346130494

0.1910360882

0.1854719

303 57

5.39

165 144

09

0.1854719303

0.

180

0698

352 58

5.55

340

09841

0.1800698352

0.1748250827 59

5.7

200

030

136

0.1748250827

0.1697

330

9 60

5.89

160

3

104

0.16973309

0.1647894078 61

6.068

351 197

2

0.1647894078

0.1599897

163 62

6.25040

173

31

0.1599897163

0.

155

3

298 216 63

6.43791

378

51

0.155

329

8216

0.1508056521 64

6.63

105

11986

0.1508056521

0.146413

254

4 65

6.8

299

8

273

46

0.1464132544

0.

142

1487907 66

7.0

348

8

221

66

0.1421487907

0.1

380

085347 67

7.2459286831

0.1380085347

0.

133

9888686 68

7.4633065436

0.13

398

88686

0.1

300

862802 69

7.687

205

7399

0.1300862802

0.1262973594 70

7.9178219

121

0.1262973594

0.

122

6187956 71

8.1553565695

0.1226187956

0.1190473743 72

8.

400

0

172

666

0.1190473743

0.

115

5799751 73

8.6520

177

846

0.1155799751

0.1122

135

68 74

8.9115783

181

0.112

213

568

0.

108

9452

117 75

9.1789256676

0.108945

211

7

0.1057720502 76

9.4542934377

0.1057720502

0.

102

6913

109 77

9.7379

222

408

0.10269

131

09

0.099700

301

8 78 1

0.03

0059908 0.0997003018

0.0967964095 79

10.3309617053

0.0967964095

0.0939770966 80

10.6408905564

0.0939770966

0.09

123

98996 81

10.9601172731

0.091

239

8996

0.0885824268 82

11.2889

207

913

0.0885824268

0.08600

235

62 83

11.6275884

151 0.0860023561 0.0834974

331 84

11.9764160675 0.0834974

332 0.0810654691 85

12.3

357

085495

0.0810654691

0.078704

338

9 86

12.705779806

0.0787043

389 0.0764119795 87

13.08695

320

02

0.0764119795

0.074186

387

9 88

13.47956

179

62

0.0741863879
89

13.8839486501 0.0720256193 90

14.3004671096 0.0699

277

857 91

14.7294811

229 0.0678910541 92

15.

171

3655566 0.06591

364

48 93

15.6

265

065233 0.06399

382

99 94

16.095301719 0.062

129

9319 95

16.5781607705 0.0603203

223 96

17.0755055936 0.0585634197 97

17.5877707615 0.056857689 98

18.1154038843 0.055

201

6398 99

18.6588660008 0.053593825 100 19.2186319809 0.05203

283

99 101 19.7951909403 0.0505173202 102

20.3890466685 0.049045942 103

21.0007180685 0.0476174194 104

21.6

307 396

106 0.046

230

5043 105

22.2796617989 0.0448839847 106

22.9480516529 0.0435766842 107

23.6364932025 0.0423074604 108

24.3455879985 0.041075

204

3 109

25.0759556

385 0.0398788391 110 25.8

282

343077 0.0387173

195 111

26.60

308

1

336

9 0.0375896306 112

27.401173777 0.036494787 113

28.2

232

089903 0.03543

183

2 114 29.06990526 0.0343998369 115

29.9420024178 0.0

333

978999 116 30.8402624903 0.032

4251455 117

31.7654703651 0.0

314

807238 118

32.7184

344

76 0.0

305

638095 119

33.6999875103 0.0

296

736015 120 34.7109871356 0.028809

321

8 121

35.752

316

7497 0.0279702154 122

36.8248862522 0.0

271

555489 123

37.9296328397 0.0

263

646106 124

39.06752

182

49 0.0

255

967093 125

40.2

395

474797 0.0248511741 126

41.4467339041 0.024127

353

5 127

42.6901359

212 0.02

342

4615 128

43.9708399988 0.0227423447 129

45.

289

9651988 0.0

220

799463 130

46.6486641547 0.02

143

68411 131

48.0481

240

794 0.0208124671 132

49.4895678018 0.020

206

2787 133

50.9742548358 0.0196177463 134

52.5034824809 0.0190463556 135

54.0785869553 0.0184916074 136

55.700944564 0.0179530169 137

57.37197

290

09 0.0174301135 138

59.09

313

20879 0.01692

244

03 139 60.8659

260

506 0.0164295537 140 62.6919038321 0.015951023 141 64.57

266

0947 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

281197 0.01

259 188

49 149

81.7987149633 0.012

225

1309 150

84.2526764122 0.0118690592

2

A

Interest Rate

at beginning of T and do not work

0.3 0.04 1

70000 0.0

2 100000 70000 70000.0

0.0 1

3 100000 70000 142800.0

1

4 100000 70000 218512.0

1

5 100000 70000 297252.5

342.6

1

6 100000 70000 379142.6

1

7 100000 70000 464308.3

1

8 100000 70000 552880.6

1

9 100000 70000 644995.8

1

10 100000 70000 740795.7

1

11 100000 70000 840427.5

1

12 100000 70000 944044.6

1

13 100000 70000 1051806.4

78.6

1

14 100000 70000 1163878.6

33.8

1

15 100000 70000 1280433.8

1

16 100000 70000 1401651.1

1

17 100000 70000 1527717.2

1

18 100000 70000 1658825.9

1

19 100000 70000 1795178.9

1

20 100000 70000 1936986.1

0

21 100000 70000 2084465.5

5044.1

0

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)
100000 70000.0
142800.0
218512.0 75712.0
297252.5 154452.5
379142.6 236
464308.3 321508.3
552880.6 410080.6
644995.8 502195.8
740795.7 597995.7
840427.5 697627.5
944044.6 801244.6
1051806.4 909006.4
1163878.6 10

210
1280433.8 11

376
1401651.1 1258851.1
1527717.2 1384917.2
1658825.9 1516025.9
1795178.9 1652378.9
1936986.1 1794186.1
2084465.5 1941665.5
2237844.1 209

3

Number

Variance SD

0.032

1

1

5

861353

2

2

0635113

3211

3

3

4

4

19

04

5

7172

5

746482

6

366

6

7

7

8

8

973051

9

9

84618

10

10

11

11

12

12

13

13

14

14

583

15

15

16

16

17

17

18

18

29

19

19

20

20

21

21

22

032

22

23

23

7993157

24

24

25

1318

25

5308987

26

26

27

27

28

28

29

29

30

30

31

31

32

32

21051

33

33

34

34

35

35

36

36

102449

37

37

38

38

1435241

39

39

904

40

14

40

41

41

42

42

43

43

44

44

45

45

46

46

47

47

48

48

49

49

50

50

51

51

52

52

53

53

54

54

55

55

56

56

57

57

58

58

59

59

60

60

61

61

62

62

63

63

64

64

65

65

66

66

67

67

68

68

69

69

70

70

71

71

72

72

73

73

74

74

75

75

76

76

77

77

78

78

79

79

80

80

81

81

82

82

83

83

84

84

85

85

86

86

87

87

88

88

89

89

90

90

91

91

92

92

93

93

94

94

95

95

96

96

97

97

98

98

99

99

100

100

101

101

102

102

103

103

104

104

105

105

106

106

107

107

108

108

109

109

110

110

111

111

112

112

113

113

114

114

115

115

116

116

117

117

118

118

119

119

120

120

121

121

122

122

123

123

124

124

125

125

126

126

127

127

128

128

129

129

130

130

131

131

132

132

133

133

134

134

135

135

136

136

137

137

138

138

139

139

140

140

141

141

142

142

143

143

144

144

145

145

146

146

147

147

148

148

149

149

150

150

151

151

152

152

153

153

154

154

155

155

156

156

157

157

158

158

159

159

160

160

161

161

162

162

163

163

164

164

165

165

166

166

167

167

168

168

169

169

170

170

171

171

172

172

173

173

174

174

175

175

176

176

177

177

178

178

179

179

180

180

181

181

182

182

183

183

184

184

185

185

186

186

187

187

188

188

189

189

190

190

191

191

192

192

193

193

194

194

195

195

196

196

197

197

198

198

199

199

200

200

201

201

202

202

203

203

204

204

205

205

206

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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
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
0.1909886181 0.2607343794 0.0284196912 0.2965640611 r_02: 0.0818629558 0.2861170

317
0.31842038 A3 -0.11

217 312 -0.2105712421 -0.29912

393 Sqaure Root (2): 1.4142135624
-0.213

192 Half of Variance: 0.0171365966 0.1975415055 0.2

373 0.4818074991
0.0491

327 P.141 Holds? 0.0159810708 0.095767706 0.1544810882 0.2650430936
0.0994614201 0.1823794595 0.1428205481 0.351247542
0.0911580267 0.1481002636 0.1586943643 0.3

302
0.2744283775 -0.16

310 0.1132522518 -0.0683286107
0.2800012322 0.1691673366 0.1878353023 0.3887782

368
0.2480456813 0.2784591323 0.2289232368 0.5711281349
0.2084834555 -0.2165552419 -0.1880896396 -0.363913084
0.1594383682 -0.1100731818 -0.0077371365 -0.1169586671
0.0634482076 0.0288598542 0.2119

270 0.2469030966
0.0450708338 0.1891123413 0.345908903 0.6004368869
0.1719530956 0.1433189595 0.0721980869 0.2258644011
0.0030173354 -0.0287350915 0.0427096173 0.012747261
0.3070944476 0.3787

153 0.3208170185 0.8210306701
0.2627844624 0.1416333773 0.1653820206 0.3304390121
0.0016959527 0.4208104289 0.2053868595 0.7126262209
0.4778106756 -0.1797399709 0.0573038485 -0.1327359145
0.124

176 0.08154223 0.3830804677 0.4958599333
-0.2206571868 -0.2476008121 0.1047336277 -0.

168
0.0617005223 0.1009341197 -0.1475125479 -0.0614674774
0.177

161 0.

311 -0.1521801548 0.1119419235
0.1852825062 0.0163475762 -0.0446368137 -0.0290189413
-0.0961296264 0.0772711311 0.098846164 0.18375525
-0.004286339 -0.0444248019 0.1458023106 0.09490027
0.3510215413 -0.0346734279 -0.0380048448 -0.0713605144
0.0884022132 0.0144872787 0.3467420706 0.3662526982
0.1443219366 0.456862864 0.0078976658 0.46836868
0.1035524541 0.3459127289 -0.14

285 0.1536462624
0.184500718 0.4063279518 0.4554021603 1.0467727391
-0.0482776425 -0.0500754926 0.1199865562 0.0639026777
0.2094580012 0.0890446991 0.0919192998 0.1891489

253
-0.1373031059 0.0483096644 0.1991709051 0.

257
0.0216112662 0.4184325639 0.2371769156 0.7548520243
0.3537363575 0.1804831442 0.1623575744 0.

372
-0.0759252911 0.0697449048 0.0323273324 0.104

326
0.21146

381 -0.046832241 0.0560989212 0.006639442
0.0859686421 0.1169592555 0.1399198046 0.2732439763
-0.0276600447 -0.361692925 -0.130512543 -0.4450000046
-0.1110657798 -0.1830324008 0.3469777848 0.100437207
0.1443456991 0.290399088 0.1777293955 0.5197409379
0.1563106552 0.1717109462 0.1872496447 0.3911134046
-0.0043913638 0.1392994211 0.247926145 0.4217615346
0.2941907603 -0.0032904958 0.2423168719 0.2382290335
0.1722775807 0.2290907149 0.3716069606 0.6858293798
-0.0218603043 -0.0964797804 0.1662837732 0.0537609709
-0.0742135374 0.2462806209 0.2713772015 0.5844927681
0.1513002884 0.3227659689 0.1789821124 0.5595174162
0.4141800549 0.0377642383 0.0652210553 0.1054483171
0.2629862613 -0.155912149 0.0807587929 -0.0877446331
0.1356450676 0.2129062532 0.2321589302 0.4944932714
0.5920735839 0.1849180459 0.3449231945 0.5936237636
-0.0282102046 0.085657868 0.0618553624 0.1528116288
0.1640638971 0.1899584466 0.3339826326 0.5873839013
-0.1072077073 0.1537170002 0.2458294298 0.4373345926
0.1042271369 0.0874052412 0.0973983908 0.1933167618
0.2987606071 -0.0899935966 0.2367903668 0.1254871534
0.158643698 0.0173090823 -0.0564912231 -0.040159952
-0.1938439874 -0.0659724593 0.174427847 0.0969479536
0.1708572427 -0.1480571419 0.141045914 -0.0278940829
0.0461252994 0.00085308 -0.1762997886 -0.1755971065
0.2311823934 0.2457957612 0.1953170046 0.4891208576
0.1540550698 -0.0529110675 0.2521606638 0.1859075064
0.1785817993 0.4212367859 0.3070372665 0.8576094437
0.1900722891 0.02199003 0.0680603053 0.0915469835
0.0382781567 0.064862169 0.4214742176 0.5136741185
-0.0559462195 0.3382556955 0.2007257493 0.6068780727
-0.2618841763 0.1309924053 -0.0679168195 0.0541789982
0.1705521863 -0.1629513807 -0.016643806 -0.1768830555
0.0212033433 0.2107766795 0.2156034661 0.4718243284
0.3538891811 0.1183286282 0.3043173247 0.4586554045
-0.0012603218 0.1965495066 0.1787623368 0.4104474925
-0.0795910626 -0.1081974281 0.0828133994 -0.0343442255
-0.0320882581 -0.1479145945 0.2247712862 0.0436097381
0.1487729279 0.2302472458 -0.015838846 0.2107615491
-0.0567791255 0.2038008095 0.1332108846 0.3641601802
0.2977585877 0.1222009423 -0.1005037914 0.009415493
0.1023831231 0.141345109 0.2575497753 0.4352982854
0.0540190261 -0.2602316262 -0.0983085598 -0.3329571896
-0.0814157561 0.1304324153 -0.0526447161 0.0709211217
-0.2644683752 -0.0905218418 0.1168676047 0.0157666921
-0.1114329549 0.2246713921 0.0632778788 0.302166
0.2148839852 0.1011500298 0.0303665101 0.1345881133
0.218713379 0.1584938701 0.0747363675 0.2450754937
0.2853361052 0.116099263 0.3978702062 0.5601619069
0.0917726807 0.262680702 -0.1530918772 0.069374543
0.3521620075 0.1052691043 0.5660098742 0.7308623311
-0.0777175669 0.0765656895 0.3470985196 0.4502400467
0.169712942 0.121163476 0.2414565349 0.391875724
0.1019668376 -0.1103421082 0.2184442752 0.0839985652
0.0214512166 -0.1791553224 0.1837039766 -0.0283628909
0.1415570044 0.1493170249 -0.0633525507 0.0765048598
0.2807733951 -0.1620211132 0.1338304639 -0.04987401
0.1942438742 0.0749292014 -0.0301318194 0.0425396288
0.0457493543 0.3246698877 0.2311021436 0.6308039383
0.2828499758 0.5126302689 0.1161551133 0.6883300092
0.2116771766 -0.0075164148 0.0832731537 0.0751308233
0.0582355458 0.4691304283 0.1136986453 0.6361685677
0.0492898119 -0.070270602 0.0468565102 -0.026706727
0.0348490452 0.0257991945 0.2371794485 0.2690976817
0.0765652469 0.4239747186 0.1146547823 0.5872402299
0.1366933042 0.1479504923 0.0637863143 0.2211740232
0.0863851313 0.0739972295 -0.0490401699 0.0213282229
-0.1521093024 0.1031051081 -0.1956245207 -0.1126893
-0.0642145945 0.1730822298 0.0219463126 0.1988270591
0.0563353652 0.1481566473 0.1127201015 0.2775769811
-0.0494148381 0.1196217587 0.2175905873 0.3632409147
0.1015623777 0.298900233 0.2740893123 0.6549149047
-0.1319313962 0.3441135406 0.2944401494 0.7398745324
-0.3555611351 0.1496908491 -0.1070344811 0.0266342856
-0.0354356245 0.3398595815 0.1505595701 0.5415882641
0.2481602697 0.1324921724 0.0092433061 0.1429601442
0.4468259749 0.3972590496 0.1158140749 0.5590813138
-0.0627419775 0.1995992058 0.2279440861 0.4730407505
0.1228687525 -0.1531857048 0.3992675796 0.1849197892
0.1027024726 0.1735091573 0.101466812 0.2925813903
0.3352381444 -0.200728814 0.2483916448 -0.0021965294
0.3717317712 -0.0214517174 0.2290640113 0.2026984774
0.1590487203 0.0651698583 0.1395100142 0.2137717204
0.3073469567 -0.2166468947 0.1246724641 -0.1189843328
0.2746859577 0.2760949862 0.1733041125 0.4972474952
0.2211339292 0.0827307601 0.2150212503 0.3155408819
-0.0777279054 -0.0124189983 0.1346946784 0.1206029071
0.0722034763 0.1456261039 0.0340722471 0.1846601596
0.1600949269 0.1875835485 0.0657397365 0.265654978
-0.3560427555 -0.0404565945 0.0339523265 -0.0078778635
0.2208503831 0.0231588822 0.2034080878 0.2312776739
0.2707060592 -0.0953577597 -0.0235400175 -0.1166530538
0.1215816876 -0.1974151616 -0.1167727765 -0.2911352216
-0.0788056223 0.0088767191 -0.0230421409 -0.0143699604
0.1927043355 0.2116130581 0.3012511325 0.576612864
0.0436699875 0.151185071 -0.0286795757 0.1181695716
-0.1428661712 -0.0322198261 -0.2777993712 -0.3010685499
-0.1352390425 0.0922202495 0.1381137974 0.2430709358
0.1395544728 0.156202341 0.0867053841 0.256451309
-0.3771741227 0.0427468098 0.3328019386 0.3897749695
0.012241747 -0.1552101095 0.3017768928 0.0997279588
0.0026267823 0.2817554803 0.1537037673 0.4787661264
0.105773786 0.0420362529 0.1539829359 0.2024920544
-0.2217157187 0.0323819152 -0.2137068875 -0.1882452106
0.102741417 -0.1936100658 0.1001434402 -0.1128554037
0.0646909978 0.3251798931 0.1626227975 0.5406843546
-0.1088207101 -0.1777841263 -0.1380018098 -0.2912514049
0.23235288 -0.0609614282 0.0285387495 -0.0341624416
0.1886606439 0.1003588764 0.3902013653 0.5297204123
-0.0963357168 0.0541671293 0.1653593524 0.2284835231
0.2039677483 0.058959214 0.2800933 0.3555665948
-0.0414071407 0.1910784718 -0.1742406095 -0.016455767
0.2203934574 -0.1803542332 0.2439992371 0.0196387087
0.0173147442 -0.0326411443 0.005148098 -0.0276610861
-0.1011653776 0.0869954506 -0.2043576632 -0.1351403996
-0.0745147917 -0.1367566286 0.0941307253 -0.0554989039
0.3472064519 -0.1193262922 0.1418632804 0.005608969
-0.0975735302 0.1486525559 0.0262356589 0.1787882126
-0.0504881533 0.2007161107 -0.0172258431 0.1800327634
0.2413231295 0.0031235629 0.3291027205 0.3332542564
0.3678955147 0.2728978877 0.2858787659 0.6367923648
-0.2514650524 0.2694577745 0.3523735971 0.7167811769
0.5148916423 0.2035714525 0.0445749498 0.2572205895
0.0830213704 0.4812059706 -0.0250228421 0.4441419875
0.5234285168 0.3146293507 0.1348748963 0.491939848
0.0409064675 0.3025858973 -0.2213414188 0.0142696866
0.2652664076 0.185859217 0.1994928929 0.4224297028
0.308319941 0.0819627772 0.1690208134 0.2648370059
-0.017332998 -0.0076359432 0.420384965 0.4095389861
-0.0117016842 0.1540035085 0.3772912581 0.589398944
0.3328846539 -0.1129416 0.269682948 0.1262829243
-0.0682695812 0.1585949 0.2918890481 0.4967760625
0.4242113461 0.3064793852 0.1244906047 0.4691237938
0.2372954521 0.2025727309 -0.1010925954 0.0810015325
0.1621948187 0.2236874925 0.3203646731 0.615713736
0.2257688014 0.1409373818 -0.0224316248 0.1153443025
-0.0820667362 0.3772675414 0.0986971749 0.5131999569
0.1967580278 0.1898200908 -0.0112619686 0.1764203743
0.0522558179 0.3359913628 0.2001803724 0.6034306113
0.2407749514 -0.3900847668 0.2115790538 -0.2610394788
0.0992581466 -0.0425072606 0.0417725806 -0.002510318
-0.2102012127 0.1032794474 0.034372128 0.1412015098
0.4105137748 0.2256066574 0.1404025517 0.3976849594
-0.1263080721 0.4715158702 0.1603797165 0.7075171683
0.0347440796 -0.2348189141 0.1325416329 -0.1334005635
-0.0029283158 0.0126860531 0.2953333636 0.3117660313
0.0433330287 0.2251673418 0.2840443382 0.5731691886
0.2359478642 0.1647534057 -0.0956584937 0.0533348493
0.2316636626 0.1717612939 -0.0838366895 0.0735247062
0.044495928 0.083422216 -0.1038295874 -0.0290690657
-0.070492704 0.4301938041 0.3262552141 0.8968019898
-0.0496206341 0.2300984068 0.3016903542 0.6012072309
0.1892347764 -0.0081921303 -0.0102124597 -0.0183209283
0.4448474071 0.3856884708 0.0182642253 0.4109969972
0.0758411472 0.0885028313 -0.0228187769 0.0636645281
0.4468425797 0.0566781227 0.012427116 0.0698095842
0.4355867114 -0.0149506414 -0.1773830358 -0.189681687
0.3265394033 0.0046676128 0.1918575783 0.197420708
0.2526247928 0.1681823715 0.0765389583 0.2575938333
-0.0094541989 0.1684221097 0.0667613158 0.2464275072
-0.2483369795 0.1997240344 0.035863763 0.2427506529
0.320058769 -0.0896839528 0.1619218406 0.057716097
-0.0733358093 -0.1227096893 0.3022893925 0.1424858657
-0.1290933963 0.200731342 0.0448150241 0.254542146
0.2570567467 0.1041669237 0.1656097581 0.2870277408
-0.0364949592 -0.1558515123 0.0796897887 -0.0885814976
0.1723867637 0.2271543234 0.1251443353 0.3807257356
-0.0780318075 -0.234640824 0.1827627524 -0.0947616745
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0.0697467245 0.2785147254 0.4759120355 0.8869752708
0.0758902886 0.3490216013 -0.0828057465 0.2373148606
0.0138660146 0.4048421176 0.1760722088 0.6521957723
0.0920067554 -0.0484322209 0.0687096563 0.0169496741
-0.0993672754 0.3139744518 0.1576114105 0.5210718185
0.0055606334 0.496865706 0.138729615 0.7045253092
0.0033181246 0.2929686268 -0.1732081888 0.0690158728
0.248921282 -0.2489494645 0.3249590411 -0.0048
0.2249009072 0.1129419744 0.0937202674 0.2172471938
0.153227594 0.3625638665 0.5862979839 1.1614323143
0.0735268876 0.1269787554 0.1479136531 0.2936743
-0.0803501861 0.2900811003 0.1511262616 0.4850462342
0.0564173965 -0.0415469991 0.0457151416 0.0022688155
0.087907633 0.3443160902 -0.1005042273 0.2092066403
0.1147976821 -0.1103993242 -0.114125107 -0.2119250965
0.2248424769 0.1580647764 0.0114836573 0.1713635955
0.3711342108 0.2522331588 -0.1628803694 0.0482689593
-0.0460503703 0.1909983745 0.2771012244 0.5210254823
-0.0211720923 -0.0377195024 -0.0644408779 -0.0997297024
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0.1249629796 0.2412099827 0.0246692439 0.2718296944
0.0898312509 0.3259523566 -0.0843747557 0.2140754505
0.1450404676 0.3278513887 -0.017548142 0.304550064
0.1175010217 -0.067958318 0.2155254972 0.132920429
0.4315386678 -0.1206704108 0.3441792854 0.1819766188
0.4496413255 0.4436369788 -0.1313326797 0.2540402659
-0.1802001185 -0.1128173655 0.3373763572 0.1864970799
0.3527387629 0.2843491847 -0.1626680361 0.0754266252
0.2773157958 0.1260283633 -0.1243719385 -0.0140179671
0.2106709912 0.1557022406 0.2458775789 0.4398635095
0.1429823529 0.0265128323 0.1237822502 0.1535769005
0.1967591219 0.2937280625 0.0742641422 0.3898056674
-0.0680588936 -0.088129262 0.0003122964 -0.0878444881
0.1997899912 0.4364479968 0.0016690966 0.4388455674
-0.0309478571 0.4420211842 0.2754924599 0.8392871475
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Signal Realized Rate of Return 2bq drift alnoe
-1 -48
0.00037504 0.00040004
0.0055769902 0.00060012
0.0007502207 0.00080024
0.0059541218 0.0010004001
0.0111850832 0.0012006002
0.0164432457 0.0014008403
0.0115643181 0.0016011204
0.0067088094 0.0018014407
0.0018766071 0.002001801
0.0070863654 0.0022022013
0.0123232145 0.0024026418
0.0074640631 0.0026031223
0.0127028762 0.0028036429
0.0179689312 0.0030042036
0.0130826803 0.0032048045
0.0082198835 0.0034054454
0.003380428 0.0036061265
0.0085980062 0.0038068478
0.0138427159 0.0040076091
0.0089762708 0.0042084106
0.0041331847 0.0044092523
-0.0006866546 0.0046101342
-0.0054833586 0.0048110562
-0.0003118721 0.0050120184
0.0048865062 0.0052130208
0.010111916 0.0054140634
0.015364498 0.0056151462
0.0206443934 0.0058162693
0.0259517442 0.0060174325
0.0210271758 0.006218636
0.0263365172 0.0064198797
0.0214101019 0.0066211637
0.0267214344 0.0068224879
0.0217931715 0.0070238524
0.0168885643 0.0072252572
0.0221763848 0.0074267023
0.0172699382 0.0076281876
0.0123870425 0.0078297132
0.0176514551 0.0080312792
0.0127667281 0.0082328854
0.0180331151 0.008434532
0.0233268873 0.0086362189
0.0184149182 0.0088379462
0.0237106758 0.0090397138
0.0187968646 0.0092415217
0.0139066396 0.00944337
0.0191789542 0.0096452587
0.0142868952 0.0098471877
0.0094183181 0.0100491572
0.0045731102 0.010251167
0.0097968903 0.0104532172
0.0049498653 0.0106553079
0.0001261059 0.0108574389
-0.0046744994 0.0110596104
-0.0094520618 0.0112618223
-0.0142066919 0.0114640747
-0.0189384998 0.0116663675
-0.023647595 0.0118687008
-0.0185705625 0.0120710745
-0.0232814238 0.0122734888
-0.0182024872 0.0124759435
-0.0130971401 0.0126784386
-0.0079652453 0.0128809743
-0.0028066645 0.0130835505
0.0023787408 0.0132861672
-0.0024326771 0.0134888245
0.0027546729 0.0136915222
-0.0020585495 0.0138942605
0.003130746 0.0140970394
-0.0016842815 0.0142998588
-0.006476197 0.0145027188
-0.0013098732 0.0147056193
-0.0061035858 0.0149085604
-0.0009353245 0.0151115422
0.0042598119 0.0153145645
0.0094819629 0.0155176274
0.0147312691 0.0157207309
0.009860559 0.015923875
0.0050132283 0.0161270598
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1.5031355934 1.4960476283
1.4911205425 1.4965468379
1.5040743693 1.4970461472
1.4920548124 1.4975455565
1.4800929493 1.4980450656
1.4681885031 1.4985446746
1.4563411983 1.4990443835
1.4691141725 1.4995441924
1.4572624245 1.5000441012
1.4700401891 1.5005441101
1.4581839962 1.5010442189
1.470966553 1.5015444277
1.483815579 1.5020447366
1.49673142 1.5025451456
1.4847471092 1.5030456546
1.4728203231 1.5035462637
1.4856789888 1.504046973
1.4986045195 1.5045477824
1.511597263 1.5050486919
1.4995415962 1.5055497017
1.4875437965 1.5060508116
1.4756035863 1.5065520218
1.4637206891 1.5070533322
1.4765320367 1.5075547428
1.4894100032 1.5080562538
1.4774608352 1.508557865
1.4655690232 1.5090595766
1.4783899821 1.5095613885
1.4664937102 1.5100633008
1.4546545404 1.5105653135
1.467418744 1.5110674265
1.4802493215 1.51156964
1.4683441248 1.5120719539
1.456496073 1.5125743683
1.4692698525 1.5130768832
1.4574173572 1.5135794986
1.4701959275 1.5140822145
1.458338987 1.5145850309
1.4465389599 1.5150879479
1.4592609625 1.5155909655
1.4720491195 1.5160940837
1.4849037749 1.5165973025
1.4978252746 1.517100622
1.4858357132 1.5176040421
1.4987620589 1.5181075629
1.4867680011 1.5186111844
1.4748315147 1.5191149067
1.4629523234 1.5196187297
1.4511301522 1.5201226534
1.4393647275 1.5206266779
1.4520494241 1.5211308033
1.4402795869 1.5216350294
1.4529690407 1.5221393564
1.4411947893 1.5226437843
1.4294770543 1.5231483131
1.4178155645 1.5236529427
1.4303882054 1.5241576733
1.418722342 1.5246625048
1.4312996982 1.5251674373
1.4439424566 1.5256724708
1.4322115328 1.5261776053
1.4448590328 1.5266828409
1.4331237094 1.5271881774
1.4214447156 1.5276936151
1.4340362282 1.5281991538
1.4466932165 1.5287047936
1.4594160213 1.5292105346
1.4476108244 1.5297163767
1.4603384007 1.5302223199
1.4731321603 1.5307283644
1.461261126 1.5312345101
1.4494470726 1.531740757
1.4621841973 1.5322471051
1.4503657132 1.5327535546
1.4386039578 1.5332601053
1.4512846983 1.5337667573
1.4395185318 1.5342735106
1.4278088428 1.5347803653
1.4404334488 1.5352873214
1.4531237028 1.5357943789
1.465879946 1.5363015378
1.4540437223 1.5368087981
1.4668047496 1.5373161598
1.4796321343 1.5378236231
1.4925262214 1.5383311878
1.5054873578 1.538838854
1.518515892 1.5393466218
1.5064270158 1.5398544911
1.5194604362 1.540362462
1.5325616305 1.5408705345
1.5204053347 1.5413787086
1.5083073891 1.5418869844
1.5213505875 1.5423953618
1.5092481047 1.5429038408
1.5222961948 1.5434124216
1.535412135 1.5439211041
1.5485962781 1.5444298883
1.5618489788 1.5449387743
1.5495521037 1.545447762
1.5373142536 1.5459568516
1.5505082877 1.546466043
1.5637709308 1.5469753362
1.5771025396 1.5474847312
1.5905034728 1.5479942282
1.6039740909 1.548503827
1.6175147562 1.5490135278
1.6311258329 1.5495233305
1.6448076872 1.5500332352
1.6321126103 1.5505432418
1.6194784698 1.5510533505
1.6330997579 1.5515635611
1.620460879 1.5520738738
1.6078826668 1.5525842886
1.59536483 1.5530948055
1.5829070788 1.5536054244
1.5963381956 1.5541161455
1.6098391542 1.5546269687
1.6234103178 1.5551378941
1.6108179483 1.5556489217
1.6243942017 1.5561600515
1.6117971095 1.5566712835
1.6253784545 1.5571826178
1.6390304224 1.5576940543
1.6263630764 1.5582055931
1.6400201644 1.5587172342
1.6273480676 1.5592289777
1.6147367969 1.5597408235
1.6021860602 1.5602527716
1.6157174278 1.5607648222
1.6293191584 1.5612769751
1.6166984264 1.5617892305
1.6303052582 1.5623015884
1.6439828456 1.5628140487
1.6577315564 1.5633266115
1.6449744449 1.5638392768
1.658728312 1.5643520447
1.6459664161 1.5648649151
1.6597254415 1.5653778881
1.6735560138 1.5658909637
1.6607229449 1.5664041419
1.6745587042 1.5669174227
1.6617208225 1.5674308062
1.6489445625 1.5679442923
1.6627190742 1.5684578812
1.6499380227 1.5689715728
1.6637177004 1.5694853671
1.6509318554 1.5699992642
1.6647167011 1.570513264
1.6519260609 1.5710273667
1.6391968158 1.5715415721
1.6265286711 1.5720558804
1.6401866202 1.5725702916
1.6275137244 1.5730848057
1.6411767958 1.5735994226
1.6284991472 1.5741141425
1.6158823513 1.5746289654
1.6294849395 1.5751438911
1.6168634118 1.5756589199
1.6043024674 1.5761740517
1.5918018156 1.5766892865
1.605279185 1.5772046244
1.5927738449 1.5777200653
1.5803285305 1.5782356093
1.5937462388 1.5787512564
1.6072337193 1.5792670067
1.5947189974 1.5797828601
1.5822643462 1.5802988167
1.5698694774 1.5808148764
1.5575341039 1.5813310394
1.5452579402 1.5818473056
1.533040702 1.5823636751
1.5462125137 1.5828801478
1.5594528188 1.5833967238
1.5471674452 1.5839134032
1.5349410415 1.5844301859
1.5481227349 1.5849470719
1.5613729731 1.5854640613
1.5490783829 1.5859811541
1.5368428066 1.5864983504
1.5246659612 1.58701565
1.5125475645 1.5875330532
1.5256128119 1.5880505598
1.5387459985 1.5885681699
1.5265600177 1.5890858835
1.5396981298 1.5896037007
1.5275075788 1.5901216214
1.5153755424 1.5906396458
1.5033017398 1.5911577737
1.4912858914 1.5916760052
1.5042405781 1.5921943404
1.4922202233 1.5927127793
1.5051797685 1.5932313219
1.4931549056 1.5937499681
1.481187762 1.5942687181
1.4692780608 1.5947875719
1.4821183067 1.5953065294
1.4702041388 1.5958255907
1.458347159 1.5963447558
1.4465470926 1.5968640248
1.4592691375 1.5973833976
1.472057337 1.5979028742
1.4601914618 1.5984224548
1.4483825428 1.5989421393
1.4366303065 1.5994619277
1.4249344811 1.5999818201
1.4375441404 1.6005018165
1.4258439285 1.6010219168
1.4384583169 1.6015421212
1.426753717 1.6020624296
1.4151052992 1.6025828421
1.4276638467 1.6031033587
1.4160110603 1.6036239794
1.4285743178 1.6041447042
1.416917161 1.6046655331
1.4053159587 1.6051864662
1.3937704421 1.6057075035
1.382280344 1.606228645
1.3946682017 1.6067498907
1.3831737944 1.6072712407
1.3955662981 1.607792695
1.4080232429 1.6083142535
1.3964647313 1.6088359164
1.3849617006 1.6093576835
1.3973635014 1.6098795551
1.4098297916 1.610401531
1.4223609065 1.6109236113
1.4107335742 1.611445796
1.4232693888 1.6119680852
1.4116376957 1.6124904788
1.4000618348 1.6130129769
1.388541538 1.6135355795
1.400961954 1.6140582866
1.4134469561 1.6145810983
1.4259968803 1.6151040145
1.4386120641 1.6156270353
1.4512928468 1.6161501607
1.4395266411 1.6166733907
1.4278169133 1.6171967254
1.4404415612 1.6177201647
1.4287274417 1.6182437088
1.41706955 1.6187673575
1.4054676162 1.619291111
1.4179760478 1.6198149692
1.4305495232 1.6203389322
1.4188828855 1.620863
1.4314610765 1.6213871726
1.4441046741 1.62191145
1.4568140184 1.6224358323
1.4450213111 1.6229603195
1.4577354219 1.6234849115
1.4459382919 1.6240096085
1.458657171 1.6245344105
1.4714421883 1.6250593173
1.4595792658 1.6255843292
1.472369078 1.6261094461
1.4852253972 1.626634668
1.4732963153 1.6271599949
1.461424493 1.6276854269
1.4742239003 1.628210964
1.4623476256 1.6287366062
1.4751518333 1.6292623535
1.4632711045 1.629788206
1.4514474032 1.6303141636
1.4641949297 1.6308402264
1.452366794 1.6313663945
1.4405954334 1.6318926678
1.4532865297 1.6324190463
1.4415107543 1.6329455301
1.4542066102 1.6334721192
1.4669684846 1.6339988136
1.4797967207 1.6345256134
1.4926916637 1.6350525185
1.5056536603 1.635579529
1.4936265228 1.6361066449
1.4816571154 1.6366338662
1.4697451613 1.637161193
1.4578903845 1.6376886253
1.4706714145 1.638216163
1.4588121917 1.6387438062
1.4715980151 1.639271555
1.4597343447 1.6397994093
1.4479276198 1.6403273692
1.4361775672 1.6408554346
1.4244839149 1.6413836057
1.4370912313 1.6419118825
1.4253931933 1.6424402648
1.438005238 1.6429687529
1.4506828652 1.6434973466
1.4634264161 1.6440260461
1.4762362335 1.6445548513
1.4891126619 1.6450837623
1.5020560477 1.645612779
1.5150667392 1.6461419016
1.5281450862 1.64667113
1.5160099898 1.6472004642
1.5039331418 1.6477299043
1.5169535942 1.6482594503
1.5048722169 1.6487891022
1.4928488303 1.64931886
1.4808831559 1.6498487238
1.4937837483 1.6503786935
1.5067514238 1.6509087692
1.494719017 1.651438951
1.5076915559 1.6519692388
1.4956546364 1.6524996326
1.5086320405 1.6530301326
1.5216769271 1.6535607386
1.5095728779 1.6540914507
1.5226226568 1.654622269
1.5357402946 1.6551531935
1.5489261442 1.6556842241
1.5366912987 1.656215361
1.5498820934 1.656746604
1.5631414803 1.6572779533
1.576469816 1.6578094089
1.5641027609 1.6583409708
1.5774360953 1.658872639
1.565064402 1.6594044135
1.5527520929 1.6599362944
1.5660264037 1.6604682817
1.579369741 1.6610003753
1.5927824637 1.6615325754
1.5803371079 1.6620648819
1.5937548608 1.6625972949
1.6072423861 1.6631298144
1.6208000465 1.6636624403
1.6344282068 1.6641951728
1.6217829514 1.6647280119
1.6354162227 1.6652609575
1.6491203871 1.6657940096
1.6628958131 1.6663271684
1.6501139132 1.6668604339
1.6373933664 1.667393806
1.6247338782 1.6679272847
1.6121351556 1.6684608702
1.5995969069 1.6689945624
1.5871188417 1.6695283613
1.6005718597 1.6700622669
1.5880891148 1.6705962794
1.575666287 1.6711303987
1.5633030888 1.6716646247
1.550999234 1.6721989577
1.56426443 1.6727333975
1.5775986051 1.6732679441
1.5910021178 1.6738025977
1.5785653077 1.6743373582
1.5661881942 1.6748722257
1.5795323728 1.6754072002
1.5929459411 1.6759422816
1.60642926 1.6764774701
1.6199826922 1.6770127655
1.6074067753 1.6775481681
1.5948912227 1.6780836777
1.6083846571 1.6786192945
1.6219482573 1.6791550183
1.6093629057 1.6796908493
1.5968379637 1.6802267875
1.6103415211 1.6807628329
1.623915297 1.6812989854
1.6375596566 1.6818352452
1.6248993702 1.6823716123
1.6122998533 1.6829080866
1.599760814 1.6834446682
1.6132795702 1.6839813571
1.626868624 1.6845181534
1.6142596546 1.685055057
1.6278538048 1.6855920681
1.6415186446 1.6861291865
1.6552545415 1.6866664123
1.6425093197 1.6872037456
1.629825275 1.6877411863
1.6435003664 1.6882787346
1.6308115646 1.6888163903
1.6444917848 1.6893541536
1.6317982242 1.6898920244
1.6191655927 1.6904300028
1.6065935979 1.6909680888
1.5940819486 1.6915062825
1.6075711748 1.6920445837
1.5950548331 1.6925829926
1.5825985699 1.6931215092
1.5702020968 1.6936601335
1.5578651267 1.6941988656
1.5711660254 1.6947377053
1.5588244285 1.6952766529
1.5721303155 1.6958157082
1.55978409 1.6963548713
1.5730949672 1.6968941423
1.5864750611 1.6974335211
1.5999247314 1.6979730079
1.61344434 1.6985126025
1.6008998072 1.699052305
1.5884154881 1.6995921154
1.6018752486 1.7001320339
1.5893862474 1.7006720603
1.5769571934 1.7012121947
1.5645877989 1.7017524371
1.5522777775 1.7022927876
1.5655496219 1.7028332462
1.5788904799 1.7033738128
1.5923007104 1.7039144876
1.6057806741 1.7044552705
1.6193307336 1.7049961615
1.6329512535 1.7055371608
1.6203130874 1.7060782682
1.6077355846 1.7066194838
1.6212958097 1.7071608077
1.6087135898 1.7077022399
1.6222789004 1.7082437803
1.6096919617 1.7087854291
1.6232623599 1.7093271862
1.6369033242 1.7098690516
1.6506152215 1.7104110254
1.6378922684 1.7109531076
1.6252303855 1.7114952983
1.6126292797 1.7120375973
1.6000886591 1.7125800048
1.5876082336 1.7131225208
1.6010637964 1.7136651453
1.6145893281 1.7142078784
1.6020392994 1.71475072
1.6155699037 1.7152936701
1.6030151682 1.7158367288
1.5905206954 1.7163798962
1.603991403 1.7169231722
1.5914922442 1.7174665568
1.6049680039 1.7180100501

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 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4(a)The realized compounded rate of return

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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

Excel Journal Format due Monday February 24th

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. 

Session 2: Extreme Early Retirement

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. 

Session 3: Arithmetic and Geometric Rates of Return

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.

5. Session 4: Signal-to-noise ratio

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
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

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
s 0.6
T 10.87572

NPV of current and future consumption (5K(1+1/r))
105000

14.7128

2

>Basis Point Simple Math

bp per day Rate Yearly

9

7

3

2

1

0

50

7

3

8

4

8

7

8

4

3

7

0

0.02

01

3

5

4

6

0

9

6

9

6

1

0

2

7

5

0

3

8

9

7

0

9

3

7

9

50

8

8

10

0.05

9

11

1

0

12

71

04

13

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

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
0.0002 0.05 6 86 38 91 10 0.01 0.

15 87 4 78
0.0003 0.07

85 18 47 150 0.015 0.

23 11 61
0.0004 0.10

60 31 16 20 0.3

17 49 57
0.0005 0.

13 24 45 250 0.025 0.39

68 26 67
0.0006 0.1

63 76 53 89 30 0.03 0.47

62 35 36
0.0007 0.

19 28 41 153 350 0.035 0.

55 56 77 75
0.0008 0.

22 32 59 71 40 0.04 0.6

34 80 14
0.0009 0.25

44 96 450 0.045 0.71

43 52 54
0.001 0.28

64 340 444 500 0.

79 37 253 33
0.0011 0.31

92 29 233 550 0.055 0.8

73 97 93 27
0.0012 0.35

285 70 600 0.06 0.

95 247 72
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

=1.0002^252)

1 0.005
2 0.0002

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

0.0002 0.005

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

0.0002 0.005

67 0.0002 -0.005
68 0.0002 0.005

0.0002 -0.005

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

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

84 0.0002 0.005
85 0.0002 -0.005
86 0.0002 -0.005
87 0.0002 -0.005

0.0002 0.005

89 0.0002 0.005

0.0002 0.005

91 0.0002 0.005
92 0.0002 -0.005
93 0.0002 -0.005

0.0002 -0.005

95 0.0002 -0.005
96 0.0002 0.005
97 0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

113 0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

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0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 -0.005

0.0002 0.005

0.0002 0.005

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
-0.005
48
66
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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
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?

12.1 Market Efficiency

A perfect market sets up stiff competition among many investors. This forces them to use all
Market efficiency means the
market uses all available
information in setting the
price.

available information as well as they possibly can. This is called market efficiency: a situation
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.

IMPORTANTA price is called efficient if the market has set the price correctly as if it were using all available
information. (PS: It is not necessary that any investor has all the information.)

Warning: Market efficiency is a different concept from mean-variance efficiency
(the efficient frontier), which was used in the context of portfolio optimization.
Economists love “efficiency” and thus use the term in many contexts.

ä Mean-variance efficiency,
Sect. 8.2, Pg.171.

Exhibit 12.1 illustrates an efficient market. Suppose the market considers an expected rate of
An example: ABC’s price
today is based on the best
estimate of future
characteristics, obtained
from a model like the CAPM.

return of 10% on ABC stock to be a fair rate of return, given ABC’s characteristics. This figure of
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

277

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.

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
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.

Efficient Market

Pricing Model

Today’s Price

The General Case

The financial markets estimate the statis-
tical distribution of future cash flows, in-
cluding their expected cash flow values,
covariances, liquidity, and anything else
possibly of interest.

The financial market determines the ap-
propriate expected rate of return, given all
value-relevant characteristics.

The market sets today’s price, so that the
expected rate of return is as the model
states.

?
?
?
?

A Specific Example: ABC

The market estimates ABC’s expected
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.

Say the CAPM is the correct pricing model.
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%.

The price today is $55/1.1 = $50 per
share.

Exhibit 12.1: Market Efficiency and Pricing Model. The critical question is If you saw a price of, say, $45.83 today, what
would you conclude has gone wrong? Is it the market or the model?

The practical use of the “efficient markets” concept begs two questions:
What is the model? What is

the information set? 1. Where does the figure of 10% come from? It has to come from some model that tells you
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.

2. If the market is not perfect and different investors have different information, then exactly
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.

What should you conclude if you can determine authoritatively that the expected rate of
If you find the expected

rate of return is really 20%:
(a) Your 10% model could be

wrong; (b) the market was
not efficient.

return is really 20%? (This can happen either if you determine that the expected payoff is $60,
not $55, or if the expected payoff is $55, but today’s price is $45.83.) You could now draw one
of two conclusions:

1. The CAPM is not the correct model. Instead, the market followed some other pricing model
and wanted to set the expected rate of return for ABC at 20% in the first place.

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.

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
Is market efficiency so
difficult to disprove that it
becomes a “faith”?

belief in market efficiency, and if you then find empirically that prices are not what your model
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.

Short-Term versus Long-Term Market Efficiency
Over long horizons (say, 1 year or longer), market efficiency is extremely difficult to disprove.

Practically useful? Rarely
over very long horizons,
where efficiency is often
more a matter of faith.

The reason is that no one knows exactly what the correct model of pricing is—the CAPM may
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.

Of course, in extreme circumstances, market efficiency can be a useful claim even on such
Okay, let me qualify this for
long horizons.long horizons. We know that no reasonable model of financial markets should give investors

great bets like “+$1 million with 99% probability” and “–$1 with 1% probability.” Expected
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.

However, over short horizons (say, a day or so), market efficiency is a surprisingly useful
Practically useful?
Definitely yes over short
horizons.

concept. The reason is that over a single day it does not matter as much whether you believe the
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:

2013-01-0

5

IMPORTANT• Over short time intervals (say, days), market efficiency is a very powerful concept. The
expected rate of return should be tiny. If it is different, the market is probably inefficient.

• Over long time intervals (say, months or years), it is difficult to pin down what the
appropriate expected rate of return is. This makes it difficult to disentangle errors in the
pricing model from market inefficiency.

• Prices should move only when there is news about future cash flows or discount rate
changes, where news is defined as the unanticipated component of new information that
is arriving. Such news can be firm-specific or market-wide.

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.

280 Perfect and Efficient Markets, and Classical and Behavioral Finance

Relation to Perfect Market
Although the efficient market concept is different from the perfect market concept, the two are

Perfect market ⇒ efficient
market. intimately linked—in fact, so much so that they are often casually confused. The reason is that if

a market is perfect, economic forces drive it instantly toward market efficiency. Put differently, 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.

The converse is not true, however. It is quite possible for an imperfect market—for example,
Efficient market 6⇒ perfect

market. one in which there are taxes or different opinions—to be efficient. You could even (crudely) think
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.

Another way to understand the difference is to compare assumptions. Of the four perfect-
Efficient market is a weak

facsimile of “same
information.”

market assumptions, only one has any overlap with and bearing on the efficient-market concept:
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.

Perhaps the most important perfect market assumption driving prices toward efficiency is
Transaction costs are often

culprits in keeping prices
from their efficient levels.

the absence of transaction costs. Without them, it is easy for you and other investors to trade
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.

Here is a practical example of how any market inefficiency would disappear quickly in a
Investor competition pushes

markets toward efficiency. perfect market: What would you do if you learned that the market always goes down on rainy
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.)

Conversely, it is easier to believe that markets are not (or less) efficient if transaction costs
Prices should be generally

efficient even in a
nonperfect financial market.
Who would be willing to hold

overpriced stuff?

are high. But even if the market is not perfect, market inefficiencies should still raise eyebrows.
For example, let’s say that the appropriate rate of return on ABC was still 10% and the price was

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12.1. Market Efficiency 28

1

still $50. Alas, when you run a few regressions, you learn that the expected future price is not
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

ä Shorting stocks,
Sect. 7.2, Pg.155.

short are too high. However, this leaves the question of why investors who already own ABC
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.

IMPORTANT
• If a market is perfect, market forces should drive it strongly and quickly toward efficiency.

• If a market is not perfect, self-interested individual behavior should still drive it toward
efficiency. But this force is much weaker, and third-party traders may not be able to aid in
the process.

Market Efficiency in Modern Financial Markets
In the United States, the financial markets for Treasuries, large corporate stocks, index mutual

You can reasonably assume
that markets are efficient
for large corporate stocks.

funds, currencies, and others, seem reasonably close to perfect and thus efficient. They are
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:

• The bid-ask spread is often high.

ä Bid-ask spread,
Sect. 11.3, Pg.252.

• The posted bid-ask spread is only guaranteed for 100 shares—if you want to trade more
shares, the price is likely to move against you.

• Commissions can be high.

• Shorting small stocks can be very costly when compared to the ideal of a perfect world in
which you have full access to the proceeds (e.g., to earn interest).

In a round-trip transaction, you will face the first three issues once when you buy and once when
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 fact that large-firm stock markets are pretty efficient means that, by and large, you
The advantage of an
efficient market: Prices can
be trusted.

can trust these financial markets to get asset values about right—at least within the limits of
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

ä Great bets,
Sect. 12.4, Pg.291.

gravy. In an inefficient market, you could not rely on market prices being fair—they could be
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

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.

282 Perfect and Efficient Markets, and Classical and Behavioral Finance

“Trading Places” and Citrus Futures
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!

and money to determine whether prices are fair. The advantage of efficient markets is that if
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.

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
that they can reject market efficiency because they have found assets that pay too much for their
risk?

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
low?

Q 12.6. Would you expect the market for the dollar-euro exchange rate to be more or less perfect
and efficient than the NYSE?

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17
.

12.2. Market Efficiency Beliefs and Behavioral Finance 28

3

How to Get Squeezed and Lose Money Even When You Are Right
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.

In 1998, I shorted Netscape. I believed that Netscape’s browser was about to be taken to the cleaners by Microsoft’s Internet
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.

Later on, I found out that I was not alone. The most reprinted article in the history of Fortune magazine was “Mr. Buffett
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.

Not everyone believes there was a bubble. The book’s website (book.ivo-welch.info) has an impromptu email conversation
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.

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,
Classical versus behavioral
finance.an outgrowth of the school of rational economics. This belief is that the evidence supports

the efficient market hypothesis, or EMH, which holds that all securities are priced efficiently.
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.

Almost all financial economists, regardless of camp, believe in basic market efficiency for
Many large financial markets
in the United States are
probably close to efficient.

large markets and liquid securities. No respectable economist believes that it is easy to get
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.

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.

284 Perfect and Efficient Markets, and Classical and Behavioral Finance

The Traditional Classification
The traditional definition of market efficiency focuses on information. In the traditional classifi-

The traditional classification
of market efficiency is

about the type of
information needed to beat

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
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.

Semistrong market efficiency says that all public information is reflected in today’s stock prices,
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.

Strong market efficiency says that all information, both public and private, is reflected in
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.

In this traditional classification, all finance professors nowadays believe that most financial
Many finance professors no

longer believe in perfect
efficiency.

markets are not strong-form efficient: Insider trading may be illegal, but it works. However,
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.

Market efficiency champions quickly point out that many of these strategies’ returns were
Why do many trading

strategies seem to have
worked historically?

spurious: They disappeared almost as quickly as they were discovered, and they probably were
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.

One conceptual question that had vexed academics for a long time was how markets could
The returns to collecting

information must be in
“balance” with their costs.

be efficient to begin with. After all, if there is no money to be made, why would anyone bother
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).

Q 12.7. Which form of market efficiency do momentum trading strategies seem to violate?

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.

12.2. Market Efficiency Beliefs and Behavioral Finance 285

The Fundamentals-Based Classification and Behavioral Finance
I prefer an alternative classification of market efficiency, which divides economists based on their

My preferred taxonomy of
market efficiency is based
on how much prices deviate
from value.

belief in whether prevailing market prices reflect underlying values:

A true believer would argue that financial prices always reflect the best net present 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.

A firm believer would argue that financial prices may sometimes deviate from the appropriate
best estimate of future cash flows. However, transaction costs make it practically impossible
for investors to find unusually good bets.

A mild believer would also argue that financial prices may sometimes deviate from the appro-
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.

A nonbeliever would argue that financial prices regularly deviate from the appropriate value,
and to an extent that allows investors to obtain great bets fairly routinely.

These classes are progressively weaker along the market efficiency dimension. For example, a
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.

Occasionally, there is evidence that refutes even the truest of believers—but this is rare.
There is even some really
weird but dramatic evidence
against market efficiency.

The most dramatic example occurred in 2000, when the network company 3COM spun off the
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.)

Where do most finance professors sit in this classification of beliefs? Virtually no academic is
This evidence as a whole
suggests that the financial
markets are usually
somewhere between mildly
and firmly efficient.

a perpetual nonbeliever, and only a very few remain in the “true believer” camp. Instead, most
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.

Let me tell you my personal view. I sit right in the middle between the two schools of thought,
Buyer beware: Here is my
own opinion.somewhere in the firm-to-mild camp. In my view, most investors believe that they are smarter

than they are—that they can predict when stocks are going to go up or down. This is why I
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.

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.

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
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.

ä Evidence on Fund Performance,
Sect. 12.5, Pg.299.

One final note: Pundits love to talk about investor psychology. And it is indeed the case that
Behavioral Finance

individuals suffer from many cognitive biases. For example, Nobel-prizing winning research
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.

Q 12.8. If you believe that market values do not always perfectly reflect underlying fundamental
values, but that trading costs nevertheless prevent you from exploiting this profitably (in large
scale), where would you classify yourself?

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
The low signal-to-noise ratio

allows our arguments about
market efficiency to

continue.

ratio in financial returns is low. The signal-to-noise description draws on an analogy from
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 explain. What are typical price change magnitudes? For example, June 17, 2016, was
Let me illustrate the

signal-to-noise ratio with a
stock’s rate of return on a

particular day.

a fairly quiet and uneventful day on the financial markets. 10-year Treasuries stood at 1.6%,
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.

The Signal
Let’s first put your statistical and financial expertise to good use: In a perfect market, if the shares

You cannot expect a
real-world trading signal to
be as strong as 1% per day:

It would amount to over
1,000% per year.

of a company cost $50 today, what do you expect them to cost tomorrow? What is a typical daily
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

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17
.

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
side would end up poor.)

So what kind of average daily returns can you expect from the U.S. stock market? Say a
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

15

basis points. The majority of stocks should allow you to earn expected rates of return of between
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.

Great Mathematicians and Gambling: The Origin of the Random Walk
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.

Later reinventions and applications of the random-walk concept abound: Jan Ingenhausz (1730–1799), a physician and
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.

Fortunately, in 1900, Louis Bachelier introduced the random-walk theory of financial market fluctuations (although Karl
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.

Let’s make this into a formula. If your expected rate of return is a small constant m, that is,
Over short intervals, the
stock price should follow a
mostly unpredictable
random walk with practically
no drift.

E

r

=[E

P1

– P0]/P0 = m, then your best expectation of the price tomorrow (P1) must be
roughly the price today (P0).

Expected Price Tomorrow = Price Today + Tiny Drift (12.1)

E

P1

= P0 + m · P0︸ ︷︷ ︸

Tiny Drift

This is customarily called a random walk with drift. As you just learned, depending on the stock,
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.

Note that price behavior very close to a random walk is a necessary consequence of an
Don’t wag the tail: Market
efficiency ⇒ random walk.
Random walk 6⇒ market
efficiency.

efficient market, but you cannot conclude that a market is (truly) efficient just because stock
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

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.

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
to outperform the EMH. The random walk only states that the known lagged price can’t be this
signal.

A Complication—Transaction Costs
The important point of perfect markets (and market efficiency) is that, given today’s information,Transaction costs destroy

the profitability of many
high turnover strategies.

no signal can be very accurate. It should not be possible to predict stock price movements
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

ä Transaction costs,
Sect. 11.3, Pg.250.

exploiting misvaluations, especially short-lived ones that require a lot of trading to exploit. You
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.

In an imperfect market with transaction costs, you can view the efficient market hypothesis
It may be best to think of

the EMH in terms of
after-transaction costs.

in one of two ways:

1. The EMH should hold if you work with post-transaction cost rates of return. One percent
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.

2. The EMH should hold if reasonably many investors have very low transaction costs, perhaps
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.

So the EMH won’t hold perfectly in an imperfect market, but it should be a fairly reasonable
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.

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
so that you can earn a positive rate of return? Assume typical real-world trading transaction
costs are about 10 basis points.

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12.3. The Random Walk and the Signal-to-Noise Ratio 289

The Noise
To put more emphasis on the noise, we can write our random walk with drift in terms of the

The daily noise in stock
returns is much larger than
the daily signal.

stock prices that you will actually observe:

Price Tomorrow = Price Today + Tiny Drift + Noise

P1 = P0 + m · P0 + ε E (ε) = 0
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:

• The typical day-to-day standard deviation of individual stocks in the market is around
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.

June 17, 2016, was on the low side in terms of volatility, but the typical noise movement of 200
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.

IMPORTANTIn the financial market context, “random walk” refers to a process in which the expected value
tomorrow is (almost) the same as the value today. Technically,

E

P1

= P0 + m · P0︸ ︷︷ ︸

Tiny Drift

⇔ P1 = P0 + m · P0︸ ︷︷ ︸
Tiny Drift

+ ε0,1︸︷︷︸
Noise

where m is a very small positive drift. (Another version of a random walk is E

P1

= P0 +m;

in practice, this version is almost indistinguishable from the one in the formula above.)
Naturally, actual values tomorrow will likely be different from their values today. The

empirical stock price evidence is highly favorable. Stock prices indeed tend to follow roughly a
random walk, at least in the short run. This means that you cannot get rich trading based on
past prices.

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
today?

Detecting an Interesting Signal in the Noise
You now know that the tiny drift is typically around 5 to 10 basis points per day, and the noise is

Detecting a signal in a lot of
noise is difficult.typically about 100 to 300 basis points per day for U.S. stocks and stock portfolios. How easy is

it to determine whether you are facing a stock with 5 basis points’ signal versus one with, say, 7
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.

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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
You cannot conclude

anything from just 1 day of
return

basis points? Obviously, 1 daily return is not going to do it. If I tell you that your investment pick
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

/Sdv


r

. If
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.

To draw reliable conclusions, you need a lot more independent daily observations. Unfortu-
You cannot consider multiple

returns from the same day
as independent observations.

nately, you cannot use the returns from many stocks from the same day as independent signals.
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.)

Fortunately, you can regard returns from different days as independent observations. You
You can use consecutive days
as independent observations.
Here is how mean, standard

deviation, and T-statistic
accumulate over time.

can therefore use sequential days of investment performance to investigate the quality of your
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

p
N

ä How risk and reward grow over
time,
Sect. 8.2, Pg.170.

times the standard deviation over 1 day. Your expected T-statistic over N days to detect your
superior excess rate of return is therefore

N-day T-Statistic =
Excess Mean

Standard Deviation
=

N · E

r

p
N · Sdv


r
� =

p
N · 1-day T-Statistic

How many trading days (N) do you need in order to expect a T-statistic of 2 if your 1-day
Only diversified strategies
that perform well for many
decades give us the chance
to learn whether they are

real.

T-statistic is 0.01? You need 2002 = 40, 000 days to have such confidence. This is about 157
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.

IMPORTANT
• The quality of your inference about a strategy’s performance increases roughly with the

square root of time.

• On an average day, the typical stock may easily move up or down by about 20 to 50 times
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.

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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
outperform the risk-adjusted financial market per typical day?

Q 12.15. Assume that the typical day-to-day noise (standard deviation) is about 100 basis points.
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.

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
above the 95% level. In Section 8.2, you learned that the standard deviation grows with the
square root of time.

4. With 252 trading days of performance, how much extra rate of return do you expect to
earn per annum?

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
statistical evidence that you have a positive ability to pick stocks.

12.4 True Arbitrage and Risk(y) Arbitrage

Measuring investment performance brushes on a closely related topic—what exactly is the
Do you understand
arbitrage?financial concept of arbitrage? Intuitively, an arbitrage is a great investment opportunity, perhaps

so great that you should not be able to find one. It is the desire of traders to exploit any arbitrage
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.

The Definition of Arbitrage
First recall that the law of one price states that two identical items at the same time and location

In a perfect market, the
market will be efficient and
the law of one price will
hold.

should have the same price. This is true in a perfect market, but even if the market is not perfect,
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

ä Law of One Price,
Sect. 1.1, Pg.2.

always hold. If it did not hold, you and the other infinitely many potential buyers could find
arbitrage opportunities. The arbitrage concept is so important that you should understand it
exactly, not just intuitively.

IMPORTANT
• A true arbitrage is a business transaction

– that offers positive net cash inflows in at least some scenarios,
– and under no circumstance—either today or in the future—has a negative net cash

flow. This means that it is risk-free.

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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
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 an ex-ante concept, not an ex-post concept—beforehand, not after the fact. For
Arbitrage is the “perpetual
motion” of economics. It is

defined in terms of (the
possibility of) negative cash

outlays.

example, it does not mean that a lottery ticket that won was an arbitrage. Ex ante, a lottery
ticket is not an arbitrage. Please also pay close attention to what the “no-negative-cash-flow”
condition means in the definition of arbitrage:

ä Ex-ante fair bet,
Sect. 6.1, Pg.106.

1. Arbitrage is not the same as “earning money without risk.” After all, Treasuries do just that,
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.

2. Arbitrage is also not the same as “receiving money today without a clear obligation to
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.

Now contemplate the difference between the examples of the true arbitrage and the risk(y)
“Risk(y)” arbitrage ≈ great

bet. Unlike a true arbitrage,
a risk(y) arbitrage could

possibly lose a little money.

arbitrage in the definition. You can lose $1 with 1% probability in the risky arbitrage, so it is
“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.

Most of all, unless financial markets are very imperfect, you should expect not to find many
There should be few

arbitrages in competitive
financial markets. Only this
fact allows us to study and

describe (sane) markets.

arbitrage opportunities of either type. If you agree with this assessment—basically that the
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.

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.

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12.4. True Arbitrage and Risk(y) Arbitrage 293

More Hypothetical Arbitrage Examples
Of course, it is difficult to find real-world examples of arbitrage. Arbitrage is principally a concept.

In a sense, positive-NPV
projects under certainty are
arbitrage.

What would a hypothetical arbitrage opportunity look like? For example, if you can buy an
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

Small arbitrages matter only
if they are scalable.times, then you could earn $10 million. Unfortunately, although you may find an arbitrage that

works once for 1 cent, it is unlikely that you can find such an arbitrage opportunity that works
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.

Another hypothetical example of arbitrage would involve stock prices that are out of sync on
Arbitrage could conceivably
occur between different
financial markets.

different stock exchanges. If PEP shares are quoted for $51 on the Frankfurt Stock Exchange,
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 before you conclude that this is an arbitrage, you still have to make sure that you have
But be skeptical. There are
many complications to take
into account.

not forgotten about costs or risks. The arbitrage may be a lot more limited than it seems—or
may not even be present at all. Consider the following issues:

1. Could the price change in between the time you buy the shares in New York and the time
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.

2. Did you account for the direct and indirect transaction costs? How much commission
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

ä Bid and ask prices,
Pg.252.

in Frankfurt and get it quickly enough from New York to Frankfurt to make the closing?
Have you accounted for the value of your own time watching the screen for opportunities?

3. Could the share prices move when you want to transact a significant amount of shares?
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.

4. Did you account for your fixed cost of setting up your business? If it costs you a million
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.

It may be that small arbitrage opportunities occur from time to time, but large financial firms are
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.

Q 12.18. Before you dedicate your life to exploiting a seeming arbitrage between financial
markets, what questions should you ask?

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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
Is the past rate of return a

good signal for the future
rate of return?

be no obvious signals to outperform the risk-adjusted appropriate expected return to the tune
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.

Weak-Form Efficiency and Technical Analysis
The main point of the traditional classification of market efficiency, specifically the “weak” version,

Could there be “cycles” in
the market? is the claim that you should not become rich by trading a strategy that relies only on historical

prices. So let me start with some trick questions. Look at the various graphs in Exhibit 12.2. Do
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.

On the other hand, graphs (c) and (d) could actually be representative. On average, each
Cycles are not reasonably
likely—although there are

ups and downs in the market,
too.

price in the next month is just a little higher than the previous (i.e., the expected rate of return
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.)

The Empirical Evidence on Trends

Traders have been trying all sorts of strategies in their efforts to become rich. So how well
Predicting with past rates

of return mostly appears to
fail.

does technical analysis—which tries to find patterns in historical stock prices—typically do? For
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

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ly
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ly
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ly
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ly
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.

12.5. Investment Consequences 295

Pattern (a) Pattern (b)

2011 2013 2015

19

20

21

22

23

Date

S
to

c
k
P

ri
c
e

2011 2013 2015
20

25

30

35

Date
S
to
c
k
P
ri
c
e

Pattern (c) Pattern (d)

2011 2013 2015
5

10

15
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

Exhibit 12.2: Potential Stock Price Patterns. If these patterns were systematic, some of them should make you rich. Which
ones? And which is the real series?

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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
1
2
3

Rate of Return Today, in

%

R
a
te

o
f

R
e
tu

rn
T

o
m

o
rr

o
w

,
in

%
−3 −2 −1 0 1 2 3
−3
−2
−1
0
1
2
3

Rate of Return Today, in %

R
a
te
o
f
R
e
tu
rn
T
o
m
o
rr
o
w
,
in
%

Exhibit 12.3: The Relation between Lagged and Current Rates of Return. The left panel is the tech-heavy Nasdaq Composite
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.

a number of financial websites, such as FINANCE—look up any stock and choose “Charts,”
then “Technical Analysis”; it is fun, but unfortunately fairly useless.

However, over annual horizons, it appears as if stocks tend to continue their pattern just a
Momentum: Firms that did

well over the last year (with
1-month lag) continue to do

well.
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.)

Are Women Better Investors Than Men?
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.

Despite strong evidence to the contrary, many investors still believe that stock prices do not follow random walks, as
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!

Odean and Barber, 2001

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12.5. Investment Consequences 297

Investment Manager Performance Evaluation
What about all the televised stock analysts who explain which stocks are undervalued and which

What about celebrity
investors?stocks are overvalued? And what about the aforementioned technical analysis, the art of seeing

patterns (shoulders, price barriers, faces, etc.) in historical prices and using them to forecast
future prices? And what about famous investors such as Warren Buffett, George Soros, and many
others? Should you trust them?

First, recall that the low signal-to-noise ratio means it is difficult to determine why a particular
What could you conclude
from their stellar past
performances? There are
three possibilities.

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
in measuring performance)? Dilbert on Hard Work, Luck, and Success:

2012-12-30

• Or was it because the market was inefficient (you have a good signal, skill, and trading
ability)?

This is not just a problem for academics. In fact, we finance professors are lucky: We can continue
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?

But the signal-to-noise ratio problem is not even the only problem that you need to consider
Here are possible objections
to believing in their magical
investment abilities (and in
inefficient markets).

when you pick an investment manager. If you believe that the market is inefficient so that your
fund manager can make you money, consider the following:

Evidence? Of course, maybe there are some investors who can pick stocks. Unfortunately, they
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

Why would they tell anyone?
find investors with superior ability and thus impossible to confirm their abilities.

Enough data? Recall our earlier conclusion that a strategy with great performance requires
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.

ä Ascertaining superior
performance,

Pg.290.

Remarkably, the most common industry standard for evaluating funds is their most recent
The industry standard of
three years’ performance is
not driven by the need to
get solid statistical
inference.

three years of investment performance. There is no disagreement that most of the 3-year
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.

What is Risk? Here is another lesson for the wise (and unwise). Until 2008, I would have sworn
Is Momentum Risk?

that investing in momentum stocks was a strategy that was reasonably well-diversified and
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?

ä “Peso” risk.,
Pg.201.

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.

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
Pure chance means that
some investors succeed

many years in a row.

ä Mutual funds,
Sect. 7.2, Pg.157.

investors’ behalf. How many of them are likely to outperform the overall stock market next
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.

Who is still alive? What happens to the funds that have underperformed several years in a row?
Good past performers grow.

They disappear quietly. (In fact, they don’t even need to appear. The SEC even allows a
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

Why funds’ average
historical performance looks

good to you as an investor
today.

offered today. First, you won’t notice funds that have performed poorly. They have already
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.

Who gets the rents from trading ability? Even if the financial markets were inefficient and
If there was superior fund

performance, the fund
manager—not the

investor—would profit the
most.

even if some fund managers could in fact systematically outperform the market, in a
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.

In sum, if you are looking for future performance, past performance may be your best guide. But
always remember that recent past performance is still a very poor guide.

Obviously, picking the right investment manager is not an easy task. Many mutual funds
Many hedge funds are

compensated on the upside.
This does not solve

investors’ problem, but the
alternative is no better.

earn fees regardless of whether they make you money or not. Would it be better to have them
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:

2013-06-30 the advice to sell it. This way, I will surely make money from one of you.) My only mistake is
that I have told you my plan.

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12.5. Investment Consequences 299

The Three Top Investment Books of 1996
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!

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,
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.

2. Matt Seto stopped publishing his stock-picking performance and decided to pursue a career as a student.
3. The Beardstown Ladies, five books richer, were found to have miscalculated their returns: Their returns were not

30%, but 9%—significantly lower than the 15% turned in by the S&P 500 stock market index during their investment
period.

How disappointing: On average, about one of them should have continued beating the market, one should have done
about the same as the market, and one should have underperformed it. Time Magazine, March 1998.

The Empirical Evidence

So what is the empirical evidence? In general, it suggests that fund managers’ luck is far more
You must realize that even
top investors seem to have
at most mild predictive
abilities.

important than their ability. Whenever academics (or the Wall Street Journal) have searched for
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.

But what about persistence? Maybe there are some funds that are better than others? True.
Are there some persistently
good performers at least?But the empirical evidence is again disappointing. Only about 54% of mutual funds that have

outperformed their benchmarks over the last 1-3 years tend to outperform their benchmarks
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

funds: 2013-04-17note—and as the evidence suggests—past performance is no predictor of future performance.
There is a whole industry full of fund managers whose job it is to allocate assets to the actual

Do Fund Managers Know?
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:

Nerdnote: There are some high-tech statistical techniques to take into account that researchers have
searched, individually and collectively, for anomalies. This is beyond our scope.

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.

300 Perfect and Efficient Markets, and Classical and Behavioral Finance

Miserable (T < (–1)) Average or Better (T > 0) Great (T > 1)
what to expect → Should be <16% Should be >50% Should be >16%

AUM Before Fees After Fees Before Fees After Fees Before Fees After Fees
< $5 million 22.4% 37.8% 48.2% 32.1% 21.2% 10.2%

–$250 million 25.0% 41.0% 44.8% 28.3% 17.4% 8.5%
> $1 billion 29.8% 45.0% 41.5% 28.3% 15.6% 7.9%

Exhibit 12.4: U.S. Equity Mutual Fund Performance, 1984–2006. This table looks at the historical performance of about
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.

Years Relative to Hiring
–2 to 0 0 to +2

Fired Funds –1.6% +3.1%
Hired Funds 7.6% +2.3%

They fire funds after they have performed poorly, not before they perform poorly. And they
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?

There are, of course, other ways to make money: Warren Buffett’s fund, Berkshire Hathaway,
For the most part, it seems

that old-fashioned work and
insurance (or liquidity)

provision work better in
earning returns than stock

picking.

for example, runs many businesses (e.g., insurance and aircraft), too. These businesses make
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

ä Business of liquidity provision,
Sect. 11.3, Pg.253.

himself would of course not attribute his own performance to luck, but to his ability. Still, even
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!

In sum, most finance professors nowadays would agree that when one particular investor
Where should the burden of

proof be? earns an unusual amount of money, even over a few years, it is usually more likely due to luck
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.

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12.6. A Cynical Perspective 301

IMPORTANTEven in an efficient market, in which no one can pick stocks better than anybody else, with a
very large number of investors, many will beat the market. A small number of investors will beat
the market again and again.

In the real world, there is little evidence that investors who did well picking stocks in the
past are better at picking stocks in the future when compared to investors who did poorly.

Q 12.19. If you want to determine whether fund managers have an ability to outperform the
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?

Q 12.20. If a firm employs 10,000 analysts, how many of them are likely to issue forecasts
that beat the market 10 years in a row if none of them has any special ability and there are no
transaction costs?

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,
Buy Low, Sell High.

they then talk more about their performance. The first targets are easiest to find at cocktail
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.)

Unfortunately, even though genetic algorithms and artificial intelligence are rather sexy
Rat Selection

high-tech sophisticated ways to pick investment assets, true genetics and intelligence seem to
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.

Most funds write monthly communiques to their investors. They are largely collection ex-post
Grandiose Claims and Dumb
Excuses.rationalizations and platitudes. Read some with an open mind. There are some patterns. Funds

on the up often write about the credit they deserve for their brillant insights. They describe
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).

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.

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
Academics are not so

different. it better than I can. I will try it anyway. If you read academic journals, you will find hundreds
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.

What about me? Am I not brillant? I placed large short bets on oil in 2013 when it traded
Intellectual Humility, please.

above $100/bl. I believed long-term supply and demand could not sustain such a high price. In
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?

Asymmetric-Pattern Strategies
But funds can wittingly or unwittingly seem even better than random gamblers. It is not difficult

Not Understanding Profit
Sources to show good historic performance. You can even do it on a roulette table. Just double up.

Choose red, and when black comes up, try again and double up. When you have won, go home
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.

The opposite of the usual pattern of hedge funds are strategies that lose money most of the
It is difficult to be a

contrarian. time but then gain a lot in a crisis. These are strategies that are very difficult to maintain. Which
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.

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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
When creating value for
your firm, there are three
different market scenarios
to consider.

are perfect, efficient, or neither? Because a perfect market implies an efficient market, you need
to think about three different cases:

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
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 (Close to) Perfect
If the financial market is perfect, the answers to these questions are simple—they are always no.

In perfect markets, all that
counts are the firm’s
underlying projects.

It does not matter how the firm communicates its earnings to investors, what its capital structure
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.

Earnings reporting: For example, if you have previously reported your foreign division’s
You cannot fool your
investors by how you report
your earnings.

ä Do reported earnings matter?,
Sect. 14.1, Pg.355.

earnings separately and now you consolidate them into your main earnings, you will indeed
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.

Capital structure: For example, say your firm is currently financed with equity only and worth
There must be no value to
changing capital structure.

ä Capital structure arbitrage,
Sect. 17.2, Pg.451.

$100, but if you had a 50-50 debt-equity ratio it would be worth $102. In this case, an
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: In a stock split, each old share becomes multiple new shares. For example, if each
Stock splits must be
irrelevant, too.

ä Stock splits,
Sect. 20.2, Pg.558.

share trading at $80 were to become two shares, the new shares should trade for $40 each
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.

Dividends: The same argument applies to dividends. In a perfect market, a $100 firm that
Still trying to fool investors,
this time with dividends?
Fugeddaboutit.

ä Stock dividends,
Sect. 20.2, Pg.558.

pays $10 in dividends should be worth $90 thereafter—no value is magically created or
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.

The lesson is simple: As a manager, you should forget about the smoke and mirrors and instead
focus exclusively on finding and executing projects with positive net present values.

Iv
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.

304 Perfect and Efficient Markets, and Classical and Behavioral Finance

If the Financial Market is Not Perfect but At Least Efficient
If markets are not perfect but efficient, the implications are not as profound. However, it

An efficient market means
“the price is right.” Thus,

you can learn from your own
market price.

means that you can still obtain valuable market intelligence. Your market price is the aggregate
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.

In addition to learning from your own company’s market price, you can also learn from all
You can also learn from

other market prices. sorts of other market prices. You can find out how good your competitors’ opportunities are, and
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.

Let’s consider a specific example of how you can learn from market prices in an efficient
Personal opinion alone

(without synergies) is not a
good argument for taking

over other companies.

market. Put yourselves in the shoes of a smart and successful manager of an aircraft manufacturer.
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 the absence of perfect markets, the efficient market does not mean that you
However, in an imperfect

market, it is possible for an
acquisition to add value. . .

should never be able to create value by buying other companies. You can indeed sometimes
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

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12.7. Corporate Consequences 305

outside arbitrageurs cannot accomplish without you. (This violates the infinitely many potential
buyers assumption of a perfect market.)

But be careful: Market efficiency means that you cannot create value for your shareholders
. . . as long as you have more
than just an opinion that the
market got prices wrong.

simply by your personal view that X is undervalued. Yes, you may be smart, but the financial
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.

The same argument applies to all sorts of other corporate actions. You may be able to create
In an imperfect market, you
can also create value with
financial transactions that
reduce market
imperfections.

value by reducing perfect market barriers. For example, you may be able to create value by
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

ä Splits as signals,
Sect. 20.4, Pg.570.

information to the market.

If the Financial Market is Not Even Efficient
Loosely speaking, financial markets tend to be reasonably, but not always perfectly, efficient.

What should you do if
markets are not efficient?Perfect market efficiency is almost surely not a good description of reality. Even in a perfectly

rational market, as an executive, you may know the firm value better than the market—for
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

ä Strong market efficiency,
Sect. 12.2, Pg.284.

appropriate market value? The right way to conceptualize your problem is to consider what you
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 your shares are undervalued, you should recognize that your cost of capital is effectively
If you are undervalued,
sometimes it is better to
pass up positive-NPV
projects. . .

too high, given the true characteristics of your project. The reason is that you cannot raise
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

ä Separation of financing and
investing,

Sect. 11.1, Pg.245.

just taking the $500 from the old project. Put differently, the opportunity cost of new
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

. . . and use your cash to
repurchase your own shares.want to do the opposite. The best use of corporate cash may now be to repurchase your

own cheap, underpriced shares—for example, from other investors. However, there is

ä Share repurchases,
Sect. 20.2, Pg.558.

an intrinsic paradox here: As an executive, you are supposed to act on behalf of your
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.)

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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
If you are overvalued,

sometimes it is better just
to issue more shares.

to take more projects. This is easiest to see if you again consider what you would do if you
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.)

These are robust insights for CEOs who are not conflicted and wish to act on behalf of their
existing shareholders.

IMPORTANT When managers have superior information:
• If the firm is undervalued, CEOs should assume a relatively high cost of capital and consider

repurchasing the firm’s own shares.

• If the firm is overvalued, CEOs should assume a relatively low cost of capital and consider
issuing more of the firm’s own shares.

A good decision rule for managers is to take projects up to the point where the marginal costs
and benefits of projects are the same as what they could obtain from repurchasing or issuing the
firm’s own shares.

(It can become a bit more complex if you see yourself as a representative of both new and
old shareholders, though.) But be careful: Most executives are notorious for always believing

ä Overconfidence,
Sect. 13.7, Pg.339.

that the financial markets do not fully reflect the value of their companies even if they have no
inside information—as an executive, you should be wary of your own perceptions and biases!

Q 12.22. For convenience, assume a zero discount rate. You have no cash on hand and can only
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).

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
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?

3. If you act on behalf of your existing investors, should you take this new project?

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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
market concepts and their
consequences.

Efficient versus inefficient markets: If the market is efficient, you can learn from financial
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.

Perfect versus imperfect markets: If the market is perfect, you can focus exclusively on your
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.

In the real world, financial markets are definitely not 100% perfect. For large firms, they are
Don’t be too dogmatic:
Nothing is perfectly
perfect, or perfectly
imperfect.

very close to efficient, but this is not necessarily so for small firms. Still, the economic magnitudes
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.

12.8 Event Studies

The immediacy of price reactions in any efficient market offers a surprisingly useful real-world
Market reactions should be
immediate and reflect all
value changes.

application: In some cases, market price reactions can allow you to estimate value consequences
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.

Capital-Structure-Related and Other Event Study Results
Researchers have run event studies on all sorts of interesting events, ranging from new legislation,

Event studies have been
used on many different
events. In finance, they
often tell us whether
corporate actions are good
news.

to corporate name changes, to analysts’ opinions, to corporate earnings, to stock splits, to
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:

• When firms announce increases in dividends, share repurchases, or stock splits (by about
0.1-1%; if you are interested, there is a longer explanation in Chapter 20).

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.

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:
Bad news…

• 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
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.

Event studies have also informed us whether certain government regulations had a positive
Government Regulation—who

benefits? who does not? or negative impact on firms. For example, we know which firms were helped and which were
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.

The Effects of Sanctions on South Africa
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.

We may all wish we could report success—that sanctions on South Africa’s racist regime had been effective. Unfortunately,
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.

Although we can conclude that, despite all its publicity, the embargo was largely ineffective economically, sanctions may
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.

Q 12.23. In a perfect market, what kind of response (“unusual” stock price change and “unusual”
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?

Q 12.24. What kind of corporate events are greeted as good news by the financial markets?
What events are greeted as bad news?

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.

End of Chapter 12 Material 309

Summary

This chapter covered the following major points:

• Market efficiency means that the market uses all avail-
able information in setting prices to offer “appropri-
ate rates of return.”

• In the short run, the appropriate expected rate of
return on stocks must be small. Therefore, market ef-
ficiency prescribes that stocks roughly follow random
walks.

• In the long run, it is rarely clear what this “appropri-
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.

• Beliefs in efficient markets come in different forms.

– The standard efficient markets classification
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).

– A more current efficient markets classification
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).

• The overall evidence suggests that it is not easy to
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—

separates finance professors into “rationalists” (or
“classical” economists) and “behavioralists.”

• In a perfect and efficient market, investors should
not find arbitrage opportunities:

– True arbitrage is a riskless bet with no nega-
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.

– Risk(y) arbitrage is more like a great bet. An
infinitely risk-averse investor would not want
to take it, because there is a chance that risk(y)
arbitrage will lose money.

– Both true and risk(y) arbitrage opportunities
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.

• Given the millions of investors, many will beat the
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.

• Managers can learn valuable information from mar-
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.

• Event studies allow you to ascertain the corporate
value impact of sharp events, such as election results,
legislative action (FDA rulings), or corporate events
(dividend increases).

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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
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.

Keywords
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.

Answers

Q 12.1 The “efficient market” phrase is shorthand for “the mar-
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.

Q 12.2 As a believer in market efficiency, you would point out
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.)

Q 12.3 Market efficiency is a much more powerful concept over
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.

Q 12.4 An efficient market is one in which the market uses all
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.

Q 12.5 Markets are more likely to be efficient when transaction
costs are low, because this makes it easier for smart investors to
compete away any unusual opportunities.

Q 12.6 The foreign currency market may well be the biggest mar-
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,

we would expect arbitrageurs to take advantage of even the smallest
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.

Q 12.7 Momentum strategies seem to violate even weak-form
market efficiency—unless you believe that their returns are just
normal because they reflect some sort of normal compensation for
risk.

Q 12.8 If you believe that market values do not always perfectly
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.

Q 12.9 The random-walk formula is on Page 287. It states that
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.

Q 12.10 There are about 250 trading days per year. More ac-
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.

Q 12.11 A daily trading strategy would have to offer above 20%
per annum in order to overcome typical transaction costs. The
calculation in the text came to about 23% per annum.

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End of Chapter 12 Material 311

Q 12.12 The typical movement (variation) of a stock is around
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.

Q 12.13 Even if the stock price follows a random walk, its actual
price can definitely—and most likely will be—different from today’s.
Only the expected price is the same as the price today.

Q 12.14 If you want to be a superstar trader who outperforms
by, say, about 4% per year, you would have to earn an extra
252
p

1.04 – 1 ≈ 1.6basis points per day.
Q 12.15 With 100 basis points per day of noise and 200 basis

points per year of excess performance:

1. With 1 day’s performance, you would expect 200/252 ≈ 0.794
basis points per day.

2. The noise was given as 100 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 ·

p
252 ≈ 1, 587 basis points.

6. The expected T would be about 200/1, 587 ≈ 0.126.
7. You need to solve (0.79 · N)/(100 ·

p
N) ≥ 1.96, or 0.0079 ·p

N ≥ 1.96. The critical N is approximately 250 years.
Q 12.16 No! Treasuries earn money without risk, but they are

not an arbitrage, because investing in them requires a negative net
cash flow upfront.

Q 12.17 If the true arbitrage opportunity can only be done once
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.

Q 12.18 Good topics to consider when thinking about how plau-
sible an arbitrage is include: time and execution risk, direct and
indirect transaction costs, price impact of trades, and fixed costs.

Q 12.19 Yes, it makes sense to look for high-ability managers
among historical high performers. However, many high-ability man-
agers will have underperformed historically, and many low-ability
managers will have outperformed historically.

Q 12.20 If each of the 10,000 analysts has a 50-50 chance
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.

Q 12.21 Survivorship bias means that you, as an investor, will
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.

Q 12.22 1. This project has a negative NPV, –$200 + $180 =
–$20, at the zero interest rate. (A positive interest rate would
make it even more negative.)

2. If you do take this second newer project, all your investors
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.

3. The true value of your firm will be ($500+$180) = $680, and
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.

Q 12.23 The immediate share price response to the news that
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.

Q 12.24 Good news: becoming an acquisition target; the an-
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.

End of Chapter Problems

Q 12.25. What kind of evidence would heretics against
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?

Q 12.26. Define “efficient market” and explain how it dif-
fers from a perfect market.

Q 12.27. Peter Lynch, a famous former fund manager for
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?

Q 12.28. Evaluate the following statement: It does not mat-
ter what portfolio you are holding in a perfect and efficient
stock market.

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312 Perfect and Efficient Markets, and Classical and Behavioral Finance

Q 12.29. A paper by Frieder and Zittrain looked at a large
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?

Q 12.30. What are the three main categories in the tradi-
tional market efficiency classification? Give an example of
what each excludes.

Q 12.31. Comment on the following statement: “An ef-
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.”

Q 12.32. Describe the fundamentals-based classification of
the strength of belief in market efficiency. Explain how one
individual can be at one level but not in the level above or
below.

Q 12.33. Does a random walk imply that the expected rate
of return on a stock is zero?

Q 12.34. Define arbitrage. How is it different from a great
bet? Is one always better than the other?

Q 12.35. Would it make sense for a model of the financial
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?

Q 12.36. Assume that the typical day-to-day noise (stan-
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.

1. With only 1 day of 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)?

4. With 252 trading days of performance, how much
extra do you expect to earn per annum?

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 statistically significant evi-
dence to prove that you have a positive ability to pick
stocks.

Q 12.37. What kind of costs should you consider when
evaluating whether an opportunity is an arbitrage?

Q 12.38. The typical hedge fund investor evaluates its fund
based on the most recent three years of performance. What
do you think of this practice?

Q 12.39. Why does the average mutual fund in the market
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?

Q 12.40. Do you expect fund managers with high ability
to prefer compensation that is more performance based?
How good an “insurance” is this for fund investors?

Q 12.41. If a corporation acquires another firm, it can
lower the firm’s uncertainty. This should lower its cost of
capital. This should create value. Is this correct?

Q 12.42. Give an example of how the cost of capital for tak-
ing a project can be too high if the market has undervalued
your firm.

Q 12.43. For convenience, assume a zero discount rate.
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

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%

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

name

of incorporation

of America

09545

Revenues $ 1,3

.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%

Do you want to override this assumption = No

Do you want to override this assumption = Yes

10%

V

50%

Do you want to override this assumption = No
Do you want to override this assumption = Yes

From last 10K

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
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.
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.
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.
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.
Check the financial statements.
If yes, enter the NOL that you are carrying over into year 1 $1,070.00

Aswath Damodaran:
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

by the sum of cells B5 and B6). Look at the industry averages as well in the worksheet.
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

% 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.
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

$ 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

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

.20

11.27%

%

4)

Ratio or reinvestment (Input cell B15)

T

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

Inputs

5

Year

-1

.98

0

0
0
0
0

Year

Current 310.06 1.00 310.06
-1 273.98

-2 208.98

-3 93.00 0.40

-4 0.00

0.00 $ – 0

-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
0 0.00 0.00 0.00 $ – 0

.19

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.
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.
R& D Expenses
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
Output
R&D Expense Unamortized portion Amortization this year
0.80 219.18 $ 54.80
0.60 12

5.39 $ 4

1.80
37.20 $ 18.60
0.20
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

Aswath Damodaran:
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

Inputs

s (From footnote to financials)

Year Commitment

is next year, ….

1

2

3

4

5

Output

7.00%

2

Year Commitment

1

2

3

4

5

6 and beyond

0

Debt outstanding =

$ 233.97

Operating Lease Converter
The yellow cells are input cells. Please enter them.
Operating lease expense in current year = $ 380.00
Operating Lease

Commitment
!

Year 1
$5

6.00
$47.00
$39.00
$35.00
$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
Present Value
$ 56.00 $ 52.34
$ 47.00 $ 4

1.05
$ 39.00 $ 3

1.84
$ 35.00 $ 26.70
$ 31.00 $ 2

2.10
$ 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

s

calculator

Inputs Computed number Country Revenues ERP

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%

Total

Debt

$ 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%

Pre-tax Cost of Debt = 7.00%

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)

Business Revenues

$ – 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
Output 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

Equity Debt Preferred Stock Capital

Market Value

$ 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
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

Estimation of Current Cost of Capital Your inputs Operating

Region 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 =
204 100.00% 9.00%
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%
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
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 =
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
Multi Business (Global Industry Averages)
$ 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
$ 148.21 1.0914

Aswath Damodaran:
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

1

$ (216.72)

2.75%

Output

.00

%

0.00%

>

≤ to Rating is Spread is

D2/D

3 100000

/AAA

0.2

9999

2.5

999

/AA

%

0.65

9999

0%

2

999

/A+

%

0.8

9999

%

1.5

999

/A

1.25

9

%

1.2 1.49999

/A-

%

1.5

9999

/B

0.9

9999

Baa2/BBB 2.00%

0.75

9999

/BB+

2

99999

/BB

0.6

9999

Ba2/BB 4.00%

2.49999 Ba1/BB+ 3.00% 0.5

9999

B1/B+ 5.50%

2.5

Baa2/BBB 2.00% 0.4

9999

B2/B 6.50%

3

A3/A- 1.30% 0.3

9999

B3/B-

4.25

A2/A 1.00% 0.2

9999

C2/C 8.75%

5.5

A1/A+

0.1 0.199999 Ca2/CC

6.5

Aa2/AA

Caa/CCC

100000 Aaa/AAA 0.40% -100000

D2/D 12.00%

If interest coverage ratio is

greater than ≤ to Rating is Spread 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

C2/C 8.75% A3/A- 1.30%

1.5 1.999999 B3/B- 7.25% Aa2/AA 0.70%
2

B2/B 6.50% Aaa/AAA 0.40%

2.5 2.999999 B1/B+ 5.50% B1/B+ 5.50%
3

Ba2/BB 4.00% B2/B 6.50%

3.5

Ba1/BB+ 3.00% B3/B- 7.25%

4

Baa2/BBB 2.00% Ba1/BB+ 3.00%

4.5

9999

A3/A- 1.30% Ba2/BB 4.00%

6

A2/A 1.00% Baa2/BBB 2.00%

7.5

A1/A+ 0.85% C2/C 8.75%

9.5

Aa2/AA 0.70% Ca2/CC 9.50%

12.5 100000 Aaa/AAA 0.40% Caa/CCC 10.50%
D2/D 12.00%
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%
0.64 Caa/CCC 1

0.50% 2.99 Aa2 0.70
0.79 Ca2/CC 9.5 2.49 A1 0.85
1.24 C2/C 8.75 1.99 A2 1.00%
1.49999 B3/B- 7.25 A3 1.30
1.74 B2 6.50% 1.19
1.75 1.999999 B1/B+ 5.50% 0.89 Ba1 3.00%
2.24 Ba2 4.00% 0.74
2.25 0.59
2.999999 0.49
4.249999 0.39 7.25%
5.499999 0.29
6.499999 0.85% 9.50%
8.499999 0.70% 0.05 0.099999 10.50%
8.50 0.049999
For smaller and riskier firms
1.499999
2.499999
3.499999
3.9999999
4.499999
5.99
7.499999
9.499999
12.499999

Aswath Damodaran:
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)

Unlevered Beta

Cost of capital

EV/Sales

DA

EV/EBIT

Advertising 32

%

%

%

%

9.00%

66

%

0.98

%

0.94

36

%

%

1.03

%

6.00

3.68

54

%

%

%

1.89

54

%

3.26%

%

0.60

Automotive 12

%

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

Computers/Peripherals 81

%

%

%

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

Internet

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

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
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
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
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
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

35.00%

Argentina 35.00%

20.00%

Australia

25.00%

0.00%

0.00%

25.00%

0.00%

Bolivia 25.00%

0.00%

10.00%

Brazil

10.00%

20.00%

Canada

0.00%

Chile

25.00%

30.00%

20.00%

10.00%

19.00%

25.00%

29.00%

Ecuador

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%

Japan

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%

New Zealand 28.00%

30.00%

28.00%

12.00%

35.00%

25.00%

30.00%

Paraguay 10.00%
Peru 30.00%

30.00%

19.00%

25.00%

10.00%

Russia 20.00%

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%

United States

25.00%

0.00%

34.00%

25.00%

20.00%

35.00%

33.00%

28.60%

Afghanistan 20.00%
Albania 10.00%
Angola
Armenia
Aruba 28.00%
30.00%
Austria
Bahamas
Bahrain
Bangladesh 2

7.50%
Barbados
Belarus 18.00%
Belgium 33.99%
Bermuda
Bonaire
Bosnia and Herzegovina
Botswana 22.00%
34.00%
Bulgaria
Cambodia
2

6.00%
Cayman Islands
1

8.50%
China
Colombia 33.00%
Costa Rica
Croatia
Curacao 27.50%
Cyprus
Czech Republic
Denmark
Dominican Republic
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
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
Nigeria
Norway
Oman
Pakistan
Panama
Papua New Guinea
Philippines
Poland
Portugal
Qatar
Romania 16.00%
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%
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

Region

Albania B1 4.00% 11.80% 6.00%

Angola

3.25%

4.88% Africa

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%

Austria Aaa 0.00% 5.80% 0.00% Western Europe

2.00% 8.80% 3.00% Eastern Europe & Russia

Bahamas

8.05%

Caribbean

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

0.70% 6.85% 1.05% Western Europe

10.00%

15.00% Central and South America

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%

Central and South America

Bulgaria Baa2 1.75% 8.43% 2.63% Eastern Europe & Russia
Cambodia B2 5.00%

7.50% Asia

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

7.00% 16.30% 10.50% Caribbean

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

B1 4.00% 11.80% 6.00% Asia

Finland Aaa 0.00% 5.80% 0.00% Western Europe
France

6.18% 0.38% Western Europe

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

9.40%

Central and South America

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%

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

B1 4.00% 11.80% 6.00% Middle East

Lithuania Baa1 1.50% 8.05% 2.25% Eastern Europe & Russia
Luxembourg Aaa 0.00% 5.80% 0.00% Western Europe

Aa3 0.70% 6.85% 1.05% Asia

Malaysia A3

7.53% 1.73% Asia

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

B3 6.00% 14.80% 9.00% Eastern Europe & Russia

B1 4.00% 11.80% 6.00% Asia

Montenegro Ba3 3.25% 10.68% 4.88% Eastern Europe & Russia

Ba1 2.40% 9.40% 3.60% Africa

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

B3 6.00% 14.80% 9.00% Central and South America

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

B1 4.00% 11.80% 6.00% Africa

Singapore Aaa 0.00% 5.80% 0.00% Asia

A2 1.00% 7.30% 1.50% Eastern Europe & Russia

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

Baa1 1.50% 8.05% 2.25% Caribbean

B2 5.00% 13.30% 7.50% Caribbean

Ba3 3.25% 10.68% 4.88% Caribbean

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

Aaa 0.00% 5.80% 0.00% North 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
Africa

Australia & New Zealand 0.00% 5.80% 0.00%
Caribbean 4.52%

6.77%

Central and South America 2.26% 9.18% 3.38%
Eastern Europe & Russia

8.48%

Middle East

6.96% 1.16%

North America 0.00% 5.80% 0.00%
Western Europe 0.70% 6.85% 1.05%

1.18% 7.58%

%

Japan 0.70% 6.85% 1.05%
Long-Term Rating Adj. Default Spread Total Risk Premium Country Risk Premium
Eastern Europe & Russia
Ba3 10.68%
Australia & New Zealand
Azerbaijan Baa3
Baa1 1.50% 2.25%
Aa3
Belize Caa3 20.80%
2.63%
13.30%
Cuba Caa1
Fiji Islands
Aa1 0.25%
2.40% 3.60%
Financial Center
Lebanon
Macao
1.15%
Moldova
Mongolia
Morocco
Nicaragua
Senegal
Slovakia
St. Maarten
St. Vincent & the Grenadines
Suriname
United States of America
Row Labels Default Spread (Weighted average) Total ERP (Weighted Average) Country Risk Premium (Weighted Average)
2.86% 10.09% 4.29%
12.57%
1.79% 2.68%
0.77%
Asia without Japan 1.78

Traiing 12 month

Revenues

.70

R&D expense

Operating income or EBIT

Book value of equity

Book value of debt

Do you have operating lease commitments?
Cash and cross holdings

Non-operating assets

$0.00

Minority interests $0.00 $0.00
Number of shares outstanding =

$121.45

Effective tax rate = 0.00%

0.00%

Marginal tax rate =
Year 1

NA

NA

.00

NA

NA

NA

NA

Last 10K First X months: Last year First X months: Current year Trailing 12 month
$413.26 $41.30 $956.74 $1,

328
$273.98 $107.17 $143.25 $310.06
-$394.28 -$194.94 -$17.38 -$216.72
Interest expenses $0.25 $2

0.23 $0.15 -$19.83
$124.70 $629.43
$452.34 $578.74
$201.89 $746.06
$0.00
$121.45
Current stock price =
22.31%
Lease commitments
$142.00
Year 2 $128.00
Year 3 $

117
Year 4 $110.00
Year 5 $102.00
Beyond year 5 $252.00

Answer keys

Synthetic rating Beta

Yes B

Direct input 1 Direct input

No V Country of incorporation Synthetic rating 2

Multibusiness(US)

Yes/No Book or Market Value ERP choices Cost of debt
Will input
Single Business(US)
Operating countries Actual rating Single Business(Global)
Operating regions
Multibusiness(Global)

Global industry averages

Industry Name Number of firms

Effective tax rate

Pre-tax Operating Margin

ROIC Sales/Capital EV/Sales

Advertising

0.98

%

3.86%

9.42%

0.94

Aerospace/Defense

0.89

20.80%

5.35% 8.91%

4.86 0.99

12.24%

Air Transport

0.60

16.15%

4.84% 6.35% 6.94% 1.67 0.79 9.50%

Apparel

1.00

15.05% 1.55 1.55 8.05%

Auto & Truck 130 0.77

16.30%

5.98%

7.83% 1.49 0.78

16.78%

Auto Parts

1.19

27.00%

4.20%

2.50 0.56 7.61% 15.87%

Bank

0.31

0.25%

%

0.09

0.44

0.00%

0.00% 0.23 3.92 4.05% 7.68%

Beverage 99 0.74

17.55%

30.71%

21.29%

1.60 2.23 9.19%

0.68

%

0.89 2.91

Biotechnology

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

Building Materials

0.81

7.58% 1.71 0.89

0.83

20.08%

4.20%

3.23 1.09

Cable TV 65 0.76

9.79%

15.33% 1.08 2.38

%

Chemical (Basic)

0.86

%

6.69%

1.32 1.06 6.76% 16.00%

Chemical (Diversified) 86 1.11

30.07%

3.43% 7.96%

10.52% 1.78 0.96 7.14%

Chemical (Specialty)

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

Computer Software

1.12 7.33% 6.83% 11.68% 27.50%

1.97

Computers/Peripherals

1.04

5.02%

0.90 0.21% 48.32%

0.75

32.69%

7.25% 7.89% 0.85 1.70

Diversified

0.67

6.18%

11.53% 7.62% 0.88 1.46 7.65%

Educational Services 145 1.10

NA

2.64 0.97 15.14%

Electrical Equipment

0.96

3.30% 6.86% 7.24%

2.10 1.01 8.43%

Electronics

1.01

2.78%

6.47% 1.85 0.74 2.24%

208 0.96

12.17% NA

2.32%

2.45 0.49

Engineering

0.81

59.23% 1.79% 4.52% 6.83% 7.93% 2.28 0.56 8.60%

Entertainment 356 0.97

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

Financial Svcs.

0.18

16.51% 21.78% 6.43%

0.38% 0.09

0.17

8.01%

3.31%

0.09 11.24

Food Processing

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%

Furn/Home Furnishings

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%

Homebuilding 155 1.00

36.75%

4.16% 6.61% 7.73% 5.94% 1.24 0.99 1.36%

Hotel/Gaming

0.84

12.19%

5.73% 11.80%

10.35% 0.95 2.24 10.03%

Household Products 456 0.82

13.98%

8.68%

2.14 2.09

16.06%

Information Services

0.98

10.40%

15.35%

3.05 6.26%

0.71

5.89% 7.96%

1.56 0.67 5.98%

Insurance (Life) 117 0.94

34.76% 3.67% 6.60% 7.68%

1.50 0.77 5.07%

Insurance (Prop/Cas.) 220 0.65

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%

Machinery

1.06

32.02%

8.92%

1.83 1.13

15.82%

Metals & Mining

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

Oil/Gas Distribution

0.70

8.92%

5.03%

8.71% 0.73 2.23

Oilfield Svcs/Equip.

1.12

4.24%

3.28 0.52

Packaging & Container

0.65

7.51% 7.73% 11.05% 1.74 0.89 9.61%

Paper/Forest Products

0.64

1.95%

3.47% 3.98% 1.02 1.06 6.17%

0.88

12.85%

1.13 2.78

18.46%

Power

15.12%

10.49% 5.23% 5.14% 0.64 1.80

Precious Metals

1.16 14.66%

4.97% 8.79% 0.58

0.75

15.27%

7.95% 0.26%

1.79 1.18 1.45%

R.E.I.T. 48 0.14

2.99%

61.89%

10.89% 0.07% 0.02

2.02% 4.94%

Railroad 56 0.46

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%

Recreation

0.86

15.30%

5.97% 11.01%

1.31 1.31 1.93%

Reinsurance 35 0.86

8.86% 12.30% 14.39% 15.67% 1.25 0.73

15.30%

Restaurant

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

Semiconductor

1.20 13.88% 12.19% 8.19%

12.92% 1.30 1.66 5.70%

Semiconductor Equip

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%

Shoe 95 1.06 7.42% 6.90% 16.82%

7.16%

16.29%

2.12 1.27 8.98% 14.72%

Steel

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%

Telecom. Equipment

1.18 15.23%

9.09%

5.90% 7.46% 9.43%

1.93 1.37

Telecom. Services

0.63

11.92%

12.33% 0.98 1.56 7.88% 8.79%

Thrift 295 0.02

18.11% 9.16%

0.59%

0.01

7.27%

Tobacco 48 0.49

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%

Trucking

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%

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
255 32.29% 24.41% 1

3.92 34.69% 8.10% 42.52% 4.53 6.82% 21.10%
210 26.27% 13.31% 33.18% 16.43% 35.50% 5.45%
160 100.92% 50.23% 51.21% 1.66% 21.78%
1166 17.84% 15.14% 13.42% 37.80% 6.48% 11.70% 12.92% 14.17%
9

3.91% 48.43% 12.66% 5.81% 18.61% 7.89%
624 37.00% 16.55% 12.54% 6.60% 13.90% 14.33%
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%
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%
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%
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%
56.80% 36.22% 1

4.42% 15.91% 18.41% 26.04% 11.67% 5.51
760 40.13% 28.64% 13.56% 5

7.82 3.79% 8.03% 7.99%
4

2.99% 20.09% 43.49% 9.84% 15.67%
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%
1068 14.49% 22.50% 16.62% 40.08% 3.22 1

0.54% 19.64%
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%
365 79.08% 44.16% 13.26% 25.92% 9.25% 1

3.98%
2

0.26% 16.84% 14.29% -1.40% 11.08% -2.57% 21.01% 20.40%
847 29.89% 23.01% 13.88% 50.70% 11.05% 20.52%
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%
1141 8

3.04% 45.37% 17.02% 15.76%
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%
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%
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%
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%
58.09% 19.22% 1

4.51% 10.35%
618 30.37% 23.29% 36.52% 8.02% 14.85%
1

4.25% 12.47% 43.82% 14.34% 16.86% 22.08% 11.76%
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%
61.35% 38.02% 1

7.28% 8.95% 12.51%
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%
1249 25.23% 20.15% 17.48% 5.32% 10.87% 1

2.83% 3.89%
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%
198 61.85% 38.21% 115.27% 10.38% 11.00% 16.37% 17.40%
570 36.67% 26.83% 14.22% 26.59% 2.36% 11.21% 11.01% 15.38% 26.79%
399 63.06% 38.67% 17.17% 43.18% 2.80% 16.01%
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%
719 0.47 105.84% 51.42% 93.77% 3.62% 1

3.97% 11.64%
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%
560.60% 84.86% 55.74% 2.67% 47.03
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%
292 31.84% 24.15% 28.25% 9.65% 10.47% 16.35%
42.79% 29.97% 11.47% 24.17% 6.02%
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%
564 38.44% 7.21% 11.30% 10.20% 17.73%
264 -1.37% -1.66%
Shipbuilding & Marine 351 90.71% 47.56% 11.28% 497.14%
18.13% 9.81% 18.16%
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%
550 13.22% 46.05% 11.82% 3.55% 18.69%
325 65.54% 39.59% 103.40% 5.58% 14.71% 9.01%
5432.46% 98.19% 39.07% -12.11% -0.00% 112.28 8.29%
15.48% 13.40% 19.70% 63.68% 44.22% 47.52%
Tranportation 32.77% 19.61% 42.98% 5.01% 11.17%
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

1

2

3

4

5

6

7

8

9

10

Base -21.857
-5.20642
45.464902
169.6272206
445.33898326
1023.92987555
2020.7215372481
3489.4661025356
5299.1581119516
7058.2476163242
8177.7425279911

Revenues

Pre-tax operating income

Revenues (in billions)
Pre-tax Operating Income
1328.696
2258.7832
3839.93144
6527.883448
11097.4018616
18865.58316472
29534.0704443692
42263.2548058923
54794.3098558393
63670.9880524853
65421.9402239286

Summary sheet

Year Revenues Pre-tax operating income
Base

1

2

$ 45

3

4

$ 445

5

6

7

8

9

10

$ 1,329 $ (22)
$ 2,259 $ (5)
$ 3,840
$ 6,528 $ 170
$ 11,097
$ 18,866 $ 1,024
$ 29,534 $ 2,021
$ 42,263 $ 3,489
$ 54,794 $ 5,299
$ 63,671 $ 7,058
$ 65,422 $ 8,178

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