· Estimating Returns

Consider the use of a probability analysis in estimating returns and determining the standard deviation. You may use a hypothetical situation and do the calculations or just describe the steps in the process.

·

Estimating Returns

Consider the use of a probability analysis in estimating returns and determining the
standard deviation. You may use a hypothetical situation and do the calculations or just
describe the steps in the process.

 Estimating Returns
Consider the use of a probability analysis in estimating returns and determining the
standard deviation. You may use a hypothetical situation and do the calculations or just
describe the steps in the process.

·

C

omplete the following problems from your textbook:

· Pages 3

0

8–309: 8-6, 8-7, 8-9, 8-11, and 8-13.

8-6 EXPECTE

D

RETURNS Stocks

A

and

B

have the following probability distributions of expected future returns:

0.2

20

a. Calculate the expected rate of return, ˆrB, for Stock B (ˆrA=12%).

b. Calculate the standard deviation of expected returns, σA, for Stock A (σB = 20.35%). Now calculate the coefficient of variation for Stock B. Is it possible that most investors will regard Stock B as being less risky than Stock A? Explain.

c. Assume the risk-free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Are these calculations consistent with the information obtained from the coefficient of variation calculations in part b? Explain.

8-7 PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $4.82 million investment fund. The fund consists of four stocks with the following investments and betas:

If the market’s required rate of return is 8% and the risk-free rate is 4%, what is the fund’s required rate of return?

8-9 REQUIRED RATE OF RETURN Stock R has a beta of 2.0, Stock S has a beta of 0.45, the required return on an average stock is 10%, and the risk-free rate of return is 5%. By how much does the required return on the riskier stock exceed the required return on the less risky stock?

8-11 CAPM AND REQUIRED RETURN Calculate the required rate of return for Mudd Enterprises assuming that investors expect a 3.6% rate of inflation in the future. The real risk-free rate is 1.0%, and the market risk premium is 6.0%. Mudd has a beta of 1.5, and its realized rate of return has averaged 8.5% over the past 5 years.

8-13 CAPM, PORTFOLIO RISK, AND RETURN Consider the following information for Stocks A, B, and C. The returns on the three stocks are positively correlated, but they are not perfectly correlated. (That is, each of the correlation coefficients is between 0 and 1.)

Beta

15

Fund P has one-third of its funds invested in each of the three stocks. The risk-free rate is 5.5%, and the market is in equilibrium. (That is, required returns equal expected returns.)

a. What is the market risk premium (rM − rRF)?

b. What is the beta of Fund P?

c. What is the required return of Fund P?

d. Would you expect the standard deviation of Fund P to be less than 15%, equal to 15%, or greater than 15%? Explain.

·

Complete the following problems from your textbook:

o

Pages 308
–
309: 8
–
6, 8
–
7, 8
–
9, 8
–
11, and 8
–
13.

8
–
6

EXPECTED RETURNS

Stocks A and B have the following probability distributions of
expected future returns:

Probability

A

B

0.1

(10%)

(35%)

0.2

2

0

0.4

12

20

0.2

20

25

0.1

38

45

a.

Calculate the expected rate of return,
ˆr
B
, for Stock B
(ˆr
A
=12
%)
.

b.

Calculate the standard deviation of expected returns, ó
A
, for Stock A (ó
B

= 20.35%). Now
calculate the coefficient of variation for Stock B. Is it possible that most investors will regard
Stock B as being less risky than Stock A? Explain.

c.

Assume the risk
–
free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Are th
ese
calculations consistent with the information obtained from the coefficient of variation
calculations in part b? Explain.

8
–
7

PORTFOLIO REQUIRED RETURN

Suppose you are the money manager of a $4.82
million investment fund. The fund consists of four stock
s with the following investments and
betas:

Stock

Investment

Beta

A

$ 460,000

1.50

B

500,000

(0.50)

C

1,260,000

1.25

D

2,600,000

0.75

If the market’s required rate of return is 8% and the risk
–
free rate is 4%, what is the fund’s
required rate of return?

8
–
9

REQUIRED RATE OF RETURN

Stock R has a beta of 2.0, Stock S has a beta of 0.45, the required
return on an average stock is 10%, and the risk
–
free rate of r
eturn is 5%. By how much does the required
return on the riskier stock exceed the required return on the less risky stock?

 Complete the following problems from your textbook:
o Pages 308–309: 8-6, 8-7, 8-9, 8-11, and 8-13.

8-6 EXPECTED RETURNS Stocks A and B have the following probability distributions of
expected future returns:
Probability A B
0.1 (10%) (35%)
0.2 2 0
0.4 12 20
0.2 20 25
0.1 38 45
a. Calculate the expected rate of return, ˆrB, for Stock B (ˆrA=12%).
b. Calculate the standard deviation of expected returns, σ
A
, for Stock A (σ
B
= 20.35%). Now
calculate the coefficient of variation for Stock B. Is it possible that most investors will regard
Stock B as being less risky than Stock A? Explain.
c. Assume the risk-free rate is 2.5%. What are the Sharpe ratios for Stocks A and B? Are these
calculations consistent with the information obtained from the coefficient of variation
calculations in part b? Explain.
8-7 PORTFOLIO REQUIRED RETURN Suppose you are the money manager of a $4.82
million investment fund. The fund consists of four stocks with the following investments and
betas:
Stock Investment Beta
A $ 460,000 1.50
B 500,000 (0.50)
C 1,260,000 1.25
D 2,600,000 0.75
If the market’s required rate of return is 8% and the risk-free rate is 4%, what is the fund’s
required rate of return?
8-9 REQUIRED RATE OF RETURN Stock R has a beta of 2.0, Stock S has a beta of 0.45, the required
return on an average stock is 10%, and the risk-free rate of return is 5%. By how much does the required
return on the riskier stock exceed the required return on the less risky stock?