Chapter 8-3



Chapter 8-3 Soln.

Use the following information for Questions 1 and 2:

A stock has a required return on 11 percent. The risk-free is 7 percent, and the market risk premium is 4 percent.

1. What is the stock’s beta?

A. 1.2

B. 1.1

C. 1.0*

D. 0.9

2. If the market risk premium increases to 6 percent, what will happen to the stock’s required rate of return?

A. 6.00%

B. 7.00%

C. 11.00%

D. 13.00%*

3. Stock R has a beta of 1.5, Stock S has a beta of 0.75, the expected rate of return on an average stock is 13 percent, and the risk-free rate of return is 7 percent. By how much does the required return on the riskier stock exceed the required return on the less risky stock?

A. 2.5%

B. 3.0%

C. 3.5%

D. 4.5%*

4. Stocks X & Y have the following probability distributions of expected future returns:

Probability X Y

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, rY, for stock Y. (rX = 12%)

b. Calculate the standard deviation of expected returns, for Stock X. (Y = 20.35%)

Now calculate the coefficient of variation for Stock Y.

a. rY= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)

= 14% versus 12% for X.

b. σ2 = (-10% – 12%)2(0.1) + (2% – 12%)2(0.2) + (12% – 12%)2(0.4)

+ (20% – 12%)2(0.2) + (38% – 12%)2(0.1) = 148.8%.

σX = 12.20% versus 20.35% for Y.

CVX = σX/ rX = 12.20%/12% = 1.02, while

CVY = 20.35%/14% = 1.45.

5. Suppose you are the money manager of a $4 million investment fund. The fund consists of 4 stocks with the following investments and betas:

Stock Investment Beta

A $400,000 1.50

B 600,000 (.50)

C 1,000,000 1.25

D 2,000,000 0.75

If the market’s required rate of return is 14% and the risk-free rate is 6%, what is the funds required rate of return?

Portfolio beta = [400,000/4,000,000](1.50) + [600,000/4,000,000] (-0.50) + [1,000,000/4,000,000] (1.25) + [2,000,000/4,000,000] (0.75)

bp = (0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.75)

= 0.15 – 0.075 + 0.3125 + 0.375 = 0.7625.

rp = rRF + (rM – rRF)(bp) = 6% + (14% – 6%)(0.7625) = 12.1%.

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