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. = (-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%.
X = 12.20% versus 20.35% for Y.
CVX = X/ 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%.