Chapter 08: Risk and Rates of Return
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126. Jim Angel holds a $200,000 portfolio consisting of the following stocks:
Stock Investment Beta
A $50,000 1.70
B $50,000 0.80
C $50,000 1.00
D $50,000 1.20
Total $200,000
What is the portfolio’s beta? Do not round your intermediate calculations.
a. 1.246
b. 1.434
c. 0.999
d. 1.210
e. 1.175
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127. Jill Angel holds a $200,000 portfolio consisting of the following stocks. The portfolio’s beta is 0.88.
Stock Investment Beta
A $50,000 0.50
B $50,000 0.80
C $50,000 1.00
D $50,000 1.20
Total $200,000
If Jill replaces Stock A with another stock, E, which has a beta of 1.30, what will the portfolio’s new beta be? Do not
round your intermediate calculations.
a. 1.40
b. 0.97
c. 0.91
d. 1.24
e. 1.08
1.08
128. Mike Flannery holds the following portfolio:
Stock Investment Beta
A $150,000 1.40
B $60,000 0.80
C $90,000 1.00
D $75,000 1.20
Total $375,000
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What is the portfolio’s beta? Do not round your intermediate calculations.
a. 1.17
b. 0.91
c. 1.27
d. 1.32
e. 1.09
129. Tom Noel holds the following portfolio:
Stock Investment Beta
A $150,000 1.40
B $50,000 0.80
C $100,000 1.00
D $75,000 1.20
Total $375,000
Tom plans to sell Stock A and replace it with Stock E, which has a beta of 0.83. By how much will the portfolio beta
change? Do not round your intermediate calculations.
a. –0.228
b. –0.219
c. –0.251
d. –0.205
e. –0.280
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131. Mikkelson Corporation’s stock had a required return of 12.00% last year, when the risk-free rate was 3% and the
market risk premium was 4.75%. Then an increase in investor risk aversion caused the market risk premium to rise by 2%.
The risk-free rate and the firm’s beta remain unchanged. What is the company’s new required rate of return? (Hint: First
calculate the beta, then find the required return.) Do not round your intermediate calculations.
a. 13.42%
b. 15.79%
c. 18.32%
d. 16.26%
e. 15.63%
132. Company A has a beta of 0.70, while Company B’s beta is 1.00. The required return on the stock market is 9.00%,
and the risk-free rate is 2.25%. What is the difference between A’s and B’s required rates of return? (Hint: First find the
market risk premium, then find the required returns on the stocks.) Do not round your intermediate calculations.
a. 2.03%
b. 2.13%
c. 1.66%
d. 1.64%
e. 1.52%
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c. 8.91%
d. 9.40%
e. 9.79%
135. Linke Motors has a beta of 1.30, the T-bill rate is 3.00%, and the T-bond rate is 6.5%. The annual return on the stock
market during the past 3 years was 15.00%, but investors expect the annual future stock market return to be 10.75%.
Based on the SML, what is the firm’s required return? Do not round your intermediate calculations.
a. 12.03%
b. 9.86%
c. 14.43%
d. 14.79%
e. 14.31%
Use the SML to determine Linke’s required return using the RPM calculated above:
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Stock Investment Beta
A $ 200,000 1.50
B 300,000 -0.50
C 500,000 1.25
D $1,000,000 0.75
a. 13.29%
b. 15.55%
c. 14.89%
d. 15.42%
e. 12.23%
138. Data for Dana Industries is shown below. Now Dana acquires some risky assets that cause its beta to increase by
15.0%. In addition, expected inflation increases by 1.10%. What is the stock’s new required rate of return? Do not round
your intermediate calculations.
Initial beta 1.00
Initial required return (rs) 10.20%
Market risk premium, RPM 6.00%
Percentage increase in beta 15.00%
Increase in inflation premium, IP 1.10%
a. 12.20%
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b. 14.03%
c. 9.64%
d. 13.18%
e. 10.13%
139. Mulherin’s stock has a beta of 1.23, its required return is 10.00%, and the risk-free rate is 2.30%. What is the required
rate of return on the market? (Hint: First find the market risk premium.) Do not round your intermediate calculations.
a. 9.59%
b. 10.02%
c. 8.56%
d. 7.96%
e. 8.99%
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2012 -12.50%
2011 17.50%
a. 21.36%
b. 21.18%
c. 18.97%
d. 18.78%
e. 18.41%
Year
Return Deviation
from Mean Squared
142. Carson Inc.’s manager believes that economic conditions during the next year will be strong, normal, or weak, and
she thinks that the firm’s returns will have the probability distribution shown below. What’s the standard deviation of the
estimated returns? (Hint: Use the formula for the standard deviation of a population, not a sample.) Do not round your
intermediate calculations.
Economic
Conditions Prob. Return
Strong 30% 32.0%
Normal 40% 10.0%
Weak 30% -16.0%
a. 18.62%
b. 16.75%
c. 19.92%
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d. 18.06%
e. 16.94%
143. Assume that your uncle holds just one stock, East Coast Bank (ECB), which he thinks has very little risk. You agree
that the stock is relatively safe, but you want to demonstrate that his risk would be even lower if he were more diversified.
You obtain the following returns data for West Coast Bank (WCB). Both banks have had less variability than most other
stocks over the past 5 years. Measured by the standard deviation of returns, by how much would your uncle’s risk have
been reduced if he had held a portfolio consisting of 57% in ECB and the remainder in WCB? (Hint: Use the sample
standard deviation formula.) Do not round your intermediate calculations.
Year ECB WCB
1 40.00% 40.00%
2 -10.00% 15.00%
3 35.00% -5.00%
4 -5.00% -10.00%
5 15.00% 35.00%
Average return = 15.00% 15.00%
Standard deviation = 22.64% 22.64%
a. 3.85%
b. 4.87%
c. 3.57%
d. 3.93%
e. 3.06%
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% ECB: Year ECB WCB Portfolio ECB/WCB
144. Assume that you manage a $10.00 million mutual fund that has a beta of 1.05 and a 9.50% required return. The risk-
free rate is 2.20%. You now receive another $8.75 million, which you invest in stocks with an average beta of 0.65. What
is the required rate of return on the new portfolio? (Hint: You must first find the market risk premium, then find the new
portfolio beta.) Do not round your intermediate calculations.
a. 7.13%
b. 8.12%
c. 9.59%
d. 7.30%
e. 8.20%
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147. CCC Corp has a beta of 1.5 and is currently in equilibrium. The required rate of return on the stock is 12.00% versus
a required return on an average stock of 10.00%. Now the required return on an average stock increases by 37.5% (not
percentage points). Neither betas nor the risk-free rate change. What would CCC’s new required return be? Do not round
your intermediate calculations.
a. 19.92%
b. 17.10%
c. 17.45%
d. 17.63%
e. 20.09%
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