Chapter 8: Risk and Rates of Return
128.
Mike Flannery 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
What is the portfolio’s beta?
a. 1.06
b. 1.17
c. 1.29
d. 1.42
e. 1.56
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 0.75. By how much will the
portfolio
beta change?
a. −0.190
b. −0.211
c. −0.234
d. −0.260
e. −0.286
0.300
0.107
0.267
0.240
130.
You hold a diversified $100,000 portfolio consisting of 20 stocks with $5,000 invested in each. The
portfolio’s beta is 1.12. You plan to sell a stock with b = 0.90 and use the proceeds to buy a new stock with b
= 1.80. What will the portfolio’s new beta be?
a. 1.286
b. 1.255
c. 1.224
d. 1.194
e. 1.165
131.
Mikkelson Corporation’s stock had a required return of 11.75% last year, when the risk-free rate was 5.50%
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.)
a. 14.38%
b. 14.74%
c. 15.11%
d. 15.49%
e. 15.87%
132.
Company A has a beta of 0.70, while Company B’s beta is 1.20. The required return on the stock market is
11.00%, and the risk-free rate is 4.25%. 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.)
a. 2.75%
b. 2.89%
c. 3.05%
d. 3.21%
e. 3.38%
133.
Stock A’s stock has a beta of 1.30, and its required return is 12.00%. Stock B’s beta is 0.80. If the risk-free
rate is
4.75%, what is the required rate of return on B’s stock? (Hint: First find the market risk premium.)
a. 8.76%
b. 8.98%
c. 9.21%
d. 9.44%
e. 9.68%
134.
Kollo Enterprises has a beta of 1.10, the real risk-free rate is 2.00%, investors expect a 3.00% future inflation
rate,
and the market risk premium is 4.70%. What is Kollo’s required rate of return?
a. 9.43%
b. 9.67%
c. 9.92%
d. 10.17%
e. 10.42%
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
13.00%. Based on the SML, what is the firm’s required return?
a. 13.51%
b. 13.86%
c. 14.21%
d. 14.58%
e. 14.95%
136.
Nagel Equipment has a beta of 0.88 and an expected dividend growth rate of 4.00% per year. The T-bill rate
is
4.00%, and the T-bond rate is 5.25%. The annual return on the stock market during the past 4 years was
10.25%.
Investors expect the average annual future return on the market to be 12.50%. Using the SML, what
is the firm’s
required rate of return?
a. 11.34%
b. 11.63%
c. 11.92%
d. 12.22%
e. 12.52%
137.
Consider the following information and then calculate the required rate of return for the Global Investment
Fund,
which holds 4 stocks. The market’s required rate of return is 13.25%, the risk-free rate is 7.00%, and
the Fund’s
assets are as follows:
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. 9.58%
b. 10.09%
c. 10.62%
d. 11.18%
e. 11.77%
Old beta:
Old rs = rRF + b(RPM
Percentage increase in beta:
Find new rRF: Old rRF + increase in IP =
138.
Data for Dana Industries is shown below. Now Dana acquires some risky assets that cause its beta to increase
by
30%. In addition, expected inflation increases by 2.00%. What is the stock’s new required rate of return?
Initial beta
1.00
Initial required return (rs)
10.20%
Market risk premium, RPM
6.00%
Percentage increase in beta
30.00%
Increase in inflation premium, IP
2.00%
a. 14.00%
b. 14.70%
c. 15.44%
d. 16.21%
e. 17.02%
139.
Mulherin’s stock has a beta of 1.23, its required return is 11.75%, and the risk-free rate is 4.30%. What is the
required rate of return on the market? (Hint: First find the market risk premium.)
a. 10.36%
b. 10.62%
c. 10.88%
d. 11.15%
e. 11.43%
140.
Suppose you hold a portfolio consisting of a $10,000 investment in each of 8 different common stocks. The
portfolio’s beta is 1.25. Now suppose you decided to sell one of your stocks that has a beta of 1.00 and to use
the
proceeds to buy a replacement stock with a beta of 1.35. What would the portfolio’s new beta be?
a. 1.17
b. 1.23
c. 1.29
d. 1.36
e. 1.43
141.
Returns for the Dayton Company over the last 3 years are shown below. What’s the standard deviation of the
firm’s returns? (Hint: This is a sample, not a complete population, so the sample standard deviation formula
should
be used.)
Year Return
2013 21.00%
2012 −12.50%
2011 25.00%
a. 20.08%
b. 20.59%
c. 21.11%
d. 21.64%
e. 22.18%
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.)
Economic
Conditions Prob. Return
Strong 30% 32.0%
Normal 40% 10.0%
Weak 30% −16.0%
a. 17.69%
b. 18.62%
c. 19.55%
d. 20.52%
e. 21.55%
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 60% in ECB and
the
remainder in WCB? (Hint: Use the sample standard deviation formula.)
Year
2009
ECB
40.00%
WCB
40.00%
2010
−10.00
15.00%
2011
35.00%
−5.00%
2012
−5.00%
−10.00%
2013
15.00%
35.00%
Average return =
15.00%
15.00%
Standard deviation =
22.64%
22.64%
a. 3.29%
b. 3.46%
c. 3.65%
d. 3.84%
e. 4.03%
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 4.20%. You now receive another $5.00 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.)
a. 8.83%
b. 9.05%
c. 9.27%
d. 9.51%
e. 9.74%
145.
A mutual fund manager has a $40 million portfolio with a beta of 1.00. The risk-free rate is 4.25%, and the
market
risk premium is 6.00%. The manager expects to receive an additional $60 million which she plans to
invest in
additional stocks. After investing the additional funds, she wants the fund’s required and expected
return to be
13.00%. What must the average beta of the new stocks be to achieve the target required rate of
return?
a. 1.68
b. 1.76
c. 1.85
d. 1.94
e. 2.04
Stock A
Stock B
Stock C
146.
Assume that you are the portfolio manager of the SF Fund, a $3 million hedge fund that contains the
following
stocks. The required rate of return on the market is 11.00% and the risk-free rate is 5.00%. What
rate of return
should investors expect (and require) on this fund?
Stock
Amount
Beta
A
$1,075,000
1.20
B
675,000
0.50
C
750,000
1.40
D
500,000
0.75
$3,000,000
a. 10.56%
b. 10.83%
c. 11.11%
d. 11.38%
e. 11.67%
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
30.0% (not percentage points). Neither betas nor the risk-free rate change. What would CCC’s
new required
return be?
a. 14.89%
b. 15.68%
c. 16.50%
d. 17.33%
e. 18.19%