CFIN4
Chapter 8 – Risk and Rates of Return
46. Assume the risk-free rate of return (rRF) is 5 percent, the market risk premium (RPM
) is 8 percent, and an
investment exists that has a beta (β) equal to 1.5. According to the Capital Asset Pricing Model (CAPM), which of
the following statements is correct?
a. The risk premium associated with the investment would be 12 percent.
b. The appropriate rate of return for the investment is 9.5 percent.
c. All investments that have betas less than 1.0 must earn a total rate of return less than 8 percent.
d. There is not enough information to answer this question.
e. None of the above is a correct statement.
47. Given the following information, compute the standard deviation for Investment A:
Investment A
Payoff Probability
20% 0.5
10% 0.4
−10% 0.1
= 13.0%
a. 85.0%
b. 5.0%
c. 9.0%
d. 17.%
e. None of the above are correct.
CFIN4
Chapter 8 – Risk and Rates of Return
48. Based on the information given below, which of the investments would be considered best based on its risk and
return relationship? Assume all investors are risk-averse and the investments will be held in isolation, not in a
portfolio.
Investment
D E F
Expected return, 10.0% 18.0% 18.0%
Standard deviation, σ 7.0% 12.0% 20.0%
a. D, because its total risk is lowest.
b. E, because its coefficient of variation is lowest.
c. F, because its standard deviation, σ, is highest.
d. E and F, because the have the same expected return, .
e. None of the above.
49. Steve Brickson currently has an investment portfolio that contains four stocks with a total value equal to $80,000.
The portfolio has a beta (β) equal to 1.4. Steve wants to invest an additional $20,000 in a stock that has β = 2.4.
After Steve adds the new stock to his portfolio, what will be the portfolio’s beta?
a. 1.6
b. 1.9
c. 2.0
d. Not enough information is given to compute the portfolio’s beta (β).
e. None of the above is correct.
CFIN4
Chapter 8 – Risk and Rates of Return
50. Stock Q has a beta (β) equal to 1.6 and Stock P has a beta equal to 0.8. Based on this information, according to the
capital asset pricing model (CAPM), which of the following statements is correct?
a. The required rate of return for Stock Q, rQ, should be 1.6 times greater than the required rate of return for
Stock P, rP.
b. The risk premium associated with Stock Q, RPQ, should be 1.6 times greater than the risk premium associated
with Stock P, RPP.
c. The required rate of return for Stock Q, rQ, should be two times greater than the required rate of return for
Stock P, rP.
d. The risk premium associated with Stock Q, RPQ, should be two times greater than the risk premium
associated with Stock P, RPP.
e. None of the above is a correct answer.
51. Given the following information, compute the coefficient of variation for Cyber Soda, Inc.:
Probability Return
0.2 2.0%
0.3 12.0%
0.5 5.0%
Expected return: = 6.5%
a. 3.78
b. 0.58
c. 0.00
d. 1.72
e. None of the above is correct.
CFIN4
Chapter 8 – Risk and Rates of Return
52. Which of the following statements is most correct?
a. According to CAPM theory, the required rate of return on a given stock can be found by use of the SML
equation:
ri = rRF + (rM − rRF)βi
Expectations for inflation are not reflected anywhere in this equation, even indirectly, and because of that the
text notes that the CAPM may not be strictly correct.
b. If the required rate of return is given by the SML equation as set forth in Answer a, there is nothing a
financial manager can do to changer his or her company’s cost of capital, because each of the elements in the
equation is determined exclusively by the market, not by the type of actions a company’s management can
take, even in the long run.
c. Assume that the required rate of return on the market is currently rM = 15%, and that rM remains fixed at
that level. If the yield curve has a steep upward slope, the calculated market risk premium would be larger if
the 30–day T-bill rate were used as the risk-free rate than if the 30-year T-bond rate were used as rRF.
d. Statements a and b are both true.
e. Statements a and c are both true.
53. Which of the following statements is most correct?
a. If investors become more risk averse, but rRF remains constant, the required rate of return on high beta stocks
will rise, the required return on low beta stocks will decline, but the required return on an average risk stock
will not change.
b. If Mutual Fund A held equal amounts of 100 stocks, each of which had a beta of 1.0, and Mutual Fund B held
equal amounts of 10 stocks with betas of 1.0, then the two mutual funds would have betas of 1.0 and thus
would be equally risky from an investor’s standpoint.
c. An investor who holds just one stock will be exposed to more risk than an investor who holds a portfolio of
stocks, assuming the stocks are all equally risky. Since the holder of the 1-stock portfolio is exposed to more
risk, he or she can expect to earn a higher rate of return to compensate for the greater risk.
d. Assume that the required rate of return on the market , rM , is given and fixed. If the yield curve were
upward-sloping, then the Security Market Line (SML) would have a steeper slope if 1-year Treasury
securities were used as the risk-free rate than if 30-year Treasury bonds were used for rRF.
e. Statements a, b, c, and d are all false.
54. Based on the information given below, which of the following statements is incorrect?
Investment
D
15.0%
E
18.0%
F
18.0%
10.0%
12.0%
20.0%
a. Based on both risk and return, Investment D and Investment E should be considered equally risky.
b. If Investment F is negatively related to both Investment D and Investment E, then combining Investment F
with both Investment D and Investment E would always produce a portfolio with lower risk than a portfolio of
Investment F and either one of the other investments combined.
c. Investment F is the most desirable security for investors who are risk averse and who want to hold a one-
security portfolio.
d. An investor can purchase positive amounts of Investment D and Investment F and form a two-security
portfolio with a return greater than 18 percent and a standard deviation less than 10 percent.
e. None of the above statements is correct.
55. Given the following probability distributions, what are the expected returns for the Market and for Security J?
State
1
PRJ
0.3
rm
−10%
rJ
40%
2
0.4
10
−20
3
0.3
30
30
a. 10.0%; 11.3%
b. 9.5%; 13.0%
c. 10.0%; 9.5%
d. 10.0%; 13.0%
e. 13.0%; 10.0%
CFIN4
Chapter 8 – Risk and Rates of Return
56. If the risk-free rate is 7 percent, the expected return on the market is 10 percent, and the expected return on
Security J is 13 percent, what is the beta of Security J?
a. 1.0
b. 1.5
c. 2.0
d. 2.5
e. 3.0
57. HR Corporation has a beta of 2.0, while LR Corporation’s beta is 0.5. The risk-free rate is 10%, and the required
rate of return on an average stock is 15%. Now the expected rate of inflation built into rRF falls by 3 percentage
points, the real risk-free rate remains constant, the required return on the market falls to 11%, and the betas remain
constant. When all of these changes are made, what will be the difference in required returns on HR’s and LR’s
stocks?
a. 1.0%
b. 2.5%
c. 4.5%
d. 5.4%
e. 6.0%
58. Stock X and the “market” had the following returns during the last three years, and the same relative volatility is
expected to exist in the future:
Year Stock X Market
1
15.0
10.0
2
5.0
5.0
3
−15.0
−5.0
The riskless rate is rRF = 8%, and the expected return on the market is 12 percent. If equilibrium exists, what is the
expected return on Stock X?
a. −4%
b. 8%
c. 12%
d. 14%
e. 16%
CFIN4
Chapter 8 – Risk and Rates of Return
59. Assume that a new law is passed which restricts investors to holding only one asset. A risk-averse investor is
considering two possible assets as the asset to be held in isolation. The assets’ possible returns and related
probabilities (i.e., the probability distributions) are as follows:
Asset X
Asset Y
Pr
r
Pr
r
0.10
−3%
0.05
−3%
0.10
2
0.10
2
0.25
5
0.30
5
0.25
8
0.30
8
0.30
10
0.25
10
Which asset should be preferred?
a. Asset X, since its expected return is higher.
b. Asset Y, since its beta is probably lower.
c. Either one, since the expected returns are the same.
d. Asset X, since its standard deviation is lower.
e. Asset Y, since its coefficient of variation is lower and its expected return is higher.
60. Calculate the standard deviation of the expected dollar returns for Ditto Copier Center, given the following
distribution of returns:
Probability Return
0.2 $50
0.5 $20
0.3 −$15
a. $36.0
b. $23.0
c. $18.0
d. $13.0
e. $30.0
CFIN4
Chapter 8 – Risk and Rates of Return
61. Consider the following information, and then calculate the required rate of return for the Scientific Investment Fund.
The total investment in the fund is $2 million. The market required rate of return is 15 percent, and the risk-free rate
is 7 percent.
Stock
Investment
Beta
A
$ 200,000
1.50
B
300,000
−0.50
C
500,000
1.25
D
a. 14.3%
1,000,000
0.75
b. 15.0%
c. 13.1%
d. 12.7%
e. 10.3%
CFIN4
Chapter 8 – Risk and Rates of Return
62. Oakdale Furniture Inc. has a beta coefficient of 0.7 and a required rate of return of 15 percent. The market risk
premium is currently 5 percent. If the inflation premium increases by 2 percentage points, and Oakdale acquires new
assets which increase its beta by 50 percent, what will be Oakdale’s new required rate of return?
a. 13.5%
b. 22.8%
c. 18.75%
d. 15.25%
e. 17.00%
63. Company X has beta = 1.6, while Company Y’s beta = 0.7. The risk-free rate is 7%, and the required rate of return
on an average stock is 12%. Now the expected rate of inflation built into rRF rises by 1 percentage point, the real
risk-free rate remains constant, the required return on the market rises to 14%, and betas remain constant. After all
of these changes have been reflected in the data, by how much will the required return on Stock X exceed that on
Stock Y?
a. 3.75%
b. 4.20%
c. 4.82%
d. 5.40%
e. 5.75%
64. You hold a diversified portfolio consisting of a $5,000 investment in each of 20 different common stocks. The
portfolio beta is equal to 1.15. You have decided to sell one of your stocks, a lead mining stock whose β = 1.0, for
$5,000 net and to use the proceeds to buy $5,000 of stock in a steel company whose β = 2.0. What will be the new
beta of the portfolio?
a. 1.12
b. 1.20
c. 1.22
d. 1.10
e. 1.15
65. You are managing a portfolio of 10 stocks which are held in equal amounts. The current beta of the portfolio is 1.64,
and the beta of Stock A is 2.0. If Stock A is sold, what would the beta of the replacement stock have to be to
produce a new portfolio beta of 1.55?
a. 1.10
b. 1.00
c. 0.90
d. 0.75
e. 0.50
66. Refer to CAPM Analysis. Calculate both stocks’ betas. What is the difference between the betas, i.e., what is the
value of betaR − betaS? (Hint: The graphical method of calculating the rise over run, or (Y2 − Y1) divided by (X2 −
X1) may aid you.)
a. 0.0
b. 1.0
c. 1.5
d. 2.0
e. 2.5
CFIN4
Chapter 8 – Risk and Rates of Return
67. Refer to CAPM Analysis. Set up the SML equation and use it to calculate both stocks’ required rates of return, and
compare those required returns with the expected returns given above. You should invest in the stock whose
expected return exceeds its required return by the widest margin. What is the widest margin, or greatest excess
return ?
a. 0.0%
b. 0.5%
c. 1.0%
d. 2.0%
e. 3.0%
CFIN4
Chapter 8 – Risk and Rates of Return
68. Here are the expected returns on two stocks:
Returns
Probability X Y
0.1 −20% 10%
0.8 20 15
0.1 40 20
If you form a 50-50 portfolio of the two stocks, what is the portfolio’s standard deviation?
a. 8.1%
b. 10.5%
c. 13.4%
d. 16.5%
e. 20.0%