127. Sherrie Hymes holds a $200,000 portfolio consisting of the following stocks. The portfolio’s beta is
0.875.
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 Sherrie replaces Stock A with another stock, E, which has a beta of 1.50, what will the portfolio’s
new beta be?
a.
1.07
b.
1.13
c.
1.18
d.
1.24
e.
1.30
Stock
Investment
Percentage
Beta
A
$ 50,000
0.50
B
0.80
C
$ 50,000
1.00
D
1.20
Total
$200,000
Beta
0.80
1.00
1.20
1.50
Total
Beta
A
$ 50,000
0.95
B
0.80
C
$ 50,000
1.00
D
$ 50,000
1.20
$200,000
128. Megan Ross 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
Stock
Investment
Percentage
Beta
A
$150,000
1.40
B
$ 50,000
0.80
C
$100,000
1.00
D
$ 75,000
1.20
$375,000
129. Paul McLaren 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
Paul 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
130. Jenna holds a diversified $100,000 portfolio consisting of 20 stocks with $5,000 invested in each. The
portfolio’s beta is 1.12. Jenna plans 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. Porter Plumbing’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. Barker Corp. 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 Barker’s required rate of return?
a.
9.43%
b.
9.67%
c.
9.92%
d.
10.17%
e.
10.42%
135. Brodkey Shoes 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. Gardner Electric 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 Universal
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%
rM
13.25%
rRF
7.00%
Find portfolio beta:
Weight
Beta
Product
= rRF + RPM
= 5.25% + RPM
= 7.25%
= rRF + RPM b
= 5.25% + 7.25% 0.88
= 11.63%
138. Data for Atwill Corporation is shown below. Now Atwill 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%
Old beta
1.00
Old rs = rRF + b(RPM)
Percentage increase in beta
Increase in IP
Find new beta after increase =
1.30
Find old rRF: Old rs = rRF+ b(RPM): 10.2% = rRF + 1.0(6.0%): rRF =
4.20%
Find new rRF: Old rRF + increase in IP =
6.20%
Find new rs = new rRF + new beta(RPM)
14.00%
139. Fiske Roofing Supplies’ 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%
= portfolio beta
d.
11.15%
e.
11.43%
140. Suppose Stan holds a portfolio consisting of a $10,000 investment in each of 8 different common
stocks. The portfolio’s beta is 1.25. Now suppose Stan decided to sell one of his 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 Alcoff 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
2010
21.00%
2009
−12.50%
2008
25.00%
a.
20.08%
b.
20.59%
c.
21.11%
d.
21.64%
e.
22.18%
142. Stuart Company’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%
Economic
Strong
32.0%
3.07%
Normal
10.0%
0.01%
Weak
−16.0%
0.97%
8.48%
Sum sqd deviations
Sum/(N − 1)
SQRT = = 20.59%
143. Assume that your cousin holds just one stock, Eastman Chemical Bonding (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 Wilder’s
Creations and Buildings (WCB). Both companies 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 cousin’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
ECB
WCB
2007
40.00%
40.00%
2008
−10.00%
15.00%
2009
35.00%
−5.00%
2010
−5.00%
−10.00%
2011
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%
ANS: D
This is a relatively technical problem. It should be used only if calculations are emphasized in class or
on a take-home exam where students have time to look up formulas or to use Excel or their calculator
functions.
Year
ECB
2007
40.00%
40.00%
2008
−10.00%
15.00%
2009
−5.00%
2010
−5.00%
−10.00%
2011
15.00%
35.00%
Average return =
15.00%
15.00%
Standard deviation =
22.64%
22.64%
Reduction in the SD vs. ECB’s SD:
144. The $10.00 million mutual fund Henry manages has a beta of 1.05 and a 9.50% required return. The
risk-free rate is 4.20%. Henry now receives another $5.00 million, which he invests 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. Hazel Morrison, 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%. Hazel 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
146. Joel Foster is 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
$3,000,000
a.
10.56%
b.
10.83%
c.
11.11%
d.
11.38%
e.
11.67%
Stock A
Stock B
Stock C
Stock D
Intermediate step
Required market return
Risk free rate
Market risk premium = rMarket − rRF =
Portfolio’s required return = rRF + b(RPM) =
13% = rRF + b(RPM); b = (13% − rRF)/RPM
beta = (Return − Risk-free)/RPM
Req. b = (Old$/Total$) Old b +
(New$/Total$) New b
147. DHF Company 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 DHF’s new required return be?
a.
14.89%
b.
15.68%
c.
16.50%
d.
17.33%
e.
18.19%