Chapter 8: Risk and Rates of Return
Learning Objectives
183
Chapter 8
Risk and Rates of Return
Learning Objectives
After reading this chapter, students should be able to:
◆ Explain the difference between stand-alone risk and risk in a portfolio context.
◆ Describe how risk aversion affects a stock’s required rate of return.
◆ Discuss the difference between diversifiable risk and market risk, and explain how each type of risk
affects well-diversified investors.
◆ Describe what the CAPM is and illustrate how it can be used to estimate a stock’s required rate of
return.
◆ Discuss how changes in the general stock and bond markets could lead to changes in the required
rate of return on a firm’s stock.
◆ Discuss how changes in a firm’s operations might lead to changes in the required rate of return on
the firm’s stock.
184
Lecture Suggestions
Chapter 8: Risk and Rates of Return
Lecture Suggestions
Risk analysis is an important topic, but it is difficult to teach at the introductory level. We just try to give
students an intuitive overview of how risk can be defined and measured, and leave a technical treatment
DAYS ON CHAPTER: 3 OF 56 DAYS (50-minute periods)
Chapter 8: Risk and Rates of Return
Answers and Solutions
185
Answers to End-of-Chapter Questions
8-1 a. No, it is not riskless. The portfolio would be free of default risk and liquidity risk, but inflation
could erode the portfolio’s purchasing power. If the actual inflation rate is greater than that
8-3 a. The expected return on a life insurance policy is calculated just as for a common stock. Each
186
Answers and Solutions
Chapter 8: Risk and Rates of Return
8-7 The risk premium on a high-beta stock would increase more than that on a low-beta stock.
8-8 According to the Security Market Line (SML) equation, an increase in beta will increase a
8-9 a. A decrease in risk aversion will decrease the return an investor will require on stocks. Thus,
Chapter 8: Risk and Rates of Return
Answers and Solutions
187
Solutions to End-of–Chapter Problems
8-1
r
ˆ
= (0.1)(-50%) + (0.2)(-5%) + (0.4)(16%) + (0.2)(25%) + (0.1)(60%)
= 11.40%.
8-3 rRF = 6%; rM = 13%; b = 0.7; r = ?
8-4 rRF = 5%; RPM = 6%; rM = ?
8-5 a. r = 11%; rRF = 7%; RPM = 4%.
188
Answers and Solutions
Chapter 8: Risk and Rates of Return
8-6 a.
=
=
N
1i
iirPr
ˆ
.
b. =
=
−
N
1i
i
2
iP)r
ˆ
r(
.
8-7 Portfolio beta =
$4,000,000
$400,000
(1.50) +
(–0.50) +
$4,000,000
$1,000,000
(1.25) +
(0.75)
Chapter 8: Risk and Rates of Return
Answers and Solutions
189
8-8 In equilibrium:
8-9 We know that bR = 1.50, bS = 0.75, rM = 13%, rRF = 7%.
8-10 An index fund will have a beta of 1.0. If rM is 12.0% (given in the problem) and the risk-free rate is
5%, you can calculate the market risk premium (RPM) calculated as rM – rRF as follows:
8-11 rRF = r* + IP = 2.5% + 3.5% = 6%.
190
Answers and Solutions
Chapter 8: Risk and Rates of Return
b. 1. rRF increases to 10%:
8-13 a. Using Stock X (or any stock):
8-14 Old portfolio beta =
$150,000
$142,500
(b) +
$150,000
$7,500
(1.00)
Chapter 8: Risk and Rates of Return
Answers and Solutions
191
8-15 bHRI = 1.8; bLRI = 0.6. No changes occur.
8-16 Step 1: Determine the market risk premium from the CAPM:
8-17 After additional investments are made, for the entire fund to have an expected return of 13%,
the portfolio must have a beta of 1.5455 as shown below:
192
Answers and Solutions
Chapter 8: Risk and Rates of Return
8-19
X
r
ˆ
= 10%; bX = 0.9; X = 35%.
Y
r
ˆ
= 12.5%; bY = 1.2; Y = 25%.
rRF = 6%; RPM = 5%.
b. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the
Y
r
ˆ
Chapter 8: Risk and Rates of Return
Answers and Solutions
193
8-20 The answers to a, b, c, and d are given below:
rA rB Portfolio
2010 (18.00%) (14.50%) (16.25%)
8-21 a.
M
r
ˆ
= 0.1(-28%) + 0.2(0%) + 0.4(12%) + 0.2(30%) + 0.1(50%) = 13%.
b. First, determine the fund’s beta, bF. The weights are the percentage of funds invested in each
stock:
A = $160/$500 = 0.32.
194
Comprehensive/Spreadsheet Problem
Chapter 8: Risk and Rates of Return
Comprehensive/Spreadsheet Problem
Note to Instructors:
The solution to this problem is not provided to students at the back of their text. Instructors
can access the
Excel
file on the textbook’s website.
8-22 a.
b.
d.
Bartman Reynolds Index
Standard deviation of return 31.5% 9.7% 13.8%
Bartman Reynolds Index
2014 24.7% –1.1% 32.8%
Year Index Bartman Reynolds
2014 32.8% 24.7% –1.1%
Chapter 8: Risk and Rates of Return
Comprehensive/Spreadsheet Problem
195
e. Bartman’s calculations:
SUMMARY OUTPUT
RESIDUAL OUTPUT
Observation Predicted Y Residuals
1 0.48239 -0.23493
Reynolds’ calculations:
SUMMARY OUTPUT
Regression Statistics
RESIDUAL OUTPUT
Observation Predicted Y Residuals
1 -0.04165 0.03113
196
Comprehensive/Spreadsheet Problem
Chapter 8: Risk and Rates of Return
f.
g. The beta of a portfolio is simply a weighted average of the betas of the stocks in the portfolio,
so this portfolio‘s beta would be:
h.
Market return = 11.000%
Beta
Portfolio
Weight
Bartman 1.539 25%
Chapter 8: Risk and Rates of Return
Integrated Case
197
Integrated Case
8-23
Merrill Finch Inc.
Risk and Return
Assume that you recently graduated with a major in finance. You just landed a
job as a financial planner with Merrill Finch Inc., a large financial services
Returns on Alternative Investments
Estimated Rate of Return
State of the
Economy
Prob.
T-Bills
High
Tech
Collec-
tions
U.S.
Rubber
Market
Portfolio
2-Stock
Portfolio
Recession
0.1
5.5%
–27.0%
27.0%
6.0%a
–17.0%
0.0%
Below Avg.
0.2
5.5
-7.0
13.0
-14.0
-3.0
Average
0.4
5.5
15.0
0.0
3.0
10.0
7.5
Above Avg.
0.2
5.5
30.0
-11.0
41.0
25.0
Boom
0.1
5.5
45.0
-21.0
26.0
38.0
12.0
r-hat (
Coeff. of Var. (CV)
13.2
1.9
1.4
0.5
198
Integrated Case
Chapter 8: Risk and Rates of Return
Merrill Finch’s economic forecasting staff has developed probability
A. (1) Why is the T–bill’s return independent of the state of the economy?
Do T-bills promise a completely risk–free return? Explain.
Answer: [Show S8–1 through S8-6 here.] The 5.5% T-bill return does not
depend on the state of the economy because the Treasury must (and