Investments
Chapters 10 & 13 Homework Problems
Homework problems reproduced from the course textbook: Bodie, Z., Kane, A., & Marcus, A. J.
(2021). Investments (12th ed). New York, NY: McGraw-Hill Education. ISBN: 978-1-260-01383-2 .
Page 1 of 3
CHAPTER 10
1. Suppose that two factors have been identified for the U.S. economy: the growth rate of industrial
production, IP, and the inflation rate, IR. IP is expected to be 3%, and IR 5%. A stock with a beta of 1
on IP and .5 on IR currently is expected to provide a rate of return of 12%. If industrial production
actually grows by 5%, while the inflation rate turns out to be 8%, what is your revised estimate of the
expected rate of return on the stock?
2. The APT itself does not provide guidance concerning the factors that one might expect to determine
risk premiums. How should researchers decide which factors to investigate? Why, for example, is
industrial production a reasonable factor to test for a risk premium?
4. Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 6%, and all
stocks have independent firm-specific components with a standard deviation of 45%.
Portfolios A and B are both well-diversified with the following properties:
Portfolio Beta on F1 Beta on F2 Expected Return
A 1.5 2.0 31%
B 2.2 −0.2 27%
What is the expected return–beta relationship in this economy?
5. (Optional Practice Problem) Consider the following data for a one-factor economy. Both portfolios
are well diversified.
Portfolio E(r ) Beta
A 12% 1.2
F 6% 0.0
Suppose that another portfolio, portfolio E, is well diversified with a beta of .6 and expected return of
8%. Would an arbitrage opportunity exist? If so, what would be the arbitrage strategy?
Continued on the next page.
Investments
Chapters 10 & 13 Homework Problems
Homework problems reproduced from the course textbook: Bodie, Z., Kane, A., & Marcus, A. J.
(2021). Investments (12th ed). New York, NY: McGraw-Hill Education. ISBN: 978-1-260-01383-2 .
Page 2 of 3
10. Consider the following multifactor (APT) model of security returns for a particular stock.
Factor Factor Beta Factor Risk Premium
Inflation 1.2 6%
Industrial production 0.5 8
Oil prices 0.3 3
a. If T-bills currently offer a 6% yield, find the expected rate of return on this stock if the market views
the stock as fairly priced.
b. Suppose that the market expects the values for the three macro factors given in column 1 below, but
that the actual values turn out as given in column 2. Calculate the revised expectations for the rate
of return on the stock once the “surprises” become known.
Factor Expected Value Actual Value
Inflation 5% 4%
Industrial production 3 6
Oil prices 2 0
11. Suppose that the market can be described by the following three sources of systematic risk with
associated risk premiums.
Factor Risk Premium
Industrial production (I ) 6%
Interest rates (R) 2
Consumer confidence (C ) 4
The return on a particular stock is generated according to the following equation:
r = 15% + 1.0I + 0.5R + 0.75C + e
Find the equilibrium rate of return on this stock using the APT. The T-bill rate is 6%. Is the stock over-
or underpriced? Explain.
Continued on the next page.
Investments
Chapters 10 & 13 Homework Problems
Homework problems reproduced from the course textbook: Bodie, Z., Kane, A., & Marcus, A. J.
(2021). Investments (12th ed). New York, NY: McGraw-Hill Education. ISBN: 978-1-260-01383-2 .
Page 3 of 3
CHAPTER 13
CFA Problem 1 (not optional): Identify and briefly discuss three criticisms of beta as used in the capital
asset pricing model.
End of document.
