• Home
  • Textbooks
  • Essentials of Investments
  • Capital Asset Pricing and Arbitrage Pricing Theory

Essentials of Investments

Bodie, Zvi; Kane, Alex; Marcus, Alan J.

Chapter 7

Capital Asset Pricing and Arbitrage Pricing Theory - all with Video Answers

Educators

Chapter Questions

Problem 1

Suppose investors believe that the standard deviation of the market-index portfolio has increased by $50 \%$. What does the CAPM imply about the effect of this change on the required rate of return on Google's investment projects?

Check back soon!
View

Problem 2

Consider the statement: “If we can identify a portfolio that beats the S&P 500 Index
portfolio, then we should reject the single-index CAPM.” Do you agree or disagree?
Explain.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
03:04

Problem 3

Are the following true or false? Explain.
a. Stocks with a beta of zero offer an expected rate of return of zero.
b. The CAPM implies that investors require a higher return to hold highly volatile securities.
c. You can construct a portfolio with a beta of .75 by investing . 75 of the investment budget in T-bills and the remainder in the market portfolio.

Md.Daniyal Arshad
Md.Daniyal Arshad
Numerade Educator
01:03

Problem 4

Here are data on two companies. The T-bill rate is 4% and the market risk premium
is 6%. (table can't copy) What would be the expected rate of return for each company, according to the capital
asset pricing model (CAPM)?

Breanna Ollech
Breanna Ollech
Numerade Educator
02:29

Problem 5

Characterize each company in the previous problem as underpriced, overpriced, or prop
erly priced.

Jacquelyn Trost
Jacquelyn Trost
Numerade Educator
02:21

Problem 6

What is the expected rate of return for a stock that has a beta of 1 if the expected return
on the market is 15%? a. $15 \%$
b. More than $15 \%$.
c. Cannot be determined without the risk-free rate.

Sanchit Jain
Sanchit Jain
Numerade Educator

Problem 7

Kaskin, Inc., stock has a beta of 1.2 and Quinn, Inc., stock has a beta of .6. Which of the
following statements is most accurate? a. The expected rate of return will be higher for the stock of Kaskin, Inc., than that of Quinn, Inc.
b. The stock of Kaskin, Inc., has more total risk than Quinn, Inc.
c. The stock of Quinn, Inc., has more systematic risk than that of Kaskin, Inc.

Check back soon!
06:55

Problem 8

Which of the following statements is true? Explain.
a. It is possible that the APT is valid and the CAPM is not.
b. It is possible that the CAPM is valid and the APT is not.

Nicholas Sacco
Nicholas Sacco
Numerade Educator

Problem 10

The market price of a security is $40. Its expected rate of return is 13%. The risk-free
rate is 7%, and the market risk premium is 8%. What will the market price of the secu-
rity be if its beta doubles (and all other variables remain unchanged)? Assume the stock
is expected to pay a constant dividend in perpetuity.

Check back soon!
01:21

Problem 11

You are a consultant to a large manufacturing corporation considering a project with the
following net after-tax cash flows (in millions of dollars): The project's beta is 1.7. Assuming $r_f=9 \%$ and $E\left(r_M\right)=19 \%$, what is the net present value of the project? What is the highest possible beta estimate for the project before its NPV becomes negative?
(table can't copy)

Nick Johnson
Nick Johnson
Numerade Educator
01:04

Problem 12

Consider the following table, which gives a security analyst’s expected return on two
stocks for two particular market returns: a. What are the betas of the two stocks?
b. What is the expected rate of return on each stock if the market return is equally likely to be $5 \%$ or $20 \%$ ?
c. If the T-bill rate is $8 \%$, and the market return is equally likely to be $5 \%$ or $20 \%$, draw the SML for this economy.
d. Plot the two securities on the SML graph. What are the alphas of each?
$e$. What hurdle rate should be used by the management of the aggressive firm for a project with the risk characteristics of the defensive firm's stock?

Achintya Suden
Achintya Suden
Numerade Educator

Problem 13

If the simple CAPM is valid, which of the situations in Problems 13–19 below are possible?
Explain. Consider each situation independently.
$$
\begin{array}{ccc}
\hline \text { Portfolio } & \text { Expected Return } & \text { Beta } \\
\hline A & 20 \% & 1.4 \\
B & 25 & 1.2 \\
\hline
\end{array}
$$

Check back soon!

Problem 14

If the simple CAPM is valid, which of the situations in Problems 13–19 below are possible?
Explain. Consider each situation independently.$$
\begin{array}{|c|c|c|}
\hline \text { Portfolio } & \text { Expected Return } & \begin{array}{l}
\text { Standard } \\
\text { Deviation }
\end{array} \\
\hline \text { A } & 30 \% & 35 \% \\
\hline B & 40 & 25 \\
\hline
\end{array}
$$

Check back soon!

Problem 15

If the simple CAPM is valid, which of the situations in Problems 13–19 below are possible?
Explain. Consider each situation independently. $$
\begin{array}{lcc}
\hline \text { Portfolio } & \text { Expected Return } & \begin{array}{c}
\text { Standard } \\
\text { Deviation }
\end{array} \\
\hline \text { Risk-free } & 10 \% & 0 \% \\
\text { Market } & 18 & 24 \\
\text { A } & 16 & 12 \\
\hline
\end{array}
$$

Check back soon!

Problem 16

If the simple CAPM is valid, which of the situations in Problems 13–19 below are possible?
Explain. Consider each situation independently. $$
\begin{array}{lcc}
\hline \text { Portfolio } & \text { Expected Return } & \begin{array}{c}
\text { Standard } \\
\text { Deviation }
\end{array} \\
\hline \text { Risk-free } & 10 \% & 0 \% \\
\text { Market } & 18 & 24 \\
\text { A } & 20 & 22 \\
\hline
\end{array}
$$

Check back soon!
01:03

Problem 17

If the simple CAPM is valid, which of the situations in Problems 13–19 below are possible?
Explain. Consider each situation independently. $$
\begin{array}{lcl}
\hline \text { Portfolio } & \text { Expected Return } & \text { Beta } \\
\hline \text { Risk-free } & 10 \% & 0 \\
\text { Market } & 18 & 1.0 \\
\text { A } & 16 & 1.5 \\
\hline
\end{array}
$$

Breanna Ollech
Breanna Ollech
Numerade Educator
01:03

Problem 18

If the simple CAPM is valid, which of the situations in Problems 13–19 below are possible?
Explain. Consider each situation independently. $$
\begin{array}{lcc}
\hline \text { Portfolio } & \text { Expected Return } & \text { Beta } \\
\hline \text { Risk-free } & 10 \% & 0 \\
\text { Market } & 18 & 1.0 \\
\text { A } & 16 & 0.9 \\
\hline
\end{array}
$$

Breanna Ollech
Breanna Ollech
Numerade Educator

Problem 19

If the simple CAPM is valid, which of the situations in Problems 13–19 below are possible?
Explain. Consider each situation independently. $$
\begin{array}{lcc}
\hline \text { Portfolio } & \text { Expected Return } & \begin{array}{c}
\text { Standard } \\
\text { Deviation }
\end{array} \\
\hline \text { Risk-free } & 10 \% & 0 \% \\
\text { Market } & 18 & 24 \\
\text { A } & 16 & 22 \\
\hline
\end{array}
$$

Check back soon!

Problem 20

Go to Connect and link to Chapter 7 materials, where you will find a spread-
sheet with monthly returns for GM, Ford, and Toyota, the S&P 500, and Treasury

bills.
a. Estimate the index model for each firm over the full five-year period. Compare the
betas of each firm.
b. Now estimate the betas for each firm using only the first two years of the sample and
then using only the last two years. How stable are the beta estimates obtained from
these shorter subperiods?

Check back soon!
02:17

Problem 21

A share of stock is now selling for $$ 100$. It will pay a dividend of $$ 9$ per share at the end of the year. Its beta is 1 . What do investors expect the stock to sell for at the end of the year?

Akash M
Akash M
Numerade Educator
01:50

Problem 22

I am buying a firm with an expected perpetual cash flow of $$ 1,0000$ but am unsure of its risk. If I think the beta of the firm is zero, when the beta is really 1 , how much more will I offer for the firm than it is truly worth?

Narayan Hari
Narayan Hari
Numerade Educator
01:03

Problem 23

A stock has an expected return of 6%. What is its beta?

Breanna Ollech
Breanna Ollech
Numerade Educator
01:31

Problem 24

Two investment advisers are comparing performance. One averaged a $19 \%$ return and the other a $16 \%$ return. However, the beta of the first adviser was 1.5 , while that of the second was 1.

a. Can you tell which adviser was a better selector of individual stocks (aside from the issue of general movements in the market)?
b. If the T-bill rate were $6 \%$ and the market return during the period were $14 \%$, which adviser would be the superior stock selector?

Breanna Ollech
Breanna Ollech
Numerade Educator
01:03

Problem 25

Suppose the yield on short-term government securities (perceived to be risk-free) is about $4 \%$. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is $12 \%$. According to the capital asset pricing model: $(2 O$ 7-2)
a. What is the expected return on the market portfolio?
b. What would be the expected return on a zero-beta stock?
c. Suppose you consider buying a share of stock at a price of $$ 40$. The stock is expected to pay a dividend of $3$ next year and to sell then for $41$. The stock risk has been evaluated at $\beta=-.5$. Is the stock overpriced or underpriced?

Breanna Ollech
Breanna Ollech
Numerade Educator
01:31

Problem 26

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios $A$ and $B$ are $11 \%$ and $14 \%$, respectively. The beta of $A$ is .8 while that of $B$ is 1.5 . The T-bill rate is currently $6 \%$, while the expected rate of return of the S&P 500 Index is $12 \%$. The standard deviation of portfolio $A$ is $10 \%$ annually, while that of $B$ is $31 \%$, and that of the index is $20 \%$. (LO 7-2)
a. If you currently hold a market-index portfolio, would you choose to add either of these portfolios to your holdings? Explain.
b. If instead you could invest only in bills and one of these portfolios, which would you choose?

Breanna Ollech
Breanna Ollech
Numerade Educator

Problem 27

Consider the following data for a one-factor economy. All portfolios are well diversified. $$
\begin{array}{lcl}
\hline \text { Portfolio } & E(r) & \text { Beta } \\
\hline \text { A } & 10 \% & 1.0 \\
\text { F } & 4 & 0 \\
\hline
\end{array}
$$ Suppose another portfolio $E$ is well diversified with a beta of $2 / 3$ and expected return of $9 \%$. Would an arbitrage opportunity exist? If so, what would the arbitrage strategy be? (LO 7-4)

Check back soon!
01:03

Problem 28

Assume both portfolios $A$ and $B$ are well diversified, that $E\left(r_A\right)=14 \%$ and $E\left(r_B\right)=14.8 \%$. If the economy has only one factor, and $\beta_A=1$ while $\beta_B=1.1$, what must be the risk-free rate?

Breanna Ollech
Breanna Ollech
Numerade Educator
01:12

Problem 29

Assume a market index represents the common factor and all stocks in the economy have a beta of 1. Firm-specific returns all have a standard deviation of $30 \%$.
Suppose an analyst studies 20 stocks and finds that one-half have an alpha of $3 \%$, and one-half have an alpha of $-3 %$. The analyst then buys $$ 1$ million of an equally weighted portfolio of the positive-alpha stocks and sells short $$ 1$ million of an equally weighted portfolio of the negative-alpha stocks. a. What is the expected profit (in dollars), and what is the standard deviation of the analyst's profit?

Dominador Tan
Dominador Tan
Numerade Educator
03:16

Problem 30

If the APT is to be a useful theory, the number of systematic factors in the economy must be small. Why?

Kaylee Mcclellan
Kaylee Mcclellan
Numerade Educator

Problem 31

The APT itself does not provide information on the factors that one might expect to determine risk premiums. How should researchers decide which factors to investigate? Is industrial production a reasonable factor to test for a risk premium? Why or why not?

Check back soon!
01:50

Problem 32

Suppose two factors are identified for the U.S. economy: the growth rate of industrial production, IP, and the inflation rate, IR. IP is expected to be $4 \%$ and IR $6 \%$. A stock with a beta of 1 on IP and .4 on IR currently is expected to provide a rate of return of $14 \%$. If industrial production actually grows by $5 \%$, while the inflation rate turns out to be $7 \%$, what is your best guess for the rate of return on the stock?
$(207-3)$

Narayan Hari
Narayan Hari
Numerade Educator

Problem 33

Suppose there are two independent economic factors, $M_1$ and $M_2$. The risk-free rate is $7 \%$, and all stocks have independent firm-specific components with a standard deviation of $50 \%$. Portfolios $A$ and $B$ are both well diversified. $$
\begin{array}{lccc}
\hline \text { Portfolio } & \text { Beta on } M_1 & \text { Beta on } M_2 & \text { Expected Return (\%) } \\
\hline A & 1.8 & 2.1 & 40 \\
B & 2.0 & 20.5 & 10 \\
\hline
\end{array}
$$

Check back soon!