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Investments

Zvi Bodie, Alex Kane, Alan J. Marcus

Chapter 9

The Capital Asset Pricing Model - all with Video Answers

Educators

Chapter Questions

Problem 1

What must be the beta of a portfolio with $E\left(r_P\right)=18 \%$, if $r_f=6 \%$ and $E\left(r_M\right)=14 \%$ ?

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02:17

Problem 2

The market price of a security is $$\$ 50$$. Its expected rate of return is $14 \%$. The risk-free rate is $6 \%$, and the market risk premium is $8.5 \%$. What will be the market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity.

Akash M
Akash M
Numerade Educator

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 beta of 75 by investing .75 of the imestment budget in T-bills and the remainder in the market portfolio.

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Problem 4

Here are data on two companies. The T-bill rate is $4 \%$ and the market risk premium is $6 \%$.
$$
\begin{array}{lcc}
\text { Company } & \$ 1 \text { Discount Store } & \text { Everything } \$ 5 \\
\hline \text { Forecasted return } & 12 \% & 11 \% \\
\text { Standard devation of returns } & 8 \% & 10 \% \\
\text { Beta } & 1.5 & 1.0
\end{array}
$$
What would be the fair return for each company according to the capital asset pricing model (CAPM)?

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Problem 5

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

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Problem 6

What is the expected rate of return for a stock that has a beta of 1.0 if the expected return on the market is $15 \%$ ?
a. $15 \%$.
b. More than $15 \%$.
c. Cannot be determined without the risk-free rate.

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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 the stock of Quinn, Inc.
c. The stock of Quinn, Inc., has more systematic risk than that of Kaskin, Inc.

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Problem 8

You are a consultant to a large manufacturing corporation that is considering a project with the following net after-tax cash flows (in millions of dollars):
$$
\begin{array}{cc}
\text { Years from Now } & \text { After-Tax Cash Flow } \\
\hline 0 & -40 \\
1-10 & 15
\end{array}
$$
The project's beta is 1.8 .
a. Assaming that $r_f=8 \%$ and $E\left(r_M\right)=16 \%$, what is the net present value of the project?
b. What is the highest possible beta estimate for the project before its NPV becomes negative?

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Problem 9

Consider the following table, which gives a security analyst's expected return on two stocks in two particular scenarios for the rate of return on the market:
$$
\begin{array}{ccc}
\text { Market Return } & \text { Aggressive Stock } & \text { Defensive Stock } \\
\hline 5 \% & -2 \% & 6 \% \\
25 & 38 & 12
\end{array}
$$
a. What are the betas of the two stocks?
b. What is the expected rate of return on each stock if the two scenarios for the market return are equally likely?
c. If the T-bill rate is $6 \%$ and the market return is equally likely to be $5 \%$ or $25 \%$, draw the SML. for this economy.
d. Plot the two securities on the SML graph. What is the alpha 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?

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Problem 10

If the simple CAPM is valid, which of the following situations are possible? Explain. Consider each situation independently.
$$
\begin{array}{ccc}
\text { Porffolio } & \text { Expected Retum } & \text { Beta } \\
\hline \text { A } & 20 \% & 1.4 \\
B & 25 \% & 1.2
\end{array}
$$

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Problem 11

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

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Problem 12

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

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Problem 13

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

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Problem 14

If the simple CAPM is valid, which of the following situations are possible? Explain. Consider each situation independently.
$$
\begin{array}{ccc}
\text { Portfolio } & \text { Expected Return } & \text { Beta } \\
\hline \text { Riskitree } & 10 \% & 0 \\
\text { Market } & 18 \% & 1.0 \\
\hline \text { A } & 16 \% & 15
\end{array}
$$

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Problem 15

If the simple CAPM is valid, which of the following situations are possible? Explain. Consider each situation independently.
$$
\begin{array}{ccc}
\text { Portfolio } & \text { Expected Return } & \text { Beta } \\
\hline \text { Risk-fiee } & 10 \% & 0 \\
\text { Market } & 18 \% & 1.0 \\
\text { A } & 16 \% & 09
\end{array}
$$

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Problem 16

If the simple CAPM is valid, which of the following situations are possible? Explain. Consider each situation independently.
$$
\begin{array}{ccc}
\text { Portfolio } & \text { Expected Retum } & \begin{array}{l}
\text { Stancard } \\
\text { Deviation }
\end{array} \\
\hline \text { Risk-ftee } & 10 \% & 0 \% \\
\text { Market } & 18 \% & 24 \% \\
\text { A } & 16 \% & 22 \%
\end{array}
$$

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Problem 17

A share of stock sells for $$\$ 50$$ today. It will pay a dividend of $$\$ 6$$ per share at the end of the year. Its beta is 1.2. What do investors expect the stock to sell for at the end of the year?

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Problem 18

I am buying a firm with an expected perpetual cash flow of $$\$ 1,000$$ but am unsure of its risk. If I think the beta of the firm is .5 , when in fact the beta is really 1 , how much more will 1 offer for the firm than it is truly worth?

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Problem 19

A stock has an expected rate of return of $4 \%$. What is its beta?

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01:31

Problem 20

Two investment advisers are comparing performance. One averaged a $19 \%$ rate of return and the other a $16 \%$ rate of return. However, the beta of the first investor was 1.5 , whereas that of the second investor was 1 .
a. Can you tell which investor was a better selector of individual stocks (aside from the issue of general movements in the market)?
b. If the T-bill rate was $6 \%$ and the market return during the period was $14 \%$, which investor would be considered the superior stock selector?
c. What if the T-bill rate was $3 \%$ and the market return was $15 \%$ ?

Breanna Ollech
Breanna Ollech
Numerade Educator

Problem 21

Suppose the rate of return on short-term government securities (perceived to be risk-free) is about $5 \%$. Suppose also that the expected rate of return required by the market for a portfolio with a beta of 1 is $12 \%$. According to the capital asset pricing model:
a. What is the expected rate of return on the market portfolio?
$b$. What would be the expected rate of return on a stock with $\beta=0$ ?
c. Suppose you consider buying a share of stock at $$\$ 40$$. The stock is expected to pay $$\$ 3$$ dividends next year and you expect it to sell then for $$\$41$$. The stock risk has been evaluated at $\beta=-.5$. Is the stock overpriced or underpriced?

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Problem 22

Suppose that borrowing is restricted so that the zero-beta version of the CAPM holds. The expected returm on the market portfolio is $17 \%$, and on the zero-beta portfolio it is $8 \%$. What is the expected return on a portfolio with a beta of .6 ?

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01:31

Problem 23

a. A mutual fund with beta of 8 has an expected rate of return of $14 \%$. If $r_f=5 \%$, and you expect the rate of return on the market portfolio to be $15 \%$, should you imvest in this fund? What is the fund's alpha?
b. What passive portfolio composed of a market-index portfolio and a money market account would have the same beta as the fund? Show that the difference between the expected rate of return on this passive portfolio and that of the fund equals the alpha from part (a).

Breanna Ollech
Breanna Ollech
Numerade Educator

Problem 24

Outline how you would incorporate the following into the CCAPM:
a. Liquidity.
b. Nontraded assets. (Do you have to worry about labor income?)

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