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CHAPTER 11
RISK AND RETURN: THE CAPITAL
ASSET PRICING MODEL (CAPM)
Answers to Concept Questions
1. Some of the risk in holding any asset is unique to the asset in question. By investing in a variety of
assets, this unique portion of the total risk can be eliminated at little cost. On the other hand, there are
2. If the market expected the growth rate in the coming year to be 2 percent, then there would be no
change in security prices if this expectation had been fully anticipated and priced. However, if the
market had been expecting a growth rate other than 2 percent and the expectation was incorporated
prices would rise if the anticipated growth rate had been less than 2 percent.
3. a. systematic
b. unsystematic
c. both; probably mostly systematic
f. systematic
4. a. a change in systematic risk has occurred; market prices in general will most likely decline.
b. no change in unsystematic risk; company price will most likely stay constant.
5. No to both questions. The portfolio expected return is a weighted average of the asset returns, so it
6. False. The variance of the individual assets is a measure of the total risk. The variance on a well-
7. Yes, the standard deviation can be less than that of every asset in the portfolio. However, p cannot be
8. Yes. It is possible, in theory, to construct a zero beta portfolio of risky assets whose return would be
equal to the risk-free rate. It is also possible to have a negative beta; the return would be less than the
diversification instrument.
9. Such layoffs generally occur in the context of corporate restructurings. To the extent that the market
10. Earnings contain information about recent sales and costs. This information is useful for projecting
future growth rates and cash flows. Thus, unexpectedly low earnings often lead market participants to
true for unexpectedly high earnings.
11. The covariance is a more appropriate measure of a security’s risk in a well-diversified portfolio
because the covariance reflects the effect of the security on the variance of the portfolio. Investors are
12. If we assume that the market has not stayed constant during the past three years, then the lack in
movement of Mid-South Electric’s stock price only indicates that the stock either has a standard
deviation or a beta that is very near to zero. The large amount of movement in Tech Flyer’s stock price
does not imply that the firm’s beta is high. Total volatility (the price fluctuation) is a function of both
Flyer is high.
13. The wide fluctuations in the price of oil stocks do not indicate that these stocks are a poor investment.
If an oil stock is purchased as part of a well-diversified portfolio, only its contribution to the risk of
the entire portfolio matters. This contribution is measured by systematic risk or beta. Since price
to a portfolio.
14. The statement is false. If a security has a negative beta, investors would want to hold the asset to reduce
the variability of their portfolios. Those assets will have expected returns that are lower than the risk-
free rate. To see this, examine the Capital Asset Pricing Model:
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this solutions
without rounding during any step in the problem.
Basic
1. The portfolio weight of an asset is the total investment in that asset divided by the total portfolio value.
First, we will find the portfolio value, which is:
Total value = $9,300
The portfolio weight for each stock is:
XB = .4892
2. The expected return of a portfolio is the sum of the weight of each asset times the expected return of
each asset. The total value of the portfolio is:
Total value = $3,850 + 6,100
E(Rp) = .1082, or 10.82%
3. The expected return of a portfolio is the sum of the weight of each asset times the expected return of
each asset. So, the expected return of the portfolio is:
4. Here we are given the expected return of the portfolio and the expected return of each asset in the
portfolio, and are asked to find the weight of each asset. We can use the equation for the expected
return of a portfolio to solve this problem. Since the total weight of a portfolio must equal 1 (100%),
the weight of Stock Y must be one minus the weight of Stock X. Mathematically speaking, this means:
E(Rp) = .109 = .124XX + .102(1 – XX)
We can now solve this equation for the weight of Stock X as:
.109 = .124XX + .102 – .102XX
So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or:
Investment in X = .3182($10,000)
And the dollar amount invested in Stock Y is:
Investment in Y = (1 – .3182)($10,000)
5. The expected return of an asset is the sum of each return times the probability of that return occurring.
So, the expected return of the asset is:
E(R) = .35(–.09) + .50(.15) + .15(.34)
6. The expected return of an asset is the sum of each return times the probability of that return occurring.
So, the expected return of each stock asset is:
E(RA) = .15(.01) + .50(.09) + .35(.13)
deviation of each stock are:
A2 =.15(.01 – .0920)2 + .50(.09 – .0920)2 + .35(.13 – .0920)2
7. The expected return of an asset is the sum of each return times the probability of that return occurring.
So, the expected return of the stock is:
by its probability, and then add all of these up. The result is the variance. So, the variance and standard
deviation of the stock are:
2 =.10(–.279 – .1012)2 + .20(–.128 – .1012)2 + .45(.141 – .1012)2 + .25(.365 – .1012)2
2 = .04307
8. The expected return of a portfolio is the sum of the weight of each asset times the expected return of
each asset. So, the expected return of the portfolio is:
E(Rp) = .25(.086) + .60(.108) + .15(.134)
If we own this portfolio, we would expect to get a return of 10.64 percent.
9. a. This portfolio does not have an equal weight in each asset. We first need to find the return of the
portfolio in each state of the economy. To do this, we will multiply the return of each asset by its
economy. Doing so, we get:
Boom: Rp = .35(.26) + .30(.40) + .35(.38) = .3440, or 34.40%
b. To calculate the standard deviation, we first need to calculate the variance. To find the variance,
we find the squared deviations from the expected return. We then multiply each possible squared
deviation by its probability, and then add all of these up. The result is the variance. So, the
variance and standard deviation of each stock are:
p2 = .15(.3440 – .0869)2 + .45(.1415 – .0869)2 + .35(–.0605 – .0869)2
10. The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. So, the beta
of the portfolio is:
p = .15(.74) + .20(1.27) + .30(1.09) + .35(1.38)
11. The beta of a portfolio is the sum of the weight of each asset times the beta of each asset. If the portfolio
is as risky as the market it must have the same beta as the market. Since the beta of the market is one,
we know the beta of our portfolio is one. We also need to remember that the beta of the risk-free asset
is zero. It has to be zero since the asset has no risk. Setting up the equation for the beta of our portfolio,
we get:
12. CAPM states the relationship between the risk of an asset and its expected return. CAPM is:
E(Ri) = Rf + [E(RM) – Rf] × i
Substituting the values we are given, we find:
13. We are given the values for the CAPM except for the of the stock. We need to substitute these values
into the CAPM, and solve for the of the stock. One important thing we need to realize is that we are
given the market risk premium. The market risk premium is the expected return of the market minus
14. Here we need to find the expected return of the market using the CAPM. Substituting the values given,
and solving for the expected return of the market, we find:
15. Here we need to find the risk-free rate using the CAPM. Substituting the values given, and solving for
the risk-free rate, we find:
Rf = .0302, or 3.02%
16. For a portfolio that is equally invested in large-company stocks and long-term bonds:
17. First, we need to find the of the portfolio. The of the risk-free asset is zero, and the weight of the
risk-free asset is one minus the weight of the stock, the of the portfolio is:
ßp = XW(1.20) + (1 – XW)(0) = 1.20XW
So, to find the of the portfolio for any weight of the stock, we multiply the weight of the stock times
100 .1090 1.200
125 .1303 1.500
150 .1515 1.800
18. There are two ways to correctly answer this question. We will work through both. First, we can use
the CAPM. Substituting in the values we are given for each stock, we find:
E(RY) = .043 + .076(1.20)
E(RY) = .1342, or 13.42%
The reward-to-risk ratio for Stock Z is too low, which means the stock plots below the SML, and the
stock is overvalued. Its price must decrease until its reward-to-risk ratio is equal to the market reward-
.10998 – .78Rf = .114 – 1.20Rf
Rf = .0096, or .96%
Intermediate
