AND RISK RATES OF RETURN
(Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard)
Please see the preface for information on the AACSB letter indicators (F, M, etc.) on the subject
lines.
Multiple Choice: True/False
(6.2) Standard deviation
1
.
FN
Answer: b
EASY
The tighter the probability distribution of its expected future returns, the
greater the risk of a given investment as measured by its standard deviation.
a. True
b. False
(6.2) Coefficient of variation
2
.
FN
Answer: a
EASY
The coefficient of variation, calculated as the standard deviation of
expected returns divided by the expected return, is a standardized measure of
the risk per unit of expected return.
a. True
b. False
(6.2) CV vs. SD
3
.
FN
Answer: b
EASY
The standard deviation is a better measure of risk than the coefficient of
variation if the expected returns of the securities being compared differ
significantly.
a. True
b. False
(6.2) Risk aversion
4
.
FN
Answer: a
EASY
Risk-averse investors require higher rates of return on investments whose
returns are highly uncertain, and most investors are risk averse.
a. True
b. False
(6.3) Portfolio risk
5
.
FN
Answer: a
EASY
When adding a randomly chosen new stock to an existing portfolio, the higher
(or more positive) the degree of correlation between the new stock and stocks
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publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 1
already in the portfolio, the less the additional stock will reduce the
portfolio's risk.
a. True
b. False
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publicly accessible website, in whole or in part.
Page 2 True/False
Chapter 6: Risk and Return
(6.3) Portfolio risk
6
.
FN
Answer: a
EASY
Diversification will normally reduce the riskiness of a portfolio of stocks.
a. True
b. False
(6.3) Portfolio risk
7
.
FN
Answer: a
EASY
In portfolio analysis, we often use ex post (historical) returns and standard
deviations, despite the fact that we are really interested in ex ante
(future) data.
a. True
b. False
(6.3) Portfolio return
8
.
FN
Answer: b
EASY
The realized return on a stock portfolio is the weighted average of the
expected returns on the stocks in the portfolio.
a. True
b. False
(6.3) Market risk
9
.
FN
Answer: a
EASY
Market risk refers to the tendency of a stock to move with the general stock
market. A stock with above-average market risk will tend to be more volatile
than an average stock, and its beta will be greater than 1.0.
a. True
b. False
(6.3) Market risk
10
.
FN
Answer: b
EASY
An individual stock's diversifiable risk, which is measured by its beta, can
be lowered by adding more stocks to the portfolio in which the stock is held.
a. True
b. False
(6.3) Risk and expected returns
11
.
FN
Answer: b
EASY
Managers should under no conditions take actions that increase their firm's
risk relative to the market, regardless of how much those actions would
increase the firm's expected rate of return.
a. True
b. False
(6.3) CAPM and risk
12
.
FN
Answer: a
EASY
One key conclusion of the Capital Asset Pricing Model is that the value of an
asset should be measured by considering both the risk and the expected return
of the asset, assuming that the asset is held in a well-diversified
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publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 3
portfolio.
CAPM.
The risk of the asset held in isolation is not relevant under the
a. True
b. False
(6.3) CAPM and risk
13
.
FN
Answer: a
EASY
According to the Capital Asset Pricing Model, investors are primarily
concerned with portfolio risk, not the risks of individual stocks held in
isolation. Thus, the relevant risk of a stock is the stock's contribution to
the riskiness of a well-diversified portfolio.
a. True
b. False
(6.5) SML and risk aversion
14
.
FN
Answer: b
EASY
If investors become less averse to risk, the slope of the Security Market
Line (SML) will increase.
a. True
b. False
(6.2) Variance
15
.
FN
Answer: a
MEDIUM
Variance is a measure of the variability of returns, and since it involves
squaring the deviation of each actual return from the expected return, it is
always larger than its square root, its standard deviation.
a. True
b. False
(6.2) Coefficient of variation
16
.
FN
Answer: a
MEDIUM
Because of differences in the expected returns on different investments, the
standard deviation is not always an adequate measure of risk. However, the
coefficient of variation adjusts for differences in expected returns and thus
allows investors to make better comparisons of investments' stand-alone risk.
a. True
b. False
(6.2) Risk aversion
17
.
FN
Answer: a
MEDIUM
"Risk aversion" implies that investors require higher expected returns on
riskier than on less risky securities.
a. True
b. False
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publicly accessible website, in whole or in part.
Page 4 True/False
Chapter 6: Risk and Return
(6.2) Risk aversion
18
.
FN
Answer: a
MEDIUM
If investors are risk averse and hold only one stock, we can conclude that
the required rate of return on a stock whose standard deviation is 0.21 will
be greater than the required return on a stock whose standard deviation is
0.10. However, if stocks are held in portfolios, it is possible that the
required return could be higher on the stock with the low standard deviation.
a. True
b. False
(6.2) Risk prem. and risk aversion
19
.
FN
Answer: a
MEDIUM
Someone who is risk averse has a general dislike for risk and a preference
for certainty. If risk aversion exists in the market, then investors in
general are willing to accept somewhat lower returns on less risky
securities. Different investors have different degrees of risk aversion, and
the end result is that investors with greater risk aversion tend to hold
securities with lower risk (and therefore a lower expected return) than
investors who have more tolerance for risk.
a. True
b. False
(6.3) Beta coefficient
20
.
FN
Answer: b
MEDIUM
A stock's beta measures its diversifiable risk relative to the diversifiable
risks of other firms.
a. True
b. False
(6.3) Beta coefficient
21
.
FN
Answer: b
MEDIUM
A stock's beta is more relevant as a measure of risk to an investor who holds
only one stock than to an investor who holds a well-diversified portfolio.
a. True
b. False
(6.3) Beta coefficient
22
.
FN
Answer: a
MEDIUM
If the returns of two firms are negatively correlated, then one of them must
have a negative beta.
a. True
b. False
(6.3) Beta coefficient
23
.
FN
Answer: b
MEDIUM
A stock with a beta equal to -1.0 has zero systematic (or market) risk.
a. True
b. False
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publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 5
(6.3) Beta coefficient
24
.
FN
Answer: a
MEDIUM
It is possible for a firm to have a positive beta, even if the correlation
between its returns and those of another firm is negative.
a. True
b. False
(6.3) Portfolio risk
25
.
FN
Answer: a
MEDIUM
Portfolio A has but one security, while Portfolio B has 100 securities.
Because of diversification effects, we would expect Portfolio B to have the
lower risk. However, it is possible for Portfolio A to be less risky.
a. True
b. False
(6.3) Portfolio risk
26
.
FN
Answer: b
MEDIUM
Portfolio A has but one stock, while Portfolio B consists of all stocks that
trade in the market, each held in proportion to its market value. Because of
its diversification, Portfolio B will by definition be riskless.
a. True
b. False
(6.3) Portfolio risk
27
.
FN
Answer: b
MEDIUM
A portfolio's risk is measured by the weighted average of the standard
deviations of the securities in the portfolio. It is this aspect of
portfolios that allows investors to combine stocks and thus reduce the
riskiness of their portfolios.
a. True
b. False
(6.3) Portfolio risk and return
28
.
FN
Answer: b
MEDIUM
The distributions of rates of return for Companies AA and BB are given below:
State of the
Economy
Boom
Normal
Recession
Probability of
This State Occurring
0.2
0.6
0.2
AA
30%
10%
-5%
BB
-10%
5%
50%
We can conclude from the above information that any rational, risk-averse
investor would be better off adding Security AA to a well-diversified
portfolio over Security BB.
a. True
b. False
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publicly accessible website, in whole or in part.
Page 6 True/False
Chapter 6: Risk and Return
(6.3) Cor. coefficient and risk
29
.
FN
Answer: b
MEDIUM
Even if the correlation between the returns on two securities is +1.0, if the
securities are combined in the correct proportions, the resulting 2-asset
portfolio will have less risk than either security held alone.
a. True
b. False
(6.3) Company-specific risk
30
.
FN
Answer: a
MEDIUM
Bad managerial judgments or unforeseen negative events that happen to a firm
are defined as "company-specific," or "unsystematic," events, and their
effects on investment risk can in theory be diversified away.
a. True
b. False
(6.3) Portfolio beta
31
.
FN
Answer: b
MEDIUM
We would generally find that the beta of a single security is more stable
over time than the beta of a diversified portfolio.
a. True
b. False
(6.3) Portfolio beta
32
.
FN
Answer: b
MEDIUM
We would almost always find that the beta of a diversified portfolio is less
stable over time than the beta of a single security.
a. True
b. False
(6.3) Diversification effects
33
.
FN
Answer: b
MEDIUM
If an investor buys enough stocks, he or she can, through diversification,
eliminate all of the market risk inherent in owning stocks, but as a general
rule it will not be possible to eliminate all diversifiable risk.
a. True
b. False
(6.3) CAPM
34
.
FN
Answer: b
MEDIUM
The CAPM is built on historic conditions, although in most cases we use
expected future data in applying it. Because betas used in the CAPM are
calculated using expected future data, they are not subject to changes in
future volatility. This is one of the strengths of the CAPM.
a. True
b. False
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publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 7
(6.5) Required return
35
.
FN
Answer: b
MEDIUM
Under the CAPM, the required rate of return on a firm's common stock is
determined only by the firm's market risk. If its market risk is known, and
if that risk is expected to remain constant, then analysts have all the
information they need to calculate the firm's required rate of return.
a. True
b. False
(6.5) Changes in beta
36
.
FN
Answer: a
MEDIUM
A firm can change its beta through managerial decisions, including capital
budgeting and capital structure decisions.
a. True
b. False
(6.5) Changes in beta
37
.
FN
Answer: a
MEDIUM
Any change in its beta is likely to affect the required rate of return on a
stock, which implies that a change in beta will likely have an impact on the
stock's price, other things held constant.
a. True
b. False
(6.5) SML
38
.
FN
Answer: b
MEDIUM
The slope of the SML is determined by the value of beta.
a. True
b. False
(6.5) SML
39
.
FN
Answer: a
The slope of the SML is determined by investors' aversion to risk.
greater the average investor's risk aversion, the steeper the SML.
MEDIUM
The
a. True
b. False
(6.5) SML
40
.
FN
Answer: a
MEDIUM
If you plotted the returns of a company against those of the market and found
that the slope of your line was negative, the CAPM would indicate that the
required rate of return on the stock should be less than the risk-free rate
for a well-diversified investor, assuming that the observed relationship is
expected to continue in the future.
a. True
b. False
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publicly accessible website, in whole or in part.
Page 8 True/False
Chapter 6: Risk and Return
(6.5) SML
41
.
FN
Answer: b
MEDIUM
If you plotted the returns on a given stock against those of the market, and
if you found that the slope of the regression line was negative, the CAPM
would indicate that the required rate of return on the stock should be
greater than the risk-free rate for a well-diversified investor, assuming
that the observed relationship is expected to continue into the future.
a. True
b. False
(6.5) SML
42
.
FN
Answer: a
MEDIUM
The Y-axis intercept of the SML represents the required return of a portfolio
with a beta of zero, which is the risk-free rate.
a. True
b. False
(6.5) SML
43
.
FN
Answer: b
MEDIUM
The SML relates required returns to firms' systematic (or market) risk. The
slope and intercept of this line can be influenced by a manager's actions.
a. True
b. False
(6.5) SML
44
.
FN
Answer: b
MEDIUM
The Y-axis intercept of the SML indicates the required return on an
individual asset whenever the realized return on an average (b = 1) stock is
zero.
a. True
b. False
(6.5) CAPM and inflation
45
.
FN
Answer: a
MEDIUM
If the price of money (e.g., interest rates and equity capital costs)
increases due to an increase in anticipated inflation, the risk-free rate
will also increase. If there is no change in investors' risk aversion, then
the market risk premium (rM rRF) will remain constant. Also, if there is no
change in stocks' betas, then the required rate of return on each stock as
measured by the CAPM will increase by the same amount as the increase in
expected inflation.
a. True
b. False
(6.5) Market risk premium
46
.
FN
Answer: a
MEDIUM
Since the market return represents the expected return on an average stock,
the market return reflects a certain amount of risk. As a result, there
exists a market risk premium, which is the amount over and above the risk-
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publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 9
free rate, that is required to compensate stock investors for assuming an
average amount of risk.
a. True
b. False
(6.3) Beta coefficient
47
.
F NAnswer: a
HARD
Assume that two investors each hold a portfolio, and that portfolio is their
only asset. Investor A's portfolio has a beta of minus 2.0, while Investor
B's portfolio has a beta of plus 2.0. Assuming that the unsystematic risks
of the stocks in the two portfolios are the same, then the two investors face
the same amount of risk. However, the holders of either portfolio could
lower their risks, and by exactly the same amount, by adding some "normal"
stocks with beta = 1.0.
a. True
b. False
(6.3) CAPM
48
.
FN
Answer: b
HARD
The CAPM is a multi-period model that takes account of differences in
securities' maturities, and it can be used to determine the required rate of
return for any given level of systematic risk.
a. True
b. False
Multiple Choice: Conceptual
(6.2) Risk aversion
49
.
CN
Answer: c
MEDIUM
You have the following data on three stocks:
Stock Standard Deviation
A
20%
B
10%
C
12%
Beta
0.59
0.61
1.29
If you are a strict risk minimizer, you would choose Stock ____ if it is to
be held in isolation and Stock ____ if it is to be held as part of a welldiversified portfolio.
a.
b.
c.
d.
e.
A;
A;
B;
C;
C;
A.
B.
A.
A.
B.
(6.2) Risk measures
50
.
CN
Answer: d
MEDIUM
Which is the best measure of risk for a single asset held in isolation, and
which is the best measure for an asset held in a diversified portfolio?
a. Variance; correlation coefficient.
b. Standard deviation; correlation coefficient.
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publicly accessible website, in whole or in part.
Page 10
True/False
Chapter 6: Risk and Return
c. Beta; variance.
d. Coefficient of variation; beta.
e. Beta; beta.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 11
(6.2) Standard deviation
51
.
CN
Answer: c
MEDIUM
A highly risk-averse investor is considering adding one additional stock to a
3-stock portfolio, to form a 4-stock portfolio. The three stocks currently
held all have b = 1.0, and they are perfectly positively correlated with the
market. Potential new Stocks A and B both have expected returns of 15%, are
in equilibrium, and are equally correlated with the market, with r = 0.75.
However, Stock A's standard deviation of returns is 12% versus 8% for Stock
B. Which stock should this investor add to his or her portfolio, or does the
choice not matter?
a.
b.
c.
d.
Either A or B, i.e., the investor should be indifferent between the two.
Stock A.
Stock B.
Neither A nor B, as neither has a return sufficient to compensate for
risk.
e. Add A, since its beta must be lower.
(6.3) Beta coefficients
52
.
CN
Answer: c
MEDIUM
Which of the following is NOT a potential problem when estimating and using
betas, i.e., which statement is FALSE?
a. The fact that a security or project may not have a past history that can
be used as the basis for calculating beta.
b. Sometimes, during a period when the company is undergoing a change such as
toward more leverage or riskier assets, the calculated beta will be
drastically different from the "true" or "expected future" beta.
c. The beta of an "average stock," or "the market," can change over time,
sometimes drastically.
d. Sometimes the past data used to calculate beta do not reflect the likely
risk of the firm for the future because conditions have changed.
e. All of the statements above are true.
(6.3) Beta coefficients
53
.
CN
Answer: d
MEDIUM
Stock A's beta is 1.5 and Stock B's beta is 0.5. Which of the following
statements must be true about these securities? (Assume market equilibrium.)
a.
b.
c.
d.
e.
When held in
Stock B must
Stock A must
The expected
The expected
isolation, Stock A has more risk than Stock B.
be a more desirable addition to a portfolio than
be a more desirable addition to a portfolio than
return on Stock A should be greater than that on
return on Stock B should be greater than that on
A.
B.
B.
A.
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publicly accessible website, in whole or in part.
Page 12
True/False
Chapter 6: Risk and Return
(6.3) Beta coefficients
54
.
CN
Answer: c
MEDIUM
Which of the following statements is CORRECT?
a. The beta of a portfolio of stocks is always smaller than the betas of any
of the individual stocks.
b. If you found a stock with a zero historical beta and held it as the only
stock in your portfolio, you would by definition have a riskless
portfolio.
c. The beta coefficient of a stock is normally found by regressing past
returns on a stock against past market returns. One could also construct
a scatter diagram of returns on the stock versus those on the market,
estimate the slope of the line of best fit, and use it as beta. However,
this historical beta may differ from the beta that exists in the future.
d. The beta of a portfolio of stocks is always larger than the betas of any
of the individual stocks.
e. It is theoretically possible for a stock to have a beta of 1.0. If a
stock did have a beta of 1.0, then, at least in theory, its required rate
of return would be equal to the risk-free (default-free) rate of return,
rRF.
(6.3) Beta coefficients
55
.
CN
Answer: b
MEDIUM
Which of the following statements is CORRECT?
a. Collections Inc. is in the business of collecting past-due accounts for
other companies, i.e., it is a collection agency. Collections' revenues,
profits, and stock price tend to rise during recessions. This suggests
that Collections Inc.'s beta should be quite high, say 2.0, because it
does so much better than most other companies when the economy is weak.
b. Suppose the returns on two stocks are negatively correlated. One has a
beta of 1.2 as determined in a regression analysis using data for the last
5 years, while the other has a beta of -0.6. The returns on the stock
with the negative beta must have been negatively correlated with returns
on most other stocks during that 5-year period.
c. Suppose you are managing a stock portfolio, and you have information that
leads you to believe the stock market is likely to be very strong in the
immediate future. That is, you are convinced that the market is about to
rise sharply. You should sell your high-beta stocks and buy low-beta
stocks in order to take advantage of the expected market move.
d. You think that investor sentiment is about to change, and investors are
about to become more risk averse. This suggests that you should rebalance your portfolio to include more high-beta stocks.
e. If the market risk premium remains constant, but the risk-free rate
declines, then the required returns on low-beta stocks will rise while
those on high-beta stocks will decline.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 13
(6.3) Beta coefficients
56
.
CN
Answer: e
MEDIUM
Which of the following statements is CORRECT?
a. If a company with a high beta merges with a low-beta company, the best
estimate of the new merged company's beta is 1.0.
b. Logically, it is easier to estimate the betas associated with capital
budgeting projects than the betas associated with stocks, especially if
the projects are closely associated with research and development
activities.
c. The beta of an "average stock," which is also "the market beta," can
change over time, sometimes drastically.
d. If a newly issued stock does not have a past history that can be used for
calculating beta, then we should always estimate that its beta will turn
out to be 1.0. This is especially true if the company finances with more
debt than the average firm.
e. During a period when a company is undergoing a change such as increasing
its use of leverage or taking on riskier projects, the calculated
historical beta may be drastically different from the beta that will exist
in the future.
(6.3) Beta coefficients
57
.
CN
Answer: e
Stock A's beta is 1.5 and Stock B's beta is 0.5. Which of the following
statements must be true, assuming the CAPM is correct.
a. Stock A would be a more desirable addition to a portfolio then
b. In equilibrium, the expected return on Stock B will be greater
on Stock A.
c. When held in isolation, Stock A has more risk than Stock B.
d. Stock B would be a more desirable addition to a portfolio than
e. In equilibrium, the expected return on Stock A will be greater
on B.
(6.3) Beta coefficients
58
.
MEDIUM
CN
Answer: c
Stock B.
than that
A.
than that
MEDIUM
Stock X has a beta of 0.5 and Stock Y has a beta of 1.5. Which of the
following statements must be true, according to the CAPM?
a. If you invest $50,000 in Stock X and $50,000 in Stock Y, your 2-stock
portfolio would have a beta significantly lower than 1.0, provided the
returns on the two stocks are not perfectly correlated.
b. Stock Y's realized return during the coming year will be higher than Stock
X's return.
c. If the expected rate of inflation increases but the market risk premium is
unchanged, the required returns on the two stocks should increase by the
same amount.
d. Stock Y's return has a higher standard deviation than Stock X.
e. If the market risk premium declines, but the risk-free rate is unchanged,
Stock X will have a larger decline in its required return than will Stock
Y.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 14
True/False
Chapter 6: Risk and Return
(6.3) Beta coefficients
59
.
a.
b.
c.
d.
e.
bA
bA
bA
bA
bA
>
>
=
<
<
MEDIUM
Market
0.03
-0.05
0.01
-0.10
0.06
Stock A
0.16
0.20
0.18
0.25
0.14
Stock B
0.05
0.05
0.05
0.05
0.05
0; bB = 1.
+1; bB = 0.
0; bB = -1.
0; bB = 0.
-1; bB = 1.
(6.3) Portfolio risk
.
Answer: d
You have the following data on (1) the average annual returns of the market
for the past 5 years and (2) similar information on Stocks A and B. Which of
the possible answers best describes the historical betas for A and B?
Years
1
2
3
4
5
60
CN
CN
Answer: e
MEDIUM
Which of the following statements is CORRECT?
a. An investor can eliminate virtually all market risk if he or she holds a
very large and well diversified portfolio of stocks.
b. The higher the correlation between the stocks in a portfolio, the lower
the risk inherent in the portfolio.
c. It is impossible to have a situation where the market risk of a single
stock is less than that of a portfolio that includes the stock.
d. Once a portfolio has about 40 stocks, adding additional stocks will not
reduce its risk by even a small amount.
e. An investor can eliminate virtually all diversifiable risk if he or she
holds a very large, well diversified portfolio of stocks.
(6.3) Portfolio risk and beta
61
.
CN
Answer: c
MEDIUM
Which of the following statements is CORRECT?
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 15
a. If you add enough randomly selected stocks to a portfolio, you can
completely eliminate all of the market risk from the portfolio.
b. If you were restricted to investing in publicly traded common stocks, yet
you wanted to minimize the riskiness of your portfolio as measured by its
beta, then according to the CAPM theory you should invest an equal amount
of money in each stock in the market. That is, if there were 10,000
traded stocks in the world, the least risky possible portfolio would
include some shares of each one.
c. If you formed a portfolio that consisted of all stocks with betas less
than 1.0, which is about half of all stocks, the portfolio would itself
have a beta coefficient that is equal to the weighted average beta of the
stocks in the portfolio, and that portfolio would have less risk than a
portfolio that consisted of all stocks in the market.
d. Market risk can be eliminated by forming a large portfolio, and if some
Treasury bonds are held in the portfolio, the portfolio can be made to be
completely riskless.
e. A portfolio that consists of all stocks in the market would have a
required return that is equal to the riskless rate.
(6.3) Market risk
62
.
CN
Answer: c
MEDIUM
Inflation, recession, and high interest rates are economic events that are
best characterized as being
a.
b.
c.
d.
systematic risk factors that can be diversified away.
company-specific risk factors that can be diversified away.
among the factors that are responsible for market risk.
risks that are beyond the control of investors and thus should not be
considered by security analysts or portfolio managers.
e. irrelevant except to governmental authorities like the Federal Reserve.
(6.3) Risk and port. divers.
63
.
CN
Answer: e
MEDIUM
Which of the following statements is CORRECT?
a. A stock's beta is less relevant as
well-diversified portfolio than to
stock.
b. If an investor buys enough stocks,
eliminate all of the diversifiable
a measure of risk to an investor with a
an investor who holds only that one
he or she can, through diversification,
risk inherent in owning stocks.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 16
True/False
Chapter 6: Risk and Return
Therefore, if a portfolio contained all publicly traded stocks, it would
be essentially riskless.
c. The required return on a firm's common stock is, in theory, determined
solely by its market risk. If the market risk is known, and if that risk
is expected to remain constant, then no other information is required to
specify the firm's required return.
d. Portfolio diversification reduces the variability of returns (as measured
by the standard deviation) of each individual stock held in a portfolio.
e. A security's beta measures its non-diversifiable, or market, risk relative
to that of an average stock.
(6.3) Risk and port. divers.
64
.
CN
Answer: b
MEDIUM
Which of the following statements is CORRECT?
a. A large portfolio of randomly selected stocks will always have a standard
deviation of returns that is less than the standard deviation of a
portfolio with fewer stocks, regardless of how the stocks in the smaller
portfolio are selected.
b. Diversifiable risk can be reduced by forming a large portfolio, but
normally even highly-diversified portfolios are subject to market (or
systematic) risk.
c. A large portfolio of randomly selected stocks will have a standard
deviation of returns that is greater than the standard deviation of a 1stock portfolio if that one stock has a beta less than 1.0.
d. A large portfolio of stocks whose betas are greater than 1.0 will have
less market risk than a single stock with a beta = 0.8.
e. If you add enough randomly selected stocks to a portfolio, you can
completely eliminate all of the market risk from the portfolio.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 17
(6.3) Port. risk, return, and beta
65
.
CN
Answer: b
MEDIUM
Which of the following statements is CORRECT?
a. A two-stock portfolio will always have a lower standard deviation than a
one-stock portfolio.
b. A portfolio that consists of 40 stocks that are not highly correlated with
"the market" will probably be less risky than a portfolio of 40 stocks
that are highly correlated with the market, assuming the stocks all have
the same standard deviations.
c. A two-stock portfolio will always have a lower beta than a one-stock
portfolio.
d. If portfolios are formed by randomly selecting stocks, a 10-stock
portfolio will always have a lower beta than a one-stock portfolio.
e. A stock with an above-average standard deviation must also have an aboveaverage beta.
(6.3) Portfolio risk concepts
66
.
CN
Answer: d
MEDIUM
Consider the following information for three stocks, A, B, and C. The
stocks' returns are positively but not perfectly positively correlated with
one another, i.e., the correlations are all between 0 and 1.
Stock
A
B
C
Expected
Return
10%
10%
12%
Standard
Deviation
20%
10%
12%
Beta
1.0
1.0
1.4
Portfolio AB has half of its funds invested in Stock A and half in Stock B.
Portfolio ABC has one third of its funds invested in each of the three
stocks. The risk-free rate is 5%, and the market is in equilibrium, so
required returns equal expected returns. Which of the following statements
is CORRECT?
a. Portfolio AB has a standard deviation of 20%.
b. Portfolio AB's coefficient of variation is greater than 2.0.
c. Portfolio AB's required return is greater than the required return on
Stock A.
d. Portfolio ABC's expected return is 10.66667%.
e. Portfolio ABC has a standard deviation of 20%.
(6.3) Port. return, CAPM, and beta
67
.
CN
Answer: b
MEDIUM
Which of the following statements is CORRECT?
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 18
True/False
Chapter 6: Risk and Return
a. If the returns on two stocks are perfectly positively correlated (i.e.,
the correlation coefficient is +1.0) and these stocks have identical
standard deviations, an equally weighted portfolio of the two stocks will
have a standard deviation that is less than that of the individual stocks.
b. A portfolio with a large number of randomly selected stocks would have
more market risk than a single stock that has a beta of 0.5, assuming that
the stock's beta was correctly calculated and is stable.
c. If a stock has a negative beta, its expected return must be negative.
d. A portfolio with a large number of randomly selected stocks would have
less market risk than a single stock that has a beta of 0.5.
e. According to the CAPM, stocks with higher standard deviations of returns
must also have higher expected returns.
(6.3) Portfolio risk and return
68
.
CN
Answer: d
MEDIUM
For a portfolio of 40 randomly selected stocks, which of the following is
most likely to be true?
a. The riskiness of the portfolio is greater than the riskiness of each of
the stocks if each was held in isolation.
b. The riskiness of the portfolio is the same as the riskiness of each stock
if it was held in isolation.
c. The beta of the portfolio is less than the average of the betas of the
individual stocks.
d. The beta of the portfolio is equal to the average of the betas of the
individual stocks.
e. The beta of the portfolio is larger than the average of the betas of the
individual stocks.
(6.3) Portfolio risk and return
69
.
CN
(6.3) Portfolio risk and return
.
MEDIUM
Which of the following statements best describes what you should expect if
you randomly select stocks and add them to your portfolio?
a. Adding more such stocks will
diversifiable, risk.
b. Adding more such stocks will
return.
c. Adding more such stocks will
thus its systematic risk.
d. Adding more such stocks will
e. Adding more such stocks will
its unsystematic risk.
70
Answer: a
reduce the portfolio's unsystematic, or
increase the portfolio's expected rate of
reduce the portfolio's beta coefficient and
have no effect on the portfolio's risk.
reduce the portfolio's market risk but not
CN
Answer: b
MEDIUM
Bob has a $50,000 stock portfolio with a beta of 1.2, an expected return of
10.8%, and a standard deviation of 25%. Becky also has a $50,000 portfolio,
but it has a beta of 0.8, an expected return of 9.2%, and a standard
deviation that is also 25%. The correlation coefficient, r, between Bob's
and Becky's portfolios is zero. If Bob and Becky marry and combine their
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 19
portfolios, which of the following best describes their combined $100,000
portfolio?
a. The combined portfolio's expected return will be less than the simple
weighted average of the expected returns of the two individual portfolios,
10.0%.
b. The combined portfolio's beta will be equal to a simple weighted average
of the betas of the two individual portfolios, 1.0; its expected return
will be equal to a simple weighted average of the expected returns of the
two individual portfolios, 10.0%; and its standard deviation will be less
than the simple average of the two portfolios' standard deviations, 25%.
c. The combined portfolio's expected return will be greater than the simple
weighted average of the expected returns of the two individual portfolios,
10.0%.
d. The combined portfolio's standard deviation will be greater than the
simple average of the two portfolios' standard deviations, 25%.
e. The combined portfolio's standard deviation will be equal to a simple
average of the two portfolios' standard deviations, 25%.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 20
True/False
Chapter 6: Risk and Return
(6.3) Portfolio risk and return
71
.
MEDIUM
a standard deviation of 30%, and its expected return is
a standard deviation less than 30%, and its beta is
a beta equal to 1.6, and its expected return is 15%.
a beta greater than 1.6, and its expected return is
a standard deviation greater than 30% and a beta equal
(6.3) Portfolio risk and return
.
Answer: c
Your portfolio consists of $50,000 invested in Stock X and $50,000 invested
in Stock Y. Both stocks have an expected return of 15%, betas of 1.6, and
standard deviations of 30%. The returns of the two stocks are independent,
so the correlation coefficient between them, rXY, is zero. Which of the
following statements best describes the characteristics of your 2-stock
portfolio?
a. Your portfolio has
15%.
b. Your portfolio has
greater than 1.6.
c. Your portfolio has
d. Your portfolio has
greater than 15%.
e. Your portfolio has
to 1.6.
72
CN
CN
Answer: a
MEDIUM
Which of the following is most likely to occur as you add randomly selected
stocks to your portfolio, which currently consists of 3 average stocks?
a. The diversifiable risk of your portfolio will likely decline, but the
expected market risk should not change.
b. The expected return of your portfolio is likely to decline.
c. The diversifiable risk will remain the same, but the market risk will
likely decline.
d. Both the diversifiable risk and the market risk of your portfolio are
likely to decline.
e. The total risk of your portfolio should decline, and as a result, the
expected rate of return on the portfolio should also decline.
(6.3) Portfolio risk and return
73
.
CN
Answer: c
MEDIUM
Jane has a portfolio of 20 average stocks, and Dick has a portfolio of 2
average stocks. Assuming the market is in equilibrium, which of the
following statements is CORRECT?
a. Jane's portfolio will have less diversifiable risk and also less market
risk than Dick's portfolio.
b. The required return on Jane's portfolio will be lower than that on Dick's
portfolio because Jane's portfolio will have less total risk.
c. Dick's portfolio will have more diversifiable risk, the same market risk,
and thus more total risk than Jane's portfolio, but the required (and
expected) returns will be the same on both portfolios.
d. If the two portfolios have the same beta, their required returns will be
the same, but Jane's portfolio will have less market risk than Dick's.
e. The expected return on Jane's portfolio must be lower than the expected
return on Dick's portfolio because Jane is more diversified.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 21
(6.3) Portfolio risk and return
74
.
Portfolio
Portfolio
Portfolio
Portfolio
Portfolio
P
P
P
P
P
has
has
has
has
has
Portfolio
Portfolio
Portfolio
Portfolio
Portfolio
AC
AC
AB
AB
AC
has
has
has
has
has
Answer: e
MEDIUM
an expected return that is less than 10%.
an expected return that is greater than 25%.
a standard deviation that is greater than 25%.
a standard deviation that is equal to 25%.
a standard deviation that is less than 25%.
(6.3) Portfolio risk and return
.
CN
Stocks A, B, and C all have an expected return of 10% and a standard
deviation of 25%. Stocks A and B have returns that are independent of one
another, i.e., their correlation coefficient, r, equals zero. Stocks A and C
have returns that are negatively correlated with one another, i.e., r is less
than 0. Portfolio AB is a portfolio with half of its money invested in Stock
A and half in Stock B. Portfolio AC is a portfolio with half of its money
invested in Stock A and half invested in Stock C. Which of the following
statements is CORRECT?
a.
b.
c.
d.
e.
76
MEDIUM
a beta that is greater than 1.2.
a standard deviation that is greater than 25%.
an expected return that is less than 12%.
a standard deviation that is less than 25%.
a beta that is less than 1.2.
(6.3) Portfolio risk and return
.
Answer: d
Stocks A and B each have an expected return of 12%, a beta of 1.2, and a
standard deviation of 25%. The returns on the two stocks have a correlation
of 0.6. Portfolio P has 50% in Stock A and 50% in Stock B. Which of the
following statements is CORRECT?
a.
b.
c.
d.
e.
75
CN
CN
Answer: b
MEDIUM
Stocks A and B each have an expected return of 15%, a standard deviation of
20%, and a beta of 1.2. The returns on the two stocks have a correlation
coefficient of +0.6. You have a portfolio that consists of 50% A and 50% B.
Which of the following statements is CORRECT?
a.
b.
c.
d.
e.
The
The
The
The
The
portfolio's
portfolio's
portfolio's
portfolio's
portfolio's
beta is less than 1.2.
expected return is 15%.
standard deviation is greater than 20%.
beta is greater than 1.2.
standard deviation is 20%.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 22
True/False
Chapter 6: Risk and Return
(6.3) Portfolio risk and return
77
.
CN
P's expected return is greater than the expected return on Stock
P's
P's
P's
P's
expected
expected
expected
expected
return
return
return
return
(6.3) Portfolio risk and return
.
MEDIUM
Stock A has a beta of 0.8, Stock B has a beta of 1.0, and Stock C has a beta
of 1.2. Portfolio P has 1/3 of its value invested in each stock. Each stock
has a standard deviation of 25%, and their returns are independent of one
another, i.e., the correlation coefficients between each pair of stocks is
zero. Assuming the market is in equilibrium, which of the following
statements is CORRECT?
a. Portfolio
B.
b. Portfolio
c. Portfolio
d. Portfolio
e. Portfolio
C.
78
Answer: d
is
is
is
is
equal to the expected return on Stock A.
less than the expected return on Stock B.
equal to the expected return on Stock B.
greater than the expected return on Stock
CN
Answer: c
MEDIUM
In a portfolio of three randomly selected stocks, which of the following
could NOT be true, i.e., which statement is false?
a. The riskiness of the portfolio is less than the riskiness of each of the
stocks if they were held in isolation.
b. The riskiness of the portfolio is greater than the riskiness of one or two
of the stocks.
c. The beta of the portfolio is lower than the lowest of the three betas.
d. The beta of the portfolio is higher than the highest of the three betas.
e. None of the above statements is obviously false, because they all could be
true, but not necessarily at the same time.
(6.5) Port. risk & ret. relationships
79
.
CN
Answer: b
Stock A has a beta = 0.8, while Stock B has a beta = 1.6.
following statements is CORRECT?
MEDIUM
Which of the
a. Stock B's required return is double that of Stock A's.
b. If the marginal investor becomes more risk averse, the required return on
Stock B will increase by more than the required return on Stock A.
c. An equally weighted portfolio of Stocks A and B will have a beta lower
than 1.2.
d. If the marginal investor becomes more risk averse, the required return on
Stock A will increase by more than the required return on Stock B.
e. If the risk-free rate increases but the market risk premium remains
constant, the required return on Stock A will increase by more than that
on Stock B.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 23
(6.5) Port. risk & ret. relationships
80
.
CN
Answer: b
MEDIUM
Stock A has an expected return of 12%, a beta of 1.2, and a standard
deviation of 20%. Stock B also has a beta of 1.2, but its expected return is
10% and its standard deviation is 15%. Portfolio AB has $900,000 invested in
Stock A and $300,000 invested in Stock B. The correlation between the two
stocks' returns is zero (that is, rA,B = 0). Which of the following
statements is CORRECT?
a. Portfolio AB's standard deviation is 17.5%.
b. The stocks are not in equilibrium based on the CAPM; if A is valued
correctly, then B is overvalued.
c. The stocks are not in equilibrium based on the CAPM; if A is valued
correctly, then B is undervalued.
d. Portfolio AB's expected return is 11.0%.
e. Portfolio AB's beta is less than 1.2.
(6.5) Port. risk & ret. relationships
81
.
CN
Answer: e
MEDIUM
Stock X has a beta of 0.7 and Stock Y has a beta of 1.3. The standard
deviation of each stock's returns is 20%. The stocks' returns are
independent of each other, i.e., the correlation coefficient, r, between them
is zero. Portfolio P consists of 50% X and 50% Y. Given this information,
which of the following statements is CORRECT?
a. Portfolio P has a standard deviation of 20%.
b. The required return on Portfolio P is equal to the market risk premium (rM
rRF).
c. Portfolio P has a beta of 0.7.
d. Portfolio P has a beta of 1.0 and a required return that is equal to the
riskless rate, rRF.
e. Portfolio P has the same required return as the market (rM).
(6.5) Market risk premium
82
.
CN
Which of the following statements is CORRECT?
rate is a constant.)
Answer: d
MEDIUM
(Assume that the risk-free
a. If the market risk premium increases by 1%, then the required return will
increase for stocks that have a beta greater than 1.0, but it will
decrease for stocks that have a beta less than 1.0.
b. The effect of a change in the market risk premium depends on the slope of
the yield curve.
c. If the market risk premium increases by 1%, then the required return on
all stocks will rise by 1%.
d. If the market risk premium increases by 1%, then the required return will
increase by 1% for a stock that has a beta of 1.0.
e. The effect of a change in the market risk premium depends on the level of
the risk-free rate.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 24
True/False
Chapter 6: Risk and Return
(6.5) Risk & ret. relationships
83
.
CN
Answer: c
MEDIUM
Over the past 75 years, we have observed that investments with the highest
average annual returns also tend to have the highest standard deviations of
annual returns. This observation supports the notion that there is a
positive correlation between risk and return. Which of the following answers
correctly ranks investments from highest to lowest risk (and return), where
the security with the highest risk is shown first, the one with the lowest
risk last?
a. Small-company stocks, long-term corporate bonds, large-company stocks,
long-term government bonds, U.S. Treasury bills.
b. Large-company stocks, small-company stocks, long-term corporate bonds,
U.S. Treasury bills, long-term government bonds.
c. Small-company stocks, large-company stocks, long-term corporate bonds,
long-term government bonds, U.S. Treasury bills.
d. U.S. Treasury bills, long-term government bonds, long-term corporate
bonds, small-company stocks, large-company stocks.
e. Large-company stocks, small-company stocks, long-term corporate bonds,
long-term government bonds, U.S. Treasury bills.
(6.5) Required return
84
.
CN
Answer: c
MEDIUM
During the coming year, the market risk premium (rM rRF), is expected to
fall, while the risk-free rate, rRF, is expected to remain the same. Given
this forecast, which of the following statements is CORRECT?
a. The required return will increase for stocks with a beta less than 1.0 and
will decrease for stocks with a beta greater than 1.0.
b. The required return on all stocks will remain unchanged.
c. The required return will fall for all stocks, but it will fall more for
stocks with higher betas.
d. The required return for all stocks will fall by the same amount.
e. The required return will fall for all stocks, but it will fall less for
stocks with higher betas.
(6.5) CAPM
85
.
CN
Answer: c MEDIUM
The risk-free rate is 6%; Stock A has a beta of 1.0; Stock B has a beta of
2.0; and the market risk premium, rM rRF, is positive. Which of the
following statements is CORRECT?
a. If the risk-free rate increases but the market risk premium stays
unchanged, Stock B's required return will increase by more than Stock A's.
b. Stock B's required rate of return is twice that of Stock A.
c. If Stock A's required return is 11%, then the market risk premium is 5%.
d. If Stock B's required return is 11%, then the market risk premium is 5%.
e. If the risk-free rate remains constant but the market risk premium
increases, Stock A's required return will increase by more than Stock B's.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 25
(6.5) CAPM and required return
86
.
CN
Answer: b
MEDIUM
Assume that in recent years both expected inflation and the market risk
premium (rM rRF) have declined. Assume also that all stocks have positive
betas. Which of the following would be most likely to have occurred as a
result of these changes?
a. The required returns on all stocks have fallen, but the decline has been
greater for stocks with lower betas.
b. The required returns on all stocks have fallen, but the fall has been
greater for stocks with higher betas.
c. The average required return on the market, rM, has remained constant, but
the required returns have fallen for stocks that have betas greater than
1.0.
d. Required returns have increased for stocks with betas greater than 1.0 but
have declined for stocks with betas less than 1.0.
e. The required returns on all stocks have fallen by the same amount.
(6.5) CAPM and required return
87
.
CN
Assume that the risk-free rate is 5%.
CORRECT?
Answer: a
MEDIUM
Which of the following statements is
a. If a stock has a negative beta, its required return under the CAPM would
be less than 5%.
b. If a stock's beta doubled, its required return under the CAPM would also
double.
c. If a stock's beta doubled, its required return under the CAPM would more
than double.
d. If a stock's beta were 1.0, its required return under the CAPM would be
5%.
e. If a stock's beta were less than 1.0, its required return under the CAPM
would be less than 5%.
(6.5) CAPM and required return
88
.
CN
Answer: b
MEDIUM
Stock HB has a beta of 1.5 and Stock LB has a beta of 0.5. The market is in
equilibrium, with required returns equaling expected returns. Which of the
following statements is CORRECT?
a. If expected inflation remains constant but the market risk premium (rM
rRF) declines, the required return of Stock LB will decline but the
required return of Stock HB will increase.
b. If both expected inflation and the market risk premium (rM rRF) increase,
the required return on Stock HB will increase by more than that on Stock
LB.
c. If both expected inflation and the market risk premium (rM rRF) increase,
the required returns of both stocks will increase by the same amount.
d. Since the market is in equilibrium, the required returns of the two stocks
should be the same.
e. If expected inflation remains constant but the market risk premium (rM
rRF) declines, the required return of Stock HB will decline but the
required return of Stock LB will increase.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 26
True/False
Chapter 6: Risk and Return
(6.5) CAPM and required return
89
.
CN
Answer: b
MEDIUM
Stock A has a beta of 0.8, Stock B has a beta of 1.0, and Stock C has a beta
of 1.2. Portfolio P has equal amounts invested in each of the three stocks.
Each of the stocks has a standard deviation of 25%. The returns on the three
stocks are independent of one another (i.e., the correlation coefficients all
equal zero). Assume that there is an increase in the market risk premium,
but the risk-free rate remains unchanged. Which of the following statements
is CORRECT?
a. The required return of all stocks will remain unchanged since there was no
change in their betas.
b. The required return on Stock A will increase by less than the increase in
the market risk premium, while the required return on Stock C will
increase by more than the increase in the market risk premium.
c. The required return on the average stock will remain unchanged, but the
returns of riskier stocks (such as Stock C) will increase while the
returns of safer stocks (such as Stock A) will decrease.
d. The required returns on all three stocks will increase by the amount of
the increase in the market risk premium.
e. The required return on the average stock will remain unchanged, but the
returns on riskier stocks (such as Stock C) will decrease while the
returns on safer stocks (such as Stock A) will increase.
(6.5) CAPM and required return
90
.
CN
Answer: e
MEDIUM
Which of the following statements is CORRECT?
a. If a company's beta doubles, then its required rate of return will also
double.
b. Other things held constant, if investors suddenly become convinced that
there will be deflation in the economy, then the required returns on all
stocks should increase.
c. If a company's beta were cut in half, then its required rate of return
would also be halved.
d. If the risk-free rate rises by 0.5% but the market risk premium declines
by that same amount, then the required rates of return on stocks with
betas less than 1.0 will decline while returns on stocks with betas above
1.0 will increase.
e. If the risk-free rate rises by 0.5% but the market risk premium declines
by that same amount, then the required rate of return on an average stock
will remain unchanged, but required returns on stocks with betas less than
1.0 will rise.
(6.5) CAPM, beta, and req. return
CN
Answer: a
MEDIUM
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 27
91
.
Assume that the risk-free rate is 6% and the market risk premium is 5%.
Given this information, which of the following statements is CORRECT?
a.
b.
c.
d.
e.
An index fund with beta = 1.0 should have a required return of 11%.
If a stock has a negative beta, its required return must also be negative.
An index fund with beta = 1.0 should have a required return less than 11%.
If a stock's beta doubles, its required return must also double.
An index fund with beta = 1.0 should have a required return greater than
11%.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 28
True/False
Chapter 6: Risk and Return
(6.5) SML
92
.
CN
The slope of the security market line is equal to the market risk premium.
Lower beta stocks have higher required returns.
A stock's beta indicates diversifiable its risk.
Diversifiable risk cannot be completely diversified away.
Two securities with the same stand-alone risk must have the same betas.
(6.5) SML
.
MEDIUM
Which of the following statements is CORRECT?
a.
b.
c.
d.
e.
93
Answer: a
CN
Answer: e
MEDIUM
Which of the following statements is CORRECT?
a. Beta is measured by the slope of the security market line.
b. If the risk-free rate rises, then the market risk premium must also rise.
c. If a company's beta is halved, then its required return will also be
halved.
d. If a company's beta doubles, then its required return will also double.
e. The slope of the security market line is equal to the market risk premium,
(rM rRF).
(6.5) SML
94
.
CN
Answer: e
MEDIUM
Stock A has a beta of 1.2 and a standard deviation of 20%. Stock B has a
beta of 0.8 and a standard deviation of 25%. Portfolio P has $200,000
consisting of $100,000 invested in Stock A and $100,000 in Stock B. Which of
the following statements is CORRECT? (Assume that the stocks are in
equilibrium.)
a. Stock A's returns are less highly correlated with the returns on most
other stocks than are B's returns.
b. Stock B has a higher required rate of return than Stock A.
c. Portfolio P has a standard deviation of 22.5%.
d. More information is needed to determine the portfolio's beta.
e. Portfolio P has a beta of 1.0.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 29
(6.5) SML
95
.
CN
Answer: d
MEDIUM
Nile Food's stock has a beta of 1.4, while Elba Eateries' stock has a beta of
0.7. Assume that the risk-free rate, rRF, is 5.5% and the market risk
premium, (rM rRF), equals 4%. Which of the following statements is CORRECT?
a. If the risk-free rate increases but the market risk premium remains
unchanged, the required return will increase for both stocks but the
increase will be larger for Nile since it has a higher beta.
b. If the market risk premium increases but the risk-free rate remains
unchanged, Nile's required return will increase because it has a beta
greater than 1.0 but Elba's required return will decline because it has a
beta less than 1.0.
c. Since Nile's beta is twice that of Elba's, its required rate of return
will also be twice that of Elba's.
d. If the risk-free rate increases while the market risk premium remains
constant, then the required return on an average stock will increase.
e. If the market risk premium decreases but the risk-free rate remains
unchanged, Nile's required return will decrease because it has a beta
greater than 1.0 and Elba's will also decrease, but by more than Nile's
because it has a beta less than 1.0.
(6.5) SML
96
.
CN
Answer: d
Stock X has a beta of 0.6, while Stock Y has a beta of 1.4.
following statements is CORRECT?
MEDIUM
Which of the
a. A portfolio consisting of $50,000 invested in Stock X and $50,000 invested
in Stock Y will have a required return that exceeds that of the overall
market.
b. Stock Y must have a higher expected return and a higher standard deviation
than Stock X.
c. If expected inflation increases but the market risk premium is unchanged,
then the required return on both stocks will fall by the same amount.
d. If the market risk premium declines but expected inflation is unchanged,
the required return on both stocks will decrease, but the decrease will be
greater for Stock Y.
e. If expected inflation declines but the market risk premium is unchanged,
then the required return on both stocks will decrease but the decrease
will be greater for Stock Y.
(6.5) SML
97
.
CN
Answer: a
MEDIUM
Stock A has a beta of 0.8 and Stock B has a beta of 1.2. 50% of Portfolio P
is invested in Stock A and 50% is invested in Stock B. If the market risk
premium (rM rRF) were to increase but the risk-free rate (rRF) remained
constant, which of the following would occur?
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publicly accessible website, in whole or in part.
Page 30
True/False
Chapter 6: Risk and Return
a. The required return would increase for both stocks but the increase would
be greater for Stock B than for Stock A.
b. The required return would decrease by the same amount for both Stock A and
Stock B.
c. The required return would increase for Stock A but decrease for Stock B.
d. The required return on Portfolio P would remain unchanged.
e. The required return would increase for Stock B but decrease for Stock A.
(6.5) SML
98
.
CN
Answer: a
MEDIUM
Stock A has a beta of 0.7, whereas Stock B has a beta of 1.3. Portfolio P
has 50% invested in both A and B. Which of the following would occur if the
market risk premium increased by 1% but the risk-free rate remained constant?
a.
b.
c.
d.
The required return on Portfolio P would increase by 1%.
The required return on both stocks would increase by 1%.
The required return on Portfolio P would remain unchanged.
The required return on Stock A would increase by more than 1%, while the
return on Stock B would increase by less than 1%.
e. The required return for Stock A would fall, but the required return for
Stock B would increase.
(6.5) SML
99
.
CN
The
The
The
The
The
required return on a stock with beta = 1.0 will not change.
required return on a stock with beta > 1.0 will increase.
return on "the market" will remain constant.
return on "the market" will increase.
required return on a stock with beta < 1.0 will decline.
(6.5) SML
.
MEDIUM
Assume that the risk-free rate remains constant, but the market risk premium
declines. Which of the following is most likely to occur?
a.
b.
c.
d.
e.
100
Answer: e
CN
Answer: c
MEDIUM
Which of the following statements is CORRECT?
a. The slope of the SML is determined by the value of beta.
b. The SML shows the relationship between companies' required returns and
their diversifiable risks. The slope and intercept of this line cannot be
influenced by a firm's managers, but the position of the company on the
line can be influenced by its managers.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 31
c. Suppose you plotted the returns of a given stock against those of the
market, and you found that the slope of the regression line was negative.
The CAPM would indicate that the required rate of return on the stock
should be less than the risk-free rate for a well diversified investor,
assuming investors expect the observed relationship to continue on into
the future.
d. If investors become less risk averse, the slope of the Security Market
Line will increase.
e. If a company increases its use of debt, this is likely to cause the slope
of its SML to increase, indicating a higher required return on the stock.
(6.5) SML
101
.
CN
The y-axis intercept would decline, and the slope would increase.
The x-axis intercept would decline, and the slope would increase.
The y-axis intercept would increase, and the slope would decline.
The SML would be affected only if betas changed.
Both the y-axis intercept and the slope would increase, leading to higher
required returns.
(6.5) SML
.
MEDIUM
Other things held constant, if the expected inflation rate decreases and
investors also become more risk averse, the Security Market Line would be
affected as follows:
a.
b.
c.
d.
e.
102
Answer: a
CN
Answer: d
MEDIUM
Assume that the risk-free rate, rRF, increases but the market risk premium,
(rM rRF), declines with the net effect being that the overall required
return on the market, rM, remains constant. Which of the following
statements is CORRECT?
a. The required return of all stocks will increase by the amount of the
increase in the risk-free rate.
b. The required return will decline for stocks that have a beta less than 1.0
but will increase for stocks that have a beta greater than 1.0.
c. Since the overall return on the market stays constant, the required return
on each individual stock will also remain constant.
d. The required return will increase for stocks that have a beta less than
1.0 but decline for stocks that have a beta greater than 1.0.
e. The required return of all stocks will fall by the amount of the decline
in the market risk premium.
(6.5) SML
103
.
CN
Answer: d
MEDIUM
Assume that to cool off the economy and decrease expectations for inflation,
the Federal Reserve tightened the money supply, causing an increase in the
risk-free rate, rRF. Investors also became concerned that the Fed's actions
would lead to a recession, and that led to an increase in the market risk
premium, (rM - rRF). Under these conditions, with other things held constant,
which of the following statements is most correct?
a. The required return on all stocks would increase by the same amount.
b. The required return on all stocks would increase, but the increase would
be greatest for stocks with betas of less than 1.0.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 32
True/False
Chapter 6: Risk and Return
c. Stocks' required returns would change, but so would expected returns, and
the result would be no change in stocks' prices.
d. The prices of all stocks would decline, but the decline would be greatest
for high-beta stocks.
e. The prices of all stocks would increase, but the increase would be
greatest for high-beta stocks.
(6.5) SML, CAPM, and beta
104
.
CN
Answer: e
MEDIUM
Which of the following statements is CORRECT?
a. If a stock has a beta of to 1.0, its required rate of return will be
unaffected by changes in the market risk premium.
b. The slope of the Security Market Line is beta.
c. Any stock with a negative beta must in theory have a negative required
rate of return, provided rRF is positive.
d. If a stock's beta doubles, its required rate of return must also double.
e. If a stock's returns are negatively correlated with returns on most other
stocks, the stock's beta will be negative.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 33
(6.5) SML and risk aversion
105
.
CN
Answer: a
MEDIUM
Assume that investors have recently become more risk averse, so the market
risk premium has increased. Also, assume that the risk-free rate and
expected inflation have not changed. Which of the following is most likely
to occur?
a. The required rate of return for an average stock will increase by an
amount equal to the increase in the market risk premium.
b. The required rate of return will decline for stocks whose betas are less
than 1.0.
c. The required rate of return on the market, rM, will not change as a result
of these changes.
d. The required rate of return for each individual stock in the market will
increase by an amount equal to the increase in the market risk premium.
e. The required rate of return on a riskless bond will decline.
(6.5) SML, CAPM, and port. risk
106
.
CN
Answer: e
MEDIUM
Which of the following statements is CORRECT?
a. A graph of the SML as applied to individual stocks would show required
rates of return on the vertical axis and standard deviations of returns on
the horizontal axis.
b. The CAPM has been thoroughly tested, and the theory has been confirmed
beyond any reasonable doubt.
c. If two "normal" or "typical" stocks were combined to form a 2-stock
portfolio, the portfolio's expected return would be a weighted average of
the stocks' expected returns, but the portfolio's standard deviation would
probably be greater than the average of the stocks' standard deviations.
d. If investors become more risk averse, then (1) the slope of the SML would
increase and (2) the required rate of return on low-beta stocks would
increase by more than the required return on high-beta stocks.
e. An increase in expected inflation, combined with a constant real risk-free
rate and a constant market risk premium, would lead to identical increases
in the required returns on a riskless asset and on an average stock, other
things held constant.
(6.5) Market equilibrium
107
.
CN
Answer: a
MEDIUM
For markets to be in equilibrium, that is, for there to be no strong pressure
for prices to depart from their current levels,
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 34
True/False
Chapter 6: Risk and Return
a. The expected rate of return must be equal to the required rate of return;
that is, = r.
b. The past realized rate of return must be equal to the expected future rate
of return; that is, = .
c. The required rate of return must equal the past realized rate of return;
that is, r = .
d. All three of the above statements must hold for equilibrium to exist; that
is = r = .
e. None of the above statements is correct.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 35
(Comp.) Risk concepts
108
.
CN
Answer: d
MEDIUM
Which of the following statements is CORRECT?
a. When diversifiable risk has been diversified away, the inherent risk that
remains is market risk, which is constant for all stocks in the market.
b. Portfolio diversification reduces the variability of returns on an
individual stock.
c. Risk refers to the chance that some unfavorable event will occur, and a
probability distribution is completely described by a listing of the
likelihoods of unfavorable events.
d. The SML relates a stock's required return to its market risk. The slope
and intercept of this line cannot be controlled by the firms' managers,
but managers can influence their firms' positions on the line by such
actions as changing the firm's capital structure or the type of assets it
employs.
e. A stock with a beta of -1.0 has zero market risk if held in a 1-stock
portfolio.
(Comp.) Risk measures
109
.
CN
Answer: b
MEDIUM
You observe the following information regarding Companies X and Y:
Company X has a higher expected return than Company Y.
Company X has a lower standard deviation of returns than Company Y.
Company X has a higher beta than Company Y.
Given this information, which of the following statements is CORRECT?
a.
b.
c.
d.
e.
Company
Company
Company
Company
Company
X has more diversifiable risk than Company Y.
X has a lower coefficient of variation than Company Y.
X has less market risk than Company Y.
X's returns will be negative when Y's returns are positive.
X's stock is a better buy than Company Y's stock.
(6.3) Portfolio risk
110
.
CN
Answer: c
MEDIUM/HARD
Stocks A and B both have an expected return of 10% and a standard deviation
of returns of 25%. Stock A has a beta of 0.8 and Stock B has a beta of 1.2.
The correlation coefficient, r, between the two stocks is 0.6. Portfolio P
has 50% invested in Stock A and 50% invested in B. Which of the following
statements is CORRECT?
a. Portfolio P has a standard deviation of 25% and a beta of 1.0.
b. Based on the information we are given, and assuming those are the views of
the marginal investor, it is apparent that the two stocks are in
equilibrium.
c. Portfolio P has more market risk than Stock A but less market risk than B.
d. Stock A should have a higher expected return than Stock B as viewed by the
marginal investor.
e. Portfolio P has a coefficient of variation equal to 2.5.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Page 36
True/False
Chapter 6: Risk and Return
(6.5) Port. risk & ret. relationships
111
.
CN
Answer: d
HARD
The risk-free rate is 6% and the market risk premium is 5%. Your $1 million
portfolio consists of $700,000 invested in a stock that has a beta of 1.2 and
$300,000 invested in a stock that has a beta of 0.8. Which of the following
statements is CORRECT?
a. If the stock market is efficient, your portfolio's expected return should
equal the expected return on the market, which is 11%.
b. The required return on the market is 10%.
c. The portfolio's required return is less than 11%.
d. If the risk-free rate remains unchanged but the market risk premium
increases by 2%, your portfolio's required return will increase by more
than 2%.
e. If the market risk premium remains unchanged but expected inflation
increases by 2%, your portfolio's required return will increase by more
than 2%.
(6.5) Port. risk & ret. relationships
112
.
Stock A's
Since the
Stock B's
Portfolio
Portfolio
HARD
beta is 0.8333.
two stocks have zero correlation, Portfolio AB is riskless.
beta is 1.0000.
AB's required return is 11%.
AB's standard deviation is 25%.
(6.5) Port. risk & ret. relationships
.
Answer: a
Stock A has an expected return of 10% and a standard deviation of 20%. Stock
B has an expected return of 13% and a standard deviation of 30%. The riskfree rate is 5% and the market risk premium, rM rRF, is 6%. Assume that the
market is in equilibrium. Portfolio AB has 50% invested in Stock A and 50%
invested in Stock B. The returns of Stock A and Stock B are independent of
one another, i.e., the correlation coefficient between them is zero. Which
of the following statements is CORRECT?
a.
b.
c.
d.
e.
113
CN
CN
Answer: c
HARD
Stock A has a beta of 1.2 and a standard deviation of 25%. Stock B has a
beta of 1.4 and a standard deviation of 20%. Portfolio AB was created by
investing in a combination of Stocks A and B. Portfolio AB has a beta of
1.25 and a standard deviation of 18%. Which of the following statements is
CORRECT?
a.
b.
c.
d.
Stock A has more
Stock A has more
Portfolio AB has
Portfolio AB has
stocks.
e. Portfolio AB has
market risk than Portfolio AB.
market risk than Stock B but less stand-alone risk.
more money invested in Stock A than in Stock B.
the same amount of money invested in each of the two
more money invested in Stock B than in Stock A.
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a
publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
True/False
Page 37
(6.5) SML
114
.
CN
Answer: e
HARD
Which of the following statements is CORRECT?
a. If Mutual Fund A held equal amounts of 100 stocks, each of which had
a beta of 1.0, and Mutual Fund B held equal amounts of 10 stocks
with betas of 1.0, then the two mutual funds would both have betas
of 1.0. Thus, they would be equally risky from an investor's
standpoint, assuming the investor's only asset is one or the other
of the mutual funds.
b. If investors become more risk averse but rRF does not change, then
the required rate of return on high-beta stocks will rise and the
required return on low-beta stocks will decline, but the required
return on an average-risk stock will not change.
c. An investor who holds just one stock will generally be exposed to
more risk than an investor who holds a portfolio of stocks, assuming
the stocks are all equally risky. Since the holder of the 1-stock
portfolio is exposed to more risk, he or she can expect to earn a
higher rate of return to compensate for the greater risk.
d. There is no reason to think that the slope of the yield curve would
have any effect on the slope of the SML.
e. Assume that the required rate of return on the market, rM, is given
and fixed at 10%. If the yield curve were upward sloping, then the
Security Market Line (SML) would have a steeper slope if 1-year
Treasury securities were used as the risk-free rate than if 30-year
Treasury bonds were used for rRF.
Problems
Generally, the SML is used to find the required return, but on occasion the required return is
given and we must solve for one of the other variables. We warn our students before the test that
to answer a number of the questions they will have to transform the SML equation to solve for
beta, the market risk premium, the risk-free rate, or the market return.
(6.2) Expected return
115
.
CN
Answer: c
EASY
Maxwell Inc.'s stock has a 50% chance of producing a 25% return, a 30%
chance of producing a 10% return, and a 20% chance of producing a -28%
return. What is the firm's expected rate of return?
a.
b.
c.
d.
e.
9.41%
9.65%
9.90%
10.15%
10.40%
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to a publicly accessible website, in whole or in part.
Page 38
Problems
Chapter 6: Risk and Return
(6.2) Expected return
116
.
CN
Answer: a
EASY
0.67
0.73
0.81
0.89
0.98
(6.3) Portfolio beta
.
EASY
Levine Inc. is considering an investment that has an expected return of
15% and a standard deviation of 10%. What is the investment's
coefficient of variation?
a.
b.
c.
d.
e.
119
Answer: a
1.20
1.26
1.32
1.39
1.46
(6.2) Coefficient of variation
.
CN
Wei Inc. is considering a capital budgeting project that has an expected
return of 25% and a standard deviation of 30%. What is the project's
coefficient of variation?
a.
b.
c.
d.
e.
118
EASY
7.72%
8.12%
8.55%
9.00%
9.50%
(6.2) Coefficient of variation
.
Answer: d
Preston Inc.'s stock has a 25% chance of producing a 30% return, a 50%
chance of producing a 12% return, and a 25% chance of producing a -18%
return. What is the firm's expected rate of return?
a.
b.
c.
d.
e.
117
CN
CN
Answer: e
EASY
Bill Dukes has $100,000 invested in a 2-stock portfolio. $35,000 is
invested in Stock X and the remainder is invested in Stock Y. X's beta
is 1.50 and Ys beta is 0.70. What is the portfolio's beta?
a.
b.
c.
d.
e.
0.65
0.72
0.80
0.89
0.98
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
Problems
Page 39
(6.3) Portfolio beta
120
.
CN
Answer: a
EASY
Tom O'Brien has a 2-stock portfolio with a total value of $100,000.
$37,500 is invested in Stock A with a beta of 0.75 and the remainder is
invested in Stock B with a beta of 1.42. What is his portfolios beta?
a.
b.
c.
d.
e.
1.17
1.23
1.29
1.35
1.42
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Page 40
Problems
Chapter 6: Risk and Return
(6.3) Portfolio beta
121
.
10.64%;
11.20%;
11.76%;
12.35%;
12.97%;
CN
Answer: c
EASY
11.36%
11.65%
11.95%
12.25%
12.55%
(6.5) Market risk premium
.
EASY
Moerdyk Company's stock has a beta of 1.40, the risk-free rate is
4.25%, and the market risk premium is 5.50%. What is the firm's
required rate of return?
a.
b.
c.
d.
e.
124
Answer: d
10.29%
10.83%
11.40%
12.00%
12.60%
(6.5) CAPM: required rate of return
.
CN
Calculate the required rate of return for Climax Inc., assuming that
(1) investors expect a 4.0% rate of inflation in the future, (2) the
real risk-free rate is 3.0%, (3) the market risk premium is 5.0%, (4)
the firm has a beta of 1.00, and (5) its realized rate of return has
averaged 15.0% over the last 5 years.
a.
b.
c.
d.
e.
123
EASY
1.17
1.23
1.29
1.36
1.42
(6.5) CAPM: required rate of return
.
Answer: b
Assume that you hold a well-diversified portfolio that has an expected
return of 11.0% and a beta of 1.20. You are in the process of buying
1,000 shares of Omega Corp at $10 a share and adding it to your
portfolio. Omega has an expected return of 13.0% and a beta of 1.50.
The total value of your current portfolio is $90,000. What will the
expected return and beta on the portfolio be after the purchase of the
Omega stock?
a.
b.
c.
d.
e.
122
CN
CN
Answer: a
EASY
Desreumaux Inc's stock has an expected return of 12.25%, a beta of 1.25,
and is in equilibrium. If the risk-free rate is 5.00%, what is the
market risk premium?
a.
b.
c.
d.
e.
5.80%
5.95%
6.09%
6.25%
6.40%
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
Problems
Page 41
(6.2) Coefficient of variation
125
.
a.
b.
c.
d.
e.
MEDIUM
Probability
of State
Occurring
0.45
0.50
0.05
Stock's
Expected
Return
25%
15%
5%
0.2839
0.3069
0.3299
0.3547
0.3813
(6.3) Portfolio beta
.
Answer: b
Choudhary Corp believes the following probability distribution exists
for its stock. What is the coefficient of variation on the company's
stock?
State of
the Economy
Boom
Normal
Recession
126
CN
CN
Answer: b
MEDIUM
Jim Angel holds a $200,000 portfolio consisting of the following stocks:
Stock
A
B
C
D
Total
Investment
$ 50,000
50,000
50,000
50,000
$200,000
Beta
0.95
0.80
1.00
1.20
What is the portfolio's beta?
a.
b.
c.
d.
e.
0.938
0.988
1.037
1.089
1.143
(6.3) Portfolio beta
CN
Answer: b
MEDIUM
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Page 42
Problems
Chapter 6: Risk and Return
127
.
Kristina Raattama holds a $200,000 portfolio consisting of the following
stocks. The portfolio's beta is 0.875.
Stock
A
B
C
D
Total
Investment
$ 50,000
50,000
50,000
50,000
$200,000
Beta
0.50
0.80
1.00
1.20
If Kristina replaces Stock A with another stock, E, which has a beta of
1.50, what will the portfolio's new beta be?
a.
b.
c.
d.
e.
1.07
1.13
1.18
1.24
1.30
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
Problems
Page 43
(6.3) Portfolio beta
128
.
CN
Answer: b
MEDIUM
Mike Flannery holds the following portfolio:
Stock
A
B
C
D
Total
Investment
$150,000
50,000
100,000
75,000
$375,000
Beta
1.40
0.80
1.00
1.20
What is the portfolio's beta?
a.
b.
c.
d.
e.
1.06
1.17
1.29
1.42
1.56
(6.3) Portfolio beta
129
.
CN
Answer: d
MEDIUM
Bruce Niendorf holds the following portfolio:
Stock
A
B
C
D
Total
Investment
$150,000
50,000
100,000
75,000
$375,000
Beta
1.40
0.80
1.00
1.20
Bruce plans to sell Stock A and replace it with Stock E, which has a
beta of 0.75. By how much will the portfolio beta change?
a.
b.
c.
d.
e.
-0.190
-0.211
-0.234
-0.260
-0.286
(6.3) Portfolio beta
130
.
CN
Answer: e
MEDIUM
You hold a diversified $100,000 portfolio consisting of 20 stocks with
$5,000 invested in each. The portfolio's beta is 1.12. You plan to
sell a stock with b = 0.90 and use the proceeds to buy a new stock with
b = 1.80. What will the portfolio's new beta be?
a.
b.
c.
d.
e.
1.286
1.255
1.224
1.194
1.165
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Page 44
Problems
Chapter 6: Risk and Return
(6.5) CAPM: req. rate of return
131
.
CN
Answer: c
MEDIUM
8.76%
8.98%
9.21%
9.44%
9.68%
(6.5) CAPM: req. rate of return
.
MEDIUM
Stock A's stock has a beta of 1.30, and its required return is 12.00%.
Stock B's beta is 0.80. If the risk-free rate is 4.75%, what is the
required rate of return on B's stock? (Hint: First find the market
risk premium.)
a.
b.
c.
d.
e.
134
Answer: e
2.75%
2.89%
3.05%
3.21%
3.38%
(6.5) CAPM: req. rate of return
.
CN
Company A has a beta of 0.70, while Company B's beta is 1.20. The
required return on the stock market is 11.00%, and the risk-free rate
is 4.25%. What is the difference between A's and B's required rates of
return? (Hint: First find the market risk premium, then find the
required returns on the stocks.)
a.
b.
c.
d.
e.
133
MEDIUM
14.38%
14.74%
15.11%
15.49%
15.87%
(6.5) CAPM: req. rate of return
.
Answer: a
Mikkelson Corporation's stock had a required return of 11.75% last
year, when the risk-free rate was 5.50% and the market risk premium was
4.75%. Then an increase in investor risk aversion caused the market
risk premium to rise by 2%. The risk-free rate and the firm's beta
remain unchanged. What is the company's new required rate of return?
(Hint: First calculate the beta, then find the required return.)
a.
b.
c.
d.
e.
132
CN
CN
Answer: d
MEDIUM
Scheuer Enterprises has a beta of 1.10, the real risk-free rate is
2.00%, investors expect a 3.00% future inflation rate, and the market
risk premium is 4.70%. What is Scheuer's required rate of return?
a.
b.
c.
d.
e.
9.43%
9.67%
9.92%
10.17%
10.42%
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
Problems
Page 45
(6.5) CAPM: req. rate of return
135
.
Answer: b
MEDIUM
and an expected dividend growth
rate is 4.00%, and the T-bond rate
stock market during the past 4
the average annual future return on
SML, what is the firm's required
11.34%
11.63%
11.92%
12.22%
12.52%
(6.5) CAPM: req. rate of return
.
CN
Engler Equipment has a beta of 0.88
rate of 4.00% per year. The T-bill
is 5.25%. The annual return on the
years was 10.25%. Investors expect
the market to be 12.50%. Using the
rate of return?
a.
b.
c.
d.
e.
137
MEDIUM
13.51%
13.86%
14.21%
14.58%
14.95%
(6.5) CAPM: req. rate of return
.
Answer: e
Linke Motors has a beta of 1.30, the T-bill rate is 3.00%, and the Tbond rate is 6.5%. The annual return on the stock market during the
past 3 years was 15.00%, but investors expect the annual future stock
market return to be 13.00%. Based on the SML, what is the firm's
required return?
a.
b.
c.
d.
e.
136
CN
CN
Answer: e
MEDIUM
Consider the following information and then calculate the required rate
of return for the Global Investment Fund, which holds 4 stocks. The
markets required rate of return is 13.25%, the risk-free rate is
7.00%, and the Fund's assets are as follows:
Stock
A
B
C
D
a.
b.
c.
d.
e.
Investment
$200,000
$300,000
$500,000
$1,000,000
Beta
1.50
-0.50
1.25
0.75
9.58%
10.09%
10.62%
11.18%
11.77%
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Page 46
Problems
Chapter 6: Risk and Return
(6.5) CAPM: req. rate of return
138
.
CN
a.
b.
c.
d.
e.
Answer: a
MEDIUM
10.36%
10.62%
10.88%
11.15%
11.43%
(6.3) Portfolio beta
.
CN
Mulherin's stock has a beta of 1.23, its required return is 11.75%, and
the risk-free rate is 4.30%. What is the required rate of return on
the market? (Hint: First find the market risk premium.)
a.
b.
c.
d.
e.
140
1.00
10.20%
6.00%
30.00%
2.00%
14.00%
14.70%
15.44%
16.21%
17.02%
(6.5) Return on the market
.
MEDIUM
Data for Dana Industries is shown below. Now Dana acquires some risky
assets that cause its beta to increase by 30%. In addition, expected
inflation increases by 2.00%. What is the stock's new required rate of
return?
Initial beta
Initial required return (rs)
Market risk premium, RPM
Percentage increase in beta
Increase in inflation premium, IP
139
Answer: a
CN
Answer: c
MEDIUM/HARD
Suppose you hold a portfolio consisting of a $10,000 investment in each
of 8 different common stocks. The portfolios beta is 1.25. Now
suppose you decided to sell one of your stocks that has a beta of 1.00
and to use the proceeds to buy a replacement stock with a beta of 1.35.
What would the portfolios new beta be?
a.
b.
c.
d.
e.
1.17
1.23
1.29
1.36
1.43
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
Problems
Page 47
(6.2) Std. dev., historical returns
141
.
CN
a.
b.
c.
d.
e.
Return
21.00%
-12.50%
25.00%
20.08%
20.59%
21.11%
21.64%
22.18%
(6.2) Std. dev., prob. data
.
HARD
Returns for the Dayton Company over the last 3 years are shown below.
What's the standard deviation of the firm's returns? (Hint: This is a
sample, not a complete population, so the sample standard deviation
formula should be used.)
Year
2008
2007
2006
142
Answer: b
CN
Answer: b
HARD
Magee Inc.'s manager believes that economic conditions during the next
year will be strong, normal, or weak, and she thinks that the firm's
returns will have the probability distribution shown below. What's the
standard deviation of the estimated returns? (Hint: Use the formula
for the standard deviation of a population, not a sample.)
Economic
Conditions
Strong
Normal
Weak
a.
b.
c.
d.
e.
Prob.
30%
40%
30%
Return
32.0%
10.0%
-16.0%
17.69%
18.62%
19.55%
20.52%
21.55%
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Page 48
Problems
Chapter 6: Risk and Return
(6.3) Portfolio risk reduction
143
.
CN
Answer: d
Assume that your uncle holds just one stock, East Coast Bank (ECB),
which he thinks has very little risk. You agree that the stock is
relatively safe, but you want to demonstrate that his risk would be
even lower if he were more diversified. You obtain the following
returns data for West Coast Bank (WCB). Both banks have had less
variability than most other stocks over the past 5 years. Measured by
the standard deviation of returns, by how much would your uncle's risk
have been reduced if he had held a portfolio consisting of 60% in ECB
and the remainder in WCB? (Hint: Use the sample standard deviation
formula.)
Year
2004
2005
2006
2007
2008
ECB
40.00%
-10.00%
35.00%
-5.00%
15.00%
WCB
40.00%
15.00%
-5.00%
-10.00%
35.00%
Average return =
Standard deviation =
15.00%
22.64%
15.00%
22.64%
a.
b.
c.
d.
e.
3.29%
3.46%
3.65%
3.84%
4.03%
(6.3) Portfolio beta
144
.
HARD
CN
Answer: a
HARD
Assume that you manage a $10.00 million mutual fund that has a beta of
1.05 and a 9.50% required return. The risk-free rate is 4.20%. You
now receive another $5.00 million, which you invest in stocks with an
average beta of 0.65. What is the required rate of return on the new
portfolio? (Hint: You must first find the market risk premium, then
find the new portfolio beta.)
a.
b.
c.
d.
e.
8.83%
9.05%
9.27%
9.51%
9.74%
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
Problems
Page 49
(6.3) Portfolio beta
145
.
CN
Answer: b
HARD
A mutual fund manager has a $40 million portfolio with a beta of 1.00.
The risk-free rate is 4.25%, and the market risk premium is 6.00%. The
manager expects to receive an additional $60 million which she plans to
invest in additional stocks. After investing the additional funds, she
wants the funds required and expected return to be 13.00%. What must
the average beta of the new stocks be to achieve the target required
rate of return?
a.
b.
c.
d.
e.
1.68
1.76
1.85
1.94
2.04
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Page 50
Problems
Chapter 6: Risk and Return
(6.5) Port. beta and req. ret.
146
.
a.
b.
c.
d.
e.
HARD
Amount
$1,075,000
675,000
750,000
500,000
$3,000,000
Beta
1.20
0.50
1.40
0.75
10.56%
10.83%
11.11%
11.38%
11.67%
(6.5) CAPM: req. rate of return
.
Answer: c
Assume that you are the portfolio manager of the SF Fund, a $3 million
hedge fund that contains the following stocks. The required rate of
return on the market is 11.00% and the risk-free rate is 5.00%. What
rate of return should investors expect (and require) on this fund?
Stock
A
B
C
D
147
CN
CN
Answer: c
HARD
CCC Corp has a beta of 1.5 and is currently in equilibrium. The
required rate of return on the stock is 12.00% versus a required return
on an average stock of 10.00%. Now the required return on an average
stock increases by 30.0% (not percentage points). Neither betas nor
the risk-free rate change. What would CCC's new required return be?
a.
b.
c.
d.
e.
14.89%
15.68%
16.50%
17.33%
18.19%
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Chapter 6: Risk and Return
Problems
Page 51
ANSWERS AND SOLUTIONS
2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted
to a publicly accessible website, in whole or in part.
Page 52
Answers
Chapter 6: Risk and Return
1.
(6.2) Standard deviation
FN
Answer: b
EASY
2.
(6.2) Coefficient of variation
FN
Answer: a
EASY
3.
(6.2) CV vs. SD
FN
Answer: b
EASY
4.
(6.2) Risk aversion
FN
Answer: a
EASY
5.
(6.3) Portfolio risk
FN
Answer: a
EASY
6.
(6.3) Portfolio risk
FN
Answer: a
EASY
7.
(6.3) Portfolio risk
FN
Answer: a
EASY
8.
(6.3) Portfolio return
FN
Answer: b
EASY
9.
(6.3) Market risk
FN
Answer: a
EASY
1
10.
(6.3) Market risk
FN
Answer: b
EASY
1
11.
(6.3) Risk and expected returns
FN
Answer: b
EASY
1
12.
(6.3) CAPM and risk
FN
Answer: a
EASY
1
13.
(6.3) CAPM and risk
FN
Answer: a
EASY
1
14.
(6.5) SML and risk aversion
FN
Answer: b
EASY
1
15.
(6.2) Variance
FN
Answer: a
MEDIUM
1
16.
(6.2) Coefficient of variation
FN
Answer: a
MEDIUM
1
17.
(6.2) Risk aversion
FN
Answer: a
MEDIUM
1
18.
(6.2) Risk aversion
FN
Answer: a
MEDIUM
1
19.
(6.2) Risk prem. and risk aversion
FN
Answer: a
MEDIUM
2
20.
(6.3) Beta coefficient
FN
Answer: b
MEDIUM
21.
(6.3) Beta coefficient
FN
Answer: b
MEDIUM
2
22.
(6.3) Beta coefficient
FN
Answer: a
MEDIUM
2
23.
(6.3) Beta coefficient
FN
Answer: b
MEDIUM
2
24.
(6.3) Beta coefficient
FN
Answer: a
MEDIUM
2
25.
(6.3) Portfolio risk
FN
Answer: a
MEDIUM
2
26.
(6.3) Portfolio risk
FN
Answer: b
MEDIUM
2
27.
(6.3) Portfolio risk
FN
Answer: b
MEDIUM
2
28.
(6.3) Portfolio risk and return
FN
Answer: b
MEDIUM
The stocks have the same expected returns, but BB does badly in booms and well in recessions. Therefore, it
would do more to reduce risk.
2
29.
(6.3) Cor. coefficient and risk
FN
Answer: b
MEDIUM
3
30.
(6.3) Company-specific risk
FN
Answer: a
MEDIUM
3
31.
(6.3) Portfolio beta
FN
Answer: b
MEDIUM
3
32.
(6.3) Portfolio beta
FN
Answer: b
MEDIUM
3
33.
(6.3) Diversification effects
FN
Answer: b
MEDIUM
3
34.
(6.3) CAPM
FN
Answer: b
MEDIUM
3
35.
(6.5) Required return
FN
Answer: b
MEDIUM
3
36.
(6.5) Changes in beta
FN
Answer: a
MEDIUM
3
37.
(6.5) Changes in beta
FN
Answer: a
MEDIUM
3
38.
(6.5) SML
FN
Answer: b
MEDIUM
3
39.
(6.5) SML
FN
Answer: a
MEDIUM
40.
(6.5) SML
FN
Answer: a
MEDIUM
4
41.
(6.5) SML
FN
Answer: b
MEDIUM
4
42.
(6.5) SML
FN
Answer: a
MEDIUM
4
43.
(6.5) SML
FN
Answer: b
MEDIUM
The slope and intercept of the SML are determined by the market, generally not the actions of a single firm.
However, managers can influence their firms' beta, and thus their firms' required returns.
4
44.
(6.5) SML
FN
Answer: b
MEDIUM
4
45.
(6.5) CAPM and inflation
FN
Answer: a
MEDIUM
4
46.
(6.5) Market risk premium
FN
Answer: a
MEDIUM
4
47.
(6.3) Beta coefficient
F NAnswer: a
HARD
Both portfolios would be twice as risky as a portfolio of average stocks. Their risks would decline if they added b
= 1.0 stocks, as those stocks would move the portfolios' betas toward 1.0.
4
48.
(6.3) CAPM
FN
Answer: b
HARD
The CAPM is a single-period model, and it does not take account of securities' maturities.
4
49.
(6.2) Risk aversion
CN
Answer: c
MEDIUM
5
50.
(6.2) Risk measures
CN
Answer: d
MEDIUM
5
51.
(6.2) Standard deviation
CN
Answer: c
MEDIUM
With only 4 stocks in the portfolio, unsystematic risk matters, and B has less.
5
52.
(6.3) Beta coefficients
CN
Answer: c
MEDIUM
5
53.
(6.3) Beta coefficients
CN
Answer: d
MEDIUM
5
54.
(6.3) Beta coefficients
CN
Answer: c
MEDIUM
5
55.
(6.3) Beta coefficients
CN
Answer: b
MEDIUM
56.
(6.3) Beta coefficients
CN
Answer: e
MEDIUM
5
57.
(6.3) Beta coefficients
CN
Answer: e
MEDIUM
5
58.
(6.3) Beta coefficients
CN
Answer: c
MEDIUM
5
59.
(6.3) Beta coefficients
CN
Answer: d
MEDIUM
First, note that B's beta must be zero, so either b or d must be correct. Second, note that A's returns are highest
when the market's returns are negative and lowest when the market's returns are positive. This indicates that A's
beta is negative. Thus, d must be correct.
6
60.
(6.3) Portfolio risk
CN
Answer: e
MEDIUM
6
61.
(6.3) Portfolio risk and beta
CN
Answer: c
MEDIUM
6
62.
(6.3) Market risk
CN
Answer: c
MEDIUM
6
63.
(6.3) Risk and port. divers.
CN
Answer: e
MEDIUM
6
64.
(6.3) Risk and port. divers.
CN
Answer: b
MEDIUM
6
65.
(6.3) Port. risk, return, and beta
CN
Answer: b
MEDIUM
6
66.
(6.3) Portfolio risk concepts
CN
Answer: d
MEDIUM
6
67.
(6.3) Port. return, CAPM, and beta
CN
Answer: b
MEDIUM
6
68.
(6.3) Portfolio risk and return
CN
Answer: d
MEDIUM
6
69.
(6.3) Portfolio risk and return
CN
Answer: a
MEDIUM
7
70.
(6.3) Portfolio risk and return
CN
Answer: b
MEDIUM
7
71.
(6.3) Portfolio risk and return
CN
Answer: c
MEDIUM
7
72.
(6.3) Portfolio risk and return
CN
Answer: a
MEDIUM
7
73.
(6.3) Portfolio risk and return
CN
Answer: c
MEDIUM
74.
(6.3) Portfolio risk and return
CN
Answer: d
MEDIUM
7
75.
(6.3) Portfolio risk and return
CN
Answer: e
MEDIUM
7
76.
(6.3) Portfolio risk and return
CN
Answer: b
MEDIUM
7
77.
(6.3) Portfolio risk and return
CN
Answer: d
MEDIUM
7
78.
(6.3) Portfolio risk and return
CN
Answer: c
MEDIUM
7
79.
(6.5) Port. risk & ret. relationships C N
Answer: b
MEDIUM
8
80.
(6.5) Port. risk & ret. relationships C N
Answer: b
MEDIUM
8
81.
(6.5) Port. risk & ret. relationships C N
Answer: e
MEDIUM
8
82.
(6.5) Market risk premium
CN
Answer: d
MEDIUM
8
83.
(6.5) Risk & ret. relationships
CN
Answer: c
MEDIUM
8
84.
(6.5) Required return
CN
Answer: c
MEDIUM
8
85.
(6.5) CAPM
CN
Answer: c
MEDIUM
8
86.
(6.5) CAPM and required return
CN
Answer: b
MEDIUM
8
87.
(6.5) CAPM and required return
CN
Answer: a
MEDIUM
8
88.
(6.5) CAPM and required return
CN
Answer: b
MEDIUM
8
89.
(6.5) CAPM and required return
CN
Answer: b
MEDIUM
9
90.
(6.5) CAPM and required return
CN
Answer: e
MEDIUM
9
91.
(6.5) CAPM, beta, and req. return C N
Answer: a
MEDIUM
9
92.
(6.5) SML
CN
Answer: a
MEDIUM
9
93.
(6.5) SML
CN
Answer: e
MEDIUM
94.
(6.5) SML
CN
Answer: e
MEDIUM
9
95.
(6.5) SML
CN
Answer: d
MEDIUM
9
96.
(6.5) SML
CN
Answer: d
MEDIUM
9
97.
(6.5) SML
CN
Answer: a
MEDIUM
9
98.
(6.5) SML
CN
Answer: a
MEDIUM
9
99.
(6.5) SML
CN
Answer: e
MEDIUM
1
100.
(6.5) SML
CN
Answer: c
MEDIUM
1
101.
(6.5) SML
CN
Answer: a
MEDIUM
1
102.
(6.5) SML
CN
Answer: d
MEDIUM
1
103.
(6.5) SML
CN
Answer: d
MEDIUM
1
104.
(6.5) SML, CAPM, and beta
CN
Answer: e
MEDIUM
1
105.
(6.5) SML and risk aversion
CN
Answer: a
MEDIUM
1
106.
(6.5) SML, CAPM, and port. risk
CN
Answer: e
MEDIUM
1
107.
(6.5) Market equilibrium
CN
Answer: a
MEDIUM
1
108.
(Comp.) Risk concepts
CN
Answer: d
MEDIUM
1
109.
(Comp.) Risk measures
CN
Answer: b
MEDIUM
1
110.
(6.3) Portfolio risk
CN
1
111.
(6.5) Port. risk & ret. relationships C N
Answer: c
MEDIUM/HARD
Answer: d
HARD
d is correct. The portfolio's beta is 1.08. Therefore, if the market risk premium increases by 2.0% the
portfolio's required return will increase by 2.16%.
1
112.
(6.5) Port. risk & ret. relationships C N
Answer: a
HARD
a is correct. Stock A's required return is 10% = 5% + b(6%), so b = 5%/6% = 0.83333.
1
113.
(6.5) Port. risk & ret. relationships C N
Answer: c
HARD
c is correct. Beta P = %A(1.2) +%B(1.4) = 1.25. If 50% is in each stock, then we would have Beta P = 0.5(1.2) +
0.5(1.4) = 1.3. But beta P < 1.3, so more money must be invested in the low beta stock, A.
1
114.
(6.5) SML
CN
Answer: e
HARD
1
115.
(6.2) Expected return
CN
Answer: c
EASY
Answer: d
EASY
Answer: a
EASY
Answer: a
EASY
Answer: e
EASY
Conditions
Good
Average
Poor
1.00
1
116.
Prob.
Return
Return
25.0%
12.50%
10.0%
3.00%
-28.0%
-5.60%
9.90% = Expected return
(6.2) Expected return
Conditions
Good
Average
Poor
1
117.
Prob.
0.50
0.30
0.20
Prob.
0.25
0.50
0.25
1.00
CN
Prob.
Return
7.50%
6.00%
-4.50%
9.00% = Expected return
Return
30.0%
12.0%
-18.0%
(6.2) Coefficient of variation
CN
Expected return
Standard deviation
Coefficient of variation = Std dev/Expected return =
1
118.
(6.2) Coefficient of variation
25.0%
30.0%
1.20
CN
Expected return
Standard deviation
Coefficient of variation = Std dev/Expected return =
1
119.
(6.3) Portfolio beta
Company
X
Y
Investment
$35,000
$65,000
$100,000
15.0%
10.0%
0.67
CN
Weight
0.35
0.65
1.00
Beta
1.50
0.70
Weight
beta
0.53
0.46
0.98 = Portfolio beta
120.
(6.3) Portfolio beta
Company
Stock A
Stock B
1
121.
Investment
$37,500
$62,500
$100,000
CN
Port.
weight
0.375
0.625
1.00
(6.3) Portfolio beta
Answer: a
Weight
beta
0.28
0.89
1.17 = Portfolio beta
Beta
0.75
1.42
CN
Answer: b
Old portfolio return
Old portfolio beta
New stock return
New stock beta
% of portfolio in new stock = $ in New/($ in Old + $ in New) = $10,000/$100,000 =
New expected portfolio return = rp = 0.1 13% + 0.9 11% =
New expected portfolio beta = bp = 0.1 1.50 + 0.9 1.20 =
1
122.
(6.5) CAPM: req. rate of return
CN
1
124.
11.0%
1.20
13.0%
1.50
10%
11.20%
1.23
EASY
CN
Answer: c
EASY
CN
(6.5) CAPM: req. rate of return
Beta
Risk-free rate
Market risk premium
Required return
EASY
Answer: d
Answer: a
EASY
Real rate (r*):
IP:
RPM:
Beta:
Required return = rRF + b(RPM) = r* + IP + b(RPM) =
1
123.
EASY
3.00%
4.00%
5.00%
1.00
12.00%
1.40
4.25%
5.50%
11.95%
(6.5) Market risk premium
Use the SML to determine the market risk premium with the given data.
rs
12.25%
7.25%
5.80%
1
125.
= rRF + bStock RPM
= 5.00% + 1.25 RPM
= RPM 1.25
= RPM
(6.2) Coefficient of variation
CN
Answer: b
MEDIUM
This is a relatively technical problem. It should be used only if calculations are emphasized in class, or on a takehome exam where students have time to look up formulas.
Probability of
Return
Deviation
Squared
State Prob.
This state
0.45
0.50
0.05
Expected return =
1
126.
from Mean
6.00%
-4.00%
-14.00%
Sq. Dev.
0.1620%
0.0800%
0.0980%
0.3400% = Expected variance
= 5.83%
Coefficient of variation = /Expected return =
0.3069
(6.3) Portfolio beta
Stock
A
B
C
D
Total
1
127.
This state
25.00%
15.00%
5.00%
19.00%
Investment
$50,000
$50,000
$50,000
$50,000
$200,000
Deviation
0.36%
0.16%
1.96%
0.34%
CN
Percentage
25.00%
25.00%
25.00%
25.00%
100.00%
(6.3) Portfolio beta
Beta
0.95
0.80
1.00
1.20
Answer: b
Product
0.238
0.200
0.250
0.300
0.988 = Portfolio beta
CN
Original Portfolio
Stock Investment Percentage
Beta
Product
A
$50,000
25.00%
0.50
0.125
B
$50,000
25.00%
0.80
0.200
C
$50,000
25.00%
1.00
0.250
D
$50,000
25.00%
1.20
0.300
E
Total $200,000
100.00%
0.875
MEDIUM
Answer: b
MEDIUM
New Portfolio
Beta
Product
25.00%
0.80
25.00%
1.00
25.00%
1.20
25.00%
1.50
New Portfolio beta =
0.200
0.250
0.300
0.375
1.125
Percentage
Alternative solution: (bE bA)(%A) + bOld = 1.125
1
128.
(6.3) Portfolio beta
Stock
A
B
C
D
Total
1
129.
Investment
$150,000
$50,000
$100,000
$75,000
$375,000
CN
Percentage
40.00%
13.33%
26.67%
20.00%
100.00%
(6.3) Portfolio beta
Stock Investment Percentage
A
$150,000
40.00%
B
$50,000
13.33%
C
$100,000
26.67%
D
$75,000
20.00%
Total $375,000
100.00%
Beta
1.40
0.80
1.00
1.20
CN
Original
Beta
Product
1.400
0.560
0.800
0.107
1.000
0.267
1.200
0.240
Old b = 1.173
Change in beta = New Old = -0.260
Alternative solution: (bE bA) %A = -0.260
Answer: b
MEDIUM
Product
0.56
0.11
0.27
0.24
1.17 = Portfolio beta
Answer: d
New
Beta
Product
0.750
0.300
0.800
0.107
1.000
0.267
1.200
0.240
New b = 0.913
MEDIUM
130.
(6.3) Portfolio beta
% in each stock:
Old stock's beta:
New stock's beta:
Old port. beta:
CN
Answer: e
MEDIUM
CN
Answer: a
MEDIUM
Answer: e
MEDIUM
Answer: c
MEDIUM
Answer: d
MEDIUM
5%
0.90
1.80
1.12
New beta = (bNew bOld) %A + bOld = 1.165
1
131.
(6.5) CAPM: req. rate of return
Risk-free rate
Old market risk premium
Old required return
b = (Old return rRF)/Old RPM
New market risk premium
New required return = rRF + b(RPM) =
1
132.
(6.5) CAPM: req. rate of return
Beta: A
Beta: B
Market return
Risk-free rate
Market risk premium
Required return A = rRF + bA(RPM) =
Required return B = rRF + bB(RPM) =
Difference
1
133.
CN
1.30
0.80
12.00%
4.75%
5.58%
9.21%
(6.5) CAPM: req. rate of return
Real risk-free rate, r*
Expected inflation, IP
Market risk premium, RPM
Beta, b
Risk-free rate = r* + IP =
CN
0.70
1.20
11.00%
4.25%
6.75%
8.98%
12.35%
3.38%
(6.5) CAPM: req. rate of return
Beta: A
Beta: B
A's required return
Risk-free rate
RPM = (A's return rRF)/betaA =
B's required return = rRF + b(RPM) =
1
134.
5.50%
4.75%
11.75%
1.32
6.75%
14.38%
CN
2.00%
3.00%
4.70%
1.10
5.00%
Required return = rRF + b(RPM) =
1
135.
10.17%
(6.5) CAPM: req. rate of return
CN
Answer: e
MEDIUM
Use SML to determine the market risk premium. Note that rRF is based on T-bonds, not short-term T-bills.
rs = rRF + RPM
13.00% = 6.50% + RPM
6.50% = RPM
Use the SML to determine the firms required return using the RPM calculated above.
rs = rRF + RPM b
= 6.50% + 6.50% 1.30
= 14.95%
1
136.
(6.5) CAPM: req. rate of return
CN
Answer: b
MEDIUM
Use SML to determine the market risk premium. Note that rRF is based on T-bonds, not short-term Tbills. Also,
note that the dividend growth rate is not needed.
rs = rRF + RPM
12.50% = 5.25% + RPM
RPM = 7.25%
Use SML to determine the firms required return using RPM calculated above.
rs = rRF + RPM b
= 5.25% + 7.25% 0.88
= 11.63%
1
137.
(6.5) CAPM: req. rate of return
rM
rRF
CN
Answer: e
13.25%
7.00%
Find portfolio beta:
$200,000
$300,000
$500,000
$1,000,000
$2,000,000
Weight
0.100
0.150
0.250
0.500
1.000
Find RPM = rM rRF = 6.25%
rs = rRF + b(RPM) = 11.77%
Beta
1.50
-0.50
1.25
0.75
Product
0.1500
-0.0750
0.3125
0.3750
0.7625
= portfolio beta
MEDIUM
138.
(6.5) CAPM: req. rate of return
CN
Answer: a
Old beta
Old rs = rRF + b(RPM)
RPM
Percentage increase in beta
Increase in IP
Find new beta after increase =
Find old rRF: Old rs = rRF+ b(RPM): 10.2% = rRF + 1.0(6.0%): rRF = 10.2% 6.0% =
Find new rRF: Old rRF + increase in IP =
Find new rs = new rRF + new beta(RPM)
1
139.
(6.5) Return on the market
CN
Beta
Risk-free rate
Required return on stock
RPM = (rStock rRF)/beta
Required return on market = rRF + RPM =
1
140.
1.00
10.20%
6.00%
30.00%
2.00%
1.30
4.20%
6.20%
14.00%
Answer: a
MEDIUM
1.23
4.30%
11.75%
6.06%
10.36%
(6.3) Portfolio beta
CN
Number of stocks
Percent in each stock = 1/number of stocks =
Portfolio beta
Stock that's sold
Stock that's bought
Change in portfolio's beta = 0.125 (b2 b1) =
New portfolio beta
1
141.
MEDIUM
(6.2) Std. dev., historical returns
Answer: c
MEDIUM/HARD
8
12.500%
1.25
1.00
1.35
0.0438
1.29
CN
Answer: b
HARD
This is a relatively technical problem. It should be used only if calculations are emphasized in class or on a takehome exam where students have time to look up formulas or to use Excel or their calculator functions.
Year
2008
2007
2006
Expected return
SQRT = = 20.59%
Return
21.00%
-12.50%
25.00%
11.17%
Deviation
from Mean
9.83%
-23.67%
13.83%
20.59% with Excel
Squared
Deviation
0.97%
5.60%
1.91%
8.48%
4.24%
Sum sqd deviations
Sum/(N 1)
142.
(6.2) Std. dev., prob. data
CN
Answer: b
HARD
This is a relatively technical problem. It should be used only if calculations are emphasized in class, or on a
take-home exam where students have time to look up formulas or to use Excel or their calculator functions.
Economic
Conditions
Strong
Normal
Weak
Prob.
30%
40%
30%
100%
= Sqrt of variance
1
143.
Return
This state
32.0%
10.0%
-16.0%
8.8%
18.62%
(6.3) Portfolio risk reduction
Dev. from
Mean
23.20%
1.20%
-24.80%
Squared
Dev.
10.24%
0.01%
6.15%
Sqd. dev.
Prob
3.07%
0.01%
1.85%
Variance 4.92%
18.62% by Excel
CN
Answer: d
HARD
This is a relatively technical problem. It should be used only if calculations are emphasized in class or on a
take-home exam where students have time to look up formulas or to use Excel or their calculator functions.
% ECB:
60%
Year
2004
2005
2006
2007
2008
Average return =
Standard deviation =
ECB
40.00%
-10.00%
35.00%
-5.00%
15.00%
WCB
40.00%
15.00%
-5.00%
-10.00%
35.00%
15.00%
22.64%
15.00%
22.64%
Reduction in the SD vs. ECB's SD:
1
144.(6.3) Portfolio beta
CN
New portfolio:
Old portfolios beta
New stocks beta
New portfolio beta
New portfolio required return = rRF + New beta(RPM) =
(6.3) Portfolio beta
15.00%
18.80%
3.84%
Old funds (millions)
New funds (millions)
Total portfolio
Req'd return, old stocks
Risk-free rate
Market risk premium:
rP = rRF + b(RPM) >> 9.5% = 4.2% + 1.05(RPM)
RPM = (9.5% 4.2%)/1.05 = 5.05%
1
145.
Portfolio ECB/WCB
40.00%
0.00%
19.00%
-7.00%
23.00%
CN
Answer: a
$10.00
$5.00
$15.00
9.50%
4.20%
5.30%
HARD
% of New Port.
66.67%
33.33%
100.00%
1.05
0.65
0.9167
8.8270%
Answer: b
HARD
Old funds (millions)
New funds (millions)
Total new funds
$40.00
$60.00
$100.00
Beta on existing portfolio
Risk-free rate
Market risk premium
Desired required return
Required new bp
Required beta, new stocks
40.00%
60.00%
100.00%
1.00
4.25%
6.00%
13.00%
1.4583
1.76
13% = rRF + b(RPM); b = (13% rRF)/RPM
beta = (Return Risk-free)/RPM
Req. b = (Old$/Total$) Old b + (New$/Total$) New b
Beta on new stocks = (Req. b (Old$/Total$) Old b)/(New$/Total$)
1
146.
(6.5) Port. beta and req. ret.
Company
Stock A
Stock B
Stock C
Stock D
Amount
$1,075,000
675,000
750,000
500,000
$3,000,000
CN
Weight
0.358
0.225
0.250
0.167
1.000
Beta
1.20
0.50
1.40
0.75
Required market return
Risk free rate
Market risk premium = rMarket rRF =
Wt beta
0.43
0.11
0.35
0.13
bPortfolio = 1.02
HARD
Intermediate step
11.00%
5.00%
6.00%
Portfolio's required return = rRF + b(RPM) =
1
147.
Answer: c
11.11%
(6.5) CAPM: req. rate of return
This problem requires some algebra:
CCC's beta
CCC's initial required return
Percentage increase in required market return
Initial required return on the market
New required return on the market
Now for the algebra:
rStock = rRF + b(RPM) = rRF + 1.5(RPM)
rMarket = rRF + b(RPM) = rRF + 1.0(RPM)
Now insert known data and transpose:
CN
Answer: c
1.50
12.00%
30.0%
10.00%
13.00%
HARD
12% = rRF + 1.5(RPM) >> 12% rRF = 1.5(RPM)
10% = rRF + (RPM) >> 10% rRF = 1.0(RPM)
Now subtract the second equation from the first. rRF and one of the RPMs cancel, leaving: 2% = 0.5(RPM)
Now solve for RPM: RPM = 2%/0.5
4.00%
Now find the risk-free rate: rRF = Initial rMarket RPM = 10% 4% =
6.00%
New RPM = New required return on the market rRF
7.00%
Now find the new return on CCC = rRF + b(new RPM) =
16.50%