<<

. 2
( 2)




Large-company stocks 13.0% 3.9% 9.1%
Small company stocks 17.3 3.9 13.4
Long-term corporate bonds 6.0 3.9 2.1
Long-term government bonds 5.7 3.9 1.8
U.S. Treasury bills 3.9 3.9 0.0
aReturn values obtained from Table 5.2.



Reviewing the risk premiums calculated above, we can see that the risk pre-
mium is highest for small-company stocks, followed by large-company stocks,
long-term corporate bonds, and long-term government bonds. This outcome
makes sense intuitively because small-company stocks are riskier than large-com-
pany stocks, which are riskier than long-term corporate bonds (equity is riskier
than debt investment). Long-term corporate bonds are riskier than long-term gov-
ernment bonds (because the government is less likely to renege on debt). And of


6. Although CAPM has been widely accepted, a broader theory, arbitrage pricing theory (APT), first described by
Stephen A. Ross, “The Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory (December 1976),
pp. 341“360, has received a great deal of attention in the financial literature. The theory suggests that the risk pre-
mium on securities may be better explained by a number of factors underlying and in place of the market return used
in CAPM. The CAPM in effect can be viewed as being derived from APT. Although testing of APT theory confirms
the importance of the market return, it has thus far failed to identify other risk factors clearly. As a result of this fail-
ure, as well as APT™s lack of practical acceptance and usage, we concentrate our attention here on CAPM.
211
CHAPTER 5 Risk and Return


course, U.S. Treasury bills, because of their lack of default risk and their very short
maturity, are virtually risk-free, as indicated by their lack of any risk premium.

Benjamin Corporation, a growing computer software developer, wishes to deter-
EXAMPLE
mine the required return on an asset Z, which has a beta of 1.5. The risk-free rate
of return is 7%; the return on the market portfolio of assets is 11%. Substituting
bz 1.5, RF 7%, and km 11% into the capital asset pricing model given in
Equation 5.7 yields a required return of
kz 7% [1.5 (11% 7%)] 7% 6% 13%

The market risk premium of 4% (11% 7%), when adjusted for the asset™s
index of risk (beta) of 1.5, results in a risk premium of 6% (1.5 4%). That risk
premium, when added to the 7% risk-free rate, results in a 13% required return.

Other things being equal, the higher the beta, the higher the required return,
and the lower the beta, the lower the required return.

The Graph: The Security Market Line (SML)
When the capital asset pricing model (Equation 5.7) is depicted graphically, it is
security market line (SML)
called the security market line (SML). The SML will, in fact, be a straight line. It
The depiction of the capital
asset pricing model (CAPM ) as a reflects the required return in the marketplace for each level of nondiversifiable
graph that reflects the required
risk (beta). In the graph, risk as measured by beta, b, is plotted on the x axis, and
return in the marketplace for
required returns, k, are plotted on the y axis. The risk“return tradeoff is clearly
each level of nondiversifiable
represented by the SML.
risk (beta).

In the preceding example for Benjamin Corporation, the risk-free rate, RF, was
EXAMPLE
7%, and the market return, km, was 11%. The SML can be plotted by using the
two sets of coordinates for the betas associated with RF and km, bRF and bm (that
is, bRF 0,7 RF 7%; and bm 1.0, km 11%). Figure 5.7 presents the resulting
security market line. As traditionally shown, the security market line in Figure
5.7 presents the required return associated with all positive betas. The market
risk premium of 4% (km of 11% RF of 7%) has been highlighted. For a beta for
asset Z, bz, of 1.5, its corresponding required return, kz, is 13%. Also shown in
the figure is asset Z™s risk premium of 6% (kz of 13% RF of 7%). It should be
clear that for assets with betas greater than 1, the risk premium is greater than
that for the market; for assets with betas less than 1, the risk premium is less than
that for the market.

Some Comments on CAPM
The capital asset pricing model generally relies on historical data. The betas may
or may not actually reflect the future variability of returns. Therefore, the
required returns specified by the model can be viewed only as rough approxima-
tions. Users of betas commonly make subjective adjustments to the historically
determined betas to reflect their expectations of the future.


7. Because RF is the rate of return on a risk-free asset, the beta associated with the risk-free asset, bRF, would equal 0.
The 0 beta on the risk-free asset reflects not only its absence of risk but also that the asset™s return is unaffected by
movements in the market return.
212 PART 2 Important Financial Concepts


FIGURE 5.7
17
Security Market Line
16
Security market line (SML)
SML
15
with Benjamin Corporation™s
14
asset Z data shown
kz = 13



Required Return, k (%)
12 Asset Z™s
km = 11 Risk
Market
10 Premium
Risk
9 (6%)
Premium
8 (4%)
RF = 7
6
5
4
3
2
1

0 .5 1.0 1.5 2.0
bR bz
bm
F

Nondiversifiable Risk, b




The CAPM was developed to explain the behavior of security prices and pro-
vide a mechanism whereby investors could assess the impact of a proposed secu-
rity investment on their portfolio™s overall risk and return. It is based on an
assumed efficient market with the following characteristics: many small investors,
efficient market
A market with the following all having the same information and expectations with respect to securities; no
characteristics: many small
restrictions on investment, no taxes, and no transaction costs; and rational
investors, all having the same
investors, who view securities similarly and are risk-averse, preferring higher
information and expectations
returns and lower risk.
with respect to securities; no
Although the perfect world of the efficient market appears to be unrealistic,
restrictions on investment, no
taxes, and no transaction costs; studies have provided support for the existence of the expectational relationship
and rational investors, who view
described by CAPM in active markets such as the New York Stock Exchange.8 In
securities similarly and are risk-
the case of real corporate assets, such as plant and equipment, research thus far
averse, preferring higher returns
has failed to prove the general applicability of CAPM because of indivisibility,
and lower risk.
relatively large size, limited number of transactions, and absence of an efficient
market for such assets.
Despite the limitations of CAPM, it provides a useful conceptual framework
for evaluating and linking risk and return. An awareness of this tradeoff and an
attempt to consider risk as well as return in financial decision making should help
financial managers achieve their goals.

8. A study by Eugene F. Fama and Kenneth R. French, “The Cross-Section of Expected Stock Returns,” Journal of
Finance 47 (June 1992), pp. 427“465, raised serious questions about the validity of CAPM. The study failed to find
a significant relationship between the historical betas and historical returns on over 2,000 stocks during 1963“1990.
In other words, it found that the magnitude of a stock™s historical beta had no relationship to the level of its histori-
cal return. Although Fama and French™s study continues to receive attention, CAPM has not been abandoned
because its rejection as a historical model fails to discredit its validity as an expectational model. Therefore, in spite
of this challenge, CAPM continues to be viewed as a logical and useful framework”both conceptually and opera-
tionally”for linking expected nondiversifiable risk and return.
213
CHAPTER 5 Risk and Return


Review Questions

5“11 How are total risk, nondiversifiable risk, and diversifiable risk related?
Why is nondiversifiable risk the only relevant risk?
5“12 What risk does beta measure? How can you find the beta of a portfolio?
5“13 Explain the meaning of each variable in the capital asset pricing model
(CAPM) equation. What is the security market line (SML)?
5“14 Why do financial managers have some difficulty applying CAPM in finan-
cial decision making? Generally, what benefit does CAPM provide them?




SUMMARY
FOCUS ON VALUE
A firm™s risk and expected return directly affect its share price. As we shall see in Chapter 7,
risk and return are the two key determinants of the firm™s value. It is therefore the financial
manager™s responsibility to assess carefully the risk and return of all major decisions in
order to make sure that the expected returns justify the level of risk being introduced.
The way the financial manager can expect to achieve the firm™s goal of increasing its
share price (and thereby benefiting its owners) is to take only those actions that earn returns
at least commensurate with their risk. Clearly, financial managers need to recognize, mea-
sure, and evaluate risk“return tradeoffs in order to ensure that their decisions contribute to
the creation of value for owners.



REVIEW OF LEARNING GOALS
of a portfolio, or collection, of assets. Sensitivity
Understand the meaning and fundamentals of
LG1
analysis and probability distributions can be used to
risk, return, and risk aversion. Risk is the
assess risk. Sensitivity analysis uses a number of
chance of loss or, more formally, the variability of
possible return estimates to assess the variability of
returns. A number of sources of firm-specific and
outcomes. Probability distributions, both bar charts
shareholder-specific risks exists. Return is any cash
and continuous distributions, provide a more quan-
distributions plus the change in value expressed as a
titative insight into an asset™s risk.
percentage of the initial value. Investment returns
vary both over time and between different types of
Discuss risk measurement for a single asset us-
investments. The equation for the rate of return is
LG3
ing the standard deviation and coefficient of
given in Table 5.12. Most financial managers are
variation. In addition to the range, which is the op-
risk-averse: They require higher expected returns as
timistic (best) outcome minus the pessimistic
compensation for taking greater risk.
(worst) outcome, the standard deviation and the co-
efficient of variation can be used to measure risk
Describe procedures for assessing and measur-
LG2
quantitatively. The standard deviation measures the
ing the risk of a single asset. The risk of a single
dispersion around an asset™s expected value, and the
asset is measured in much the same way as the risk
214 PART 2 Important Financial Concepts


TABLE 5.12 Summary of Key Definitions and Formulas for Risk and Return


Definitions of variables

bj beta coefficient or index of nondiversifiable risk for asset j
bp portfolio beta
Ct cash received from the asset investment in the time period t 1 to t
CV coefficient of variation
k expected value of a return
kj return for the jth outcome; return on asset j; required return on asset j
km market return; the return on the market portfolio of assets
kt actual, expected, or required rate of return during period t
n number of outcomes considered
Pt price (value) of asset at time t
Pt price (value) of asset at time t 1
1
Prj probability of occurrence of the jth outcome
RF risk-free rate of return
standard deviation of returns
k
wj proportion of total portfolio dollar value represented by asset j

Risk and return formulas

Coefficient of variation:
Rate of return during period t:

Ct Pt Pt k
1
CV [Eq. 5.4]
kt [Eq. 5.1]
k
Pt 1

Total security risk Nondiversifiable risk
Expected value of a return:
Diversifiable risk [Eq. 5.5]
for probabilistic data:

Portfolio beta:
n
k kj Prj [Eq. 5.2]
j1 n
bp wj bj [Eq. 5.6]
general formula: j1


Capital asset pricing model
n
kj
(CAPM):
j1
k n [Eq. 5.2a]
kj RF [bj (km RF)] [Eq. 5.7]
Standard deviation of return:
for probabilistic data:
n
k)2
(kj Prj [Eq. 5.3]
k
j1


general formula:
n
k)2
(kj
j1
[Eq. 5.3a]
k
n 1
215
CHAPTER 5 Risk and Return


coefficient of variation uses the standard deviation risk of both an individual security and a portfolio.
to measure dispersion on a relative basis. The key The total risk of a security consists of nondiversifi-
equations for the expected value of a return, the able and diversifiable risk. Nondiversifiable risk is
standard deviation of return, and the coefficient of the only relevant risk; diversifiable risk can be
variation are summarized in Table 5.12. eliminated through diversification. Nondiversifiable
risk is measured by the beta coefficient, which is a
Understand the risk and return characteristics relative measure of the relationship between an as-
LG4
of a portfolio in terms of correlation and diver- set™s return and the market return. Beta is derived
sification, and the impact of international assets on by finding the slope of the “characteristic line”
a portfolio. The financial manager™s goal is to create that best explains the historical relationship be-
an efficient portfolio that maximizes return for a tween the asset™s return and the market return. The
given level of risk or minimizes risk for a given level beta of a portfolio is a weighted average of the be-
of return. The risk of a portfolio of assets may be tas of the individual assets that it includes. The
reduced through diversification. New investments equations for total risk and the portfolio beta are
must be considered in light of their effect on the risk given in Table 5.12.
and return of the portfolio. Correlation, which is
the statistical relationship between asset returns, Explain the capital asset pricing model
LG6
affects the diversification process. The more nega- (CAPM), and its relationship to the security
tive (or less positive) the correlation between asset market line (SML). The capital asset pricing model
returns, the greater the risk-reducing benefits of (CAPM) uses beta to relate an asset™s risk relative to
diversification. International diversification can be the market to the asset™s required return. The equa-
used to reduce a portfolio™s risk further. With for- tion for CAPM is given in Table 5.12. The graphical
eign assets come the risk of currency fluctuation and depiction of CAPM is the security market line
political risks. (SML). Although it has some shortcomings, CAPM
provides a useful conceptual framework for evaluat-
Review the two types of risk and the deriva- ing and linking risk and return.
LG5
tion and role of beta in measuring the relevant




SELF-TEST PROBLEMS (Solutions in Appendix B)
ST 5“1 Portfolio analysis You have been asked for your advice in selecting a portfolio
LG3 LG4
of assets and have been given the following data:

Expected return
Year Asset A Asset B Asset C

2004 12% 16% 12%
2005 14 14 14
2006 16 12 16


No probabilities have been supplied. You have been told that you can create two
portfolios”one consisting of assets A and B and the other consisting of assets A
and C”by investing equal proportions (50%) in each of the two component
assets.
a. What is the expected return for each asset over the 3-year period?
b. What is the standard deviation for each asset™s return?
216 PART 2 Important Financial Concepts


c. What is the expected return for each of the two portfolios?
d. How would you characterize the correlations of returns of the two assets
making up each of the two portfolios identified in part c?
e. What is the standard deviation for each portfolio?
f. Which portfolio do you recommend? Why?

ST 5“2 Beta and CAPM Currently under consideration is a project with a beta, b, of
LG5 LG6
1.50. At this time, the risk-free rate of return, RF, is 7%, and the return on the
market portfolio of assets, km, is 10%. The project is actually expected to earn
an annual rate of return of 11%.
a. If the return on the market portfolio were to increase by 10%, what would
you expect to happen to the project™s required return? What if the market
return were to decline by 10%?
b. Use the capital asset pricing model (CAPM) to find the required return on
this investment.
c. On the basis of your calculation in part b, would you recommend this invest-
ment? Why or why not?
d. Assume that as a result of investors becoming less risk-averse, the market
return drops by 1% to 9%. What impact would this change have on your
responses in parts b and c?


PROBLEMS
5“1 Rate of return Douglas Keel, a financial analyst for Orange Industries, wishes to
LG1
estimate the rate of return for two similar-risk investments, X and Y. Keel™s
research indicates that the immediate past returns will serve as reasonable esti-
mates of future returns. A year earlier, investment X had a market value of
$20,000, investment Y of $55,000. During the year, investment X generated cash
flow of $1,500 and investment Y generated cash flow of $6,800. The current mar-
ket values of investments X and Y are $21,000 and $55,000, respectively.
a. Calculate the expected rate of return on investments X and Y using the most
recent year™s data.
b. Assuming that the two investments are equally risky, which one should Keel
recommend? Why?

5“2 Return calculations For each of the investments shown in the following table,
LG1
calculate the rate of return earned over the unspecified time period.

Cash flow Beginning-of- End-of-
Investment during period period value period value

A $ 100 $ 800 $ 1,100
B 15,000 120,000 118,000
C 7,000 45,000 48,000
D 80 600 500
E 1,500 12,500 12,400


5“3 Risk aversion Sharon Smith, the financial manager for Barnett Corporation,
LG1
wishes to evaluate three prospective investments: X, Y, and Z. Currently, the
217
CHAPTER 5 Risk and Return


firm earns 12% on its investments, which have a risk index of 6%. The three
investments under consideration are profiled in terms of expected return and
expected risk in the following table. If Sharon Smith is risk-averse, which invest-
ment, if any, will she select? Explain why.

Expected Expected
Investment return risk index

X 14% 7%
Y 12 8
Z 10 9




5“4 Risk analysis Solar Designs is considering an investment in an expanded prod-
LG2
uct line. Two possible types of expansion are being considered. After investigat-
ing the possible outcomes, the company made the estimates shown in the follow-
ing table

Expansion A Expansion B

Initial investment $12,000 $12,000
Annual rate of return
Pessimistic 16% 10%
Most likely 20% 20%
Optimistic 24% 30%


a. Determine the range of the rates of return for each of the two projects.
b. Which project is less risky? Why?
c. If you were making the investment decision, which one would you choose?
Why? What does this imply about your feelings toward risk?
d. Assume that expansion B™s most likely outcome is 21% per year and
that all other facts remain the same. Does this change your answer to part
c? Why?

5“5 Risk and probability Micro-Pub, Inc., is considering the purchase of one of
LG2
two microfilm cameras, R and S. Both should provide benefits over a 10-year
period, and each requires an initial investment of $4,000. Management has con-
structed the following table of estimates of rates of return and probabilities for
pessimistic, most likely, and optimistic results:

Camera R Camera S
Amount Probability Amount Probability

Initial investment $4,000 1.00 $4,000 1.00
Annual rate of return
Pessimistic 20% .25 15% .20
Most likely 25% .50 25% .55
Optimistic 30% .25 35% .25
218 PART 2 Important Financial Concepts


a. Determine the range for the rate of return for each of the two
cameras.
b. Determine the expected value of return for each camera.
c. Purchase of which camera is riskier? Why?

5“6 Bar charts and risk Swan™s Sportswear is considering bringing out a line of
LG2
designer jeans. Currently, it is negotiating with two different well-known design-
ers. Because of the highly competitive nature of the industry, the two lines of
jeans have been given code names. After market research, the firm has estab-
lished the expectations shown in the following table about the annual rates
of return


Annual rate of return
Market acceptance Probability Line J Line K

Very poor .05 .0075 .010
Poor .15 .0125 .025
Average .60 .0850 .080
Good .15 .1475 .135
Excellent .05 .1625 .150



Use the table to:
a. Construct a bar chart for each line™s annual rate of return.
b. Calculate the expected value of return for each line.
c. Evaluate the relative riskiness for each jean line™s rate of return using the bar
charts.

5“7 Coefficient of variation Metal Manufacturing has isolated four alternatives for
LG3
meeting its need for increased production capacity. The data gathered relative to
each of these alternatives is summarized in the following table.


Expected Standard
Alternative return deviation of return

A 20% 7.0%
B 22 9.5
C 19 6.0
D 16 5.5



a. Calculate the coefficient of variation for each alternative.
b. If the firm wishes to minimize risk, which alternative do you recommend?
Why?

5“8 Assessing return and risk Swift Manufacturing must choose between two asset
LG2 LG3
purchases. The annual rate of return and the related probabilities given in the
following table summarize the firm™s analysis to this point.
219
CHAPTER 5 Risk and Return


Project 257 Project 432
Rate of return Probability Rate of return Probability

10% .01 10% .05
10 .04 15 .10
20 .05 20 .10
30 .10 25 .15
40 .15 30 .20
45 .30 35 .15
50 .15 40 .10
60 .10 45 .10
70 .05 50 .05
80 .04
100 .01


a. For each project, compute:
(1) The range of possible rates of return.
(2) The expected value of return.
(3) The standard deviation of the returns.
(4) The coefficient of variation of the returns.
b. Construct a bar chart of each distribution of rates of return.
c. Which project would you consider less risky? Why?

5“9 Integrative”Expected return, standard deviation, and coefficient of variation
LG3
Three assets”F, G, and H”are currently being considered by Perth Industries.
The probability distributions of expected returns for these assets are shown in
the following table.

Asset F Asset G Asset H
j Prj Return, kj Prj Return, kj Prj Return, kj

1 .10 40% .40 35% .10 40%
2 .20 10 .30 10 .20 20
3 .40 0 .30 20 .40 10
4 .20 5 .20 0
5 .10 10 .10 20



a. Calculate the expected value of return, k , for each of the three assets. Which
provides the largest expected return?
b. Calculate the standard deviation, k, for each of the three assets™ returns.
Which appears to have the greatest risk?
c. Calculate the coefficient of variation, CV, for each of the three assets™
returns. Which appears to have the greatest relative risk?

5“10 Portfolio return and standard deviation Jamie Wong is considering building a
LG4
portfolio containing two assets, L and M. Asset L will represent 40% of the
dollar value of the portfolio, and asset M will account for the other 60%. The
220 PART 2 Important Financial Concepts


expected returns over the next 6 years, 2004“2009, for each of these assets, are
shown in the following table.


Expected return
Year Asset L Asset M

2004 14% 20%
2005 14 18
2006 16 16
2007 17 14
2008 17 12
2009 19 10



a. Calculate the expected portfolio return, kp, for each of the 6 years.
b. Calculate the expected value of portfolio returns, kp, over the 6-year period.
c. Calculate the standard deviation of expected portfolio returns, k , over the
p
6-year period.
d. How would you characterize the correlation of returns of the two assets L
and M?
e. Discuss any benefits of diversification achieved through creation of the
portfolio.

5“11 Portfolio analysis You have been given the return data shown in the first table
LG4
on three assets”F, G, and H”over the period 2004“2007.


Expected return
Year Asset F Asset G Asset H

2004 16% 17% 14%
2005 17 16 15
2006 18 15 16
2007 19 14 17



Using these assets, you have isolated the three investment alternatives shown in
the following table:


Alternative Investment

1 100% of asset F
2 50% of asset F and 50% of asset G
3 50% of asset F and 50% of asset H



a. Calculate the expected return over the 4-year period for each of the three
alternatives.
b. Calculate the standard deviation of returns over the 4-year period for each of
the three alternatives.
221
CHAPTER 5 Risk and Return


c. Use your findings in parts a and b to calculate the coefficient of variation for
each of the three alternatives.
d. On the basis of your findings, which of the three investment alternatives do
you recommend? Why?

5“12 Correlation, risk, and return Matt Peters wishes to evaluate the risk and return
LG4
behaviors associated with various combinations of assets V and W under three
assumed degrees of correlation: perfect positive, uncorrelated, and perfect nega-
tive. The expected return and risk values calculated for each of the assets are
shown in the following table.


Expected Risk (standard
Asset return, k deviation), k

V 8% 5%
W 13 10



a. If the returns of assets V and W are perfectly positively correlated (correla-
tion coefficient 1), describe the range of (1) expected return and (2) risk
associated with all possible portfolio combinations.
b. If the returns of assets V and W are uncorrelated (correlation coefficient 0),
describe the approximate range of (1) expected return and (2) risk associated
with all possible portfolio combinations.
c. If the returns of assets V and W are perfectly negatively correlated (correla-
tion coefficient 1), describe the range of (1) expected return and (2) risk
associated with all possible portfolio combinations.

5“13 Total, nondiversifiable, and diversifiable risk David Talbot randomly selected
LG5
securities from all those listed on the New York Stock Exchange for his portfo-
lio. He began with a single security and added securities one by one until a total
of 20 securities were held in the portfolio. After each security was added, David
calculated the portfolio standard deviation, k . The calculated values are shown
p
in the following table.


Number of Portfolio Number of Portfolio
securities risk, k securities risk, k
p p

1 14.50% 11 7.00%
2 13.30 12 6.80
3 12.20 13 6.70
4 11.20 14 6.65
5 10.30 15 6.60
6 9.50 16 6.56
7 8.80 17 6.52
8 8.20 18 6.50
9 7.70 19 6.48
10 7.30 20 6.47
222 PART 2 Important Financial Concepts


a. On a set of “number of securities in portfolio (x axis)“portfolio risk (y axis)”
axes, plot the portfolio risk data given in the preceding table.
b. Divide the total portfolio risk in the graph into its nondiversifiable and diver-
sifiable risk components and label each of these on the graph.
c. Describe which of the two risk components is the relevant risk, and
explain why it is relevant. How much of this risk exists in David Talbot™s
portfolio?

5“14 Graphical derivation of beta A firm wishes to estimate graphically the betas
LG5
for two assets, A and B. It has gathered the return data shown in the following
table for the market portfolio and for both assets over the last ten years,
1994“2003.


Actual return
Year Market portfolio Asset A Asset B

1994 6% 11% 16%
1995 2 8 11
1996 13 4 10
1997 4 3 3
1998 8 0 3
1999 16 19 30
2000 10 14 22
2001 15 18 29
2002 8 12 19
2003 13 17 26



a. On a set of “market return (x axis)“asset return (y axis)” axes, use the data
given to draw the characteristic line for asset A and for asset B.
b. Use the characteristic lines from part a to estimate the betas for assets A
and B.
c. Use the betas found in part b to comment on the relative risks of assets A
and B.

5“15 Interpreting beta A firm wishes to assess the impact of changes in the market
LG5
return on an asset that has a beta of 1.20.
a. If the market return increased by 15%, what impact would this change be
expected to have on the asset™s return?
b. If the market return decreased by 8%, what impact would this change be
expected to have on the asset™s return?
c. If the market return did not change, what impact, if any, would be expected
on the asset™s return?
d. Would this asset be considered more or less risky than the market?
Explain.

5“16 Betas Answer the following questions for assets A to D shown in the following
LG5
table.
223
CHAPTER 5 Risk and Return


Asset Beta

A .50
B 1.60
C .20
D .90



a. What impact would a 10% increase in the market return be expected to have
on each asset™s return?
b. What impact would a 10% decrease in the market return be expected to have
on each asset™s return?
c. If you were certain that the market return would increase in the near future,
which asset would you prefer? Why?
d. If you were certain that the market return would decrease in the near future,
which asset would you prefer? Why?

5“17 Betas and risk rankings Stock A has a beta of .80, stock B has a beta of 1.40,
LG5
and stock C has a beta of .30.
a. Rank these stocks from the most risky to the least risky.
b. If the return on the market portfolio increased by 12%, what change would
you expect in the return for each of the stocks?
c. If the return on the market portfolio decreased by 5%, what change would
you expect in the return for each of the stocks?
d. If you felt that the stock market was just ready to experience a significant
decline, which stock would you probably add to your portfolio? Why?
e. If you anticipated a major stock market rally, which stock would you add to
your portfolio? Why?

5“18 Portfolio betas Rose Berry is attempting to evaluate two possible portfolios,
LG5
which consist of the same five assets held in different proportions. She is particu-
larly interested in using beta to compare the risks of the portfolios, so she has
gathered the data shown in the following table.


Portfolio weights
Asset Asset beta Portfolio A Portfolio B

1 1.30 10% 30%
2 .70 30 10
3 1.25 10 20
4 1.10 10 20
5 .90 40 20
Totals 100% 100%



a. Calculate the betas for portfolios A and B.
b. Compare the risks of these portfolios to the market as well as to each other.
Which portfolio is more risky?
224 PART 2 Important Financial Concepts


5“19 Capital asset pricing model (CAPM) For each of the cases shown in
LG6
the following table, use the capital asset pricing model to find the required
return.


Risk-free Market
Case rate, RF return, km Beta, b

A 5% 8% 1.30
B 8 13 .90
C 9 12 .20
D 10 15 1.00
E 6 10 .60



5“20 Beta coefficients and the capital asset pricing model Katherine Wilson is won-
LG5 LG6
dering how much risk she must undertake in order to generate an acceptable
return on her portfolio. The risk-free return currently is 5%. The return on the
average stock (market return) is 16%. Use the CAPM to calculate the beta coef-
ficient associated with each of the following portfolio returns.
a. 10%
b. 15%
c. 18%
d. 20%
e. Katherine is risk-averse. What is the highest return she can expect if she is
unwilling to take more than an average risk?

5“21 Manipulating CAPM Use the basic equation for the capital asset pricing model
LG6
(CAPM) to work each of the following problems.
a. Find the required return for an asset with a beta of .90 when the risk-free rate
and market return are 8% and 12%, respectively.
b. Find the risk-free rate for a firm with a required return of 15% and a beta of
1.25 when the market return is 14%.
c. Find the market return for an asset with a required return of 16% and a beta
of 1.10 when the risk-free rate is 9%.
d. Find the beta for an asset with a required return of 15% when the risk-free
rate and market return are 10% and 12.5%, respectively.

5“22 Security market line, SML Assume that the risk-free rate, RF, is currently 9%
LG6
and that the market return, km, is currently 13%.
a. Draw the security market line (SML) on a set of “nondiversifiable risk
(x axis)“required return (y axis)” axes.
b. Calculate and label the market risk premium on the axes in part a.
c. Given the previous data, calculate the required return on asset A having a
beta of .80 and asset B having a beta of 1.30.
d. Draw in the betas and required returns from part c for assets A and B on the
axes in part a. Label the risk premium associated with each of these assets,
and discuss them.
225
CHAPTER 5 Risk and Return


5“23 Integrative”Risk, return, and CAPM Wolff Enterprises must consider several
LG6
investment projects, A through E, using the capital asset pricing model (CAPM)
and its graphical representation, the security market line (SML). Relevant infor-
mation is presented in the following table.


Item Rate of return Beta, b

Risk-free asset 9% 0
Market portfolio 14 1.00
Project A ” 1.50
Project B ” .75
Project C ” 2.00
Project D ” 0
Project E ” .50



a. Calculate the required rate of return and risk premium for each project, given
its level of nondiversifiable risk.
b. Use your findings in part a to draw the security market line (required return
relative to nondiversifiable risk).
c. Discuss the relative nondiversifiable risk of projects A through E.




CHAPTER 5 CASE Analyzing Risk and Return
on Chargers Products™ Investments

J unior Sayou, a financial analyst for Chargers Products, a manufacturer of sta-
dium benches, must evaluate the risk and return of two assets, X and Y. The
firm is considering adding these assets to its diversified asset portfolio. To assess
the return and risk of each asset, Junior gathered data on the annual cash flow
and beginning- and end-of-year values of each asset over the immediately pre-
ceding 10 years, 1994“2003. These data are summarized in the accompanying
table. Junior™s investigation suggests that both assets, on average, will tend to
perform in the future just as they have during the past 10 years. He therefore
believes that the expected annual return can be estimated by finding the average
annual return for each asset over the past 10 years.
Junior believes that each asset™s risk can be assessed in two ways: in isolation
and as part of the firm™s diversified portfolio of assets. The risk of the assets in
isolation can be found by using the standard deviation and coefficient of varia-
tion of returns over the past 10 years. The capital asset pricing model (CAPM)
can be used to assess the asset™s risk as part of the firm™s portfolio of assets.
Applying some sophisticated quantitative techniques, Junior estimated betas for
assets X and Y of 1.60 and 1.10, respectively. In addition, he found that the risk-
free rate is currently 7% and that the market return is 10%.
226 PART 2 Important Financial Concepts


Return Data for Assets X and Y, 1994“2003

Asset X Asset Y

Value Value

Year Cash flow Beginning Ending Cash flow Beginning Ending

1994 $1,000 $20,000 $22,000 $1,500 $20,000 $20,000
1995 1,500 22,000 21,000 1,600 20,000 20,000
1996 1,400 21,000 24,000 1,700 20,000 21,000
1997 1,700 24,000 22,000 1,800 21,000 21,000
1998 1,900 22,000 23,000 1,900 21,000 22,000
1999 1,600 23,000 26,000 2,000 22,000 23,000
2000 1,700 26,000 25,000 2,100 23,000 23,000
2001 2,000 25,000 24,000 2,200 23,000 24,000
2002 2,100 24,000 27,000 2,300 24,000 25,000
2003 2,200 27,000 30,000 2,400 25,000 25,000




Required
a. Calculate the annual rate of return for each asset in each of the 10 preceding
years, and use those values to find the average annual return for each asset
over the 10-year period.
b. Use the returns calculated in part a to find (1) the standard deviation and (2)
the coefficient of variation of the returns for each asset over the 10-year
period 1994“2003.
c. Use your findings in parts a and b to evaluate and discuss the return and risk
associated with each asset. Which asset appears to be preferable? Explain.
d. Use the CAPM to find the required return for each asset. Compare this value
with the average annual returns calculated in part a.
e. Compare and contrast your findings in parts c and d. What recommendations
would you give Junior with regard to investing in either of the two assets?
Explain to Junior why he is better off using beta rather than the standard
deviation and coefficient of variation to assess the risk of each asset.



WEB EXERCISE Go to the RiskGrades Web site, www.riskgrades.com. This site, from
WW RiskMetrics Group, provides another way to assess the riskiness of stocks and
W
mutual funds. RiskGrades provide a way to compare investment risk across all
asset classes, regions, and currencies. They vary over time to reflect asset-specific
information (such as the price of a stock reacting to an earnings release) and gen-
eral market conditions. RiskGrades operate differently from traditional risk mea-
sures, such as standard deviation and beta.

1. First, learn more about RiskGrades by clicking on RiskGrades Help Center
and reviewing the material. How are RiskGrades calculated? What differ-
227
CHAPTER 5 Risk and Return


ences can you identify when you compare them to standard deviation and
beta techniques? What are the advantages and disadvantages of this mea-
sure, in your opinion?

2. Get RiskGrades for the following stocks using the Get RiskGrade pull-down
menu at the site™s upper right corner. You can enter multiple symbols sepa-
rated by commas. Select all dates to get a historical view.


Company Symbol

Citigroup C
Intel INTC
Microsoft MSFT
Washington Mutual WM


What do the results tell you?

3. Select one of the foregoing stocks and find other stocks with similar risk
grades. Click on By RiskGrade to pull up a list.

4. How much risk can you tolerate? Use a hypothetical portfolio to find out.
Click on Grade Yourself, take a short quiz, and get your personal
RiskGrade measure. Did the results surprise you?




Remember to check the book™s Web site at
www.aw.com/gitman
for additional resources, including additional Web exercises.

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