ńňđ. 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, â€śThe Arbitrage Theory of Capital Asset Pricing,â€ť Journal of Economic Theory (December 1976),

pp. 341â€“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 APTâ€™s lack of practical acceptance and usage, we concentrate our attention here on CAPM.

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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 assetâ€™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 riskâ€“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 Zâ€™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 assetâ€™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 Corporationâ€™s

14

asset Z data shown

kz = 13

Required Return, k (%)

12 Asset Zâ€™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 portfolioâ€™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, â€śThe Cross-Section of Expected Stock Returns,â€ť Journal of

Finance 47 (June 1992), pp. 427â€“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 1963â€“1990.

In other words, it found that the magnitude of a stockâ€™s historical beta had no relationship to the level of its histori-

cal return. Although Fama and Frenchâ€™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 frameworkâ€”both conceptually and opera-

tionallyâ€”for linking expected nondiversifiable risk and return.

213

CHAPTER 5 Risk and Return

Review Questions

5â€“11 How are total risk, nondiversifiable risk, and diversifiable risk related?

Why is nondiversifiable risk the only relevant risk?

5â€“12 What risk does beta measure? How can you find the beta of a portfolio?

5â€“13 Explain the meaning of each variable in the capital asset pricing model

(CAPM) equation. What is the security market line (SML)?

5â€“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 firmâ€™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 firmâ€™s value. It is therefore the financial

managerâ€™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 firmâ€™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 riskâ€“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 assetâ€™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 assetâ€™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- setâ€™s return and the market return. Beta is derived

sification, and the impact of international assets on by finding the slope of the â€ścharacteristic lineâ€ť

a portfolio. The financial managerâ€™s goal is to create that best explains the historical relationship be-

an efficient portfolio that maximizes return for a tween the assetâ€™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 assetâ€™s risk relative to

diversification. International diversification can be the market to the assetâ€™s required return. The equa-

used to reduce a portfolioâ€™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 5â€“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

portfoliosâ€”one consisting of assets A and B and the other consisting of assets A

and Câ€”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 assetâ€™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 5â€“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 projectâ€™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

5â€“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. Keelâ€™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 yearâ€™s data.

b. Assuming that the two investments are equally risky, which one should Keel

recommend? Why?

5â€“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

5â€“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

5â€“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 Bâ€™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?

5â€“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?

5â€“6 Bar charts and risk Swanâ€™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 lineâ€™s annual rate of return.

b. Calculate the expected value of return for each line.

c. Evaluate the relative riskiness for each jean lineâ€™s rate of return using the bar

charts.

5â€“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?

5â€“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 firmâ€™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?

5â€“9 Integrativeâ€”Expected return, standard deviation, and coefficient of variation

LG3

Three assetsâ€”F, G, and Hâ€”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

â€“

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 assetsâ€™ returns.

Which appears to have the greatest risk?

c. Calculate the coefficient of variation, CV, for each of the three assetsâ€™

returns. Which appears to have the greatest relative risk?

5â€“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, 2004â€“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.

5â€“11 Portfolio analysis You have been given the return data shown in the first table

LG4

on three assetsâ€”F, G, and Hâ€”over the period 2004â€“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?

5â€“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.

5â€“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 â€śnumber of securities in portfolio (x axis)â€“portfolio risk (y axis)â€ť

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 Talbotâ€™s

portfolio?

5â€“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,

1994â€“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 â€śmarket return (x axis)â€“asset return (y axis)â€ť 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.

5â€“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 assetâ€™s return?

b. If the market return decreased by 8%, what impact would this change be

expected to have on the assetâ€™s return?

c. If the market return did not change, what impact, if any, would be expected

on the assetâ€™s return?

d. Would this asset be considered more or less risky than the market?

Explain.

5â€“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 assetâ€™s return?

b. What impact would a 10% decrease in the market return be expected to have

on each assetâ€™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?

5â€“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?

5â€“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

5â€“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

5â€“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?

5â€“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.

5â€“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 â€śnondiversifiable risk

(x axis)â€“required return (y axis)â€ť 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

5â€“23 Integrativeâ€”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 â€” 1.50

Project B â€” .75

Project C â€” 2.00

Project D â€” 0

Project E â€” .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 Productsâ€™ 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, 1994â€“2003. These data are summarized in the accompanying

table. Juniorâ€™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 assetâ€™s risk can be assessed in two ways: in isolation

and as part of the firmâ€™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 assetâ€™s risk as part of the firmâ€™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, 1994â€“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 1994â€“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 siteâ€™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 bookâ€™s Web site at

www.aw.com/gitman

for additional resources, including additional Web exercises.

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