Solution manual financial management 10e by keown chapter 06

The only portfolio with returns consistently exceeding the inflation rate has been common stocks.. The required rate of return is the minimum rate necessary to compensate an investor for

CHAPTER 6

Risk and Rates of Return

CHAPTER ORIENTATION

This chapter introduces the concepts that underlie the valuation of securities and their rates

of return We are specifically concerned with common stock, preferred stock, and bonds

We also look at the concept of the investor's expected rate of return on an investment

CHAPTER OUTLINE

I The relationship between risk and rates of return

A Data have been compiled by Ibbotson and Sinquefield on the actual returns

for various portfolios of securities from 1926-2002

B The following portfolios were studied

1 Common stocks of small firms

2 Common stocks of large companies

3 Long-term corporate bonds

4 Long-term U.S government bonds

5 U.S Treasury bills

C Investors historically have received greater returns for greater risk-taking

with the exception of the U.S government bonds

D The only portfolio with returns consistently exceeding the inflation rate has

been common stocks

II Effects of Inflation on Rates of Return

A When a rate of interest is quoted, it is generally the nominal or, observed

rate The real rate of interest represents the rate of increase in actualpurchasing power, after adjusting for inflation

B Consequently, the nominal rate of interest is equal to the sum of the real rate

of interest, the inflation rate, and the product of the real rate and the

The relationship between a debt security’s rate of return and the length of time untilthe debt matures is known as the term structure of interest rates or the yield tomaturity.

IV Expected Return

A The expected benefits or returns to be received from an investment come in

the form of the cash flows the investment generates

B Conventionally, we measure the expected cash flow, X , as follows:

X = XiP(Xi)

where N = the number of possible states of the economy

Xi = the cash flow in the ith state of the economy.

P(Xi) = the probability of the ith cash flow.

V Riskiness of the cash flows

A Risk can be defined as the possible variation in cash flow about an expected

cash flow

B Statistically, risk may be measured by the standard deviation about the

expected cash flow

C Risk and diversification

1 Total variability can be divided into:

a The variability of returns unique to the security (diversifiable

or unsystematic risk)

b The risk related to market movements (nondiversifiable or

systematic risk)

2 By diversifying, the investor can eliminate the "unique" security risk

The systematic risk, however, cannot be diversified away

3 The market rewards diversification We can lower risk without

sacrificing expected return, and/or we can increase expected returnwithout having to assume more risk

4 Diversifying among different kinds of assets is called asset

allocation Compared to diversification within the different assetclasses, the benefits received are far greater through effective assetallocation

5 Risk and being patient

a An investor in common stocks must often wait longer to earn

the higher returns than those provided by bonds

b The capital markets reward us not just for diversifying, but

6 The characteristic line tells us the average movement in a firm's

stock price in response to a movement in the general market, such asthe stock market The slope of the characteristic line, which has

come to be called beta, is a measure of a stock's systematic or

market risk The slope of the line is merely the ratio of the "rise" ofthe line relative to the "run" of the line

7 If a security's beta equals one, a 10 percent increase (decrease) in

market returns will produce on average a 10 percent increase(decrease) in security returns

8 A security having a higher beta is more volatile and thus more risky

than a security having a lower beta value

9 A portfolio's beta is equal to the average of the betas of the stocks in

the portfolio

VI Required rate of return

A The required rate of return is the minimum rate necessary to compensate an

investor for accepting the risk he or she associates with the purchase andownership of an asset

B Two factors determine the required rate of return for the investor:

1 The risk-free rate of interest which recognizes the time value of

money

2 The risk premium which considers the riskiness (variability of

returns) of the asset and the investor's attitude toward risk

C Capital asset pricing model-CAPM

1 The required rate of return for a given security can be expressed as

= + beta x or

kj = krf + βj (km - krf)

2 Security market line

a Graphically illustrates the CAPM

b Designates the risk-return trade-off existing in the market,

where risk is defined in terms of beta according to the CAPMequation

ANSWERS TO END-OF-CHAPTER QUESTIONS

6-1 Data have been compiled by Ibbotson and Sinquefield on the actual returns for the

following portfolios of securities from 1926-2002

1 U.S Treasury bills

2 U.S government bonds

3 Corporate bonds

4 Common stocks for large firms

5 Common stocks for small firms

Investors historically have received greater returns for greater risk-taking with theexception of the U.S government bonds Also, the only portfolio with returnsconsistently exceeding the inflation rate has been common stocks

6.2 When a rate of interest is quoted, it is generally the nominal or, observed rate The

real rate of interest represents the rate of increase in actual purchasing power, afteradjusting for inflation Consequently, the nominal rate of interest is equal to thesum of the real rate of interest, the inflation rate, and the product of the real rate andthe inflation rate

6-3 The relationship between a debt security’s rate of return and the length of time until

the debt matures is known as the term structure of interest rates or the yield tomaturity In most cases, longer terms to maturity command higher returns or yields.6-4 (a) The investor's required rate of return is the minimum rate of return

necessary to attract an investor to purchase or hold a security

(b) Risk is the potential variability in returns on an investment Thus, the

greater the uncertainty as to the exact outcome, the greater is the risk Riskmay be measured in terms of the standard deviation or by the variance term,which is simply the standard deviation squared

(c) A large standard deviation of the returns indicates greater riskiness

associated with an investment However, whether the standard deviation islarge relative to the returns has to be examined with respect to otherinvestment opportunities Alternatively, probability analysis is a meaningfulapproach to capture greater understanding of the significance of a standarddeviation figure However, we have chosen not to incorporate such ananalysis into our explanation of the valuation process

6-5 (a) Unique risk is the variability in a firm's stock price that is associated with

the specific firm and not the result of some broader influence An employeestrike is an example of a company-unique influence

6-6 Beta indicates the responsiveness of a security's returns to changes in the market

returns Beta is multiplied by the market risk premium and added to the risk-freerate of return to calculate a required rate of return

6-7 The security market line is a graphical representation of the risk-return trade-off

that exists in the market The line indicates the minimum acceptable rate of returnfor investors given the level of risk Since the security market line results fromactual market transactions, the relationship not only represents the risk-returnpreferences of investors in the market but also represents the investors' availableopportunity set

6-8 The beta for a portfolio is equal to the weighted average of the individual stock

betas, weighted by the percentage invested in each stock

6-9 If a stock has a great amount of variability about its characteristic line (the graph of

the stock's returns against the market's returns), then it has a high amount ofunsystematic or company-unique risk If, however, the stock's returns closelyfollow the market movements, then there is little unsystematic risk

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

Solutions to Problems Set A

Probability Return Expected Return Deviation

Probability Return Expected Return Deviation

Probability Return Expected Return Deviation

6-5A

Common Stock A:

Probability Return Expected Return Deviation

Probability Return Expected Return Deviation

(b) The 18 percent "fair rate" compensates the investor for the time value of

money and for assuming risk However, only nondiversifiable risk is beingconsidered, which is appropriate

6-7A Eye balling the characteristic line for the problem, the rise relative to the run is

about 0.5 That is, when the S & P 500 return is eight percent Aram's expectedreturn would be about four percent Thus, the beta is also approximately 0.5 (4 ÷

= 7.5% + (11.5% - 7.5%) x 0.765

= 10.56%

6-10A If the expected market return is 12.8 percent and the risk premium is 4.3 percent, the

riskless rate of return is 8.5 percent (12.8% - 4.3%) Therefore;

Time Price Return Price Return

6-12A.a Zemin Market

c Zemin's historical return of 24 percent exceeds what we would consider a

fair return of 17.24 percent, given the stock's systematic risk

6-13A

a The portfolio expected return, kp, equals a weighted average of the

individual stock's expected returns

kp = (0.20)(16%) + (0.30)(14%) + (0.15)(20%) + (0.25)(12%) +

(0.10)(24%)

= 15.8%

b The portfolio beta, ßp, equals a weighted average of the individual stock

d A "winner" may be defined as a stock that falls above the security market

line, which means these stocks are expected to earn a return exceeding whatshould be expected given their beta or systematic risk In the above graph,these stocks include 1, 3, and 5 "Losers" would be those stocks fallingbelow the security market line, which are represented by stocks 2 and 4 ever

so slightly

e Our results are less than certain because we have problems estimating the

security market line with certainty For instance, we have difficulty inspecifying the market portfolio

6-14A a.

Market Mathews

Month Price kt (kt - k )2 Price kt (kt - k )2

Aug-02 1320.41 -0.63% 0.0002 41.09 19.10% 0.0170Sep-02 1282.71 -2.86% 0.0013 37.16 -9.56% 0.0244Oct-02 1362.93 6.25% 0.0031 38.72 4.20% 0.0003Nov-02 1388.91 1.91% 0.0001 38.34 -0.98% 0.0050Dec-02 1469.25 5.78% 0.0026 41.16 7.36% 0.0002Jan-03 1394.46 -5.09% 0.0034 49.47 20.19% 0.0199Feb-03 1366.42 -2.01% 0.0007 56.50 14.21% 0.0066Mar-03 1498.58 9.67% 0.0080 65.97 16.76% 0.0114Apr-03 1452.43 -3.08% 0.0014 63.41 -3.88% 0.0099May-03 1420.60 -2.19% 0.0008 62.34 -1.69% 0.0060Jun-03 1454.60 2.39% 0.0003 66.84 7.22% 0.0001Jul-03 1430.83 -1.63% 0.0005 66.75 -0.13% 0.0038

d Mathews returns seem to correlate to the market returns during the majority

of the year, but show great volatility

6-15A

Stock 1

Probability Return Expected Return Deviation

Probability Return Expected Return Deviation

Probability Return Expected Return Deviation

Williams Davis

Time Price Return Price Return

SOLUTION TO INTEGRATIVE PROBLEM

1 Holding-period returns for Market, Reynolds Computer, and Andrews

Market Reynolds Computer Andrews Price kt (kt - k )2 Price kt (kt - k )2 Price kt (kt - k )2

June 1133.84 3.94% 0.0007 23.20 12.62% 0.0067 26.72 11.33% 0.0065July 1120.67 -1.16% 0.0006 27.15 17.03% 0.0158 20.94 -21.63% 0.0619Aug 957.28 -14.58% 0.0251 25.00 -7.92% 0.0153 15.78 -24.64% 0.0778Sept 1017.01 6.24% 0.0025 32.88 31.52% 0.0733 18.09 14.64% 0.0130Oct 1098.67 8.03% 0.0046 32.75 -0.40% 0.0023 21.69 19.90% 0.0277Nov 1163.63 5.91% 0.0022 30.41 -7.15% 0.0134 23.06 6.32% 0.0009Dec 1229.23 5.64% 0.0019 36.59 20.32% 0.0252 28.06 21.68% 0.034002Jan 1279.64 4.10% 0.0008 50.00 36.65% 0.1037 26.03 -7.23% 0.0110Feb 1238.33 -3.23% 0.0020 40.06 -19.88% 0.0592 26.44 1.58% 0.0003Mar 1286.37 3.88% 0.0007 40.88 2.05% 0.0006 28.06 6.13% 0.0008Apr 1335.18 3.79% 0.0006 41.19 0.76% 0.0014 36.94 31.65% 0.0806May 1301.84 -2.50% 0.0014 34.44 -16.39% 0.0434 36.88 -0.16% 0.0012June 1372.71 5.44% 0.0018 37.00 7.43% 0.0009 37.56 1.84% 0.0002July 1328.72 -3.20% 0.0020 40.88 10.49% 0.0037 23.25 -38.10% 0.1710Aug 1320.41 -0.63% 0.0004 48.81 19.40% 0.0224 22.88 -1.59% 0.0023Sept 1282.71 -2.86% 0.0017 41.81 -14.34% 0.0353 24.78 8.30% 0.0026Oct 1362.93 6.25% 0.0025 40.13 -4.02% 0.0072 27.19 9.73% 0.0042Nov 1388.91 1.91% 0.0000 43.00 7.15% 0.0007 26.56 -2.32% 0.0031Dec 1469.25 5.78% 0.0021 51.00 18.60% 0.0201 24.25 -8.70% 0.014303Jan 1394.46 -5.09% 0.0040 38.44 -24.63% 0.0845 32.00 31.96% 0.0824Febr 1366.42 -2.01% 0.0011 40.81 6.17% 0.0003 35.13 9.78% 0.0043Mar 1498.58 9.67% 0.0071 53.94 32.17% 0.0769 44.81 27.55% 0.0591Apr 1452.43 -3.08% 0.0019 50.13 -7.06% 0.0132 30.23 -32.54% 0.1281May 1420.60 -2.19% 0.0012 43.13 -13.96% 0.0339 34.00 12.47% 0.0085

3.

Reynolds vs Market

-0.3-0.2-0.100.10.20.30.4

4 Reynolds’s returns have a great amount of volatility with some correlation to the

12.29%

We see in this new graph where both stocks are included as a single portfolio that therelationship of the stocks with the market approximates an average of the relationshipstaken alone Note the reduction in volatility that occurs when risk is diversified evenbetween just two stocks

Reynolds and Andrews

7 Monthly holding-period returns for long-term government bonds

(ki - k )2

2001 June 5.70% 0.48% 0.000000%July 5.68% 0.47% 0.000001%August 5.54% 0.46% 0.000004%September 5.20% 0.43% 0.000023%October 5.01% 0.42% 0.000041%November 5.25% 0.44% 0.000020%December 5.06% 0.42% 0.000036%

2002 January 5.16% 0.43% 0.000027%February 5.37% 0.45% 0.000012%March 5.58% 0.47% 0.000003%April 5.55% 0.46% 0.000004%

June 6.04% 0.50% 0.000005%July 5.98% 0.50% 0.000003%August 6.07% 0.51% 0.000006%September 6.07% 0.51% 0.000006%October 6.26% 0.52% 0.000016%November 6.15% 0.51% 0.000009%December 6.35% 0.53% 0.000022%

2003 January 6.63% 0.55% 0.000050%February 6.23% 0.52% 0.000014%March 6.05% 0.50% 0.000005%April 5.85% 0.49% 0.000000%

AverageMonthly

Standard

8 Monthly portfolio returns when portfolio consists of equal amounts invested in

Reynolds, Andrews, and long-term government bonds

(ki - k )2

2001 June 8.14% 0.0029

August -10.69% 0.0180September 15.53% 0.0164October 6.63% 0.0015November -0.13% 0.0008December 14.15% 0.0131

2002 January 9.94% 0.0052February -5.95% 0.0075

2003 January 2.63% 0.0000February 5.49% 0.0008March 20.08% 0.0301April -13.04% 0.0248