Explain the capital asset pricing model (CAPM), its relationship to the

LG 6 Explain the capital asset pricing model (CAPM), its relationship to the

security market line (SML), and the major forces causing shifts in the SML. The CAPM uses beta to relate an asset’s risk relative to the market to the asset’s required return. The graphical depiction of the CAPM is SML, which shifts over time in response to changing inflationary expectations and/or changes in investor risk aversion. Changes in inflationary expectations result in parallel shifts in the SML. Increasing risk aversion results in a steepening in the slope of the SML. Decreasing risk aversion reduces the slope of the SML. Although it has some shortcomings, the CAPM provides a useful conceptual framework for evaluating and linking risk and return.

Opener-in-Review

The table below shows the annual returns in each year from 2007 through 2009 of the Close Special Situations Fund (a British fund specializing in small stocks), and the Financial Times Stock Index (FTSE), an index that tracks the perform- ance of the 100 largest companies on the U.K. stock market:

Year

Close Fund

FTSE

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Risk and Return

For both the Close Fund and the FTSE, calculate the average annual return and its standard deviation. What are the general patterns that you see? Provide one reason that the performance of the FTSE differs from that of the Close Fund.

Self-Test Problems (Solutions in Appendix)

LG 3 LG 4 ST8–1 Portfolio analysis You have been asked for your advice in selecting a portfolio of

assets and have been given the following data:

Expected return

Year

Asset A

Asset B

Asset C

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? 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?

LG 5 LG 6 ST8–2 Beta and CAPM Currently under consideration is an investment with a beta, b, of 1.50. At this time, the risk-free rate of return, R F , is 7%, and the return on the market portfolio of assets, r m , is 10%. You believe that this investment will 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 investment’s 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

PART 4

Risk and the Required Rate of Return

Warm-Up Exercises All problems are available in

LG 1 E8–1 An analyst predicted last year that the stock of Logistics, Inc., would offer a total return of at least 10% in the coming year. At the beginning of the year, the firm had a stock market value of $10 million. At the end of the year, it had a market value of $12 million even though it experienced a loss, or negative net income, of $2.5 mil- lion. Did the analyst’s prediction prove correct? Explain using the values for total annual return.

LG 2 E8–2 Four analysts cover the stock of Fluorine Chemical. One forecasts a 5% return for the coming year. A second expects the return to be negative 5%. A third predicts a 10% return. A fourth expects a 3% return in the coming year. You are relatively confident that the return will be positive but not large, so you arbitrarily assign probabilities of being correct of 35%, 5%, 20%, and 40%, respectively, to the analysts’ forecasts. Given these probabilities, what is Fluorine Chemical’s expected return for the coming year?

LG 2 E8–3 The expected annual returns are 15% for investment 1 and 12% for investment 2. The standard deviation of the first investment’s return is 10%; the second invest- ment’s return has a standard deviation of 5%. Which investment is less risky based solely on standard deviation? Which investment is less risky based on coefficient of variation? Which is a better measure given that the expected returns of the two investments are not the same?

LG 3 E8–4 Your portfolio has three asset classes. U.S. government T-bills account for 45% of the portfolio, large-company stocks constitute another 40%, and small-company stocks make up the remaining 15%. If the expected returns are 3.8% for the T-bills, 12.3% for the large-company stocks, and 17.4% for the small-company stocks, what is the expected return of the portfolio?

LG 5 E8–5 You wish to calculate the risk level of your portfolio based on its beta. The five stocks in the portfolio with their respective weights and betas are shown in the accompanying table. Calculate the beta of your portfolio.

Stock

Portfolio weight

LG 6 E8–6 a. Calculate the required rate of return for an asset that has a beta of 1.8, given a risk-free rate of 5% and a market return of 10%.

b. If investors have become more risk-averse due to recent geopolitical events, and the market return rises to 13%, what is the required rate of return for the same asset?

c. Use your findings in part a to graph the initial security market line (SML), and then use your findings in part b to graph (on the same set of axes) the shift in

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Risk and Return

Problems All problems are available in

LG 1 P8–1 Rate of return Douglas Keel, a financial analyst for Orange Industries, wishes to estimate the rate of return for two similar-risk investments, X and Y. Douglas’s research indicates that the immediate past returns will serve as reasonable estimates of future returns. A year earlier, investment X had a market value of $20,000; investment Y had a market value of $55,000. During the year, investment X gener- ated cash flow of $1,500 and investment Y generated cash flow of $6,800. The cur- rent market 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 Douglas

recommend? Why? LG 1 P8–2 Return calculations For each of the investments shown in the following table, cal-

culate the rate of return earned over the unspecified time period.

Cash flow

during period

period value

period value

LG 1 P8–3 Risk preferences Sharon Smith, the financial manager for Barnett Corporation, wishes to evaluate three prospective investments: X, Y, and Z. Sharon will evaluate

each of these investments to decide whether they are superior to investments that her company already has in place, which have an expected return of 12% and a stan- dard deviation of 6%. The expected returns and standard deviations of the invest- ments are as follows:

a. If Sharon were risk neutral, which investments would she select? Explain why. b. If she were risk averse, which investments would she select? Why? c. If she were risk seeking, which investments would she select? Why? d. Given the traditional risk preference behavior exhibited by financial managers,

which investment would be preferred? Why? LG 2 P8–4 Risk analysis Solar Designs is considering an investment in an expanded product

line. Two possible types of expansion are being considered. After investigating the

PART 4

Risk and the Required Rate of Return

Expansion A

Expansion B

Initial investment

Annual rate of return

Most likely

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? LG 2 P8–5 Risk and probability Micro-Pub, Inc., is considering the purchase of one of 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 constructed the accompanying table of estimates of rates of return and probabilities for pessimistic, most likely, and optimistic results.

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?

Camera R

Camera S

Amount

Probability

Amount Probability

Initial investment

Annual rate of return

Most likely

LG 2 P8–6 Bar charts and risk Swan’s Sportswear is considering bringing out a line of designer jeans. Currently, it is negotiating with two different well-known designers. 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 established the expecta- tions shown in the following table about the annual rates of return:

Annual rate of return

Market acceptance

Probability

Line J

Line K

Very poor

Poor

Average

Good

Excellent

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Risk and Return

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.

LG 2 P8–7 Coefficient of variation Metal Manufacturing has isolated four alternatives for meeting its need for increased production capacity. The following table summarizes data gathered relative to each of these alternatives.

Expected

Standard deviation

Alternative

return

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?

LG 2 P8–8 Standard deviation versus coefficient of variation as measures of risk Greengage,

Inc., a successful nursery, is considering several expansion projects. All of the alternatives promise to produce an acceptable return. Data on four possible projects follow.

2.9% B 12.5 5.0 3.2 C 13.0 6.0 3.5 D 12.8 4.5 3.0

a. Which project is least risky, judging on the basis of range? b. Which project has the lowest standard deviation? Explain why standard devia-

tion may not be an entirely appropriate measure of risk for purposes of this com- parison.

c. Calculate the coefficient of variation for each project. Which project do you think Greengage’s owners should choose? Explain why.

Personal Finance Problem LG 1 LG 2 P8–9 Rate of return, standard deviation, coefficient of variation Mike is searching for a stock to include in his current stock portfolio. He is interested in Hi-Tech Inc.; he

has been impressed with the company’s computer products and believes Hi-Tech is an innovative market player. However, Mike realizes that any time you consider a technology stock, risk is a major concern. The rule he follows is to include only

PART 4

Risk and the Required Rate of Return

Mike has obtained the following price information for the period 2009 through 2012. Hi-Tech stock, being growth-oriented, did not pay any dividends during these

4 years.

Stock price

a. Calculate the rate of return for each year, 2009 through 2012, for Hi-Tech stock. b. Assume that each year’s return is equally probable, and calculate the average

return over this time period. c. Calculate the standard deviation of returns over the past 4 years. (Hint: Treat

these data as a sample.) d. Based on b and c determine the coefficient of variation of returns for the security. e. Given the calculation in d what should be Mike’s decision regarding the inclusion

of Hi-Tech stock in his portfolio?

LG 2 P8–10 Assessing return and risk Swift Manufacturing must choose between two asset pur- chases. The annual rate of return and the related probabilities given in the following

table summarize the firm’s analysis to this point.

Project 257

Project 432

Rate of return

Probability

Rate of return

a. For each project, compute: (1) The range of possible rates of return. (2) The expected 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.

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Risk and Return

LG 2 P8–11 Integrative—Expected return, standard deviation, and coefficient of variation Three assets—F, G, and H—are currently being considered by Perth Industries. The proba-

bility distributions of expected returns for these assets are shown in the following table.

Asset H j

Asset F

Asset G

Pr j

Return, r j

Pr j

Return, r j

Pr j Return, r j

4 0.20 - 5 0.20 0 5 0.10 - 10 0.10 - 20

a. Calculate the expected value of return, for each of the three assets. Which pro- r, vides the largest expected return?

b. Calculate the standard deviation, s r , 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?

LG 2 P8–12 Normal probability distribution Assuming that the rates of return associated with a given asset investment are normally distributed; that the expected return, is r,

18.9%; and that the coefficient of variation, CV, is 0.75; answer the following questions:

a. Find the standard deviation of returns, s r . b. Calculate the range of expected return outcomes associated with the following

probabilities of occurrence: (1) 68%, (2) 95%, (3) 99%.

c. Draw the probability distribution associated with your findings in parts a and b.

Personal Finance Problem LG 3 P8–13 Portfolio return and standard deviation Jamie Wong is considering building an investment portfolio containing two stocks, L and M. Stock L will represent 40% of the dollar value of the portfolio, and stock M will account for the other 60%. The expected returns over the next 6 years, 2013–2018, for each of these stocks are shown in the following table.

Expected return

Year

Stock L

Stock M

PART 4

Risk and the Required Rate of Return

a. Calculate the expected portfolio return, r p , for each of the 6 years. b. Calculate the expected value of portfolio returns, , over the 6-year period. r p c. Calculate the standard deviation of expected portfolio returns, s r p , over the

6-year period. d. How would you characterize the correlation of returns of the two stocks L and M? e. Discuss any benefits of diversification achieved by Jamie through creation of the

portfolio.

LG 3 P8–14 Portfolio analysis You have been given the expected return data shown in the first table on three assets—F, G, and H—over the period 2013–2016.

Expected return

Year

Asset F

Asset G

Asset H

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. 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?

LG 4 P8–15 Correlation, risk, and return Matt Peters wishes to evaluate the risk and return behaviors associated with various combinations of assets V and W under three assumed degrees of correlation: perfect positive, uncorrelated, and perfect negative. The expected returns and standard deviations calculated for each of the assets are shown in the following table.

Expected

Risk (standard

Asset

return, deviation), r S r

V 8%

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Risk and Return

a. If the returns of assets V and W are perfectly positively correlated (correlation coefficient =+ 1 ), describe the range of (1) expected return and (2) risk associ- ated 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 (correlation coefficient =- 1 ), describe the range of (1) expected return and (2) risk associ- ated with all possible portfolio combinations.

Personal Finance Problem LG 1 LG 4 P8–16 International investment returns Joe Martinez, a U.S. citizen living in Brownsville, Texas, invested in the common stock of Telmex, a Mexican corporation. He pur- chased 1,000 shares at 20.50 pesos per share. Twelve months later, he sold them at

24.75 pesos per share. He received no dividends during that time. a. What was Joe’s investment return (in percentage terms) for the year, on the basis of the peso value of the shares?

b. The exchange rate for pesos was 9.21 pesos per US$1.00 at the time of the pur- chase. At the time of the sale, the exchange rate was 9.85 pesos per US$1.00. Translate the purchase and sale prices into US$.

c. Calculate Joe’s investment return on the basis of the US$ value of the shares. d. Explain why the two returns are different. Which one is more important to Joe?

Why? LG 5 P8–17 Total, nondiversifiable, and diversifiable risk David Talbot randomly selected securi-

ties from all those listed on the New York Stock Exchange for his portfolio. 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, s r p . The calculated values are shown in the following table.

Number of

Portfolio securities

Portfolio

Number of

risk, securities s r p

risk, s r p

a. Plot the data from the table above on a graph that has the number of securities on the x-axis and the portfolio standard deviation on the y-axis.

b. Divide the total portfolio risk in the graph into its nondiversifiable and diversifiable 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

PART 4

Risk and the Required Rate of Return

LG 5 P8–18 Graphical derivation of beta

A firm wishes to estimate graphically the betas 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 10 years, 2003–2012.

Actual return

Year

Market portfolio

Asset A

Asset B

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.

LG 5 P8–19 Graphical derivation and interpreting beta You are analyzing the performance of two stocks. The first, shown in Panel A, is Cyclical Industries Incorporated. Cyclical

Return on Overall Market Return on Overall Market

10 Return on

10 Return on

Panel A

CHAPTER 8

Risk and Return

Industries makes machine tools and other heavy equipment, the demand for which rises and falls closely with the overall state of the economy. The second stock, shown in Panel B, is Biotech Cures Corporation. Biotech Cures uses biotechnology to develop new pharmaceutical compounds to treat incurable diseases. Biotech’s for- tunes are driven largely by the success or failure of its scientists to discover new and effective drugs. Each data point on the graph shows the monthly return on the stock of interest and the monthly return on the overall stock market. The lines drawn through the data points represent the characteristic lines for each security.

a. Which stock do you think has a higher standard deviation? Why? b. Which stock do you think has a higher beta? Why? c. Which stock do you think is riskier? What does the answer to this question

depend on?

LG 5 P8–20 Interpreting beta

A firm wishes to assess the impact of changes in the market 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. LG 5 P8–21 Betas Answer the questions below for assets A to D shown in the table.

Asset

Beta

A 0.50 B 1.60

C - 0.20 D 0.90

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 believed that the market return would increase in the near future, which asset would you prefer? Why?

d. If you believed that the market return would decrease in the near future, which asset would you prefer? Why?

Personal Finance Problem LG 5 P8–22 Betas and risk rankings You are considering three stocks—A, B, and C—for pos- sible inclusion in your investment portfolio. Stock A has a beta of 0.80, stock B has

a beta of 1.40, and stock C has a beta of 0.30. - 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

PART 4

Risk and the Required Rate of Return

d. If you felt that the stock market was getting 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? Personal Finance Problem

LG 5 P8–23 Portfolio betas Rose Berry is attempting to evaluate two possible portfolios, which consist of the same five assets held in different proportions. She is particularly

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

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?

LG 6 P8–24 Capital asset pricing model (CAPM) For each of the cases shown in the following table, use the capital asset pricing model to find the required return.

rate, R F return, r m

Beta, b

C 9 12 - 0.20 D 10 15 1.00 E 6 10 0.60

Personal Finance Problem

LG 5 LG 6 P8–25 Beta coefficients and the capital asset pricing model Katherine Wilson is wondering how much risk she must undertake to generate an acceptable return on her portfolio. The risk-free return currently is 5%. The return on the overall stock market is 16%. Use the CAPM to calculate how high the beta coefficient of Katherine’s portfolio would have to be to achieve each of the following expected portfolio returns.

a. 10% b. 15% c. 18% d. 20%

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Risk and Return

LG 6 P8–26 Manipulating CAPM Use the basic equation for the capital asset pricing model

(CAPM) to work each of the following problems.

a. Find the required return for an asset with a beta of 0.90 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. Personal Finance Problem

LG 1 LG 3 P8–27 Portfolio return and beta Jamie Peters invested $100,000 to set up the following LG

portfolio one year ago:

Beta at purchase

Yearly income Value today

a. Calculate the portfolio beta on the basis of the original cost figures. b. Calculate the percentage return of each asset in the portfolio for the year. c. Calculate the percentage return of the portfolio on the basis of original cost,

using income and gains during the year. d. At the time Jamie made his investments, investors were estimating that the market

return for the coming year would be 10%. The estimate of the risk-free rate of return averaged 4% for the coming year. Calculate an expected rate of return for each stock on the basis of its beta and the expectations of market and risk-free returns.

e. On the basis of the actual results, explain how each stock in the portfolio per- formed relative to those CAPM-generated expectations of performance. What factors could explain these differences?

LG 6 P8–28 Security market line (SML) Assume that the risk-free rate, R F , is currently 9% and

that the market return, r m , 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

0.80 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.

LG 6 P8–29 Shifts in the security market line Assume that the risk-free rate, R F , is currently 8%, the market return, r m , is 12%, and asset A has a beta, b A , of 1.10. a. Draw the security market line (SML) on a set of “nondiversifiable risk ( x axis)–

required return ( y axis)” axes.

PART 4

Risk and the Required Rate of Return

c. Assume that as a result of recent economic events, inflationary expectations have declined by 2%, lowering R F and r m to 6% and 10%, respectively. Draw the new SML on the axes in part a, and calculate and show the new required return for asset A.

d. Assume that as a result of recent events, investors have become more risk averse, causing the market return to rise by 1%, to 13%. Ignoring the shift in part c, draw the new SML on the same set of axes that you used before, and calculate and show the new required return for asset A.

e. From the previous changes, what conclusions can be drawn about the impact of (1) decreased inflationary expectations and (2) increased risk aversion on the required returns of risky assets?

LG 6 P8–30 Integrative—Risk, return, and CAPM Wolff Enterprises must consider several investment projects, A through E, using the capital asset pricing model (CAPM) and

its graphical representation, the security market line (SML). Relevant information is presented in the following table.

Item

Rate of return

Beta, b

Risk-free asset

Market portfolio

Project A

Project B

Project C

Project D

Project E

a. Calculate (1) the required rate of return and (2) the 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 rela-

tive to nondiversifiable risk). c. Discuss the relative nondiversifiable risk of projects A through E. d. Assume that recent economic events have caused investors to become less risk-

averse, causing the market return to decline by 2%, to 12%. Calculate the new required returns for assets A through E, and draw the new security market line on the same set of axes that you used in part b.

e. Compare your findings in parts a and b with those in part d. What conclusion can you draw about the impact of a decline in investor risk aversion on the required returns of risky assets?

LG 1 P8–31 ETHICS PROBLEM Risk is a major concern of almost all investors. When share- holders invest their money in a firm, they expect managers to take risks with those funds. What do you think are the ethical limits that managers should observe when taking risks with other people’s money?

CHAPTER 8

Risk and Return

Spreadsheet Exercise

Jane is considering investing in three different stocks or creating three distinct two- stock portfolios. Jane considers herself to be a rather conservative investor. She is able to obtain forecasted returns for the three securities for the years 2013 through 2019. The data are as follows:

Year

Stock A

Stock B

Stock C

In any of the possible two-stock portfolios, the weight of each stock in the portfolio will be 50%. The three possible portfolio combinations are AB, AC, and BC.