Ch11 End of Chapter Questions

CHAPTER 11RISK AND RETURN 359

11.3 If we compute the reward-to-risk ratios, we get (19% – 8%)/1.6 = 6.875% for Beef Ltd versus 6.67% for Flowers Ltd. Relative to that of Beef, Flowers’ expected return is too low, so its price is too high.

If they are correctly priced, then they must offer the same reward-to-risk ratio. The risk-free rate would have to be such that:

( 19 % − R f ) / 1.6 = ( 16 % − R f ) / 1.2

With a little algebra, we fi nd that the risk-free rate must be 7%:

(19% − Rf )/1.6 = (16% − Rf )(1.6/1.2)

19% − 16% × 4⁄3 = Rf − Rf × 4⁄3

Rf = 7%

11.4 Since the expected return on the market is 14%, the market risk premium is 14% − 8% = 6% (the risk-free rate is 8%). The fi rst share has a beta of 0.60, so its expected return is 8% + 0.60 × 6% = 11.6%.

For the second share, notice that the risk premium is 20% − 8% = 12%. Since this is twice as large as the market risk premium, the beta must be exactly equal to 2. We can verify this using the CAPM:

E(Ri ) = Rf + [E(RM) − Rf ] × βi

20% = 8% + (14% − 8%) × βi

βi = 12%/6% = 2.0

CRITICAL THINKING AND CONCEPTS REVIEW 11.1 Diversifi able and Non-diversifi able Risks. In broad terms, why is some risk diversifi able? Why

are some risks non-diversifi able? Does it follow that an investor can control the level of unsystematic risk in a portfolio, but not the level of systematic risk? LO 2

11.2 Information and Market Returns. Suppose the government announces that, based on a just-completed survey, the growth rate in the economy is likely to be 2% in the coming year, as compared with 5% for the year just completed. Will security prices increase, decrease or stay the same following this announcement? Does it make any difference whether the 2% fi gure was anticipated by the market? Explain. LO 3

11.3 Systematic versus Unsystematic Risk. Classify the following events as mostly systematic or mostly unsystematic. Is the distinction clear in every case? a. Short-term interest rates increase unexpectedly. b. The interest rate a company pays on its short-term debt borrowing is increased by its

bank. c. Oil prices unexpectedly decline. d. An oil tanker ruptures, creating a large oil spill. e. A manufacturer loses a multimillion-dollar product liability suit. f. A Supreme Court decision substantially broadens producer liability for injuries suffered by

product users. LO 3 11.4 Systematic versus Unsystematic Risk. Indicate whether the following events might cause share

prices in general to change, and whether they might cause Big Widget Ltd’s share price to change. a. The government announces that infl ation unexpectedly jumped by 2% last month. b. Big Widget’s half-yearly earnings report, just issued, generally fell in line with analysts’

expectations. c. The government reports that economic growth last year was at 3%, which generally agreed

with most economists’ forecasts.

Continued

Ross_Ch11.indd 359 9/14/10 1:22:22 AM

Essentials of Corporate Finance, Second Australian Edition 381

McGraw-Hill Create™ Review Copy for Instructor S. Not for distribution.

360 PART 6 RISK AND RETURN

d. The directors of Big Widget die in a plane crash. e. The government passes changes to the tax laws that will increase the corporate tax rate.

The legislation had been debated for the previous six months. LO 3 11.5 Expected Portfolio Returns. If a portfolio has a positive investment in every asset, can the

expected return on the portfolio be greater than that on every asset in the portfolio? Can it be less than that on every asset in the portfolio? If you answer yes to one or both of these questions, give an example to support your answer. LO 1

11.6 Diversifi cation. True or false: the most important characteristic in determining the expected return of a well-diversifi ed portfolio is the variances of the individual assets in the portfolio? Explain. LO 2

11.7 Portfolio Risk. If a portfolio has a positive investment in every asset, can the standard deviation on the portfolio be less than that on every asset in the portfolio? What about the portfolio beta? LO 3

11.8 Beta and CAPM. Is it possible that a risky asset could have a beta of zero? Explain. Based on the CAPM, what is the expected return on such an asset? Is it possible that a risky asset could have a negative beta? What does the CAPM predict about the expected return on such an asset? Can you give an explanation for your answer? LO 4

11.9 Corporate Downsizing. In recent years it has been common for companies to experience signifi cant share price changes in reaction to announcements of massive layoffs. Critics charge that such events encourage companies to fi re long-time employees and that the share market is cheering them on. Do you agree or disagree? LO 2

11.10 Earnings and Share Returns. As indicated by a number of examples in this chapter, earnings announcements by companies are closely followed by, and frequently result in, share price revisions. Two issues should come to mind. First, earnings announcements concern past periods. If the market values shares are based on expectations of the future, why are numbers summarising past performance relevant? Second, these announcements concern accounting earnings. Going back to Chapter 2 , such earnings may have little to do with cash fl ow, so, again, why are they relevant? LO 1

QUESTIONS AND PROBLEMS BASIC QUESTIONS (1-31) 1. Determining Portfolio Weights. What are the portfolio weights for a portfolio that has ninety shares

of Firm A that sell for $84 per share and fi fty shares of Firm B that sell for $58 per share? LO 1 2. Portfolio Expected Return. You own a portfolio that has $700 invested in Alpha Ltd and $2 500

invested in Better Ltd. If the expected returns on these fi rms are 10% and 16%, respectively, what is the expected return on the portfolio? LO 1

3. Portfolio Expected Return. You own a portfolio that is 20% invested in Share X, 45% in Share Y and 35% in Share Z. The expected returns on these three shares are 10%, 14% and 16%, respectively. What is the expected return on the portfolio? LO 1

4. Portfolio Expected Return. You have $10 000 to invest in a share portfolio. Your choices are shares in FIJ Ltd, with an expected return of 16%, and shares in HLP Ltd, with an expected return of 11%. If your goal is to create a portfolio with an expected return of 14.25%, how much money will you invest in FIJ? In HLP? LO 1

5. Calculating Expected Return. Based on the following information, calculate the expected return. LO 1

(1) STATE OF

ECONOMY

(2) PROBABILITY OF

STATE OF ECONOMY

(3) RATE OF RETURNIF STATE OCCURS

Recession 0.15 –0.09

Boom 0.85 0.18

Selected problems are available in

McGraw-Hill Connect Plus.

Ross_Ch11.indd 360 9/13/10 3:26:07 PM

382 FINS




(1) STATE OF

ECONOMY

(2) PROBABILITY OF

STATE OF ECONOMY

(3) RATE OF RETURNIF STATE OCCURS


Normal 0.55 0.13

Boom 0.25 0.30

7. Calculating Returns and Standard Deviations. Based on the following information, calculate the expected return and standard deviation for the two investments. LO 1

STATE OF ECONOMY

PROBABILITY OF STATE OF ECONOMY

RATE OF RETURN IF STATE OCCURS

ANT LTD BELL LTD

Recession 0.15 0.01 –0.25

Normal 0.55 0.09 0.15

Boom 0.30 0.14 0.38

8. Calculating Expected Returns. A portfolio is invested 20% in shares of Gabba Ltd, 35% in shares of Jumbuck Ltd and 45% in shares of Kanga Ltd. The expected returns on these shares are 9%, 13% and 19%, respectively. What is the portfolio’s expected return? How do you interpret your answer? LO 1

9. Returns and Standard Deviations. Consider the following information:

STATE OF ECONOMY



ADD LTD BTE LTD COL LTD

Boom 0.65 0.08 0.02 0.33

Bust 0.35 0.14 0.24 –0.06

a. What is the expected return on an equally weighted portfolio of these three fi rms? b. What is the variance of a portfolio invested 20% each in ADD and BTE and 60% in COL?

LO 3 & LO 2 10. Returns and Standard Deviations. Consider the following information:

STATE OF ECONOMY



FIRM A FIRM B FIRM C

Boom 0.15 0.30 0.45 0.33

Good 0.45 0.12 0.10 0.15

Poor 0.35 0.01 –0.15 –0.05

Bust 0.05 –0.20 –0.30 –0.09

a. Your portfolio is invested 30% each in A and C and 40% in B. What is the expected return of the portfolio?

b. What is the variance of this portfolio? The standard deviation? LO 1 & LO 2 11. Calculating Portfolio Betas. You own a share portfolio invested 25% in shares of Q, 20% in shares

in R, 45% in shares in S and 10% in shares in T. The betas for these four shares are 0.73, 0.86, 1.25 and 1.84, respectively. What is the portfolio beta? LO 3

12. Calculating Portfolio Betas. You own a portfolio equally invested in a risk-free asset and two fi rms. If one of the fi rms has a beta of 1.65 and the total portfolio is equally as risky as the market, what must the beta be for the other fi rm in your portfolio? LO 3

Continued

Ross_Ch11.indd 361 9/13/10 3:26:11 PM




13. Using CAPM. A share has a beta of 0.9, the expected return on the market is 13% and the risk-free rate is 6%. What must the expected return on this share be? LO 4

14. Using CAPM. A share has an expected return of 17%, the risk-free rate is 5.5% and the market risk premium is 8%. What must the beta of this share be? LO 4

15. Using CAPM. A share has an expected return of 17%, its beta is 1.45 and the risk-free rate is 5.5%. What must the expected return on the market be? LO 4

16. Using CAPM. A share has an expected return of 11.9% and a beta of 0.85 and the expected return on the market is 13%. What must the risk-free rate be? LO 4

17. Using CAPM. A share has a beta of 1.4 and an expected return of 16%. A risk-free asset currently earns 6.25%. a. What is the expected return on a portfolio that is equally invested in the two assets? b. If a portfolio of the two assets has a beta of 0.8, what are the portfolio weights? c. If a portfolio of the two assets has an expected return of 12%, what is its beta? d. If a portfolio of the two assets has a beta of 2.80, what are the portfolio weights?

How do you interpret the weights for the two assets in this case? Explain. LO 4 18. Using the SML. Asset W has an expected return of 16.5% and a beta of 1.25. If the risk-free rate

is 6%, complete the following table for portfolios of Asset W and a risk-free asset. Illustrate the relationship between portfolio expected return and portfolio beta by plotting the expected returns against the betas. What is the slope of the line that results? LO 4

PERCENTAGE OF PORTFOLIO IN ASSET W

PORTFOLIO EXPECTED

RETURNPORTFOLIO

BETA

0%

25

50

75

100

125

150

19. Reward-to-Risk Ratios. Dingo Ltd shares have a beta of 1.5 and an expected return of 16%. Shares in White Shark Ltd have a beta of 0.70 and an expected return of 11.5%. If the risk-free rate is 5.5% and the market risk premium is 8%, are these shares correctly priced? LO 4

20. Reward-to-Risk Ratios. In the previous problem, what would the risk-free rate have to be for the two shares to be correctly priced relative to each other? LO 4

21. Portfolio Returns. Using information from Table 10.2 on capital market history, determine the return on a portfolio that was equally invested in large-company shares and government bonds. What was the return on a portfolio that was equally invested in government bonds and cash? LO 1

22. Portfolio Expected Return. You have $250 000 to invest in a share portfolio. Your choices are shares in Homestead Ltd, with an expected return of 16%, and shares in Limestone Ltd, with an expected return of 9.5%. If your goal is to create a portfolio with an expected return of 12%, how much money will you invest in Homestead? In Limestone? LO 1

23. Calculating Expected Return Based on the following information, calculate the expected return. LO 1

STATE OF ECONOMY


RATE OF RETURNIF STATE OCCURS


Boom 0.80 0.21

Ross_Ch11.indd 362 9/13/10 3:26:16 PM

384 FINS




STATE OF ECONOMY


RATE OF RETURNIF STATE OCCURS


Normal 0.40 0.10

Boom 0.35 0.34

25. Calculating Returns and Deviations. Based on the following information, calculate the expected return and standard deviation for the two shares. LO 1 & LO 2

STATE OF ECONOMY


SHARE PIPRATE OF RETURN

SHARE SQUID RATE OF RETURN

Recession 0.15 0.04 –0.20

Normal 0.65 0.08 0.20

Boom 0.20 0.16 0.60

26. Calculating Expected Returns. A portfolio is invested 20% in House, 40% in Door and 40% in Window. The expected returns on these investments are 9%, 17% and 23%, respectively. What is the portfolio’s expected return? LO 1

27. Returns and Deviations. Consider the following information:

STATE OF ECONOMY


SHARE A RATE OF RETURN

SHARE B RATE OF RETURN

SHARE C RATE OF RETURN

Boom 0.75 0.04 0.03 0.26

Bust 0.25 0.12 0.18 –0.02

a. What is the expected return on an equally weighted portfolio of these three shares? b. What is the variance of a portfolio invested 25% in A and B and 50% in C? LO 1 & LO2

28. Returns and Deviations. Consider the following information:

STATE OF ECONOMY





Boom 0.10 0.18 0.35 0.20

Good 0.60 0.11 0.15 0.11

Poor 0.20 0.06 –0.05 0.02

Bust 0.10 0.01 –0.40 –0.08

a. Your portfolio is invested 20% each in B and C and 60% in A. What is the portfolio’s expected return?

b. What is the variance of this portfolio? The standard deviation? LO 1 & LO2 29. Calculating Portfolio Returns. Avalon Ltd shares have an average return of 12%, Bondi Ltd shares

have an average return of 19.5%, and Cairns Ltd shares have an average return of 31%. If your portfolio weights are 30%, 50% and 20%, respectively, what is the expected return of your portfolio? LO 1

30. Calculating Portfolio Weights. Share J has a beta of 1.35 and an expected return of 17%, while Share K has a beta of 0.8 and an expected return of 10%. You want a portfolio with the same risk as the market. How much will you invest in each share? What is the expected return of your portfolio? LO 1

Continued

Ross_Ch11.indd 363 9/13/10 3:26:16 PM




31. Calculating Portfolio Weights and Expected Return. You have a portfolio with the following:

COMPANY NUMBER OF SHARES PRICE EXPECTED RETURN

North 500 $41 12%

South 300 27 16

East 250 65 14

West 625 49 15

What is the expected return of your portfolio? LO 1

INTERMEDIATE QUESTIONS (32–35) 32. Analysing a Portfolio. You have $100 000 to invest in Darwin Ltd shares, Frankston Ltd shares or

a risk-free asset. You must invest all of your money. Your goal is to create a portfolio that has an expected return of 12%. If Darwin has an expected return of 16%, Frankston has an expected return of 10.5% and the risk-free rate is 6%, and if you invest $50 000 in Darwin, how much will you invest in Frankston? LO 2

33. Portfolio Returns and Deviations. Consider the following information on a portfolio of three shares:

STATE OF ECONOMY





Boom 0.25 0.05 0.25 0.60

Normal 0.55 0.09 0.12 0.20

Bust 0.20 0.12 –0.13 –0.40

a. If your portfolio is invested 40% each in A and B, and 20% in C, what is the portfolio’s expected return? The variance? The standard deviation?

b. If the expected risk-free rate is 4.25%, what is the expected risk premium on the portfolio? LO 1 & LO2

34. CAPM. Using the CAPM, show that the ratio of the risk premiums on two assets is equal to the ratio of their betas. LO 4

35. Portfolio Returns and Deviations. Consider the following information on three shares:

STATE OF ECONOMY



SHARE A SHARE B SHARE C

Boom 0.2 0.38 0.02 0.60

Normal 0.7 0.14 0.10 0.05

Bust 0.1 –0.05 0.15 –0.50

a. If your portfolio is invested 30% each in A and B and 40% in C, what is the portfolio expected return? The variance? The standard deviation?

b. If the expected risk-free rate is 3.60%, what is the expected risk premium on the portfolio? LO 1 & LO 2

CHALLENGE QUESTIONS (36–38) 36. Analysing a Portfolio. You want to create a portfolio equally as risky as the market, and you have

$500 000 to invest. Given this information, fi ll in the rest of this table:

ASSET INVESTMENT BETA LO 2

Share A $120 000 0.85

Share B 150 000 1.20

Share C 1.45

Risk-free asset

Ross_Ch11.indd 364 9/13/10 3:26:17 PM

386 FINS


Ch11 End of Chapter Questions

Documents

Transcript of Ch11 End of Chapter Questions