Questions and Problems

Returns

9.1 Last year, you bought 500 shares of Twedt El Dee stock at $37 per share. You have received total dividends of $1,000 during the year. Currently, Twedt El Dee stock sells for $38.

a. How much did you earn in capital gains?

b. What was your total dollar return?

c. What was your percentage return?

d. Must you sell the Twedt El Dee stock to include the capital gains in your return? Explain.

9.2 Mr. Alexander Bell invested $10,400 in 200 shares of First Industries stock a year ago and has received total dividends of $600 during the period. He sold the stock today at $54.25.

a. What was his total dollar return?

b. What was his capital gain?

c. What was his percentage return?

d. What was the stock's dividend yield?

9.3 Suppose a stock had an initial price of $42 per share. During the year, the stock paid a dividend of $2.40 per share. At the end of the year, the price is $31 per share. What is the percentage return on this stock?

9.4 Lydian Stock currently sells for $52 per share. You intend to buy the stock today and hold it for two years. During those two years, you expect to receive dividends at the year-ends that total $5.50 per share. Finally, you expect to sell the Lydian stock for $54.75 per share. What is your expected holding-period return on Lydian stock?

9.5 Use the information from Ibbotson and Sinquefield provided in the text to compute the nominal and real annual returns from 1926 to 1997 for each of the following items.

a. Common stock b. Long-term corporate bonds c. Long-term government bonds d. U.S. Treasury bills

9.6 Suppose the current interest rate on U.S. Treasury bills is 6.2 percent. Ibbotson and Sinquefield found the average return on Treasury bills from 1926 through 1997 to be 3.8 percent. The average return on common stock during the same period was 13.0 percent. Given this information, what is the current expected return on common stocks?

9.7 Two stocks, Koke and Pepsee, had the same prices two years ago. During the last two years, Koke's stock price had first increased by 10 percent and then dropped by 10 percent, while Pepsee's stock price had first dropped by 10 percent and then increased by 10 percent. Do these two stocks have the same prices today? Explain.

9.8 S&P 500 index returns of common stocks for the period 1981-1985 are as follows. Calculate the five-year holding-period return.

1981 1982 1983 1984 1985

S&P 500 index return (%) -4.91 21.41 22.51 6.27 32.16

9.9 The Wall Street Journal announced yesterday that the current rate for one-year Treasury bills is 4.36 percent, while an Ibbotson and Sinquefield study shows that the average return on Treasury bills for the period 1926-1997 is 3.8 percent. During the same period the average return on long-term corporate bonds is 6.1 percent. What is the risk premium of the long-term corporate bonds? What is the expected return on the market of long-term corporate bonds?

Ross-Westerfield-Jaffe: I III. Risk I 9. Capital Market Theory: I I © The McGraw-Hill

Corporate Finance, Sixth An Overview Companies, 2002

Edition

238 Part III Risk

Average Returns, Expected Returns, and Variance

9.10 During the past seven years, the returns on a portfolio of long-term corporate bonds were the following:

Year Long-Term Corporate Bonds

Last 19.9

a. Calculate the average return for long-term corporate bonds over this period.

b. Calculate the variance and the standard deviation of the returns for long-term corporate bonds during this period.

9.11 The following are the returns during the past seven years on a market portfolio of common stocks and on Treasury bills.

Year

Common Stocks

Treasury Bills

-7

32.4%

11.2%

-6

-4.9

14.7

-5

21.4

10.5

-4

22.5

8.8

-3

6.3

9.9

-2

32.2

7.7

Last

18.5

6.2

The realized risk premium is the return on the common stocks less the return on the Treasury bills.

a. Calculate the realized risk premium of common stocks over T-bills in each year.

b. Calculate the average risk premium of common stocks over T-bills during the period.

c. Is it possible that this observed risk premium can be negative? Explain.

9.12 The probability that the economy will experience moderate growth next year is 0.6. The probability of a recession is 0.2, and the probability of a rapid expansion is also 0.2. If the economy falls into a recession, you can expect to receive a return on your portfolio of 5 percent. With moderate growth your return will be 8 percent. If there is a rapid expansion, your portfolio will return 15 percent.

a. What is your expected return?

b. What is the standard deviation of that return?

9.13 The probability that the economy will experience moderate growth next year is 0.4. The probability of a recession is 0.3, and the probability of a rapid expansion is also 0.3. If the economy falls into a recession, you can expect to receive a return on your portfolio of 2 percent. With moderate growth your return will be 5 percent. If there is a rapid expansion, your portfolio will return 10 percent.

a. What is your expected return?

b. What is the standard deviation of that return?

9.14 The returns on the market and on Trebli stock are shown below for the five possible states of the economy that might prevail next year.

Ross-Westerfield-Jaffe: I III. Risk I 9. Capital Market Theory: I I © The McGraw-Hill

Corporate Finance, Sixth An Overview Companies, 2002

Edition

Chapter 9 Capital Market Theory: An Overview 239

Market

Trebli

Economic Condition

Probability

Return

Return

Rapid expansion

0.12

0.23

0.12

Moderate expansion

0.40

0.18

0.09

No growth

0.25

0.15

0.05

Moderate contraction

0.15

0.09

0.01

Serious contraction

0.08

0.03

-0.02

a. What is the expected return on the market?

b. What is the expected return on Trebli stock?

9.15 Four equally likely states of the economy may prevail next year. Below are the returns on the stocks of P and Q companies under each of the possible states.

State P Stock Q Stock

a. What is the expected return on each stock?

b. What is the variance of the returns of each stock?

9.16 The returns on the small-company stocks and on the S&P composite index of common stocks from 1935 through 1939 are tabulated below.

Small-Company Market Index of

Year Stocks Common Stocks

1936 33.9 64.8

1938 31.0 32.8

a. Calculate the average return for the small-company stocks and the market index of common stocks.

b. Calculate the variance and standard deviation of returns for the small-company stocks and the market index of common stocks.

9.17 The following data are the returns for 1980 through 1986 on five types of capital-market instruments: common stocks, small-capitalization stocks, long-term corporate bonds, long-term U.S. government bonds, and U.S. Treasury bills.

Year

Stocks

Long-Term Corporate Bonds

Treasury Bills

1980

0.3242

0.3988

-0.0262

-0.0395

0.1124

1981

-0.0491

0.1388

-0.0096

0.0185

0.1471

1982

0.2141

0.2801

0.4379

0.4035

0.1054

1983

0.2251

0.3967

0.0470

0.0068

0.0880

1984

0.0627

-0.0667

0.1639

0.1543

0.0985

1985

0.3216

0.2466

0.3090

0.3097

0.0772

1986

0.1847

0.0685

0.1985

0.2444

0.0616

Calculate the average return and variance for each type of security.

Calculate the average return and variance for each type of security.

Ross-Westerfield-Jaffe: I III. Risk I 9. Capital Market Theory: I I © The McGraw-Hill

Corporate Finance, Sixth An Overview Companies, 2002

Edition

240 Part III Risk

Return and Risk Statistics

9.18 Ibbotson and Sinquefield have reported the returns on small-company stocks and U.S. Treasury bills for the period 1986-1991 as follows.

Small-Company U.S. Treasury

Year Stocks Bills

1988 22.87 6.35

1989 10.18 8.37

1991 44.63 5.60

a. Calculate the average returns on small-company stocks and U.S. Treasury bills.

b. Calculate the variances and standard deviations of the returns on small-company stocks and U.S. Treasury bills.

c. Compare the returns and risks of these two types of securities.

9.19 Suppose International Trading Company's stock returns follow a normal distribution with a mean of 17.5 percent and a standard deviation of 8.5 percent. What is the range of returns in which about 95 percent of International Trading's stock returns are located?

9.20 The returns on the market of common stocks and on Treasury bills are contingent on the economy as follows.

Economic Condition Probability Market Return Treasury Bills

Normal 0.50 12.3 3.5

a. Calculate the expected returns on the market and Treasury bills.

b. Calculate the expected risk premium.

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