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Chapter10: Risk and Return:Lessons from Market History

Questions and Problems

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BASIC
(Questions 1-18)

  1. Calculating Returns Suppose a stock had an initial price of $92 per share, paid a dividend of $1.45 per share during the year, and had an ending share price of $104. Compute the percentage total return.

  2. Calculating Yields In Problem 1, what was the dividend yield? The capital gains yield?

  3. Calculating Returns Rework Problems 1 and 2 assuming the ending share price is $81.

  4. Calculating Returns Suppose you bought an 8 percent coupon bond one year ago for $1,090. The bond sells for $1,056 today.

    1. Assuming a $1,000 face value, what was your total dollar return on this investment over the past year?

    2. What was your total nominal rate of return on this investment over the past year?

    3. If the inflation rate last year was 3 percent, what was your total real rate of return on this investment?

  5. Nominal versus Real Returns What was the arithmetic average annual return on large-company stocks from 1926 through 2008

    1. In nominal terms?

    2. In real terms?

  6. Bond Returns What is the historical real return on long-term government bonds? On long-term corporate bonds?

    p. 324

  7. Calculating Returns and Variability Using the following returns, calculate the average returns, the variances, and the standard deviations for X and Y:

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  8. Risk Premiums Refer to Table 10.1 in the text and look at the period from 1973 through 1978.

    1. Calculate the arithmetic average returns for large-company stocks and T-bills over this period.

    2. Calculate the standard deviation of the returns for large-company stocks and T-bills over this period.

    3. Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. What was the arithmetic average risk premium over this period? What was the standard deviation of the risk premium over this period?

  9. Calculating Returns and Variability You've observed the following returns on Mary Ann Data Corporation's stock over the past five years: 34 percent, 16 percent, 19 percent, −21 percent, and 8 percent.

    1. What was the arithmetic average return on Mary Ann's stock over this five-year period?

    2. What was the variance of Mary Ann's returns over this period? The standard deviation?

  10. Calculating Real Returns and Risk Premiums In Problem 9, suppose the average inflation rate over this period was 4.2 percent, and the average T-bill rate over the period was 5.1 percent.

    1. What was the average real return on Mary Ann's stock?

    2. What was the average nominal risk premium on Mary Ann's stock?

  11. Calculating Real Rates Given the information in Problem 10, what was the average real risk-free rate over this time period? What was the average real risk premium?

  12. Holding Period Return A stock has had returns of 18.43 percent, 16.82 percent, 6.83 percent, 32.19 percent, and −19.87 percent over the past five years, respectively. What was the holding period return for the stock?

  13. Calculating Returns You purchased a zero coupon bond one year ago for $77.81. The market interest rate is now 9 percent. If the bond had 30 years to maturity when you originally purchased it, what was your total return for the past year?

  14. Calculating Returns You bought a share of 5 percent preferred stock for $92.85 last year. The market price for your stock is now $94.63. What was your total return for last year?

  15. Calculating Returns You bought a stock three months ago for $75.15 per share. The stock paid no dividends. The current share price is $82.01. What is the APR of your investment? The EAR?

    p. 325

  16. Calculating Real Returns Refer to Table 10.1. What was the average real return for Treasury bills from 1926 through 1932?

  17. Return Distributions Refer back to Table 10.2. What range of returns would you expect to see 68 percent of the time for long-term corporate bonds? What about 95 percent of the time?

  18. Return Distributions Refer back to Table 10.2. What range of returns would you expect to see 68 percent of the time for large-company stocks? What about 95 percent of the time?


INTERMEDIATE
(Questions 19-26)

  1. Calculating Returns and Variability You find a certain stock that had returns of 19 percent, −27 percent, 6 percent, and 34 percent for four of the last five years. If the average return of the stock over this period was 11 percent, what was the stock's return for the missing year? What is the standard deviation of the stock's returns?

  2. Arithmetic and Geometric Returns A stock has had returns of 34 percent, 18 percent, 29 percent, −6 percent, 16 percent, and −48 percent over the last six years. What are the arithmetic and geometric returns for the stock?

  3. Arithmetic and Geometric Returns A stock has had the following year-end prices and dividends:

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    What are the arithmetic and geometric returns for the stock?

  4. Calculating Returns Refer to Table 10.1 in the text and look at the period from 1973 through 1980.

    1. Calculate the average return for Treasury bills and the average annual inflation rate (consumer price index) for this period.

    2. Calculate the standard deviation of Treasury bill returns and inflation over this period.

    3. Calculate the real return for each year. What is the average real return for Treasury bills?

    4. Many people consider Treasury bills to be risk-free. What do these calculations tell you about the potential risks of Treasury bills?

  5. Calculating Investment Returns You bought one of Bergen Manufacturing Co.'s 7 percent coupon bonds one year ago for $943.82. These bonds make annual payments and mature six years from now. Suppose you decide to sell your bonds today when the required return on the bonds is 8 percent. If the inflation rate was 4.8 percent over the past year, what would be your total real return on the investment?

  6. Using Return Distributions Suppose the returns on long-term government bonds are normally distributed. Based on the historical record, what is the approximate probability that your return on these bonds will be less than −3.3 percent in a given year? What range of returns would you expect to see 95 percent of the time? What range would you expect to see 99 percent of the time?

    p. 326

  7. Using Return Distributions Assuming that the returns from holding small-company stocks are normally distributed, what is the approximate probability that your money will double in value in a single year? Triple in value?

  8. Distributions In the previous problem, what is the probability that the return is less than −100 percent? (Think.) What are the implications for the distribution of returns?


CHALLENGE (Questions 27-28)

  1. Using Probability Distributions Suppose the returns on large-company stocks are normally distributed. Based on the historical record, use the NORMDIST function in Excel® to determine the probability that in any given year you will lose money by investing in common stock.

  2.  Using Probability Distributions Suppose the returns on long-term corporate bonds and T-bills are normally distributed. Based on the historical record, use the NORMDIST function in Excel® to answer the following questions:

    1. What is the probability that in any given year, the return on long-term corporate bonds will be greater than 10 percent? Less than 0 percent?

    2. What is the probability that in any given year, the return on T-bills will be greater than 10 percent? Less than 0 percent?

    3. In 1979, the return on long-term corporate bonds was −4.18 percent. How likely is it that this low of a return will recur at some point in the future? T-bills had a return of 10.56 percent in this same year. How likely is it that this high of a return on T-bills will recur at some point in the future?

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