Risk Premiums, Market Indexes, Discount Rates, Rate of Return

1. Risk Premiums. Here are stock market and Treasury bill returns between 2000 and 2004:

Year Stock Market Return T-Bill Return

2000 -10.89 5.89
2001 -10.97 3.83
2002 -20.86 1.65
2003 31.64 1.02
2004 12.62 1.20

a. What was the risk premium on common stock in each year?

b. What was the average risk premium?

c. What was the standard deviation of the risk premium?

Hint: Calculate the variance: the sum of squared deviations from the mean divided by the number of observations or N (ignore the concept of degrees of freedom, N-1)

Calculate the standard deviation: the square root of the variance

2. Market Indexes. In 1990, the Dow Jones Industrial Average was at a level of about 2,600. In 2005, it was about 10,000. Would you expect the Dow in 2005 to be more or less likely to move up or down by more than 40 points in a day than in 1990? Does this mean the market was riskier in 2005 than it was in 1990?

3. What will happen to the opportunity cost of capital if investors suddenly become especially conservative and less willing to bear investment risk?

4. Risk Premiums and Discount Rates. You believe that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $50. The stock will pay a dividend at year-end of $2. What price will you be willing to pay for the stock today? Hint: Start by checking today's 1-year Treasury rates.

Assume that the risk premium is 7.6% and the risk free rate is 3.5%

5. Scenario Analysis. Consider the following scenario analysis:

Rate of Return

Scenario Probability Stocks Bonds

Recession .20 -5% +14%

Normal economy .60 +15 +8

Boom .20 +25 +4

a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?

b. Calculate the expected rate of return and standard deviation for each investment.

c. Which investment would you prefer?

6. Risk and Return. A stock will provide a rate of return of either -20% or +28%.

a. If both possibilities are equally likely, calculate the expected return and standard deviation.

b. If the Treasury bills yield 4% and investors believe that the stock offers a satisfactory expected return, what must the market risk of the stock be?