# 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?

© BrainMass Inc. brainmass.com October 25, 2018, 4:26 am ad1c9bdddfhttps://brainmass.com/business/finance/risk-premiums-market-indexes-discount-rates-rate-return-378641

#### Solution Preview

** Please see the attached document for the complete solution response **

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 ...

#### Solution Summary

This solution provides a complete computation of the given finance problem formatted in Excel.

Investments: Expected return, volatility, beta and risk premium, PV of cash flow, hedge

1. Compute the expected return and volatility of return for a portfolio that has a portfolio share of 0.9 in the S&P 500 and 0.1 in an emerging market index. The S&P 500 has a volatility of return of 15 percent and an expected return of 12 percent. The emerging market has a return volatility of 30 percent and an expected return of 10 percent. The correlation between the emerging market index return and the S&P 500 is 0.1.

2. If the S&P 500 is a good proxy for the market portfolio in the CAPM, and the CAPM applies to the emerging market index, use the information in previous question to compute the beta and risk premium for emerging market index.

3. A firm has an expected cash flow of $500 million in one year. The beta of the common stock of the firm is 0.8 and this cash flow has the same risk as the firm as a whole. Using a risk-free rate of 5 percent and a risk premium on the market portfolio of 6 percent, what is the present value of the cash flow? If the beta of the firm doubles, what happens to the present value of the cash flow?

4. Using the data in the previous question, consider how hedging the cash flow against systematic risk might affect the firm. If management wants to eliminate the systematic risk of the cash flow completely, how could it do so? How much would the firm have to pay investors to bear the systematic risk of the cash flow?

5. Consider problem 3. To hedge the firm's systematic risk, management has to pay investors to bear this risk. Why is it that the value of the firm for shareholders does not fall when the firm pays other investors to bear the cash flow's systematic risk?

View Full Posting Details