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Top hedge fund manager Sally Buffit believes that a stock with the same market risk as the S&P 500 will sell at year-end at a price of $59. The stock will pay a dividend at year-end of $4.00. Assume that risk-free Treasury securities currently offer an interest rate of 1.6%.
Average rates of return on Treasury bills, government bonds, and common stocks, 1900–2017 (figures in percent per year) are as follows.
Rate of Return (%)Average Premium (Extra return
versus Treasury bills) (%)Treasury bills 3.8 Treasury bonds 5.3 1.5 Common stocks 11.5 7.7
a. What is the discount rate on the stock? (Enter your answer as a percent rounded to 2 decimal places.)
b. What price should she be willing to pay for the stock today? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Consider the following scenario analysis:
Rate of ReturnScenarioProbabilityStocksBondsRecession0.2-4%15%Normal economy0.716 11 Boom0.125 3
Assume a portfolio with weights of 0.60 in stocks and 0.40 in bonds.
a. What is the rate of return on the portfolio in each scenario? (Enter your answer as a percent rounded to 1 decimal place.)
b. What are the expected rate of return and standard deviation of the portfolio? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)
Consider the following two scenarios for the economy and the expected returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D.
Rate of ReturnScenario Market Aggressive
Stock A Defensive
Stock D Bust –8% –11% –6% Boom 30 40 24
Required:a. Find the beta of each stock.b. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock.c. If the T-bill rate is 3%, what does the CAPM say about the fair expected rate of return on the two stocks?d. Which stock seems to be a better buy on the basis of your answers to (a) through (c)?
a. The discount rate on the stock is (4.00 / 59) + 1.6% = 6.78%.
b. The price she should be willing to pay for the stock today is 59 / (1 + 0.0678) = 55.17.
a. The rate of return on the portfolio in each scenario would be: Recession: 0.60 * -4% + 0.40 * 15% = -1.6% Normal economy: 0.60 * 16% + 0.40 * 11% = 14.4% Boom: 0.60 * 3% + 0.40 * 24% = 9.6%
b. The expected rate of return on the portfolio is: (0.2 * -1.6%) + (0.7 * 14.4%) + (0.125 * 9.6%) = 12.32%. The standard deviation of the portfolio is: sqrt((0.2 * (-1.6% – 12.32%)^2) + (0.7 * (14.4% – 12.32%)^2) + (0.125 * (9.6% – 12.32%)^2)) = 5.03%.
a. The beta of each stock can be calculated as follows: Aggressive Stock A: (40% – 30%) / (30% – (-8%)) = 2.5 Defensive Stock D: (24% – 30%) / (30% – (-8%)) = 0.75
b. If each scenario is equally likely, the expected rate of return on the market portfolio is: (1/3) * (-8%) + (1/3) * 30% + (1/3) * 40% = 20%. The expected rate of return on Aggressive Stock A is: (1/3) * (-11%) + (1/3) * 30% + (1/3) * 40% = 23.33%. The expected rate of return on Defensive Stock D is: (1/3) * (-6%) + (1/3) * 30% + (1/3) * 24% = 18%.
c. According to the Capital Asset Pricing Model (CAPM), the fair expected rate of return on Aggressive Stock A is: 3% + 2.5 * (23.33% – 3%) = 34.83%. The fair expected rate of return on Defensive Stock D is: 3% + 0.75 * (23.33% – 3%) = 10.08%.
d. On the basis of the calculations above, Aggressive Stock A seems to be a better buy as it has a higher expected rate of return and a higher fair expected rate of return according to the CAPM.
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