Problem 1. Is the following statement True, False, or Ambiguous? Provide a short justification for your answer (you are evaluated on the justification).
"In the CAPM model, since investors are compensated for holding risk, two securities with the same standard deviation should have the same expected return."
Problem 2. Suppose there are two types of risky assets in the market: high growth and low growth stocks. High growth stocks have a standard deviation of .5 and make up 35% of the market while low growth stocks have a standard deviation of .2 and make up 65% of the market. The correlation between the two stocks is .5. The coefficient of relative risk aversion for the average investor is 2.5 and the risk free rate of return is .07. What is the risk premium on high growth stocks according to the CAPM?
Problem 3. Assume the following properties for two stocks (stock 1 and stock 2) and of the market.
E(rm) = 0.10, σ1 = 0.20, ρ1,m = 0.4, σm = 0.15, σ2 = 0.30, ρ2,m = 0.7. Suppose further that the risk-free rate is 5%
a) According to the Capital Asset Pricing Model, what should be the expected return of stock 1 and of stock 2?
b) Suppose that the correlation between the return of stock 1 and the return of stock 2 is 0.5. What is the expected return and the standard deviation of the return of a portfolio that has a 40% investment in stock 1 and a 60% investment in stock 2?
c) Assume that the Capital Asset Pricing Model is valid. How could you construct a new portfolio using the market portfolio and the risk-free asset that has the same expected return as the portfolio you considered in 2(b), but has the lowest standard deviation possible? What is the standard deviation of the return of this portfolio?
d) Suppose that the correlation between the return of stock 1 and the return of stock 2 is -0.7. What is the expected return and the standard deviation of the return of a portfolio that has a 40% investment in stock 1 and a 60% investment in stock 2?
Problem 4.
a) A futures contract on a non-dividend paying stock with a current price $150 has a maturity of 1 year. If the T-bill rate is 6%, what should the futures price be?
b) What should the futures price be if the maturity of the contract is lengthened to 3 years?
Problem 5. Are the following statements True, False, or Ambiguous? Provide a short justification for your answers (you are evaluated on the justification).
a) All else equal, the futures price on a stock index with a high dividend yield should be higher than the futures price on an index with a low dividend yield.
b) All else equal, the futures price on a high-beta stock should be higher than the futures price on a low-beta shock.
c) "The current price of Digital stock is $44 a share. You are offered a forward price for Digital stock to be delivered in one year of $42. The forward price is lower than the spot price because the market anticipates a sharp decline in the price of Digital stock, and the contract offers a way to hedge this risk. There is no arbitrage opportunity."
Problem 6. Consider the following option strategy:
- Long one call with $100 strike price bought for $6
- Long one call with $90 strike price bought for $20
- Short one call with $105 strike price sold for $8
- Short one call with $95 strike price sold for $16
a) Draw a picture of the payoff of this option strategy at expiration as a function of the stock price.
b) Draw a picture of the investor's profit at expiration as a function of the stock price. (Hint: The profit includes the cost of the strategy)