1. Suppose the CAPM holds, RF =4%, and the expected return on the market portfolio is 6%. Assume continuous compounding. A company will sell 1 unit of gold a year from today. Assume the mean price of gold GT to be $100 in a year, and the standard deviation of the gold price GT to be $20. Assume that the gold β = .9. (a) Find the value of the firm if it did no hedging. (b) If the firm went short $ β times the value of the firm in (a) of the market portfolio, and invested the proceeds in riskless debt, then what would be the hedged firm’s beta? What would be its expected return, and what would be the market value of the firm? (c) Find the forward price of a 1-year forward contract on a unit of gold. Find the value of the firm if it hedged its gold price risk in the forward market.
2. Suppose the market portfolio consists of weights w1 = 0.30, and, w2 = 0.70 in two stocks. Assume that E[R˜ 1]= 10% and E[R˜ 2]=20%, Var[R˜ 1]=25%,Var[R˜ 2]=45%. Assume that the correlation between the two stock returns is 0.5. (a) Compute the variance of the market portfolio (you might look at Properties 10 and 11 of “Review of Variances and Covariances” posted on Blackboard). (b) Find the beta of each stock with respect to the market portfolio. Also find the quantity w1 · β1 + w2 · β2.