You hold an $8 million stock portfolio with a beta of 1.0. You believe that the risk-adjusted abnormal return on the portfolio (the alpha) over the next three months is 2 percent. The S&P/TSX 60 index currently is at 800 and the risk-free rate is 1 percent per quarter.

1. What will be the futures price on the three-month maturity S&P/TSX 60 futures contract?
2. How many S&P/TSX 60 futures contracts are needed to hedge the stock portfolio?
3. What will be the profit on that futures position in three months as a function of the value of the S&P/TSX 60 index on the maturity date?
4. If the alpha of the portfolio is 2 percent, show that the expected rate of return (in decimal form) on the portfolio as a function of the market return isr_p= .03 + 1.0 (r_M.01).
5. LetS_Tbe the value of the index in three months. ThenS_T/S₀=S_T/800 = 1 +r_M. (We are ignoring dividends here to keep things simple.) Substitute this expression in the equation for the portfolio return,r_p, and calculate the expected value of the hedged (stock-plus-futures) portfolio in three months as a function of the value of the index.
6. Show that the hedged portfolio provides an expected rate of return of 3 percent over the next three months.
7. What is the beta of the hedged portfolio? What is the alpha of the hedged portfolio?