Question 11. Hedging with Stock Index Futures (10 marks) You manage a portfolio that is currently all invested in equities in companies in five major Canadian industries. The market value involved and beta for each industry are shown in the table below. Industry Oil and Gas Technology Utilities Financial Pharmaceutical Market Value $1,100,000 900,000 1,500,000 1,000,000 800,000 Beta 1.2 1.5 0.8 1.3 1.1 You believe that the Canadian equity market is on the verge of a big but short-lived downturn. You would move your portfolio temporarily into T-bills, but you do not want to incur the transaction costs of liquidating and re-establishing your equity position. Instead, you decide to hedge your portfolio with three-month S&P/TSX 60 index futures contracts for one month. Currently, the level of the S&P/TSX 60 index is 851.38, the three-month futures price of the S&P/TSX 60 is 856.40, and one contract is for $200 times the index. The annual simple risk-free rate of return is 1%. a. Should you long or short the S&P/TSX 60 futures? (0.5 mark) b. C. How many futures contracts should you use? (5 marks) Suppose the return on the S&P/TSX 60 index is -5% in one month, and the S&P/TSX index futures price falls to 830 in one month. Calculate your net gain or loss on your hedged portfolio in part (a). (Hint: Use the CAPM formula to derive the portfolio return. Then use the portfolio return to obtain gain/loss on the portfolio). (4.5 marks)