The S&P 500 Index is currently at 1,200. You manage a $6 million indexed equity portfolio. The

Question:

The S&P 500 Index is currently at 1,200. You manage a $6 million indexed equity portfolio. The S&P 500 futures contract has a multiplier of $250.

a. If you are temporarily bearish on the stock market, how many contracts should you sell to fully eliminate your exposure over the next six months?

b. If T-bills pay 2% per six months and the semiannual dividend yield is 1%, what is the parity value of the futures price? Show that if the contract is fairly priced, the total risk-free proceeds on the hedged strategy in part (a) provide a return equal to the T-bill rate?

c. How would your hedging strategy change if, instead of holding an indexed portfolio, you hold a portfolio of only one stock with a beta of .6? How many contracts would you now choose to sell? Would your hedged position be riskless? What would be the beta of the hedged position?

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