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Hedging with futures A fund manager has a portfolio worth $50 million with a...

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Finance

Hedging with futures

A fund manager has a portfolio worth $50 million with a beta of 0.87. The manager is concerned about the performance of the market over the next two months and plans to use three-month futures contracts on the S&P 500 to hedge the risk. The current level of the index is 1250, one contract is on $250 times the index, the risk-free rate is 6% per annum (continuously compounded), and the dividend yield on the index is 3% per annum (continuously compounded). The current 3-month futures price is 1259.

a). What position should the fund manager take to eliminate all exposure to the market over the next two months?

b). Assume the level of the index in two months is 1000. Using the CAPM, show that your strategy delivers an overall return on the combined portfolio (i.e., original portfolio plus futures position) close to the risk-free rate.

c). What is the beta of the combined portfolio?

d). In light of your answer to (c), is your answer to (b) surprising?

e). How would you generate a beta for the combined portfolio equal to half the beta of the original portfolio?

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