A portfolio manager runs a $500 million equity fund and wishes to hedge her stock portfolio over the final two months of the year. The beta of her stock portfolio is 1.6. Her portfolio has performed quite well relative to comparable funds over the first 10 months of the year and she now wants to hedge against a possible market-wide crash during the final two months of the year. Rather than liquidating her stock portfolio or purchasing put options, she wants to use stock index futures with a three-month maturity to hedge her portfolio. Each futures contract is for delivery of $250 times the index. The stock index currently stands at 16,000 and its dividend yield is 2.5%. The risk-free rate is 1%. The manager wishes to lower the beta of her portfolio to 0.5 (from its current level of 1.6).

a) What position in the three-month futures contract should she take?

b) If the stock index drops to 15,200 by yearend, how does the hedge work out? Assume there is no change in either the risk-free rate or the dividend yield on the stock index.