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

a)      What position should thefund manager take to eliminate all exposure to the market over the next twomonths?

b)      Calculate the effect ofyour strategy on the fund manager’s returns if the level of the market in twomonths is 1,000, 1,100, 1,200, 1,300, and 1,400. Assume that the one-monthfutures price is 0.25% higher than the index level at this time. (Hint: to findout portfolio return, use CAPM: expected portfolio return = RF + β(RM-RF).)