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 2 months and plans to use 3-month futures contracts on a well-diversified index to hedge its risk. The current level of the index is 1,250 , one contract is on 250 times the index, the risk-free rate is $6 \% \mathrm{per}$ annum, and the dividend yield on the index is $3 \%$ per annum. The current 3-month futures price is 1,259 .
(a) What position should the fund manager take to hedge all exposure to the market over the next 2 months?
(b) Calculate the effect of your strategy on the fund manager's returns if the index in 2 months is $$1,000,1,100,1,200,1,300$$, and 1,400 . Assume that the 1 -month futures price is $0.25 \%$ higher than the index level at thime.