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 the S\&P \(\$ 00\) 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, and the dividend
yield on the index is \(3 \%\) per annum. 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 2 months?
(b) Calculate the effect of your strategy on the fund manager's returns if the
level of the market 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 this time.