A fund manager has a diversified equity portfolio worth $$50$ million and a beta of $0\mathrm{.}87$ to

the market. The manager is concerned about the performance of the market over the next

two months and plans to use three$-$month futures contracts on a well$-$diversified index to

hedge its 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 two months?

b$.$ Calculate the effect of your strategy on the fund manager's returns if the level of

the market in two months is $1,000($i$.$e$.,$ what is your return in dollars and $\%)?$