A fund manager has a portfolio worth $$95$ million with a beta of $1\mathrm{.}16.$ The manager is concerned about the performance of the market over the next two months and plans to use three$-$month futures contracts on the S&P $500$ to hedge the risk.

The current level of the S&P $500$ index is $2,675,$ the risk$-$free rate is

$2\%$ per annum, and the dividend yield on the index is $4\%$ per annum. The current $3-$month S&P $500$ index futures price is $2,660,$ and one contract is on $250$ times the index.

$($a$)$ What position should the fund manager take to eliminate all risk exposure to the market over the next two months? $($B$\text{'}=0)$ How many three$-$month S&P $500$ futures contracts should the fund manager buy or sell now? $($Rounding to the nearest whole number.$)$

$($b$)$ Calculate the effect of your strategy on the fund manager's returns if the level of the S&P $500$ index in two months is $2,585.$ Assume that the $3-$month S&P $500$ index futures price is $2,570$ in two months.

What would be the expected value of the fund manager's hedged portfolio $($including the spot and futures positions$)$ in two months?