A fund manager has a portfolio worth $50$ million with a beta of $0\mathrm{.}87.$ The manager is concerned about the performance of the market over the next two months and plans to use three$-$month future contract on NSE to hedge the risk. The current level of the index is $8,400,$ one contract is on $200$ times the index, the risk free rate is $6\%$ per annum, and the dividend yield on the index is $4\%$ per annum. The current $3-$month future price is $4270.$

$($a$)$ What position should the fund manager take to eliminate all exposure to the market over the next $2$ years?

$($b$)$ Calculate the effect of your strategy on the fund manager's returns if the level of market in $2$ months is $8,000,8,200$ and $8,600$ respectively. Assume that the $1-$month future is $0\mathrm{.}25\%$ higher than the index level at this time