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 futures contracts on the S&P $500$ 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 $1259.$

Calculate the effect of your strategy on the fund manager$$s returns if the level of the market in two months is $1400.$ Assume that the one$-$month futures price is $0\mathrm{.}25\%$ higher than the index level at this time.

If the index in two months is $1400,$ what is the total gain? $$517,250.$ Please show the steps to get to this answer