A fund has a portfolio worth $$50$ million with a beta of $0\mathrm{.}75.$ The manageger is concerned about the performace of the market over the next $2$ months and plans to use $3-$month futures contracts on the S&P $500$ to hedge the risk. The current level of the index is $2,000,$ one contract is onn $250$ times the index, the risk$-$ free rate $8\%$ per annum, and the dividend yield on the index is $3\%$ per annum. $($A$).$ calculate the theoretical futures prices for the $3-$months index futures, assuming continuous compounding. Round to the nearest $100$th$.($B$).$ How many contracts should the fund manager buy or sell to hedge all exposure to the market over the next $2$ months? Round to a whole number. $($C$).$ Describe an arbitrage stretegy and payoff if the current $3-$months index futures price is at $2050.$