The SP$500$ today is at $2667\mathrm{.}55$ and the SP$500$ futures settlement price for December is at $2649\mathrm{.}2.$ A person decides to invest $$662,300$ in a mutual fund which tracks the SP$500$ and, at the same time, enter in one SP$500$ futures contract. The standard deviation of the SP $500$ returns is $10\mathrm{.}2\%.$ Decide if the investor should enter the short or long position in the futures contract. Calculate the expected value and standard deviation of gains$/$losses for the mutual fund alone and the fund plus futures for all range of probabilities. Suppose the SP$500$ can vary by one STD in either direction. Is there a combination of probabilities for which the combination of futures contracts and index is better? How do the standard deviation for the three alternatives compare?