Suppose you manage a portfolio with a current market value of $64,845,000. You and your analyst team actively manage a long/short equity fund, which is benchmarking the S\&P 500 . Over the past three years your fund exhibits an annual continuously compounded retum of 17.92%. Over the same period of time the S\&P 500 returned an average annual continuously compounded retum of 16.39\%. You and your team estimate the beta of the portfolio over the same time period using daily retums is 0.885 . Your boss, the hedge fund manager, wants to "port" the alpha out of your portfolio and apply it to the retums of the hedge fund in a risk-less fashion using futures contracts as the hedging mechanism. Currently the risk-free rate is 4.13% (one-year treasury rate) and the current spot price of the S\&P 500 futures contract is 4149.5. You assume CAPM correctly prices the portfolio. A) What is the portfolio alpha? 5 points B) How many contracts are needed to hedge the portfolio in the most effective way? 5 points C) Show the expected cash value of the portfolio symbolically. 9 points D) What is the cash payoff of the futures pos fion? 7 points E) Show that the portfolio position hedged with the futures contract provides a return equal to the risk-free rate plus the portfolio alpha. 9 points