Suppose you manage a portfolio with a current market value of $58,715,000. 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 return of 13.27%. Over the same period of time, the S&P 500 returned an average annual continuously compounded return of 14.17%. You and your team estimate the beta of the portfolio over the same time period using daily returns is 0.745. Your boss, the hedge fund manager, wants to port the alpha out of your portfolio and apply it to the returns of the hedge fund in a risk-less fashion using futures contracts as the hedging mechanism. Currently, the risk-free rate is 2.63% and the current spot price of the S&P 500 futures contract is 2,952.50. You assume CAPM correctly prices the portfolio.

1. Show the expected cash value of the portfolio symbolically. What is the cash payoff of the futures position?

2. Show that the portfolio position hedged with the futures contract provides a return equal to the risk-free rate plus the portfolio alpha.