Question

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.

Answer 1

1) Current market value of the portfolio is = $58,715,000

If we manage a portfolio with S&P 500 we have to make more 0.9%. Current market value included the compounded return of 13.27% and the S&P 500 avg return was 14.17%. Yes, the risk-free rate is 2.63% and other portfolio's return is more than the risk-free rate, so the investing both of them is an intelligent investment opportunity for investors, but there is some kind of risk has to be followed. For 1 future contract we have to pay $2952.50, with this portfolio we have to buy 19886.54 Future contract.

2) We will earn a profit if only the future contract executed our expectation. The average annual compounded return is 14.17%, then if we buy the future contract with the expectation of the price of the S&P 500 Index will go up. So buy holding this our portfolio will increase more 0.9% then will make a profit, we are successfully hedged the portfolio with S&P.

Thank you For asking.