Index futures are often used to hedge portfolios that are not exactly the index. This is called cross-hedging. Suppose that we have a portfolio that is not the S&P 500, and we wish to shift the portfolio into T-bills. Assume that the portfolio and the S&P 500 are perfectly correlated. Suppose that we own $200 million of stocks with a beta relative to the S&P 500 of 1.2. Assume that the S&P 500 is 1200 with a zero dividend yield and the effective annual rate of 10%.
(a) Find the future price
(b) You believe that the S&P 500 index price will drop in the future and you decide to hedge your portfolio. You need to short some quantity of the S&P 500. How many S&P 500 index futures can you short?