(Use continuous compounding)

We are expecting a volatile year in the financial markets. You are a manager of a $100 million pension fund. Retirees already rely on the fund for the payment; therefore, you want to avoid any risk to the portfolio and hedge against a market decline. Your portfolio beta is .90. The S&P 500 current level is 4,050.0, the S&P 500 dividend yield is 1.60% and the risk free rate is 4.0%. You consider hedging using the March 2023 (three months to maturity). a. Price the future contract (time should be by months). b. Describe your hedge (using the standard $250 multiple contract); how many contracts will buy or sell? One month later the S&P 500 index is down 5%. c. Compute the March 2023 future contract value (risk-free rate and dividend yield remain the same) and the short future position gains. d. Compute the equity portfolio value (assume the portfolio return follow exactly the CAPM formula). e. Compute the total portfolio value (including the hedge).