2. 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