c) A mutual fund currently holds a $100 million portfolio of stocks resembling the S&P 500: which has a beta of 1 .CI. 1) How many S&P 500 Jtures contracts does the fund need to hedge this portfolio= if each S&P index point is worth S250? Round your answer to the nearest whole contract ( decimals). (2 points) 2) Instead of hedging= suppose that the fund would like to use futures to adjust the portfolio's beta from the current 1.0 to a less volatile 0.85. How many S&P 500 futures contracts does the md need\"? Round your answer to the nearest whole contract (0 decimals). Should these contracts be long or short? (2 points) 3) What is the beta of the illy-hedged portfolio (stocks + futures) in Part c) 1) above? What is the beta of a short S&P 500 futures contract? (2 points) PROBLEM 4 16 points): At Time 0 you observe the following zero coupon bond prices: hiaturity Implied Forward Rate Forward Price 1year 2 {ea 1' 3 }-'ea 1' a) For each maturity in the table above, calculate the implied forward rate for the nal year of the bond, and the forward zero-coupon bond price for the nal year of the bond. (6 points)