7. Suppose the S\&P500 index has a value of 1985 . Time to maturity is 4 months and the continuously compounded interest rate is 2% p.a. (a.) What is the no-arbitrage price of the futures contract? (b.) Show that you get the same futures price using the simple rate. (c.) Suppose you are long a diversified stock portfolio of $20m with a beta of 1.2 . Each futures contract has a value of $250 times the index. The no-arbitrage futures price (calculated in (a.) equals the actual futures price. How many contracts would you buy/sell