Hedging with Futures. Suppose we want to hedge $10,000,000 worth of stock using a position in S\&P500 futures. Each futures contract is worth 250 times the index value at expiry and the current index value is 800 . Suppose that the stock's beta (relative to the S\&P 500) is 1.5, its standard deviation is p=0.3 and its correlation with the S&P500 is =0.5. (a) (5) Compute the optimal number of futures contracts to hedge this position. Be sure to indicate long or short. (b) (5) What is the variance of the hedged position? Hedging with Futures. Suppose we want to hedge $10,000,000 worth of stock using a position in S\&P500 futures. Each futures contract is worth 250 times the index value at expiry and the current index value is 800 . Suppose that the stock's beta (relative to the S\&P 500) is 1.5, its standard deviation is p=0.3 and its correlation with the S&P500 is =0.5. (a) (5) Compute the optimal number of futures contracts to hedge this position. Be sure to indicate long or short. (b) (5) What is the variance of the hedged position