The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S\&P 500 index. A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2.5% over the coming month. a. If he holds a $3 million portfolio of Waterworks stock, and wishes to hedge market exposure for the next month using 1-month maturity S\&P 500 futures contracts, how many contracts should he enter? Should he buy or sell contracts? The S\&P 500 currently is at 1,000 and the contract multiplier is $250. b. What is the standard deviation of the monthly return of the hedged portfolio? c. Assuming that monthly returns are approximately normally distributed, what is the probability that this market-neutral strategy will lose money over the next month? Assume the risk-free rate is .2% per month. The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S\&P 500 index. A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2.5% over the coming month. a. If he holds a $3 million portfolio of Waterworks stock, and wishes to hedge market exposure for the next month using 1-month maturity S\&P 500 futures contracts, how many contracts should he enter? Should he buy or sell contracts? The S\&P 500 currently is at 1,000 and the contract multiplier is $250. b. What is the standard deviation of the monthly return of the hedged portfolio? c. Assuming that monthly returns are approximately normally distributed, what is the probability that this market-neutral strategy will lose money over the next month? Assume the risk-free rate is .2% per month