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 2.3% over the coming month. Beta 0.75 R-square 0.65 Standard Deviation of Residuals 0.12 (i.e., 12% monthly) a-1. If he holds a $4 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? The S&P 500 currently is at 600 and the contract multiplier is $250. Number of contracts

The following is part of the computer output from a regression of monthly retums on Waterworks stock against the S\&P 50Q index. hedge fund manager believes that Waterworks is underpriced, with an alpha of 2.3% over the coming month. a-1. If he holds a \$4 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? The S\&P 500 currently is at 600 and the contract multiplier is $250. b. What is the standard deviation of the monthly retum of the hedged portfolio? c. Assuming that monthly retums 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 0.2% per month. (Enter your answer as percent rounded to 2 decimol places, e.g., enter " 12.53% " and not "0.1253.")