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% over the coming month.

Beta: 0.75

R-square: 0.65

Standard Deviaiton of Residuals: 0.06 (i.e., 6% monthly)

a-1 If he holds a $6 million portfolio of Waterworks stock and wishes to hedge market exposure for the next month using one-month maturity S&P 500 futures contracts, how many contracts should he enter? The S&P 500 currently is at 2,000 and the contract multiplier is $250.

a-2. Should he buy or sell contracts? Explain why he should buy or sell.

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 0.5% per month.