The following is part of the computer output from a regression of monthly returns on Waterworks stock

Question:

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.

Standard Devlation of Residuals Beta R-square 0.06 (i.e., 6% monthly) 0.75 0.65

a. 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? Should he buy or sell contracts? The S&P 500 currently is at 2,000 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 .5% per month.

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