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 believes that Waterworks is underpriced, with an alpha of 2% over the coming month.

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

a. If the fund holds a $4 million position in 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 it enter? Should it buy or sell contracts? The S&P 500 currently is at 4,000 and the contract multiplier is $50.

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.

d. Suppose you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviation as Waterworks. Assume the residual returns (the e terms in Equations 26.1 and 26.2) on each of these stocks are independent of each other. What is the residual standard deviation of the portfolio?

e. Recalculate the probability of a loss on a market-neutral strategy involving equally weighted, market-hedged positions in the 100 stocks over the next month.

 P-68