Refer to problem 36.
a. 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 23.1 and 23.2) on each of these stocks are independent of each other. What is the residual standard deviation of the portfolio?
b. 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.
In Problem 36.
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 percent over the coming month.

Beta Rsquared Standard Deviation of Residuals 75 65 06 (ie, 6% monthly)