Assuming that monthly returns are approximately normally distributed, what is the probability that this market-neutral strategy will lose money over the next month

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 Deviation of Residuals = 0.06 (i.e., 6% monthly)

Assuming that monthly returns are approximately normally distributed, what is theprobability that this market-neutral strategy will lose money over the next month?

Assume the risk-free rate is .5% per month.

0.33853

Explanation:

Given that, the expected rate of return of the market-neutral position is equal to the risk-free rate plus the alpha:

0.5%+ 2.0% = 2.5%

Hence, since we assume that monthly returns are approximately normally distributed.

The z-value for a rate of return of zero is

−2.5%/6.0% = −0.4167

Therefore, the probability of a negative return is N(−0.4167) = 0.33853