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.
Answer:
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
