NO.PZ2023101902000011
问题如下：
An analyst regresses the returns of 100 stocks against the returns of a major market index. The resulting pool of 100 alphas has a residual risk of 18% and an information coefficient of 9%. If the alphas are normally distributed with a mean of 0%, roughly how many stocks have an alpha greater than 4% or less than -4%?选项：
A.5 B.10 C.20 D.25解释：
The standard deviation (std) of the alphas = Residual Risk (volatility) x Information Coefficient (IC) = 0.20 * 0.10 = 0.02. So, 4% is twice the standard deviation of the alphas. The alphas follow normal distribution with mean 0, so about 5% of the alphas are out of the interval [-4%, 4%]. The total number of stocks is 100, so roughly there are 5 alphas that are out of the range.
