An analyst regresses the returns of 200 stocks against the returns of a major market index.The resulting pool of 200 alphas has a residual risk of 25%and an information coefficient of 8%.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%?
A.8
B.10
C.16
D.25
Answer:B
Explanation:
The standard deviation(std)of the alphas=Residual Risk(volatility)*Information Coefficient(IC)=0.25*0.08=0.02.4%is twice of 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 200,so roughly there are 10 alphas that are out of the range.