Explanation:
According to the Fundamental Law of Active Management, the standard deviation of alphas can be roughly approximated by: Standard Deviation of Alpha = Information Coefficient (IC) × Residual Risk = 0.10 × 0.18 = 0.018 = 1.8%. The question asks for the number of stocks with an alpha greater than 3.6% or less than -3.6%. Since the mean is 0%, 3.6% is exactly two standard deviations away from the mean (2 × 1.8% = 3.6%). Assuming a normal distribution, the probability of an observation being more than two standard deviations from the mean is approximately 5% (more precisely 4.55%). Number of stocks = 500 × 5% = 25.
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Q.62 An analyst regresses the returns of 500 stocks against the returns of the S&P 500 index. The resulting pool of 500 alphas has a residual risk of 18% and an information coefficient of 10%. Assuming that the alphas are normally distributed with a mean of 0%, roughly how many stocks have an alpha greater than 3.6% or less than -3.6%?
A
5
B
250
C
475
D
25
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