P1.T2.310. Probability Distributions II, Miller Chapter 4

[Giulia.Geraci]

Hi David, surely it is a stupid question. How do you calculate 1,64 standard deviation into this excercise (end of chapter 6 MIller question 3)?

****
Assume the annual returns of Fund A are normally distributed with a mean and standard deviation of 30%. The annual returns of Fund B are also normally distributed, but with a mean and standard deviation of 40%. The returns of both funds are independent of each other. What is the mean and standard deviation of the difference of the returns of the two funds, Fund B
minus Fund A? At the end of the year, Fund B has returned 80%, and Fund A has lost 12%. How likely is it that Fund B outperforms Fund A by this much or more?
Answer:
(...)
The mean of this distribution is 10%, and the standard deviation is 50%. At the end of the year, the difference in the expected returns is 92%. This is 82% above the mean, or 1.64 standard deviations.

 

[David Harper CFA FRM]

Hi @Giulia.Geraci (X - µ)/σ = (92% - 10%)/50% = 1.64, where 50% = sqrt(30%^2 + 40%^2 + 0), as ρ=0