A young investment manager tells his client that the probability of making a pos

Question

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 90%. What is the risk (standard deviation) that this investment manager has assumed in his calculation if it is known that returns are normally distributed with a mean of 5.6%?

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 90%. What is the risk (standard deviation) that this investment manager has assumed in his calculation if it is known that returns are normally distributed with a mean of 5.6%?

Explanation / Answer

We take the pdf of the normal distribution with a mean of 5.6%, integrate from 0 to +inf, and then set the result equal to 90%.

(1.25331*erf(3.9598/a) + 1.25331) = .9 * sqrt(2 pi)

Solving by computer, we get that the standard deviation is 4.37%

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