An investment consultant tells her client that the probability of making a posit

Question

An investment consultant tells her client that the probability of making a positive return with her suggested portfolio is 0.90. What is the risk, measured by standard deviation, that this investment manager has assumed in his calculation if it is known that returns from her suggested portfolio are normally distributed with a mean of 6%?

I already have the answer but can you please explain this question like you're explaining it to someone who has never done this before because thats how i feel right now :/ Thank you

Explanation / Answer

answer

The probability of a positive return is

1Pr[1Pr[negative return]]

so

Pr[Pr[negative return]=0.1]=0.1

The z-score associated with a probability of 0.1 is (looking this up in the table)

z=1.28155z=1.28155

z=00.06=1.28155

z=00.06=1.28155

=0.061.28155=0.04681824.68%

=0.061.28155=0.04681824.68%

looks like they are actually off by 0.01% but it's closer than the other answers.

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