Question

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 80%. If it is known that returns are normally distributed with a mean of 8%, what is the risk, measured by standard deviation, that this investment manager assumes in his calculation

Answer 1

9.5%

Step-by-step explanation:

we solve for the z value using

z = barX - μ/σ

= 0-0.08/σ

= p(x>0) = 0.80

1-0.80 = 0.20

0-0.08/σ = 0.20

using the z calculator we find the z score using a p value of 0.20

= -0.842

0-0.08/σ = -0.842

-0.08 = -0.842σ

Divide through by -0.842

0.08/0.842 = σ

0.095 = σ

The risk measured by the standard deviation at 80%= 9.5%

Thank you