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 her calculation if it is known that returns from her suggested portfolio are normally distributed with a mean of 6%?
A) 1.28%
B) 4.69%
C) 6.00%
D) 10.0%

Question

Quizplus · Accepted Answer

We can use the inverse normal distribution function to find the z-score corresponding to a probability of 0.90:
z = invNorm(0.90) = 1.2816
We can then use the z-score formula to solve for the standard deviation:
z = (x - mu) / sigma
1.2816 = (0 - 0.06) / sigma
sigma = (0.06) / 1.2816 = 0.0469 or 4.69%
Therefore, the investment manager has assumed a risk of 4.69% in her calculation.

An Investment Consultant Tells Her Client That the Probability of Making