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%?
A) 1.28%
B) 4.69%
C) 6.00%
D) 10.0%

Question

Quizplus · Accepted Answer

We need to use the standard normal distribution table to find the z-score that corresponds to a probability of 0.90. The closest value to 0.90 in the table is 0.8997, which corresponds to a z-score of 1.28.

z-score = (x - mean) / standard deviation

1.28 = (x - 6) / standard deviation

Solving for the standard deviation:

standard deviation = (x - 6) / 1.28

To find x, we can use the fact that the expected return is 6%:

0 = (6 - 6) / 1.28

Therefore, x = 6 + 0 = 6.

substitute x and the z-score back into the standard deviation formula:

standard deviation = (6 - 6) / 1.28 = 0 / 1.28 = 0

Therefore, the investment consultant has assumed a standard deviation of 0, which is not possible. This means that there is an error in the question, and none of the answer choices are correct.

An Investment Consultant Tells Her Client That the Probability of Making