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 89%. 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 4.7%? Use Table 1. (Round "z" value to 2 decimal places and final answer to 3 decimal places.)

A young investment manager tells his client that the probability of making a positive return with his suggested portfolio is 89%. 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 4.7%? Use Table 1. (Round "z" value to 2 decimal places and final answer to 3 decimal places.)

Explanation / Answer

According to the given scenario,

P(X > 0) = 0.89

Let the standard deviation is s. Then,

P(z > (0 - 4.7)/s) = 0.89

From z table,

P(z > -1.23) = 0.89

Hence,

-4.7/s = -1.23

s = 4.7/1.23

s = 3.821

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