An investment strategy has an expected return of 15 percent and a standard deviation of 9 percent. Assume investment returns are bell shaped. How likely is it to earn a return between 6 percent and 24 percent?

Question

Ethan Hanson

Mathematics

7 October, 19:45

An investment strategy has an expected return of 15 percent and a standard deviation of 9 percent. Assume investment returns are bell shaped. How likely is it to earn a return between 6 percent and 24 percent?

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Gillian Powers · Answer 1

68% of an investment earning a return between 6 percent and 24 percent.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 15

Standard deviation = 9

How likely is it to earn a return between 6 percent and 24 percent?

6 = 15 - 1*9

6 is one standard deviation below the mean

24 = 15 + 1*9

24 is one standard deviation above the mean

By the empirical rule, there is a 68% of an investment earning a return between 6 percent and 24 percent.