A return series has an arithmetic mean of 12.8% and standard deviation of 7.8%. Assuming the returns are normally distributed what is the range of returns that an investor would expect to receive 90% of the time?

Question

Quizplus · Accepted Answer

To find the range of returns that an investor would expect to receive 90% of the time, we first need to determine the z-score associated with the 90th percentile. This can be found using a standard normal distribution table or by using a calculator.

Using a calculator, we can use the following formula:

z = invNorm(0.9) ≈ 1.28

Next, we need to find the corresponding return values using the given mean and standard deviation.

The lower expected return is:

12.8% - (1.28 x 7.8%) ≈ 2.8%

The upper expected return is:

12.8% + (1.28 x 7.8%) ≈ 22.8%

Thus, the range of returns that an investor would expect to receive 90% of the time is 2.8% to 22.8%. The closest answer choice to this range is C, which is F1F1F1S1F1F1F102.8% to 28.4%.

A Return Series Has an Arithmetic Mean of 12