A return series has an arithmetic mean of 10.5% and standard deviation of 13%. 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 calculate the range of returns that an investor would expect to receive 90% of the time, we need to find the two return values that have a cumulative probability of 5% on both ends (since 100% - 90% = 10% and we need to split that among both tails).

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a 5% cumulative probability is -1.645. From there, we can use the formula:

return = mean + (z-score * standard deviation)

Upper Range:
return = 10.5% + (-1.645 * 13%) = 7.37%
Lower Range:
return = 10.5% + (1.645 * 13%) = 13.63%

Therefore, an investor would expect to receive returns between 7.37% and 13.63% 90% of the time. So, the best choice is D.

A Return Series Has an Arithmetic Mean of 10