Question

An asset has an average return of 10.25 percent and a standard deviation of 22.56 percent. What is the most you should expect to earn in any given year with a probability of 2.5 percent?

Answer 1

In the question, probability of 2.5% means 95% confidence interval.

Upper end value of 95% confidence interval is calculated as:
= Average Return + 2*Standard Deviation

Similarly, lower end value is calculated as:
= Average Return - 2*Standard Deviation

We need to determine, how much we should expect to earn in any given year. It means, we need to calculate the upper end value.

Given that;
Average Return is 10.25%
Standard Deviation is 22.56%

In a given year, we should expect to earn:
=10.25% + 2*22.56%
=10.25% + 0.4512
=0.5537 or 55.37%