Assume that historical returns and future returns are independently and identically distributed and drawn from the same distribution.
a. Calculate the 95% confidence intervals for the expected annual return of the four different investments included in the following table.
b. Assume the data in the table represents the true expected return and volatility and that these returns are normally distributed. For each investment, calculate the probability that an investor will not lose more than 5% in the next year.
Investment Average Annual Return Return Volatility (std dev)
Firm A 20.9% 41.5%
Firm B 11.6% 20.6%
Firm C 6.6% 7.0%
Firm D 3.9% 3.1%