Suppose the returns on an asset are normally distributed Sup

Suppose the returns on an asset are normally distributed. Suppose the historical average annual return for the asset was 5.7 percent and the standard deviation was 18.3 percent. What is the probability that your return on this asset will be less than –4.1 percent in a given year? Use the NORMDIST function in Excel® to answer this question. What range of returns would you expect to see 95 percent of the time? What range would you expect to see 99 percent of the time?

Solution

P(X<-4.1%) = normdist(-4.1,5.7,18.3) = 0.2961

95% range is

norminv(0.025,5.7,18.3) and norminv(0.975,5.7,18.3)

-30.167% and 41.567%

99% range is

norminv(0.005,5,7,18.3) and norminv(0.995,5.7,18.3)

-41.438% and 52.838%