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# Returns and the Bell Curve and Using Returns Distributions

Returns and the Bell Curve
An investment has an expected return of 8 percent per year with a standard deviation of 4 percent. Assuming that the returns on this investment are at least roughly normally distributed, how frequently do you expect to lose money?

Using Returns Distributions
Based on the historical record, if you invest in long- term U. S. Treasury bonds, what is the approximate probability that your return will be less than 6.0 percent in a given year? What range of returns would you expect to see 95 percent of the time? 99 percent of the time?

#### Solution Preview

1. We use the normal calculator which I used in the last question. Using mean = 0.08 and std. dev. = 0.04 and x1 = 0, we see that P(x<x1) = 0.0228. the probability of losing money is roughly 2.28%.

2. We refer back to the 4 sources for data on long term US treasury bonds. We have

Return Standard deviation

Long Term Bond ...

#### Solution Summary

Returns and the Bell Curve and Using Returns Distributions

\$2.19