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

... 1. Modern portfolio theory for stock returns, assumes that ... calculate the probability that your return will be ... is supposed to be the "bell curve", the graphical ...

... When returns from a project can be assumed to be ... in Figure 136 (represented by a symmetrical, bell-shaped curve), the areas under the curve can be ...

Using the data given, find the time of day that has the shortest ... 43.5 44 8am Sunday 45 60 42 11pm Monday Return trip 47 58 ... (3) You can't get a bell curve (nor. ...

... mean which makes both sides of the bell equal. ... b. Find the probability that the return for common ... Mean returns 15.40% Standard deviation of returns 24.50% Test ...

... Therefore, Stock 2 has the more reliable expected return. ... you might get very large or very small returns.). ... is the sample symmetrical, skewed, bell-shaped, etc ...

... 2) Mound or Bell-shaped curve. ... 8) The total area under the normal curve is equal to 1. ... Modern portfolio theory commonly assumes that the returns of a ...

... the following problems I have used excel function NORMDIST(x, mean ,std dev , 1) returns. ... f ( x) = e σ 2π The graph of f(x)is famous bell shaped curve. ...

... discount rate, which equates expected future returns for the ... instructed on a proxy properly executed and returned. ... Web site this ratio is labeled Return on Net ...