Question

Assume the returns from an asset are normally distributed. The average annual return for the asset is 17.4 percent and the standard deviation of the returns is 27.5 percent. What is the approximate probability that your money will double in value in a single year?

Answer 1

Answer:

0.13%

Step-by-step explanation:

Mean, u = 17.4%

standard deviation, sd = 27.5%

We are looking for the probability that the money will double in value. Therefore we are looking for the value of x = 100% (meaning the value is 100% more that the previous year)

Find the value of z-score

z = (x-u)/sd

  = (100 - 17.4) / 27.5 = 3.003

Find the z score using the z-table

From z-table at P(z<3.003) = 0.9987

So, for the probability that it the money will be double is

P (Z>2.8982) = 1 - P(z<2.8982)

                      = 1- 0.9987

                      = 0.0013  = 0.13%