Assume that the returns from an asset are normally distributed The average annua

Question

Assume that the returns from an asset are normally distributed The average annual return for this asset over a specific period was 17 percent and the standard deviation of those returns in this period was 43 68 percent What is the approximate probability that your money will double in value in a single year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g.. 32.18.) Probability of doubling 2 87 percentage What about triple m value? (Do not round intermediate calculations. Enter your answer as a percent rounded to 6 decimal places, e.g.. 32.161616.)

Explanation / Answer

Doubling the money means return of 100% and tripling the money means return of 200%. So, if the return is normally distributed we can use z-statistic.

Formula: Z = (X - µ)/

When 100%
Z = (100% - 17%) / 43.68 = 1.900 standard deviation above the mean
the correspondent probability = 0.0287 or 2.87% approximately

When 200%
Z = (200% - 17%) / 43.68 = 4.189 standard deviation above the mean
the correspondent probability = 0.000014 or 0.0014%% approximately

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