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

Question

Assume that the returns from an asset are normally distributed. The average annual return for this asset over a specific period was 17.1 percent and the standard deviation of those returns in this period was 41.7 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., 32.16.)

Probability of doubling %

What about triple in value?

(Do not round intermediate calculations. Enter your answer as a percent rounded to 6 decimal places, e.g., 32.161616.) Probablity of tripling %

Explanation / Answer

We need to use the Normal Distribution Table for calculation.

Doubling the value means a return of 100% and Tripling means a return of 200%.

Converting to Z-score using the Normal Distribution Table.

Double your Money :

Z= (X - µ)/ = (Value – Mean)/ Standard Deviation

                      = (100-17.1)/41.7

                     = 82.9/41.7 = 1.98

We have look up 1.98 in the Normal Distribution table and we find 0.9761

Triple your Money :

Z= (X - µ)/ = (Value – Mean)/ Standard Deviation

= (200-17.1)/41.7

= 182.9/41.7 = 4.38

Using table 1 we have to cut off at 4 i.e less than 0.003%

Probability of Doubling = (P return>100) = P(Z>1.89) = 1-0.9706 = 0.0294 or 2.94%

Probability of Tripling = (P return>200) = P(Z>4.38) = <0.003%{cut off at Z=4}

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