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 17.2 percent and the standard deviation of those returns in this period was 43.92 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.)

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.)

Explanation / Answer

Doubling is a return of 100%. Tripling is a return of 200%. Convert to Z-score, then refer to the table.

Z = ( value - mean ) / sd = ( 100 - 17.2 ) / 43.92 = 1.885

here, value = 100%, mean = average annual rate = 17.2% and sd is nothing but standard deviation = 43.92% already given

Look up 1.89 on the table to find .9706

P(double) = P(return > 100) = P( Z > 1.89 ) = 1 - .9706 = .0294 or 2.94%
P(triple) = P(return > 200) = P(Z > 4.162 ) = less than 0.003% (table I used cut off at 4)

note: the figure 4.1759 we got by this calculation i.e, Z = ( value - mean ) / sd

= (200 - 17.2) / 43.92 = 4.162

here, Iam assuming you know how to use a Normal Distribution Table from your class.

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