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 43.53 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.)

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 43.53 percent.

Explanation / Answer

Answer: The mean return for shares was 17.2%, with a standard deviation of 43.53%.

Doubling your money is a 100% return, so if the return distribution is normal, we can use the z-statistic. So:

z = (X – µ)/s

z = (100% – 17.2)/43.53% = 1.902136 standard deviations above the mean

This corresponds to a probability of approximately 2.857666%.

Answer: Tripling your money would be:

z = (200% – 17.2)/43.53% = 4.19940 standard deviations above the mean.

This corresponds to a probability of almost 0.001338%.

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