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 43.8 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.)

Explanation / Answer

1) Approximate probability that money will double in value in a single year.

Z value = (100 - 17.1)/43.8 = 1.89269

Table area to the left = 0.97080045

So probability that money will double = 1 - 0.97080045 = 0.02919955 = 2.92%

2) Approximate probability that money will triple in value in a single year.

Z value = (200 - 17.1)/43.8 = 4.17578

Table area to the left =0.99998515

So probability that money will triple = 1 - 0.99998515 = 0.00001485 = 0.001485%

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