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., 32.16.) 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

1. Suppose that the asset price is $50. Doubling will make it $50*2 = $100. Return = (100-50)/50 = 100%.

Mean = 17% and standard deviation = 43.68%.

Now using the Z formula, Z = (value-mean)/standard deviation = (100-17)/43.68

= 1.90

Using the Z table for 1.90 we get the figure of 0.9713.

Now probability of doubling = probability that the return is greater than 100% = P(Z>1.90) = 1-0.9713 = 0.0287 or 2.87%

2. Probability of tripling: return = 200%. (Using the same method as shown in 1 above). Thus Z = (200-17)/43.68

= 4.1895 or 4.19

Using the Z table for 4.19 we get the figure of 0.99999. Now probability of tripling = probability that the return is greater than 200% = P(Z>4.19) = 1-0.99999 = 0.00001 or 0.001000%.

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