Question

Assume that the returns from an asset are normally distributed. The average annual return for this asset over a specific period was 14.7 percent and the standard deviation of those returns in this period was 43.59 percent.

a. What is the approximate probability that your money will double in value in a single year? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b. What about triple in value? (Do not round intermediate calculations and enter your answer as a percent rounded to 6 decimal places, e.g., .161616.)

Answer 1

(a) Let the interest rate to double amount in one year be r

Initial Investment = P, Investment Value after 1 year = 2P

FV = PV(1+r)

=> 2P = P(1+r) => r = 100%

The return should be more than 100% for the amount to double in one year

Let the Probability be P(x)

z = (X - mean)/stdev = (100 - 14.7)/43.59 = 1.957

from z table, P(z) = 0.9748

P(x) = 1 - 0.9748 = 0.0252 or 2.52%

Hence, probability that the investment would double in one year is 2.52%

(b) Let the interest rate to triple amount in one year be r

Initial Investment = P, Investment Value after 1 year = 3P

FV = PV(1+r)

=> 3P = P(1+r) => r = 200%

The return should be more than 200% for the amount to double in one year

Let the Probability be P(x)

z = (X - mean)/stdev = (200 - 14.7)/43.59 = 4.252

from z table, P(z) = 0.99998

P(x) = 1 - 0.99998 = 0.00002 or 0.002%

Hence, probability that the investment would double in one year is 0.002%