Question

You have found an asset with an arithmetic average return of
13.60 percent and a geometric average return of 10.44 percent. Your
observation period is 30 years. What is your best estimate of the
return of the asset over the next 5 years? 10 years? 20 years?
**(Do not round intermediate calculations. Enter your answers
as a percent rounded to 2 decimal places.)**

Answer #1

If arithmetic mean and geometric mean are given for a period of x and if we need to estimate mean for period of y, then we can use the formula: ((y-1/x-1)*geometric mean)+((x-y/x-1)*arithmetic mean.

Given arithmetic average return and geometric average return for a period of 30 years is 13.6% and 10.44% respectively.

So, estimate of return over next 5 years will be ((5-1)/30-1)*10.44%+((30-5)/30-1)*13.6%= 13.16%

estimate of return over next 10 years will be ((10-1/30-1)*10.44%+((30-10)/30-1)*13.6%= 12.62%

estimate of return over next 20 years will be ((20-1/30-1)*10.44%+((30-20)/30-1)*13.6%= 11.53%

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