Question

Suppose that, from 25 years of annual returns data, we calculate an arithmetic average return of 12 percent and a geometric average of 9 percent. Calculate average return forecasts 1 year, 5-year, and 10 year into the future.

Answer 1

R(T) = [ T-1 / N-1 ] × geometric average + [ N-T / N-1 ] × arithmetic average

Given Geometric Average = 12%

Arithmetic Average = 19%

N = 40

(i) Given T = 1

R(1) = [ (1 - 1) / (25 -1) ] * 12% + [ (25 - 1) / ( 25 - 1) ] * 9%

= 9%

(ii) Given T = 5

R(5) = [ (5 - 1) / (25 -1) ] * 12% + [ (25 - 5) / ( 25 - 1) ] * 9%

= 2.0% + 7.5%

= 9.5%

(iii) Given T = 10

R(10) = [ (10 - 1) / (25 -1) ] * 12% + [ (25 - 10) / ( 25 - 1) ] * 9%

= 4.5% + 5.625%

= 10.125%

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