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An asset has had an arithmetic return of 10.3 percent and a geometric return of 8.3 percent over the last 90 years. What return would you estimate for this asset over the next 10 years? 25 years? 30 years?

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Answer:

Blume's formula combines the geometric and arithmetic means of an asset to be able to predict its returns in a given period.

The formula is;

= Geometric Mean*(T-1)/(N-1) + Arithmatic Mean *(N-T)/(N-1)

Where;

T = Period in question

N = Total period

10 years

= 8.3%*(10-1)/(90-1) + 10.3%*(90-10)/(90-1)

= 10.1 %

25 years

= 8.3%*(25-1)/(90-1) + 10.3%*(90-25)/(90-1)

= 9.76%

30 years

= 8.3%*(30-1)/(90-1) + 10.3%*(90-30)/(90-1)

= 9.65%

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