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Over a 38-year period an asset had an arithmetic return of 12.4 percent and a geometric return of 10.3 percent. Using Blume’s formula, what is your best estimate of the future annual returns over 6 years? 10 years? 19 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

6 years

= 10.3%*(6-1)/(38-1) + 12.4%*(38-6)/(38-1)

= 12.1 %

10 years

= 10.3%*(10-1)/(38-1) + 12.4%*(38-10)/(38-1)

= 11.89%

19 years

= 10.3%*(19-1)/(38-1) + 12.4%*(38-19)/(38-1)

= 11.38%

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