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over a 25-year period an asset had an arithmetic return of 13.1 percent and a geometric return of 12.6 percent. using blume's formula, what is your best estimate of the future annual returns over the next 10 years?

Respuesta :

The estimated future annual returns over the next 10 years is 8.73%

Blume's Formula is a statistical formula used to forecast the future returns of an asset. The formula used past return information, in particular, both the arithmetic average return and the geometric average return. The forecast for a future return is the weighted average the arithmetic average and the geometric average.

Blume's formula is as follows:

[tex]R(T) = \frac{T - 1}{N - 1}\times \text{Geometric Average} + \frac{N - T}{N - 1} \times \text{Arithmetic Average} , where[/tex]

T is the number of periods to the forest into the future

N is the number of periods with observed returns

In this question, we have 50 periods of observed returns, i.e., N = 25. Applying this formula, the estimate of the future annual return over 10 years, i.e., T = 10, is:

[tex]\frac{10 - 1}{25 - 1} * 12.6\% + \frac{25 - 10}{50 - 1} * 13.1\% = 8.73\%[/tex]

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