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28 August, 09:21

Over a 30-year period an asset had an arithmetic return of 13 percent and a geometric return of 10.5 percent. Using Blume's formula, what is your best estimate of the future annual returns over the next 10 years?

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  1. 28 August, 09:54
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    12.22% will be the forecast rate over the next 10-years framework.

    Explanation:

    Blume's formula is used to do an average of both, the arithmetic and geometric mean. The formula is as follow:

    (T-1) / (N-1) * Geometric average + (N-T) / (N-1) * Arithmetic average

    Where:

    T = forecast period = 10 years for this case

    N = the data we have samples = 30 years for this particular project

    Then we have thegeometric and arthmetic mean

    We place them on the formula and solve for Return on Equity

    Return = (10-1) / (30-1) * 0.105 + (30-10) / (30-1) * 0.13

    Return = (9/29) *.105 + (20/29) *.13 = 0.122241379 = 12.22%

    12.22% will be the forecast rate over the next 10-years framework.
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