Geometric Mean ReturnWhen measuring property investment performance over several periods the simple average, which is also referred to as arithmetic mean, does not provide a good measure of investment performance because it does not take into account the compounding of returns through time. In such case one needs to calculate the constant rate of return per period which when applied to the beginning value of the investment at a compounding fashion would result in the same ending value of the investment. This compounded periodic constant rate implied by the beginning and ending value of the investment is referred to as the geometric mean return. The geometric mean return can be calculated in two ways: 1) Using periodic returns 2) using the beginning and ending value of the investment.
GMR = [(1+R1) * (1+R2) * (1+R3)]1/3 - 1 Then the more generalized formula for n periods (months, quarters, or years) is: GMR = [(1+R1) * (1+R2) * (1+R3)….(1+Rn)]1/n - 1 Consider the following example of annual returns for three years: Example: R1 = 10% R2 = 40% R3= -30% Then the geometric mean annual return can be calculated as: GMR = [(1+0.10) * (1+0.4) * (1-0.3)]1/3 - 1 GMR = (EV/BV) (1/3) -1 To demonstrate the application of the formula let' s assume that the beginning value BV in the above example is 100. With this beginning value and given the annual returns the respective investment values at the end of each year can be calculated as: Thus the ending value EV is 107.8 and GMR can be calculated as: GMR = (107.8 /100) o.333 -1 = .0254 This example verifies that both formulas give the same result.
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