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Note: Geometric vs Arithmetic Mean

September 26, 2009

To avoid confusion, GAMDO looks at the product of momentums which is the geometric cumulative return versus the arithmetic mean of short term returns. The derivation of the geometric mean would be to take the power of of the geometric cumulative return (P) as:

P^ 1/(number of data points)

One of our astute readers Eber Terandst pointed out that the geometric mean is never larger than the arithmetic mean which is true, however I was referring to the geometric cumulative return series which does in fact fluctuate between being higher or lower than the arithmetic mean of returns. My own terminology was the source  of confusion, nonetheless the results are accurate . Here is a breakdown:

Last 3000 bars (10/20/1997-Present) 17.50% 0.764 0.795
Last 13000 bars 5.10% 0.01 0.392
Previous 10000 bars 1.50% 0.015 0.12
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