Geometric Mean for Measuring Compounded Growth

Summary

The document explains the geometric mean as a way to summarize values that compound or multiply over time. It contrasts this approach with the arithmetic mean, which averages values by summing them, and notes that the geometric mean is suited to proportional growth, including investment growth rates. Applied across periods, it gives the constant rate that would produce the same cumulative change as the varying period-by-period rates. The document also connects this calculation to the familiar business measure of compound annual growth rate and mentions benchmarking speedup ratios as another use.

The explanation is conceptual and provides no worked trading example, dataset, or empirical comparison. It does not discuss how to calculate returns with losses, handle zero or negative values, or use the measure to evaluate risk. Traders can take away when compounded performance calls for a geometric average, but need additional guidance to apply it correctly to a particular return series.

Key ideas

• The geometric mean summarizes values through their product rather than their sum.
• It is suited to proportional growth and other quantities that compound across periods.
• The geometric mean of period growth describes an equivalent constant rate leading to the same ending amount.
• Compound annual growth rate is a business application of geometric averaging.
• The document gives a conceptual explanation without investment data or calculation guidance for edge cases.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.