Measuring Investment Returns: Arithmetic Mean vs. Geometric Mean

$25.00

Inspired by the fact that arithmetic means are always higher than geometric means, the author derives the mathematical relationship using Taylor’s Expansion. Real U.S. historical data are used to validate the relationship across different investment classes. This mathematical relationship reveals that variance (risk) plays an important role in calculating geometric mean.

Author: Jim Zhang, Ph.D.

Inspired by the fact that arithmetic means are always higher than geometric means, the author derives the mathematical relationship using Taylor's Expansion. Real U.S. historical data are used to validate the relationship across different investment classes. This mathematical relationship reveals that variance (risk) plays an important role in calculating geometric mean.

 

Measuring Investment Returns: Arithmetic Mean vs. Geometric Mean.

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