The Interpretation of the Geometric Mean: A Note

Stewart Hodges and Stephen Schaefer

Journal of Financial and Quantitative Analysis, 1974, vol. 9, issue 3, 497-504

Abstract: It has been said [2,4,5,6,7, and 8], and it seems to be widely accepted, that the geometric mean of the price relatives of a group of securities can be interpreted as the return which would have been earned on a portfolio of those securities, managed continuously over time to maintain an equal money investment in each security. This is a theoretical concept which could not be implemented literally by a portfolio manager, but it can still be treated rigorously in a mathematical sense. In a recent paper in this journal Rothstein [8] defined continuous reallocation as the limiting case of a policy which does have an operational definition. He showed that the index corresponding to a policy of the equalization of dollar investments approaches the geometrically averaged index as its limiting value. We shall argue that this interpretation of the geometric mean is a misleading one, since it depends upon assumptions which imply serious market inefficiencies.

Date: 1974
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