On the Relationship between Arithmetic and Geometric Returns

Abstract

For a conventional portfolio of risky assets, the paper presents four approximate relationships between the portfolio's arithmetic expected return, geometric expected return, and variance. The paper provides simple quantitative explanations for all four relationships. The results of these formulas are compared to historic data and to each other. The paper identifies the relationship that should be expected to produce the most reliable results.

Keywords: arithmetic expected return, arithmetic average, geometric expected return, geometric average

JEL Classification: G00, G10, G11