Using a modified geometric mean

In this paper, we examine the use of geometric versus arithmetic assumptions when constructing return expectations for use in mean-variance optimization and the generation of expected portfolio returns.

In a mean-variance framework, we observe that an expected return derived from an arithmetic mean tends to overstate the long-term realized returns, while an expected return derived from a geometric mean tends to understate the realized return. Accordingly, we recommend using a blended approach that we call a modified geometric mean.