Risk-Return Analysis: The Theory and Practice of Rational Investing (Volume One)

3MEAN-VARIANCE APPROXIMATIONS TO THE GEOMETRIC MEAN

INTRODUCTION

Summaries of return series typically report their “geometric mean” return as well as their arithmetic mean. In general, if A₁, …, A_n are n nonnegative numbers, their geometric mean is defined as the nth root of their product,

This is to be distinguished from their arithmetic mean, or ordinary average,

The so-called geometric mean return in financial summaries is not literally the geometric mean of the return series r₁, r₂, …, r_T. (It couldn’t be, since returns are sometimes negative.) ...