Geometric Return and Portfolio Analysis

Abstract

Expected geometric return is routinely reported as a summary measure of the prospective performance of asset classes and investment portfolios. It has intuitive appeal because its historical counterpart, the geometric average, provides a useful annualised measure of the proportional change in wealth that actually occurred over a past time series, as if there had been no volatility in return. However, as a prospective measure, expected geometric return has limited value and often the expected annual arithmetic return is a more relevant statistic for modelling and analysis. Despite this, the distinction between expected annual arithmetic return and expected geometric return is not well understood, both in respect of individual asset classes and in respect of portfolios. This confusion persists even though it is explained routinely in finance textbooks and other reference sources. Even the supposedly straightforward calculation of weighted average portfolio return becomes somewhat complicated, and can produce counterintuitive results, if the focus of future-orientated reporting is expected geometric return. This paper explains these issues and applies them in the context of the calculations underlying the projections for the New Zealand Superannuation Fund.