The Treasury

Global Navigation

Personal tools

You are here: Home > Publications > Research and Policy > Working Papers > 2003 > Geometric Return and Portfolio Analysis (WP 03/28)


Geometric Return and Portfolio Analysis - WP 03/28

Publication Details

  • Geometric Return and Portfolio Analysis
  • Published: Dec 2003
  • Status: Current
  • Author: McCulloch, Brian
  • JEL Classification: C53; D84; G10; H55
  • Hard copy: Available in HTML and PDF formats only.

Geometric Return and Portfolio Analysis

New Zealand Treasury Working Paper 03/28

Published December 2003

Author: Brian McCulloch


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.


Browse section/chapter Download/Page range


Table of Contents

List of Tables

List of Figures

1 Introduction

2 Expected geometric return and expected arithmetic return

3 Expected portfolio return

4 Expected future size of an investment fund

5 Calculation of the required capital contribution rate for the New Zealand Superannuation Fund

6 Conclusion

Appendix One: Derivation of Median Returns

Appendix Two: Lognormal Distribution of Annual Returns


twp03-28.pdf (397 KB) pp. 1–12

List of Tables

List of Figures


This Treasury Working Paper is an expanded version of a practice note that was published on the Treasury internet at the time that the strategic investment policy for the New Zealand Superannuation Fund was announced (McCulloch 2003).


The views expressed in this Working Paper are those of the author and do not necessarily reflect the views of the New Zealand Treasury. The paper is presented not as policy, but with a view to inform and stimulate wider debate.

Page top