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Geometric Return and Portfolio Analysis




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 futureorientated 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.

Suggested Citation

  • Brian McCulloch, 2003. "Geometric Return and Portfolio Analysis," Treasury Working Paper Series 03/28, New Zealand Treasury.
  • Handle: RePEc:nzt:nztwps:03/28

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    References listed on IDEAS

    1. Ian Cooper, 1996. "Arithmetic versus geometric mean estimators: Setting discount rates for capital budgeting," European Financial Management, European Financial Management Association, vol. 2(2), pages 157-167.
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    More about this item


    Arithmetic; geometric; returns; portfolio; lognormal distribution.;

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • H55 - Public Economics - - National Government Expenditures and Related Policies - - - Social Security and Public Pensions

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