The pension separation theorem

Roger Gay

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    The Tobin s separation theorem, a pillar of classic portfolio theory asserts that single-period mean variance efficient (MVE) investment portfolios, consist of combinations of the risk-free asset (the single period zero coupon bond ( ZCB )) and the market portfolio. In this paper the theorem is generalised to combinations of the market portfolio and risk-free assets such as bonds and annuities; securities with cash payoffs before end-of-term over the same single period. This apparently simple extension has immediate and far-reaching application to worlda??s multi-trillion dollar pension industry, for retirees exiting defined contribution (DC) funds with their individual lump sum which they must convert to a retirement income stream (RIS). An optimal pension portfolio under the mean variance criterion (MVC) is formed by splitting the lump sum into two parts. With one part, a riskless income asset (government-issued annuity bond for instance) is purchased, while the residual is invested in the market portfolio over the annuity term to reinstate capital. MVE pension portfolios can be used to mitigate investment, inflation, liquidity and longevity risk and are preferable under criteria other than mean-variance to account-based drawdown currently favoured by many lump sum retirees. A case study in the Australian pension context is provided. Existence of efficient RIS portfolios has policy implications for government infrastructure provision to support lump sum retirees in the pension phase.
    Original languageEnglish
    Pages (from-to)19 - 30
    Number of pages12
    JournalInvestment Management and Financial Innovations
    Volume8
    Issue number1
    Publication statusPublished - 2011

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