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Mean-Preserving-Spread Risk Aversion and The CAPM

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  • Phelim P. Boyle
  • Chenghu Ma

Abstract

This paper establishes conditions under which the classical CAPM holds in equilibrium. Our derivation uses simple arguments to clarify and extend results available in the literature. We show that if agents are risk averse in the sense of mean-preserving-spread (MPS) the CAPM will necessarily hold, along with two-fund separation. We derive this result without imposing any distributional assumptions on asset returns. The CAPM holds even when the market contains an infinite number of securities and when investors only hold finite portfolios. Our paper complements the results of Duffie(1988) who provided an abstract derivation of the CAPM under some somewhat more technical assumptions. In addition we use simple arguments to prove the existence of equilibrium with MPS-risk-averse investors without assuming that the market is complete. Our proof does not require any additional restrictions on the asset returns, except that the co-variance matrix for the returns on the risky securities is non-singular.

Suggested Citation

  • Phelim P. Boyle & Chenghu Ma, 2013. "Mean-Preserving-Spread Risk Aversion and The CAPM," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    • Handle: RePEc:wyi:wpaper:001969
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    References listed on IDEAS

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    More about this item

    Keywords

    CAPM equilibrium; two-fund separation; generalized efficient portfolio; MPS-risk-aversion. JEL;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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