Mean-Preserving-Spread Risk Aversion and The CAPM

Phelim P. Boyle and Chenghu Ma

No 2013-10-14, Working Papers from Wang Yanan Institute for Studies in Economics (WISE), Xiamen University

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.

Keywords: CAPM equilibrium; two-fund separation; generalized efficient portfolio; MPS-risk-aversion. JEL (search for similar items in EconPapers)
JEL-codes: D50 D81 G10 G11 (search for similar items in EconPapers)
Date: 2013-10-14
New Economics Papers: this item is included in nep-upt
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