The Capital Asset Pricing Model as a General Equilibrium with Incomplete Markets
We recast the capital asset pricing model (CAPM) in the broader context of general equilibrium with incomplete markets (GEI). In this setting we give proofs of three properties of CAPM equilibria: they are eﬀicient, asset prices lie on a “security market line,” and all agents hold the same two mutual funds. The ﬁrst property requires a riskless asset, the latter two do not. We show that across all GEI only one of these three properties of equilibrium is generally valid: asset prices depend on covariances, not variances. We extend CAPM to many consumption goods in such a way that all three properties hold. But now the deﬁnition of a riskless asset depends on preferences and endowments, and so cannot be speciﬁed a priori.
Geanakoplos, John and Shubik, Martin, "The Capital Asset Pricing Model as a General Equilibrium with Incomplete Markets" (1989). Cowles Foundation Discussion Papers. 1157.