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.