Necessary and Sufficient Conditions for the CAPM

Abstract

The general restrictions on all economic primitives (for example, (a) endowments, (b) preferences and (c) asset return distributions) that yield either the CAPM or derived preferences over mean and variance alone in equilibrium are provided. These results are then used to derive necessary and sufficient conditions on preferences and the distribution of asset returns alone that provide the CAPM. In particular we show that the CAPM can hold in the class of polynomial utility functions and pseudo-elliptical asset return distributions. This class includes the already known conditions under which the CAPM holds (quadratic utility or two-fund separating distributions). Furthermore, we show that the CAPM cannot hold for analytic utility functions and return distributions that are not in this class. Unfortunately, this class of restrictions is no more appealing, empirically, than the already well known restrictions that provide the CAPM. Consequently, this paper shows that no set of empirically appealing conditions on primitives exist that can provide the CAPM.

JEL Classification: G11, G12