On the Distributional Conditions for A Consumption Oriented Three Moment CAPM

In this paper we develop sufficient conditions on probability distributions for a three moment (mean, variance, skewness) consumption oriented capital asset pricing model (CAPM) to price correctly a subset of assets. The assumptions that individuals in an allocationally efficient capital market have identical probability beliefs and monotone increasing strictly concave utility functions displaying non-increasing absolute risk aversion imply an aggregate preference function that exhibits preference for expected return, aversion to variance of return and preference for positive skewness. For otherwise arbitrary preferences, show that quadratic characteristic lines are sufficient for a subset of assets to be priced according to a three moment consumption oriented CAPM.