A Characterization of the Coskewness-Cokurtosis Pricing Model

The coskewness-cokurtosis pricing model is equivalent to there not being any return for which the alpha is positive and for which the residual risk has positive coskewness and negative cokurtosis with the market. Such returns would be extremely attractive to investors with mean-variance-skewness-kurtosis preferences who hold the market portfolio. This result establishes a parallel to the CAPM, which is equivalent to the absence of positive alpha returns. It also establishes a parallel to the fundamental theorem of asset pricing, because it relates absence of portfolios with unusually good costs/payoffs to the existence of a stochastic discount factor of a particular type