Many people find the mean-variance assumption of the CAPM hard to justify. This paper replaces the mean-variance assumption with a weaker assumption based on the class of consistent risk measures. This class of risk measures is chosen because there is a weak form of equivalence between the mean consistent risk and the expected utility approaches to portfolio optimization. The general form for mean-consistent risk asset pricing models is derived, and the generalized mean-risk beta provided. The CAPM and a number of other well-known mean-risk asset pricing models arise as special cases.