Purpose: To incorporate preference asymmetries in asset pricing theory. Originality: High. New theorem and pricing models introduced. Clarifications on Tier 1 literature provided. Two areas of literature bridged. Key literature / theoretical perspective: Hogan & Warren (1974), Bawa & Lindenberg (1977), Harvey & Siddique (2000), Dittmar (2002), Vanden (2006), Smith (2007) and Guidolin & Timmermann (2008). Design/methodology/approach: Primarily theoretical. Results developed in the pricing kernel framework of Ross (1978), Harrison & Kreps (1979) and Kreps (1981). Tests conducted using Hansen’s GMM. Findings: This paper contributes to the theoretical development of nonlinear asset pricing kernels. I bridge the current kernel framework with the early partial moment pricing models of the beta framework—thereby reconciling and clarifying these bodies of literature. By forming a generalized nonlinear asset pricing kernel involving powered min and max functions I generate a generalized multi-beta model. I derive and test the partial-moment analogue to the Black CAPM. This is a new result. A model involving both lower and upper partial-moments, accommodating various kernel shapes, is developed and tested in the context of preference regularity conditions. Research limitations/implications: Much research can be conducted using the new models and generalized kernel presented. Practical and Social implications: Previously, if a market did not have a risk-free asset, pricing using partial-moments was not possible. The new model makes this possible.