[show abstract][hide abstract] ABSTRACT: I bridge the current pricing kernel framework with the early partial-moment pricing models of the beta framework, thereby reconciling and clarifying these bodies of literature. I argue for the inclusion of powers of min and max functions within a generalized kernel, and form a generalized beta model. Polynomial kernels and the kernel underpinning the partial-moment analogue of the Sharpe-Lintner CAPM are nested. I derive the partial-moment analogue to the Black CAPM, thus completing a theoretical parallelism, and compare the kernel-implied and canonical risk-neutral probabilities. A new model involving both lower and upper partial-moments, accommodating various kernel shapes present in the literature, is developed in the context of preference regularity conditions.
[show abstract][hide abstract] ABSTRACT: The mean-lower partial-moment CAPM is an analogue of the Sharpe-Lintner CAPM. The partial-moment analogue of the Black CAPM has to date proven illusive. In this paper, the mean-threshold probability weighted lower partial-moment framework is introduced. A new pricing model is derived in this framework, building on new theorems on stochastic dominance and zero-beta separation. This model is the partial-moment analogue of the Black CAPM and completes a parallelism in the literature. Unlike the Black CAPM, the model is not rejected under a generalized method of moments test. A Bonferroni correction adds weight to this conclusion.