The stochastic discount factor model provides a general framework for pricing assets. A suitably specified discount factor encompasses most of the theories currently in use, including the CAPM, consumption CAPM, higher-moment CAPM and their conditional versions. In this thesis, we focus on the empirical admissibility of alternative SDFs under restrictions that ensure that investors’ risk-preferences are well behaved. More innovatively, we explore whether the SDF implied by the 3 and 4-moment CAPM is plausible under restrictions that are weaker than those considered by Dittmar (2002) yet sufficient to rule out implausible curvature of the representative investor’s utility functions. We find that, even under these weaker restrictions, the 3 and 4-moment CAPM cannot solve well known puzzles which plague the empirical performance of extant rational asset pricing models, even though the higher order terms do generate considerable additional explanatory power. Faced with this difficulty, we then explore whether the failure to fully account for cross-sectional differences in average returns can be explained by the presence of either transaction costs or a behavioural component of the SDF, reflecting investors’ systematic mistakes in processing information. We find evidence of both problems, though our analysis is not conclusive in this respect. Finally, in a more applied exercise, we apply the SDF-framework to test whether Chinese fund managers generate superior investment performance, and find that Chinese fund managers have not achieved better performance than the individual investors under either the unconditional or the conditional measure.