The primary objective of this dissertation is to revisit the CAPM and the Fama-French multi-factor models with a view to evaluate the validity of the probabilistic assumptions imposed (directly or indirectly) on the particular data used. By thoroughly testing the assumptions underlying these models, several departures are found and the original linear regression models are respecified. The respecification results in a family of heterogeneous Student's t models which are shown to account for all the statistical regularities in the data. This family of models provides an appropriate basis for revisiting the empirical adequacy of the CAPM and the Fama-French multi-factor models, as well as other models, such as alternative asset pricing models and risk evaluation models. Along the lines of providing a sound basis for reliable inference, the respecified models can serve as a coherent basis for selecting the relevant factors from the set of possible ones. The latter contributes to the enhancement of the substantive adequacy of the CAPM and the multi-factor models. / Ph. D.