Evaluating alternative methods for testing asset pricing models with historical data

We follow the correct Jagannathan and Wang (2002) framework for comparing the estimates and specification tests of the classical Beta and Stochastic Discount Factor/Generalized Method of Moments (SDF/GMM) methods. We extend previous studies by considering not only single but also multifactor models, and by taking into account some of the prescriptions for improving empirical tests suggested by Lewellen, Nagel and Shanken (2009). Our results reveal that SDF/GMM first-stage estimators lead to lower pricing errors than OLS, while SDF/GMM second-stage estimators display higher pricing errors than the classical Beta GLS method. While Jagannathan and Wang (2002), and Cochrane (2005) conclude that there are no differences when estimating and testing by the Beta and SDF/GMM methods for the CAPM, we show that their conclusion can not be extensible for multifactor models. Moreover, the Beta method (OLS and GLS) seem to dominate the SDF/GMM (first and second-stage) procedure in terms of estimators’ properties. These results are consistent across benchmark portfolios and sample periods.