| Multivariate statistics used to test factor-based asset pricing models often rely on the presumption that returns are independent and identically distributed multivariate normal or that factor-mimicking portfolio returns are independent of model residuals, assumptions that are strongly rejected in stock return data. I propose simple to calculate asymptotic corrections to these multivariate tests of asset pricing factor models that allow returns to remain within the elliptical class of distributions—the class of distributions closely associated with mean-variance separation—having finite fourth moments and containing the multivariate normal distribution as a special case. The generalized tests presented therefore nest many previous tests yet are computationally simple to implement. In addition, it is shown through simulations that the adjusted tests perform well when simulated data are multivariate normal. The adjustment provides good inference when returns are elliptical but not normal. Furthermore, the proposed adjusted statistics perform as well as or better from a test size perspective than competing generalizations including some GMM-based and bootstrap-based approaches. Moreover, the work discusses how the power of the adjusted tests may be improved through the use of M-estimators. With the adjustment, the three-factor model of Fama and French (1993) is no longer strongly rejected. In addition, the work shows how Stein's Lemma, frequently used in deriving the factor models like the CAPM, does not hold under discrete ellipticity. |
