Testing Linear Factor Pricing Models With Large Cross Sections: A Distribution-Free Approach

Abstract

We develop a finite-sample procedure to test the beta-pricing representation of linear factor pricing models that is applicable even if the number of test assets is greater than the length of the time series. Our distribution-free framework leaves open the possibility of unknown forms of non-normalities, heteroskedasticity, time-varying correlations, and even outliers in the asset returns. The power of the proposed test procedure increases as the time-series lengthens and/or the cross-section becomes larger. This stands in sharp contrast to the usual tests that lose power or may not even be computable if the crosssection is too large. Finally, we revisit the CAPM and the Fama-French three factor model. Our results strongly support the mean-variance efficiency of the market portfolio. JEL classification: C12, C14, C33, G11, G12 Bank classification: Econometric and statistical methods; Financial markets RésuméLes auteurs élaborent une procédure permettant de tester, en échantillon fini, la représentation des coefficients bêta donnés par les modèles linéaires d'évaluation factorielle, et ce, même si le nombre des actifs dépasse celui des valeurs de la série chronologique. Leur cadre autorise des formes inconnues de distribution autres que la loi normale ainsi que la présence d'hétéroscédasticité, de structures de corrélation variables dans le temps, voire de rendements aberrants. La puissance de la procédure s'accroît avec l'allongement de la série chronologique et la hausse du nombre des actifs. Cette propriété tranche avec les limites des tests habituels, qui perdent de leur puissance ou peuvent même devenir inexécutables si le nombre des actifs est trop élevé. Pour finir, les auteurs réexaminent le modèle d'évaluation des actifs financiers et le modèle trifactoriel de Fama et French. Leurs résultats indiquent clairement que le portefeuille de marché se situe sur la frontière efficiente dans le plan moyenne-variance.

Bootstrap Tests of Mean-Variance Efficiency with Multiple Portfolio Groupings

“…The effect of increasing the number of test assets on test power is discussed in Gibbons et al (1989), Campbell et al (1997, p. 206), Sentana (2009), andGungor andLuger (2013).…”

Robust Factor Models with Explanatory Proxies

“…The GRS test and related tests, in contrast, are designed to test the "zero-alpha" hypothesis (H 0 : α i = 0 for all i = 1, ..., N ) using w t as the factors in the empirical asset pricing model. The "zero-alpha" test is used to assess the proxy of the true factors only when the market is mean-variance efficient (Gungor and Luger, 2013). In contrast, our proposed test aims directly at the question whether the observed proxy w t is adequate or not, without assuming the efficient market hypothesis.…”

“…The proposed test provides a diagnostic tool for the specification of common factors in empirical studies, and complements the "efficiency test" in the financial econometric literature (e.g., Gibbons et al (1989); Pesaran and Yamagata (2012); Gungor and Luger (2013); Fan et al (2015a)). While the efficiency test aims to test whether the alphas of excess returns are simultaneously zero for the specified factors, here we directly test whether the factor proxies are correctly specified.…”

Finite-Sample Sign-Based Inference in Linear and Nonlinear Regression Models with Applications in Finance

“…As shown in Gungor and Luger (2009) Finally, an extension of the mean-variance efficiency sign-based test of Gungor and Luger (2009) can be found in Gungor and Luger (2013). The latter provide a sign-based statistical procedure that allows one to test the beta-pricing representation of linear factor pricing models, instead of the single market factor model in (40).…”

“…The latter provide a sign-based statistical procedure that allows one to test the beta-pricing representation of linear factor pricing models, instead of the single market factor model in (40). Exploiting results from Coudin andDufour (2009), Gungor andLuger (2013) obtain tests of multi-beta pricing representations that relax three assumptions of the prominent mean-variance efficiency test of Gibbons, Ross, and Shanken (1989): (i) the assumption of identically distributed disturbances, (ii) the assumption of normally distributed disturbances, and (iii) the restriction on the number of assets. A very attractive feature of Gungor and Luger's (2013) test is that it is applicable even if the number of assets is greater than the length of the time series.…”