Cross-section and GMM/SDF tests of linear factor models

ABSTRACT

This study follows the appropriate Cochrane (2005) framework for comparing the estimates’ standard errors, $t$-statistics and ${\chi }^2$ statistics that pricing errors are jointly zero of the beta and the Generalized Method of Moments/Stochastic Discount Factor (GMM/SDF) methods in testing linear factor models. I extend his work by using the Fama-French three-factor model. The study finds that the GMM/SDF estimators’ standard errors and $t$-statistics behave very similarly to those obtained by the beta method, and the methods give almost exactly the same ${\chi }^2$ statistics. Unlike Rubio and Lozano (2011) conclusion, I find that Cochrane (2005) results are extensible to the Fama-French three-factor model. The results are robust using an extended sample period that ends in February 2020.

KEYWORDS:

• GMM/SDF
• beta
• cross-section
• Fama-French three-factor
• asset pricing

JEL CLASSIFICATION:

• G
• G1
• G12

Acknowledgments

I thank the late Professor John Nankervis for his constructive comments. I also thank the Editor (David Peel) and the anonymous reviewer for their valuable comments. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ For a detailed explanation of the methods, I refer the reader to Cochrane (2005), Chapter 12, section 12.2, pages 235–239 for the beta method. It is Chapter 13, section 13.2, pages 256–257, for the GMM/SDF method.

² Dividends are included.

³ http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.

⁴ The results are available upon request.