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Beta Matrix and Common Factors in Stock Returns

  • Seung C. Ahn, Alex R. Horenstein and Na Wang


We consider the estimation methods for the rank of a beta matrix corresponding to a multifactor model and study which method would be appropriate for data with a large number of assets. Our simulation results indicate that a restricted version of Cragg and Donald’s (1997) Bayesian information criterion estimator is quite reliable for such data. We use this estimator to analyze some selected asset pricing models with U.S. stock returns. Our results indicate that the beta matrix from many models fails to have full column rank, suggesting that risk premiums in these models are underidentified.


Corresponding author

* Ahn (corresponding author),, Arizona State University Carey School of Business; Horenstein,, University of Miami Business School; and Wang,, Hofstra University Zarb School of Business.


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We are grateful to Stephen Brown (the editor), Raymond Kan (the referee), George Korniotis, Alok Kumar, Todd Pronno, Richard Roll, Aurelio Vazquez, and the participants at Columbia University, Instituto Tecnológico Autónomo de México, Universidad Autónoma de Nuevo León, Sogang University, Hofstra University, Arizona State University, the University of Miami, Hitotsubashi University, and numerous conferences at which we presented this paper. We also thank Laura Xiaolei Liu, Jonathan Lewellen, and Stefan Nagel for sharing their data with us.



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Beta Matrix and Common Factors in Stock Returns

  • Seung C. Ahn, Alex R. Horenstein and Na Wang


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