Innovated Power Enhancement for Testing Multi-factor Asset Pricing Models

24 Pages Posted: 8 Apr 2021

See all articles by Xiufan Yu

Xiufan Yu

University of Notre Dame

Jiawei Yao

Princeton University

Lingzhou Xue

Pennsylvania State University - Department of Statistics

Date Written: November 4, 2019

Abstract

Testing multi-factor asset pricing models is instrumental for the asset pricing theory and practice. Due to the accumulation of errors in estimating high-dimensional parameters, traditional quadratic-form tests such as the Wald test perform poorly against the sparse alternative hypothesis in the presence of a few mispriced assets. Fan et al. (2015) introduced a powerful testing procedure by adding a power enhancement component to the Wald test statistic and proved the power enhancement properties. To provide a promising alternative to Fan et al. (2015), we first introduce a new maximum-form test statistic and then study the asymptotic joint distribution of the Wald test statistic and the maximum test statistic. We prove that these two test statistics are asymptotically independent. Given their asymptotic independence, we propose an innovative power-enhanced testing procedure to combine their respective power based on Fisher’s method (Fisher, 1925). Theoretically, we prove that the innovated power enhancement retains the desired nominal significance level and achieves the asymptotically consistent power against the more general alternative. Furthermore, we demonstrate the finite-sample performance of our proposed innovated power enhancement test in simulation studies and an empirical study for testing market efficiency using asset returns of the Russel-2000 portfolio.

Keywords: high-dimensional hypothesis testing; multi-factor pricing model; sparse alter-natives; Fisher’s method; power enhancement.

JEL Classification: C12, C58

Suggested Citation

Yu, Xiufan and Yao, Jiawei and Xue, Lingzhou, Innovated Power Enhancement for Testing Multi-factor Asset Pricing Models (November 4, 2019). Available at SSRN: https://ssrn.com/abstract=3809369 or http://dx.doi.org/10.2139/ssrn.3809369

Xiufan Yu

University of Notre Dame

Notre Dame, IN 46556
United States

Jiawei Yao

Princeton University ( email )

22 Chambers Street
Princeton, NJ 08544-0708
United States

Lingzhou Xue (Contact Author)

Pennsylvania State University - Department of Statistics ( email )

326 Thomas Building
University Park, PA 16802
United States

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