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Nonparametric testing for anomaly effects in empirical asset pricing models

Abstract

In this paper, we propose a class of nonparametric tests for anomaly effects in empirical asset pricing models in the framework of nonparametric panel data models with interactive fixed effects. Our approach has two prominent features: one is the adoption of nonparametric functional form to capture the anomaly effects of some asset-specific characteristics and the other is the flexible treatment of both observed/constructed and unobserved common factors. By estimating the unknown factors, betas, and nonparametric function simultaneously, our setup is robust to misspecification of functional form and common factors and avoids the well-known “error-in-variable” problem associated with the commonly used two-pass procedure. We apply our method to a publicly available data set and divide the full sample into three subsamples. Our empirical results show that size and book-to-market ratio affect the excess returns of portfolios significantly for the full sample and two of the three subsamples in all five factor pricing models under investigation. In particular, nonparametric component is significantly different from zero, meaning that the constructed common factors (e.g., small minus big and high minus low) cannot capture all the size and book-to-market ratio effects. We also find strong evidence of nonlinearity of the anomaly effects in the Fama–French 3-factor model and the augmented 4-factor and 5-factor models in the full sample and two of the three subsamples.

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Fig. 1

Notes

  1. 1.

    Website: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/det_100_port_sz.html.

  2. 2.

    Website: http://faculty.chicagobooth.edu/lubos.pastor/research/liq_data_1962_2012.txt.

  3. 3.

    See Lu et al. (2014) for the performance of Bai and Ng’s (2002) information criteria in linear panel data models with interactive fixed effects.

  4. 4.

    This weight function can be replaced by the constant 1 since we truncate the 2.5 % tail observations before implementing the sieve-based and kernel-based tests.

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Acknowledgments

We sincerely thank Subal Kumbhakar and two anonymous referees for their many insightful comments and suggestions that lead to a substantial improvement of the presentation. The first and second authors gratefully acknowledge the Singapore Ministry of Education for Academic Research Fund under Grant Number MOE2012-T2-2-021.

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Correspondence to Liangjun Su.

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Cite this article

Jin, S., Su, L. & Zhang, Y. Nonparametric testing for anomaly effects in empirical asset pricing models. Empir Econ 48, 9–36 (2015). https://doi.org/10.1007/s00181-014-0846-2

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Keywords

  • Anomaly effects
  • Asset pricing
  • CAPM
  • Common factors
  • EIV
  • Fama–French three-factor
  • Interactive fixed effects
  • Nonparametric panel data model
  • Sieve method
  • Specification test

JEL Classification

  • C14
  • C33
  • C58