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Testing and Ranking of Asset Pricing Models Using the GRS Statistic

Author

Listed:
  • Mark J. Kamstra

    (Schulich School of Business, Room N204-C, York University, 4700 Keele St., Toronto, ON M3J 1P3, Canada
    These authors contributed equally to this work.)

  • Ruoyao Shi

    (Department of Economics, University of California Riverside, 900 University Avenue, Riverside, CA 92521, USA
    These authors contributed equally to this work.)

Abstract

We clear up an ambiguity in the statement of the GRS statistic by providing the correct formula of the GRS statistic and the first proof of its F-distribution in the general multiple-factor case. Casual generalization of the Sharpe-ratio-based interpretation of the single-factor GRS statistic to the multiple-portfolio case makes experts in asset pricing studies susceptible to an incorrect formula. We illustrate the consequences of using the incorrect formulas that the ambiguity in GRS leads to—over-rejecting and misranking asset pricing models. In addition, we suggest a new approach to ranking models using the GRS statistic p -value.

Suggested Citation

  • Mark J. Kamstra & Ruoyao Shi, 2024. "Testing and Ranking of Asset Pricing Models Using the GRS Statistic," JRFM, MDPI, vol. 17(4), pages 1-25, April.
    • Handle: RePEc:gam:jjrfmx:v:17:y:2024:i:4:p:168-:d:1379260
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    References listed on IDEAS

    as
    1. Kan, Raymond & Wang, Xiaolu & Zheng, Xinghua, 2024. "In-sample and out-of-sample Sharpe ratios of multi-factor asset pricing models," Journal of Financial Economics, Elsevier, vol. 155(C).
    2. Zaremba, Adam & Czapkiewicz, Anna, 2017. "Digesting anomalies in emerging European markets: A comparison of factor pricing models," Emerging Markets Review, Elsevier, vol. 31(C), pages 1-15.
    3. Leite, André Luis & Klotzle, Marcelo Cabus & Pinto, Antonio Carlos Figueiredo & da Silva, Aldo Ferreira, 2018. "Size, value, profitability, and investment: Evidence from emerging markets," Emerging Markets Review, Elsevier, vol. 36(C), pages 45-59.
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    5. repec:bla:jfinan:v:44:y:1989:i:4:p:889-908 is not listed on IDEAS
    6. Eugene F. Fama & Kenneth R. French, 2016. "Dissecting Anomalies with a Five-Factor Model," The Review of Financial Studies, Society for Financial Studies, vol. 29(1), pages 69-103.
    7. Tim A. Kroencke, 2017. "Asset Pricing without Garbage," Journal of Finance, American Finance Association, vol. 72(1), pages 47-98, February.
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    Cited by:

    1. Koichiro Moriya & Akihiko Noda, 2026. "Finite-Sample Properties of Model Specification Tests for Multivariate Dynamic Regression Models," Papers 2601.21272, arXiv.org, revised Apr 2026.

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