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Testing and Ranking of Asset Pricing Models Using the GRS Statistic

Author

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  • 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. K. Geert Rouwenhorst, 1999. "Local Return Factors and Turnover in Emerging Stock Markets," Journal of Finance, American Finance Association, vol. 54(4), pages 1439-1464, August.
    3. Fama, Eugene F. & French, Kenneth R., 2015. "A five-factor asset pricing model," Journal of Financial Economics, Elsevier, vol. 116(1), pages 1-22.
    4. repec:bla:jfinan:v:44:y:1989:i:4:p:889-908 is not listed on IDEAS
    5. Frank Kleibergen & Zhaoguo Zhan, 2020. "Robust Inference for Consumption‐Based Asset Pricing," Journal of Finance, American Finance Association, vol. 75(1), pages 507-550, February.
    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. Frank Kleibergen & Lingwei Kong & Zhaoguo Zhan, 2023. "Identification Robust Testing of Risk Premia in Finite Samples," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 263-297.
    Full references (including those not matched with items on IDEAS)

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