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A Note on the GRS Test

Author

Listed:
  • Mark Kamstra

    (Schulich School of Business, York University)

  • Ruoyao Shi

    (Department of Economics, University of California Riverside)

Abstract

We clear up an ambiguity in Gibbons, Ross and Shanken (1989, GRS hereafter) by providing the correct formula of the GRS test statistic and proving its exact F distribution in the general multiple portfolio case. We generalize the Sharpe ratio based interpretation of the GRS test to the multiple portfolio case, which we argue paradoxically makes experts in asset pricing studies more susceptible to an incorrect formula. We theoretically and empirically illustrate the consequences of using the incorrect formula -- over-rejecting and mis-ranking asset pricing models.

Suggested Citation

  • Mark Kamstra & Ruoyao Shi, 2021. "A Note on the GRS Test," Working Papers 202111, University of California at Riverside, Department of Economics.
    • Handle: RePEc:ucr:wpaper:202111
    as

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    File URL: https://economics.ucr.edu/repec/ucr/wpaper/202111.pdf
    File Function: First version, 2021
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    References listed on IDEAS

    as
    1. Francisco Barillas & Jay Shanken, 2018. "Comparing Asset Pricing Models," Journal of Finance, American Finance Association, vol. 73(2), pages 715-754, April.
    2. Baek, Seungho & Bilson, John F.O., 2015. "Size and value risk in financial firms," Journal of Banking & Finance, Elsevier, vol. 55(C), pages 295-326.
    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. Sha, Yezhou & Gao, Ran, 2019. "Which is the best: A comparison of asset pricing factor models in Chinese mutual fund industry," Economic Modelling, Elsevier, vol. 83(C), pages 8-16.
    5. Mardy Chiah & Daniel Chai & Angel Zhong & Song Li, 2016. "A Better Model? An Empirical Investigation of the Fama–French Five-factor Model in Australia," International Review of Finance, International Review of Finance Ltd., vol. 16(4), pages 595-638, December.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Pankaj Agrrawal, 2023. "The Gibbons, Ross, and Shanken Test for Portfolio Efficiency: A Note Based on Its Trigonometric Properties," Mathematics, MDPI, vol. 11(9), pages 1-19, May.

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    More about this item

    Keywords

    GRS test; asset pricing; CAPM; multivariate test; portfolio efficiency; Sharpe ratio; over-rejection; model ranking;
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