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A Robust Estimation of the CAPM with a Heavy-tailed Distribution

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  • Chikashi Tsuji

Abstract

This study quantitatively explores the linear standard capital asset pricing model (CAPM) and a non-linear CAPM by using ten US representative firms’ monthly stock returns. By the maximum likelihood estimation, we derive the following useful findings. (1) First, when the stock return distribution is fat-tailed, our non-linear CAPM application is highly effective. Because our non-linear CAPM parameters very well capture the behavior of fat-tailed returns, the non-linear CAPM estimation derives more reliable beta value estimates than the standard linear CAPM. (2) Second, conducting the Wald tests based on both the standard linear CAPM and non-linear CAPM estimators, we clarify that when the stock return distribution is fat-tailed, the Wald test result based on the non-linear CAPM estimators is more reliable than that based on the standard linear CAPM estimators.

Suggested Citation

  • Chikashi Tsuji, 2017. "A Robust Estimation of the CAPM with a Heavy-tailed Distribution," International Journal of Social Science Studies, Redfame publishing, vol. 5(5), pages 79-86, May.
    • Handle: RePEc:rfa:journl:v:5:y:2017:i:5:p:79-86
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    References listed on IDEAS

    as
    1. Tsai, Hsiu-Jung & Chen, Ming-Chi & Yang, Chih-Yuan, 2014. "A time-varying perspective on the CAPM and downside betas," International Review of Economics & Finance, Elsevier, vol. 29(C), pages 440-454.
    2. Chikashi Tsuji, 2012. "Do industries contain predictive information for the Fama--French factors?," Quantitative Finance, Taylor & Francis Journals, vol. 12(6), pages 969-991, March.
    3. Fama, Eugene F. & French, Kenneth R., 1993. "Common risk factors in the returns on stocks and bonds," Journal of Financial Economics, Elsevier, vol. 33(1), pages 3-56, February.
    4. Guermat, Cherif, 2014. "Yes, the CAPM is testable," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 31-42.
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    More about this item

    Keywords

    fat-tail; non-linear CAPM; Student’s t-distribution; US stock market; Wald test;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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