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Higher Co-Moment CAPM and Hedge Fund Returns

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Abstract

This paper uses a higher moment capital asset pricing model to characterize the returns of several types of hedge fund indices. The quantile regression approach is used to test for any possible changes in the coefficients of the model. The hypothesis that the parameters are stable across the distribution of returns is tested and rejected. The most stable coefficient is the second moment (beta) coefficient. The higher moment coefficients vary considerably. Alpha returns tend to be positive and significant at the center of the distribution. The importance of higher co-moments (i.e., co-skewness and co-kurtosis) is more prevalent at the tails of the distribution of returns suggesting that there are significant tail risks. These findings could potentially have important implications for portfolio strategies and performance evaluation.

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Notes

  1. This study covers a much larger time period than Ranaldo and Favre (2005) which included more market cycles. More importantly however, our methodology examines the importance of the market portfolio as well as the co-moments across the entire distribution of returns.

  2. See Getmansky et al. (2015) for an excellent review on the evolution of the hedge fund industry.

  3. It should be noted that the co-skewness and co-kurtosis factors have very low and insignificant correlations with the well-known Fama-French factors. The correlation values range between −0.09 to 0.17.

  4. A complete description of investment styles corresponding to each index is available at the website of the Credit Swiss (2018) Hedge Fund Database.

  5. The intercept in the quantile regression equation is meaningful only at the center of the distribution i.e., for τ = .5.

  6. The use of the AR(1) term in the regression is used to correct for serial correlation in the error term.

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Authors and Affiliations

  1. Hanken, School of Economics, P.O. Box 287, F, IN-65101, Vaasa, Finland

    Johan Knif

  2. Worcester Polytechnic Institute, 100 Institute Road, 01609, –2280, Worcester, MA, United States

    Dimitrios Koutmos

  3. Gerald M. Levin Professor of Finance, Charles F. Dolan School of Business, Fairfield University, 06430, Fairfield, CT, United States

    Gregory Koutmos

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  1. Johan Knif
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  2. Dimitrios Koutmos
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  3. Gregory Koutmos
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Correspondence to Gregory Koutmos.

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Knif, J., Koutmos, D. & Koutmos, G. Higher Co-Moment CAPM and Hedge Fund Returns. Atl Econ J 48, 99–113 (2020). https://doi.org/10.1007/s11293-020-09659-1

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