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