Higher moment CAPM and hedge fund returns

Objectives: Higher moment capital asset pricing models (CAPM) have been used successfully to characterize the market risk premium. The seminal papers by  Kraus and Litzenberger (1976) and Friend and Westerfield (1980) showed that the traditional one-factor CAPM fails to provide an adequate description of the market premium. They showed that significant improvements can be achieved by extending the model to include co-skewness and co-kurtosis. Several other studies have shown the importance of using higher co-moments to price risky assets. Most studies of this nature have focused on individual stocks or, portfolios of stocks.  No attention has been paid to the potential significance of higher market co-moments in the determination of hedge fund risk premia.  This is an important omission given that hedge funds are actively managed and they are more likely to exhibit significant market co-skewness and co-kurtosis. This paper aims to fill this void in the literature by investigating the importance of higher moments in hedge fund returns.

 More specifically this study aims to provide answers to the following questions:

1)  Are higher market co-moments important determinants of hedge fund returns?

 2) Are co-factor loadings stable across the ditribution of hedge fund returns?

 3) Are alpha-returns at least partially explained by higher market co-moments?

Data and Methodology: That data used in this study are monthly returns on hedge funds indices covering the period 1994:1 till 10/31/2015 for total of 262 monthly observations. The return series data are obtained from the TASS Hedge Funds Data Base which produces indexes of investment performance of several hedge fund classes.

The model use in this study is based on Kraus and Litzenberger (1976) and Friend and Westerfield (1980). Typically, the model in the literature is estimated using simple regression methods. Such an approach however, does not allow for testing of stability of parameters across the conditional distribution.  As such a suitable methodology is to use the Quantile regression approach of Koenker and Basset (1978). 

Expected Findings: We expect the higher co-moments to be significant in explaining the risk premia in hedge fund returns. Moreover, it is likely that part of alpha returns (excess returns) can be explained by the exposure to higher co-moments. The findings could potentially have important implications for portfolio strategies and performance evaluation.