Testing non-linear dependence in the hedge fund industry

Abstract

This paper proposes a parsimonious approach to test non-linear dependence on the conditional mean and variance of hedge funds with respect to several market factors. My approach introduces non-linear dependence by means of empirically relevant polynomial functions of the factors. For comparison purposes, I also consider multifactor extensions of tests based on piecewise linear alternatives. I apply these tests to a database of monthly returns on 1,071 hedge funds. I fi nd that non-linear dependence on the mean is highly sensitive to the factors that I consider. However, I obtain a much stronger evidence of non-linear dependence on the conditional variance