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.