Are higher-order factors useful in pricing the cross-section of hedge fund returns?

Abstract

This paper investigates hedge funds’ exposures to various risk factors across different investment strategies through models with both linear and second-order factors. Despite many efforts to search for the set of risk factors that best explains cross-sectional hedge fund returns, no consensus has been reached. In this study, we extend the analysis from an augmented linear model based on Fama and French (1993) and Fung and Hsieh (2001) to second-order models that include all quadratic and interaction terms by adopting a novel multistep strategy that combines the variable selection capabilities of the lasso regression with the Fama-MacBeth (1973) two-step method. We find that several quadratic and interaction terms are statistically significant for some strategies; however, there is no evidence that the second-order models have more overall explanatory or predictive power than the linear model. Moreover, while both the linear and second-order models perform well for directional funds, missing factors may still remain for semidirectional funds.