Are Higher-Order Factors Useful in Pricing the Cross-Section of Hedge Fund Returns?

This paper investigates hedge funds' exposures to various risk factors across different investment strategies through models with both linear and second-order factors. 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, for some strategies, several quadratic and interaction terms are statistically significant. Nonetheless, there is no evidence that the second-order models have more overall explanatory or predictive power than the linear model. Moreover, while both linear and second-order models perform well for directional funds (like emerging markets, event driven and managed futures), missing factors may still remain for semi-directional funds, such as fund of funds, long/short equity hedge and multi-strategy