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 di↵erent investment strategies through models with both linear and second-order factors. De- spite many efforts to search for the set of risk factors that best explains cross-sectional hedge fund returns, no consensus has been reached regarding how many and which factors should be used. With little knowledge of the model’s functional form, most existing research presumes that cross-sectional hedge fund returns are linearly related to risk factors. In this study, we contribute to the hedge fund literature by extend- ing 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. To overcome the large number of factors and high correlations between them, we adopt 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 strate- gies; however, there is no evidence that the second-order models have more overall explanatory or predictive power than the linear model. Moreover, although several factors are widely shared by all strategies, funds in each strategy are exposed to additional strategy-specific risk factors. Finally, while both the linear and second- order models perform well for directional funds, missing factors may still remain for semi-directional funds.