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Straight Talk on Nonlinearities in Linear Factor Models

Linear regression models have been the workhorses of finance and economics. However, given increasing attention to nonlinear methods, we investigate the extent to which nonlinearities not captured by standard linear models within equity factor risk models are present. Adding nonlinear factors in simple polynomial functions of their linear counterparts contributed some additional explanatory power to the cross-section of security returns. Furthermore, some generated factor returns and information ratios higher than corresponding linear factors. Overall, we found linear models created a robust framework to identify relationships between factor exposures and security returns through simple linear factors or transformed (e.g., polynomial) variants.


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