Nonlinear dependencies in the Fama and French three-factor model

This article addresses the topic of nonlinear dependencies in the Fama and French three-factor model. Five time-series models, including nonlinear terms, are assessed using US and European data and compared with a benchmark linear model. The analysis found that nonlinear dependencies in the modified Fama and French three-factor model were statistically significant and provided additional explanatory power for the underlying return-generating process. However, these nonlinear dependencies are of secondary importance in the economic sense.