Machine Learning Factors: Capturing Non Linearities in Linear Factor Models

The linear factor model has been a workhorse for understanding portfolio exposures, risk and performance for many years. But the idea that relationships between factor exposures and returns must be linear is not etched in stone. We investigate the extent to which machine-learning (ML) algorithms can detect significant nonlinearities and interactions in these relationships after the linear components have been removed.

We shine a light inside the “black box” to gain insight into the relationships the ML algorithms identified. For example, we found that interactions between style factors had a significant influence on the ML models’ output, particularly those factors that showed strong feature importance, including the interaction between momentum and size, as shown below.

Momentum-Size Interaction

We defined bi-variate interaction as the ML model’s predicted response minus the univariate partial dependence contributions from each of the two inputs, which is plotted in the contours.