Benefit of Complexity in Machine Learning Models

Is model complexity (large number of parameters) more an analytical benefit in predicting asset returns, or more an avenue to discover in-sample luck? In their March 2023 paper entitled "Complexity in Factor Pricing Models", Antoine Didisheim, Shikun Ke, Bryan Kelly and Semyon Malamud examine the theoretical relationship between input complexity and output accuracy for machine learning asset pricing models. They focus on a complexity wedge, the combination of overfitting (data snooping) and limits to learning that causes in-sample performance of a trained model to exceed out-of-sample performance. They apply ridge shrinkage (controlled by a regularization parameter that sets the strength of an overfitting penalty) to suppress data snooping bias and improve the limits to learning. They assess model performance by out-of-sample Sharpe ratio and out-of-sample pricing errors of optimal portfolios. They test theoretical conclusions on a broad sample of publicly traded U.S. stocks and a set of 110 monthly stock return factors, the latter augmented by a random feature generator that expands the 110 raw factors to any desired number of derivative factors. Using monthly data for the 110 stock return predictors and monthly U.S. stock returns during February 1963 through December 2019, they find that: