Beyond the Ellipse - The Virtue of Nonlinearity in Asset Pricing

While machine learning (ML) and deep learning (DL) models are increasingly applied to predict both cross-section and time series of stock returns, the underlying sources of the nonlinearities they capture remain largely unexplored. This study develops a simple theoretical framework to identify conditions under which nonlinear modeling is critical. Specifically, we show that when the data-generating process (DGP) of stock payoffs deviates from elliptical distributions, nonlinear models can offer distinct advantages. Our theoretical model predicts that firms exhibiting higher exposure to non-elliptical components are more likely to benefit from nonlinear modeling. Guided by these insights, we conduct empirical tests using portfolio analysis, sorting stocks based on ML-based predictions and firm characteristics. The results demonstrate that nonlinear machine learning models significantly outperform linear models, particularly among stocks with high positive skewness and growth-related attributes, proxies for non-elliptical exposure. We run several robustness checks and explore the underlying mechanisms across different firm characteristics, including financial health and other intangible factors.