Beyond the Ellipse - The Virtue of Nonlinearity in Asset Pricing

Nonlinear machine learning (ML) models are increasingly used to predict the cross-section of stock returns, yet the economic justification for their nonlinear gains remains underexplored. Building on an equilibrium-based framework, this study shows that nonlinear MLs are most valuable when stock payoffs deviate from elliptical distributions (e.g., regime-switching) and that nonlinear gains arise when there is uncertainty about the likelihood of such deviations. Consistent with the model’s predictions, empirical tests show that nonlinear models significantly outperform linear ones among stocks with high idiosyncratic skewness and growth-related attributes, and during periods of elevated market volatility. In terms of explainability, the predictive edge of nonlinear ML models over their linear counterparts arises from their superior ability to capture well-documented firm-level anomaly signals.