Pricing Complexity in the Cross Section of Stock Returns
We evaluate the pricing performance of a robust SDF spanned by a broad cross‑section of factor returns. Methodologically, we combine kernel principal component analysis—which extracts factors as nonlinear functions of a high‑dimensional set of firm characteristics—with novel regularization techniques. Allowing for nonlinearities enhances the model’s performance in explaining a wide range of cross‑sectional stock‑return anomalies and reduces pricing errors. We further decompose the mean–variance efficient portfolio into linear and nonlinear components and study their relative contributions across different states of the economy. Out‑of‑sample, incorporating nonlinearities increases the Sharpe ratio of the mean–variance efficient portfolio by roughly 25% to 2.15.