N°26-36: Recursive Portfolio Machines

We introduce the Recursive Portfolio Machine (RPM), an asset-pricing framework for learning the characteristic directions most relevant for the stochastic discount factor (SDF). Our theory shows that the risk-weighted gradient outer product (RWGOP) recovers the pricing-relevant subspace of characteristic space, while its eigenvectors define principal pricing directions that rank this subspace by pricing importance. The RPM operationalizes this theory by first estimating the RWGOP and then using it within a closed-form large factor model to construct the SDF. In U.S. equity data, the RPM improves out-of-sample performance relative to benchmark models. Low-rank versions retain much of the full-rank performance, suggesting that the pricing-relevant space is effectively low-dimensional.