Scaling Prediction and Investment in Financial Machine Learning

Financial machine learning typically follows a predict-then-optimize pipeline: forecast returns, then construct portfolios. We study how model capacity should scale when returns are noisy and cross-sectionally dependent. We derive a finance-specific scaling law that separates diversifiable estimation error from the additional cost induced by common shocks. On a panel of 1,800 U.S. stocks with 153 characteristics, the law raises log-loss $R^2$ from $0.315$ to $0.888$ relative to an i.i.d. law and captures finite loss-minimizing model widths. A natural response is to select the loss-minimizing model, but our portfolio results show that this can discard useful information: smaller models achieve lower prediction loss, while larger models generate higher cumulative long–short returns. Together, these results show that financial scaling cannot be reduced to model selection alone; further scaling beyond the loss optimum requires better supervision. We therefore introduce hybrid weak-to-strong (W2S) learning, which combines smaller-model forecasts with realized returns to supervise the larger model. Under conditional orthogonality, prediction loss is quadratic in the mixing weight and admits an interior optimum. Empirically, hybrid W2S reduces prediction loss relative to direct strong learning and achieves higher terminal cumulative long–short returns than both the weak and directly trained strong models.