Multi-Hypothesis Prediction for Portfolio Optimization: A Structured Ensemble Learning Approach to Risk Diversification

This work proposes a unified framework for portfolio allocation, covering both asset selection and optimization, based on a multiple-hypothesis predict-then-optimize approach. The portfolio is modeled as a structured ensemble, where each predictor corresponds to a specific asset or hypothesis. Structured ensembles formally link predictors' diversity - captured via ensemble loss decomposition - to out-of-sample risk diversification. A structured dataset of predictor outputs is constructed with a parametric diversity control, influencing both the training process and diversification outcomes. This dataset feeds a supervised ensemble model whose target portfolio must align with the ensemble combiner rule implied by the loss. For squared loss, the arithmetic mean applies, yielding the equal-weighted portfolio as the optimal target. For asset selection, a novel method is introduced that prioritizes assets from more diverse predictor sets, even at the cost of lower average predicted returns, via a diversity-quality trade-off. This diversity is applied prior to optimization and can integrate into other allocation techniques. Experiments on SP500 stocks validate the theoretical framework and show that both sources of diversity expand the limits of portfolio diversification, achieving strong performance across one-step and multi-step allocation tasks.