Multi-hypothesis prediction for portfolio optimization: A structured ensemble learning approach to risk diversification

Speaker: Dr. Alejandro Rodriguez Dominguez, Director of Quantitative Analysis and Artificial Intelligence, Miralta Finance Bank, Madrid.

Abstract: We introduce a novel framework for portfolio construction, covering both selection and optimization, based entirely on ensemble learning theory. A portfolio is modelled as an ensemble in a multi-hypothesis prediction setting, with each constituent (base learner) focused on a specific hypothesis. This formulation connects the Bias–Variance–Diversity trade-off in ensemble models with out-of-sample portfolio performance. Diversity in the training of base learners translates to out-of-sample diversification, allowing control over portfolio diversification via model training.

Portfolio optimization is reframed as a supervised learning task, where the target portfolio follows an ensemble combiner rule derived from Bregman divergences and ensemble model properties. When using Mean Squared Error, the equal-weighted portfolio emerges as the target. Also,it enables the use of alternative loss functions—treating the problem as classification or regression, where targets follow ensemble combiner rules defined by Bregman divergences. A second source of out-of-sample diversification is also identified: the diversity in return predictions across base learners. Controlling this diversity at decision time further improves performance. When base learners exhibit similar error levels, portfolios built from asset sets with more diverse return predictions, but lower average sets forecasts, outperform those with higher average sets predictions but less diversity. This defines a diversity-quality trade-off in predicted returns. Together, these two sources of diversification expand the traditional boundaries of portfolio construction, enabling meaningful diversification even within single-asset portfolios, benefiting constrained strategies and redefining conventional notions of diversification. Theoretical results are empirically validated using full historical data from all S&P 500 constituents and a globally diversified set of 1,300 bonds across multiple categories, spanning over two decades and diverse market regimes. The diversity-quality trade-off is shown to be applicable across a wide range of portfolio optimization methods.