Building an efficient portfolio starts with a deceptively simple question: how do assets move together? In real markets, however, these relationships are never observed cleanly because genuine collective movements are mixed with sampling noise. Even small errors in this risk map can lead to unstable portfolio allocations.

In a study published in The Journal of Finance and Data Science, researchers from CentraleSupélec, University of Catania and University of Palermo developed a neural-network approach that learns how to clean these co-movement patterns before portfolios are constructed. Rather than replacing portfolio theory, the method integrates AI into a transparent allocation framework.

The study focuses on global minimum-variance portfolios designed to control risk. The neural network is trained on the realized risk after allocation, allowing covariance cleaning to be optimized for the portfolio it ultimately produces while keeping the core process explicit and interpretable.

A key idea is that a covariance matrix contains more than pairwise correlations. It also reflects broader collective market patterns. Some capture general market movements, others represent more specific structures, while some are largely noise. Cleaning the matrix means deciding how much confidence each collective pattern deserves before influencing portfolio allocation.

The researchers argue that this principle extends beyond portfolio construction. Whenever a noisy covariance matrix is transformed before guiding a decision, the process can be viewed as correcting collective market patterns. Their neural network learns these corrections while remaining grounded in the mathematical structure of the problem.

The method is designed to respect the symmetries of covariance matrices. Portfolio results should not depend on the order in which stocks are listed or on arbitrary representations of the same risk structure. By incorporating these invariances, the network learns a general cleaning rule instead of memorizing a fixed set of assets.

In out-of-sample tests on U.S. equities from 2000 to 2024, a model calibrated on a few hundred stocks was successfully applied, without retraining, to roughly one thousand stocks. The resulting portfolios achieved lower realized volatility, smaller drawdowns and higher Sharpe ratios than competing covariance estimators, including advanced nonlinear shrinkage methods. These advantages remained in realistic trading simulations that included transaction costs, slippage, exchange fees and financing costs, suggesting that neural networks may be most useful in finance when designed around the symmetries and constraints of the systems they aim to learn.

More information: Christian Bongiorno et al, End-to-end large portfolio optimization for variance minimization with neural networks through covariance cleaning, The Journal of Finance and Data Science. DOI: 10.1016/j.jfds.2026.100179

Journal information: The Journal of Finance and Data Science Provided by KeAi Communications Co., Ltd.