Covariance Matrix

End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning ArXiv ID: 2507.01918 “View on arXiv” Authors: Christian Bongiorno, Efstratios Manolakis, Rosario Nunzio Mantegna Abstract We develop a rotation-invariant neural network that provides the global minimum-variance portfolio by jointly learning how to lag-transform historical returns and how to regularise both the eigenvalues and the marginal volatilities of large equity covariance matrices. This explicit mathematical mapping offers clear interpretability of each module’s role, so the model cannot be regarded as a pure black-box. The architecture mirrors the analytical form of the global minimum-variance solution yet remains agnostic to dimension, so a single model can be calibrated on panels of a few hundred stocks and applied, without retraining, to one thousand US equities-a cross-sectional jump that demonstrates robust out-of-sample generalisation. The loss function is the future realized minimum portfolio variance and is optimized end-to-end on real daily returns. In out-of-sample tests from January 2000 to December 2024 the estimator delivers systematically lower realised volatility, smaller maximum drawdowns, and higher Sharpe ratios than the best analytical competitors, including state-of-the-art non-linear shrinkage. Furthermore, although the model is trained end-to-end to produce an unconstrained (long-short) minimum-variance portfolio, we show that its learned covariance representation can be used in general optimizers under long-only constraints with virtually no loss in its performance advantage over competing estimators. These gains persist when the strategy is executed under a highly realistic implementation framework that models market orders at the auctions, empirical slippage, exchange fees, and financing charges for leverage, and they remain stable during episodes of acute market stress. ...

Topological Portfolio Selection and Optimization ArXiv ID: 2310.14881 “View on arXiv” Authors: Unknown Abstract Modern portfolio optimization is centered around creating a low-risk portfolio with extensive asset diversification. Following the seminal work of Markowitz, optimal asset allocation can be computed using a constrained optimization model based on empirical covariance. However, covariance is typically estimated from historical lookback observations, and it is prone to noise and may inadequately represent future market behavior. As a remedy, information filtering networks from network science can be used to mitigate the noise in empirical covariance estimation, and therefore, can bring added value to the portfolio construction process. In this paper, we propose the use of the Statistically Robust Information Filtering Network (SR-IFN) which leverages the bootstrapping techniques to eliminate unnecessary edges during the network formation and enhances the network’s noise reduction capability further. We apply SR-IFN to index component stock pools in the US, UK, and China to assess its effectiveness. The SR-IFN network is partially disconnected with isolated nodes representing lesser-correlated assets, facilitating the selection of peripheral, diversified and higher-performing portfolios. Further optimization of performance can be achieved by inversely proportioning asset weights to their centrality based on the resultant network. ...