Searcharxiv⌕ Search

arXiv subjects

Christian Bongiorno

Publications and source records attributed to Christian Bongiorno.

At least 19 recordsLinked to original sources
arXiv2026

End-to-End Neural Shrinkage of Indefinite Pairwise Correlation Matrices for Small-Cap-Inclusive Portfolios

Small-cap-inclusive equity universes contain recently listed and intermittently traded securities, so enforcing a common look-back discards a substantial fraction of the available information. Pairwise-complete estimation preserves the longest overlap for each asset pair, but the resulting correlation matrix can be indefinite because its entries are computed on different samples. This prevents direct use in Markowitz optimization and falls outside the assumptions of standard random-matrix shrinkage. We adapt a rotation-invariant neural covariance estimator to this setting. The model computes mask-aware marginal moments and a pairwise correlation matrix proxy, processes its signed spectrum, and uses a bidirectional gated recurrent unit conditioned on factor-aligned effective sample lengths derived from the overlap matrix and eigenvector loadings. It maps all eigenvalues, including negative ones, to a positive inverse spectrum. The reconstructed covariance is positive definite and is trained end-to-end to minimize five-day realized global-minimum-variance risk. We evaluate 26 expanding-window models from 2000 to 2025 on up to 1,500 U.S. equities in a closing-auction simulator with point-in-time selection, commissions, financing, corporate actions, and market impact. Across the 26-year out-of-sample period, the neural estimator reduces annualized five-day volatility by approximately 20\% and increases the Sharpe ratio by approximately 40\% relative to the next-best covariance estimator. These improvements are consistent across realized risk, risk-adjusted performance, and drawdown control, remain after the modeled execution frictions, and are supported by a 99.9\% Model Confidence Set that retains only the neural estimator.

q-fin.PM↗
arXiv2026

Physics-Informed Singular-Value Learning for Cross-Covariances Forecasting in Financial Markets

Recent advances in nonlinear shrinkage yield asymptotically optimal cleaners for large covariance matrices and have been extended to empirical cross-covariances via singular-value shrinkage. However, these approaches rely on stationarity and bounded-spectrum assumptions that are violated by real equity returns, which exhibit dependence drift and macroscopic common modes. We propose a physics-informed neural estimator that parameterizes the cleaned cross-covariance matrix in the empirical singular-vector basis and learns a nonlinear map from empirical singular values and marginal projections to cleaned singular values, recovering the cleaning performances of the analytical solution as a limiting case. On U.S. equity data, the learned correction not only improves out-of-sample cross-covariance prediction but also translates these statistical gains into better tracking-error minimization for portfolio replication. Furthermore, it remains stable in regimes where the analytical cross-covariance estimation deteriorates with universe size, suggesting an interpolation between sample-size denoising and a learned forecast correction under non-stationary dependence.

q-fin.ST↗
arXiv2026

Neural Network-Driven Volatility Drag Mitigation under Aggressive Leverage

This paper introduces a compact reformulation of a modular end-to-end neural network for global minimum-variance portfolio optimization that decouples model complexity from both look-back window length and universe size. A five-parameter hyperbolic weighted moving average combined with a saturating exponential replaces the original 2,400-parameter lag-transformation layer, and a bidirectional gated-recurrent-unit eigencleaning module together with a streamlined marginal-volatility network reduce total learnable parameters from 39,586 to just 2,175. In out-of-sample tests against state-of-the-art nonlinear-shrinkage and risk-parity benchmarks, the compact network attains the lowest realized portfolio variance without compromising expected return. Under long-only constraints, the variance reduction supports substantially higher leverage while maintaining comparable drawdown control. Validation in a high-fidelity trading simulator that incorporates realistic margin-call dynamics confirms enhanced over-leverage resilience. These findings demonstrate that end-to-end variance-minimization architectures can achieve substantial parameter efficiency and robust capital-efficiency gains without sacrificing risk-adjusted performance.

q-fin.PM↗
arXiv2026

End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning

We develop a rotation-invariant neural network that provides the global minimum-variance portfolio by jointly learning how to lag-transform historical returns and marginal volatilities and how to regularise the eigenvalues 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 indicates robust generalization capability. The loss function is the future short-term realized minimum variance and is optimized end-to-end on real returns. In out-of-sample tests from January 2000 to December 2024, the estimator delivers systematically lower realized volatility, smaller maximum drawdowns, and higher Sharpe ratios than the best competitors, including state-of-the-art non-linear shrinkage, and these advantages persist across both short and long evaluation horizons despite the model's training focus is short-term. Furthermore, although the model is trained end-to-end to produce an unconstrained 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 advantages 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.

q-fin.PM↗
arXiv2025

Noise-proofing Universal Portfolio Shrinkage

We enhance the Universal Portfolio Shrinkage Approximator (UPSA) of Kelly et al. (2023) by making it more robust with respect to estimation noise and covariate shift. UPSA optimizes the realized Sharpe ratio using a relatively small calibration window, leveraging ridge penalties and cross-validation to yield better portfolios. Yet, it still suffers from the staggering amount of noise in financial data. We propose two methods to make UPSA more robust and improve its efficiency: time-averaging of the optimal penalty weights and using the Average Oracle correlation eigenvalues to make covariance matrices less noisy and more robust to covariate shift. Combining these two long-term averages outperforms UPSA by a large margin in most specifications.

q-fin.RM↗
arXiv2025

Optimal Data Splitting for Holdout Cross-Validation in Large Covariance Matrix Estimation

Cross-validation is a statistical tool that can be used to improve large covariance matrix estimation. Although its efficiency is observed in practical applications and a convergence result towards the error of the non linear shrinkage is available in the high-dimensional regime, formal proofs that take into account the finite sample size effects are currently lacking. To carry on analytical analysis, we focus on the holdout method, a single iteration of cross-validation, rather than the traditional $k$-fold approach. We derive a closed-form expression for the expected estimation error when the population matrix follows a white inverse Wishart distribution, and we observe the optimal train-test split scales as the square root of the matrix dimension. For general population matrices, we connected the error to the variance of eigenvalues distribution, but approximations are necessary. In this framework and in the high-dimensional asymptotic regime, both the holdout and $k$-fold cross-validation methods converge to the optimal estimator when the train-test ratio scales with the square root of the matrix dimension which is coherent with the existing theory.

math.ST↗
arXiv2025

Functional Decomposition and Estimation of Irreversibility in Time Series via Machine Learning

This work introduces a novel, simple, and flexible method to quantify irreversibility in generic high-dimensional time series based on the well-known mapping to a binary classification problem. Our approach utilizes gradient boosting for estimation, providing a model-free, nonlinear analysis able to handle large-dimensional systems while requiring minimal or no calibration. Our procedure is divided into three phases: trajectory encoding, Markovian order identification, and hypothesis testing for variable interactions. The latter is the key innovation that allows us to selectively switch off variable interactions to discern their specific contribution to irreversibility. When applied to financial markets, our findings reveal a distinctive shift: during stable periods, irreversibility is mainly related to short-term patterns, whereas in unstable periods, these short-term patterns are disrupted, leaving only contributions from stable long-term ones. This observed transition underscores the crucial importance of high-order variable interactions in understanding the dynamics of financial markets, especially in times of turbulence.

cond-mat.stat-mech↗
arXiv2024

Quantifying the information lost in optimal covariance matrix cleaning

Obtaining an accurate estimate of the underlying covariance matrix from finite sample size data is challenging due to sample size noise. In recent years, sophisticated covariance-cleaning techniques based on random matrix theory have been proposed to address this issue. Most of these methods aim to achieve an optimal covariance matrix estimator by minimizing the Frobenius norm distance as a measure of the discrepancy between the true covariance matrix and the estimator. However, this practice offers limited interpretability in terms of information theory. To better understand this relationship, we focus on the Kullback-Leibler divergence to quantify the information lost by the estimator. Our analysis centers on rotationally invariant estimators, which are state-of-art in random matrix theory, and we derive an analytical expression for their Kullback-Leibler divergence. Due to the intricate nature of the calculations, we use genetic programming regressors paired with human intuition. Ultimately, using this approach, we formulate a conjecture validated through extensive simulations, showing that the Frobenius distance corresponds to a first-order expansion term of the Kullback-Leibler divergence, thus establishing a more defined link between the two measures.

stat.CO↗
arXiv2023

Covariance matrix filtering and portfolio optimisation: the Average Oracle vs Non-Linear Shrinkage and all the variants of DCC-NLS

The Average Oracle, a simple and very fast covariance filtering method, is shown to yield superior Sharpe ratios than the current state-of-the-art (and complex) methods, Dynamic Conditional Covariance coupled to Non-Linear Shrinkage (DCC+NLS). We pit all the known variants of DCC+NLS (quadratic shrinkage, gross-leverage or turnover limitations, and factor-augmented NLS) against the Average Oracle in large-scale randomized experiments. We find generically that while some variants of DCC+NLS sometimes yield the lowest average realized volatility, albeit with a small improvement, their excessive gross leverage and investment concentration, and their 10-time larger turnover contribute to smaller average portfolio returns, which mechanically result in smaller realized Sharpe ratios than the Average Oracle. We also provide simple analytical arguments about the origin of the advantage of the Average Oracle over NLS in a changing world.

q-fin.ST↗
arXiv2023

Optimal Covariance Cleaning for Heavy-Tailed Distributions: Insights from Information Theory

In optimal covariance cleaning theory, minimizing the Frobenius norm between the true population covariance matrix and a rotational invariant estimator is a key step. This estimator can be obtained asymptotically for large covariance matrices, without knowledge of the true covariance matrix. In this study, we demonstrate that this minimization problem is equivalent to minimizing the loss of information between the true population covariance and the rotational invariant estimator for normal multivariate variables. However, for Student's t distributions, the minimal Frobenius norm does not necessarily minimize the information loss in finite-sized matrices. Nevertheless, such deviations vanish in the asymptotic regime of large matrices, which might extend the applicability of random matrix theory results to Student's t distributions. These distributions are characterized by heavy tails and are frequently encountered in real-world applications such as finance, turbulence, or nuclear physics. Therefore, our work establishes a connection between statistical random matrix theory and estimation theory in physics, which is predominantly based on information theory.

cs.IT↗
arXiv2023

Reactive Global Minimum Variance Portfolios with $k-$BAHC covariance cleaning

We introduce a $k$-fold boosted version of our Boostrapped Average Hierarchical Clustering cleaning procedure for correlation and covariance matrices. We then apply this method to global minimum variance portfolios for various values of $k$ and compare their performance with other state-of-the-art methods. Generally, we find that our method yields better Sharpe ratios after transaction costs than competing filtering methods, despite requiring a larger turnover.

q-fin.PM↗
arXiv2023

Cleaning the covariance matrix of strongly nonstationary systems with time-independent eigenvalues

We propose a data-driven way to reduce the noise of covariance matrices of nonstationary systems. In the case of stationary systems, asymptotic approaches were proved to converge to the optimal solutions. Such methods produce eigenvalues that are highly dependent on the inputs, as common sense would suggest. Our approach proposes instead to use a set of eigenvalues totally independent from the inputs and that encode the long-term averaging of the influence of the future on present eigenvalues. Such an influence can be the predominant factor in nonstationary systems. Using real and synthetic data, we show that our data-driven method outperforms optimal methods designed for stationary systems for the filtering of both covariance matrix and its inverse, as illustrated by financial portfolio variance minimization, which makes out method generically relevant to many problems of multivariate inference.

stat.AP↗
arXiv2022

Non-linear shrinkage of the price return covariance matrix is far from optimal for portfolio optimisation

Portfolio optimization requires sophisticated covariance estimators that are able to filter out estimation noise. Non-linear shrinkage is a popular estimator based on how the Oracle eigenvalues can be computed using only data from the calibration window. Contrary to common belief, NLS is not optimal for portfolio optimization because it does not minimize the right cost function when the asset dependence structure is non-stationary. We instead derive the optimal target. Using historical data, we quantify by how much NLS can be improved. Our findings reopen the question of how to build the covariance matrix estimator for portfolio optimization in realistic conditions.

q-fin.PM↗
arXiv2022

Statistical inference of lead-lag at various timescales between asynchronous time series from p-values of transfer entropy

Symbolic transfer entropy is a powerful non-parametric tool to detect lead-lag between time series. Because a closed expression of the distribution of Transfer Entropy is not known for finite-size samples, statistical testing is often performed with bootstraps whose slowness prevents the inference of large lead-lag networks between long time series. On the other hand, the asymptotic distribution of Transfer Entropy between two time series is known. In this work, we derive the asymptotic distribution of the test for one time series having a larger Transfer Entropy than another one on a target time series. We then measure the convergence speed of both tests in the small sample size limits via benchmarks. We then introduce Transfer Entropy between time-shifted time series, which allows to measure the timescale at which information transfer is maximal and vanishes. We finally apply these methods to tick-by-tick price changes of several hundreds of stocks, yielding non-trivial statistically validated networks.

q-fin.ST↗
arXiv2021

Vector-based Pedestrian Navigation in Cities

How do pedestrians choose their paths within city street networks? Researchers have tried to shed light on this matter through strictly controlled experiments, but an ultimate answer based on real-world mobility data is still lacking. Here, we analyze salient features of human path planning through a statistical analysis of a massive dataset of GPS traces, which reveals that (1) people increasingly deviate from the shortest path when the distance between origin and destination increases, and (2) chosen paths are statistically different when origin and destination are swapped. We posit that direction to goal is a main driver of path planning and develop a vector-based navigation model that is a statistically better predictor of human paths than a model based on minimizing distance with stochastic effects. Our findings generalize across two major US cities with different street networks, hinting to the fact that vector-based navigation might be a universal property of human path planning.

q-bio.NC↗
arXiv2021

A multi-layer network model to assess school opening policies during the COVID-19 vaccination campaign

We propose a multi-layer network model for the spread of COVID-19 that accounts for interactions within the family, between schoolmates, and casual contacts in the population. We utilize the proposed model-calibrated on epidemiological and demographic data-to investigate current questions concerning the implementation of non-pharmaceutical interventions (NPIs) during the vaccination campaign. Specifically, we consider scenarios in which the most fragile population has already received the vaccine, and we focus our analysis on the role of schools as drivers of the contagions and on the implementation of targeted intervention policies oriented to children and their families. We perform our analysis by means of a campaign of Monte Carlo simulations. Our findings suggest that, in a phase with NPIs enacted but in-person education, children play a key role in the spreading of COVID-19. Interestingly, we show that children's testing might be an important tool to flatten the epidemic curve, in particular when combined with enacting temporary online education for classes in which infected students are detected. Finally, we test a vaccination strategy that prioritizes the members of large families and we demonstrate its good performance. We believe that our modeling framework and our findings could be of help for public health authorities for planning their current and future interventions, as well as to increase preparedness for future epidemic outbreaks.

physics.soc-ph↗
arXiv2020

Bootstraps Regularize Singular Correlation Matrices

I show analytically that the average of $k$ bootstrapped correlation matrices rapidly becomes positive-definite as $k$ increases, which provides a simple approach to regularize singular Pearson correlation matrices. If $n$ is the number of objects and $t$ the number of features, the averaged correlation matrix is almost surely positive-definite if $k> \frac{e}{e-1}\frac{n}{t}\simeq 1.58\frac{n}{t}$ in the limit of large $t$ and $n$. The probability of obtaining a positive-definite correlation matrix with $k$ bootstraps is also derived for finite $n$ and $t$. Finally, I demonstrate that the number of required bootstraps is always smaller than $n$. This method is particularly relevant in fields where $n$ is orders of magnitude larger than the size of data points $t$, e.g., in finance, genetics, social science, or image processing.

stat.CO↗