Correlation Matrices

Signed network models for portfolio optimization ArXiv ID: 2510.05377 “View on arXiv” Authors: Bibhas Adhikari Abstract In this work, we consider weighted signed network representations of financial markets derived from raw or denoised correlation matrices, and examine how negative edges can be exploited to reduce portfolio risk. We then propose a discrete optimization scheme that reduces the asset selection problem to a desired size by building a time series of signed networks based on asset returns. To benchmark our approach, we consider two standard allocation strategies: Markowitz’s mean-variance optimization and the 1/N equally weighted portfolio. Both methods are applied on the reduced universe as well as on the full universe, using two datasets: (i) the Market Champions dataset, consisting of 21 major S&P500 companies over the 2020-2024 period, and (ii) a dataset of 199 assets comprising all S&P500 constituents with stock prices available and aligned with Google’s data. Empirical results show that portfolios constructed via our signed network selection perform as good as those from classical Markowitz model and the equal-weight benchmark in most occasions. ...

Eigenvalue Distribution of Empirical Correlation Matrices for Multiscale Complex Systems and Application to Financial Data ArXiv ID: 2507.14325 “View on arXiv” Authors: Luan M. T. de Moraes, Antônio M. S. Macêdo, Giovani L. Vasconcelos, Raydonal Ospina Abstract We introduce a method for describing eigenvalue distributions of correlation matrices from multidimensional time series. Using our newly developed matrix H theory, we improve the description of eigenvalue spectra for empirical correlation matrices in multivariate financial data by considering an informational cascade modeled as a hierarchical structure akin to the Kolmogorov statistical theory of turbulence. Our approach extends the Marchenko-Pastur distribution to account for distinct characteristic scales, capturing a larger fraction of data variance, and challenging the traditional view of noise-dressed financial markets. We conjecture that the effectiveness of our method stems from the increased complexity in financial markets, reflected by new characteristic scales and the growth of computational trading. These findings not only support the turbulent market hypothesis as a source of noise but also provide a practical framework for noise reduction in empirical correlation matrices, enhancing the inference of true market correlations between assets. ...

Coarse graining correlation matrices according to macrostructures: Financial markets as a paradigm ArXiv ID: 2402.05364 “View on arXiv” Authors: Unknown Abstract We analyze correlation structures in financial markets by coarse graining the Pearson correlation matrices according to market sectors to obtain Guhr matrices using Guhr’s correlation method according to Ref. [“P. Rinn {"\it et. al.”}, Europhysics Letters 110, 68003 (2015)"]. We compare the results for the evolution of market states and the corresponding transition matrices with those obtained using Pearson correlation matrices. The behavior of market states is found to be similar for both the coarse grained and Pearson matrices. However, the number of relevant variables is reduced by orders of magnitude. ...

Improved Data Generation for Enhanced Asset Allocation: A Synthetic Dataset Approach for the Fixed Income Universe ArXiv ID: 2311.16004 “View on arXiv” Authors: Unknown Abstract We present a novel process for generating synthetic datasets tailored to assess asset allocation methods and construct portfolios within the fixed income universe. Our approach begins by enhancing the CorrGAN model to generate synthetic correlation matrices. Subsequently, we propose an Encoder-Decoder model that samples additional data conditioned on a given correlation matrix. The resulting synthetic dataset facilitates in-depth analyses of asset allocation methods across diverse asset universes. Additionally, we provide a case study that exemplifies the use of the synthetic dataset to improve portfolios constructed within a simulation-based asset allocation process. ...

Permutation invariant Gaussian matrix models for financial correlation matrices ArXiv ID: 2306.04569 “View on arXiv” Authors: Unknown Abstract We construct an ensemble of correlation matrices from high-frequency foreign exchange market data, with one matrix for every day for 446 days. The matrices are symmetric and have vanishing diagonal elements after subtracting the identity matrix. For this case, we construct the general permutation invariant Gaussian matrix model, which has 4 parameters characterised using the representation theory of symmetric groups. The permutation invariant polynomial functions of the symmetric, diagonally vanishing matrices have a basis labelled by undirected loop-less graphs. Using the expectation values of the general linear and quadratic permutation invariant functions of the matrices in the dataset, the 4 parameters of the matrix model are determined. The model then predicts the expectation values of the cubic and quartic polynomials. These predictions are compared to the data to give strong evidence for a good overall fit of the permutation invariant Gaussian matrix model. The linear, quadratic, cubic and quartic polynomial functions are then used to define low-dimensional feature vectors for the days associated to the matrices. These vectors, with choices informed by the refined structure of small non-Gaussianities, are found to be effective as a tool for anomaly detection in market states: statistically significant correlations are established between atypical days as defined using these feature vectors, and days with significant economic events as recognized in standard foreign exchange economic calendars. They are also shown to be useful as a tool for ranking pairs of days in terms of their similarity, yielding a strongly statistically significant correlation with a ranking based on a higher dimensional proxy for visual similarity. ...