Inferring financial stock returns correlation from complex network analysis

ArXiv ID: 2407.20380 “View on arXiv”

Authors: Unknown

Abstract

Financial stock returns correlations have been studied in the prism of random matrix theory, to distinguish the signal from the “noise”. Eigenvalues of the matrix that are above the rescaled Marchenko Pastur distribution can be interpreted as collective modes behavior while the modes under are usually considered as noise. In this analysis we use complex network analysis to simulate the “noise” and the “market” component of the return correlations, by introducing some meaningful correlations in simulated geometric Brownian motion for the stocks. We find that the returns correlation matrix is dominated by stocks with high eigenvector centrality and clustering found in the network. We then use simulated “market” random walks to build an optimal portfolio and find that the overall return performs better than using the historical mean-variance data, up to 50% on short time scale.

Keywords: Random matrix theory, Complex network analysis, Eigenvalue decomposition, Eigenvector centrality, Portfolio optimization, Equities

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced random matrix theory and network science (eigenvector centrality, Marchenko-Pastur distribution) with mathematical derivations, but it also includes real S&P500 data, specific timeframes, and portfolio backtesting results.

  flowchart TD
    A["Research Goal<br>Simulate noise & market<br>components of stock correlations"] --> B["Data Generation<br>Geometric Brownian Motion<br>with simulated correlations"]
    B --> C["Correlation Matrix Analysis<br>Random Matrix Theory<br>Marchenko-Pastur distribution"]
    C --> D["Complex Network Analysis<br>Build correlation network<br>Calculate Eigenvector Centrality"]
    D --> E["Portfolio Optimization<br>Use 'market' random walks<br>to construct optimal portfolio"]
    E --> F["Performance Evaluation<br>Compare portfolio returns<br>vs historical mean-variance"]
    F --> G["Key Outcomes<br>1. Correlations dominated by high centrality stocks<br>2. Portfolio return improved by up to 50%<br>on short time scales"]