Finding Core Balanced Modules in Statistically Validated Stock Networks

TL;DR

This paper introduces statistically validated stock correlation networks and a novel module detection method, LSCBM, to identify stable, core market groups with potential hedging opportunities, validated through theoretical and empirical analysis.

Contribution

It proposes a new structure, LSCBM, and an efficient heuristic algorithm, MaxBalanceCore, for detecting core modules in stock networks, addressing limitations of traditional threshold-based methods.

Findings

LSCBM size increases during market stress periods.

MaxBalanceCore scales efficiently to large networks.

Empirical analysis reveals dynamic reorganization of core modules across economic regimes.

Abstract

Traditional threshold-based stock networks suffer from subjective parameter selection and inherent limitations: they constrain relationships to binary representations, failing to capture both correlation strength and negative dependencies. To address this, we introduce statistically validated correlation networks that retain only statistically significant correlations via a rigorous t-test of Pearson coefficients. We then propose a novel structure termed the largest strong correlation balanced module (LSCBM), defined as the maximum-size group of stocks with structural balance (i.e., positive edge-sign products for all triplets) and strong pairwise correlations. This balance condition ensures stable relationships, thus facilitating potential hedging opportunities through negative edges. Theoretically, within a random signed graph model, we establish LSCBM's asymptotic existence, size scaling, and multiplicity under various parameter regimes. To detect LSCBM efficiently, we develop MaxBalanceCore, a heuristic algorithm that leverages network sparsity. Simulations validate its efficiency, demonstrating scalability to networks of up to 10,000 nodes within tens of seconds. Empirical analysis demonstrates that LSCBM identifies core market subsystems that dynamically reorganize in response to economic shifts and crises. In the Chinese stock market (2013-2024), LSCBM's size surges during high-stress periods (e.g., the 2015 crash) and contracts during stable or fragmented regimes, while its composition rotates annually across dominant sectors (e.g., Industrials and Financials).