Higher-Order Network Reveals Risk in Chinese Stocks

Shanghai Jiao Tong University Journal Center

Background and Motivation

Systemic financial risk remains a critical challenge for modern economies, underscored by recurring crises such as the 2008 global financial meltdown, the 2015 Chinese stock market crash, and the COVID-19 pandemic. Traditional research has often examined sectors in isolation or focused on pairwise risk spillovers, overlooking the complex, multi-sector dependencies that can amplify systemic threats. This study addresses that gap by exploring higher-order interactions—where risks resonate simultaneously across multiple sectors—within China's stock market. By moving beyond conventional dyadic models, the research provides a more nuanced understanding of how collective risk behaviour shapes financial stability.

Methodology and Scope

Using the Reconstructing the Higher Order Structure of Time Series (RHOSTS) method, the authors construct dynamic higher-order networks to capture risk co-movement among 24 Chinese stock sectors from 2007 to 2024. Sectoral volatility is estimated via GJR-GARCH models, and hyperedges represent synchronised risk resonance across multiple sectors. Network topology metrics—such as higher-order degree, systemic importance, and clustering coefficient—are analysed at both sector and system levels. The study further integrates these metrics into a coupled-map-lattice model to quantify time-varying resilience during major crises, including the 2008 financial crisis, the 2015 market crash, and the COVID-19 pandemic.

Key Findings and Contributions

  • Dominant Third-Order Resonance: The most prevalent risk pattern involves synchronous resonance among four sectors (third-order hyperedges), highlighting limitations of traditional pairwise models.
  • Sectoral Heterogeneity: The insurance (INS) sector consistently shows high systemic importance, while energy (ENE) becomes central during geopolitical crises like the Russia-Ukraine conflict.
  • Crisis-Specific Clusters: Core resonance groups shift with each crisis—e.g., {ENE, INS, DFI, TSE} post-2008, {TSE, RES, ACO, INS} post-2015, and {DFI, TSE, THA, SSE} post-COVID-19.
  • Network Resilience: System-wide resilience exhibits an upward long-term trend, though it fluctuates significantly during stress periods. Financial sectors generally demonstrate higher shock-absorption capacity, while retailing (RET) and capital goods (CGO) are among the most vulnerable.
  • Structural Shifts: Major events drastically alter network density, connectivity, and cluster formation, confirming that external shocks reconfigure risk transmission pathways.

Why It Matters

The study offers a paradigm shift in systemic risk analysis by capturing group-level risk synchronisation that traditional models miss. This approach reveals how multi-sector co-movements can accelerate contagion and create hidden vulnerabilities. By identifying crisis-specific resonance clusters and tracking resilience in real time, the research provides a more precise tool for monitoring and mitigating systemic threats in increasingly interconnected financial systems.

Practical Applications

  • For Regulators: Enables dynamic monitoring of higher-order risk clusters and informs targeted policies, such as cross-sector exposure limits or circuit-breaker mechanisms for highly synchronised sectors.
  • For Investors: Highlights the danger of over-concentrating portfolios in sectors prone to collective resonance—e.g., avoiding simultaneous heavy exposure to TSE, RES, ACO, and INS during turbulent periods.
  • For Risk Management: Provides a framework to design hedging strategies that account for multi-sector dependencies, particularly for energy and climate-related financial risks.
  • For Global Financial Stability: Demonstrates a scalable methodology for building real-time risk resonance surveillance systems in other markets.

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