Structural Dynamics of G5 Stock Markets During Exogenous Shocks: A Random Matrix Theory-Based Complexity Gap Approach

Paper: arXiv 2604.19107

Authors: Kundan Mukhia, Imran Ansari, Md. Nurujjaman

Abstract

We identify a robust structural signature of stock markets during exogenous shock events by analyzing collective return dynamics across G5 countries. Using Random Matrix Theory, we introduce the complexity gap, defined as the difference between the normalized largest eigenvalue and the average pairwise correlation, to quantify changes in market structure. This measure reveals a consistent three-phase pattern across multiple shocks, including the 2025 U.S. tariff event, the COVID-19 crisis, and country-specific shocks in Japan and China during 2024. Before a shock, markets show a positive complexity gap, reflecting a rich structure with multiple interacting factors. During shocks, the gap collapses to near zero, signaling strong synchronization under a single dominant mode. Post-shock recovery follows a nonmonotonic path: an initial widening (a false recovery), a temporary recollapse, and final sustained restoration. This pattern holds at both market and sector levels and across global and local shocks. Ordinal entropy analysis confirms the same sequence of collapse and false recovery in directional diversity. We further demonstrate that lower complexity gap values predict higher future portfolio volatility, especially after shocks, establishing its value as a state-dependent risk indicator. For investors, initial gap widening may mislead, while sustained widening signals genuine structural stabilization. These findings reveal a robust structural signature governing financial market dynamics during crisis and recovery periods.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The research employs advanced Random Matrix Theory and ordinal entropy analysis to extract market signals, while providing a multi-event empirical validation across several recent global shocks. The methodology bridges sophisticated theoretical physics techniques with concrete, actionable risk indicators suitable for market analysis.

Research Flowchart

  flowchart TD
    A[<b>Goal:</b> Analyze G5 Market Dynamics<br/>During Exogenous Shocks] --> B[<b>Data:</b> G5 Collective<br/>Return Dynamics]
    B --> C[<b>Method:</b> Random Matrix Theory<br/>& Complexity Gap Calculation]
    C --> D[<b>Processes:</b> Ordinal Entropy Analysis<br/>& Synchronization Mapping]
    D --> E[<b>Finding 1:</b> Three-Phase Pattern<br/>(Collapse, False Recovery, Stabilization)]
    D --> F[<b>Finding 2:</b> Risk Metric: Low Gap<br/>Predicts High Future Volatility]
    E --> G[<b>Outcome:</b> Structural Signature<br/>as Decision Support Tool]
    F --> G

Cited References (46)

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4. Dynamics of market correlations: Taxonomy and portfolio analysis (2003)
5. Econometric measures of connectedness and systemic risk in the finance and insurance sectors (2012)
6. Why stock markets crash: critical events in complex financial systems (2017)
7. A tool for filtering information in complex systems (2005)
8. Correlation of financial markets in times of crisis (2012)

4 of 46 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.