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

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.