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

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Highly relevant for quantitative trading and risk management. The complexity gap provides a state-dependent risk indicator that predicts future portfolio volatility, particularly after shocks. The three-phase recovery pattern (collapse → false recovery → sustained restoration) offers actionable timing signals for portfolio rebalancing and risk position rebuilding. The finding that initial gap widening is misleading (false recovery) while sustained widening signals genuine stabilization is directly applicable to post-crisis trading strategies. The quintile analysis showing up to 4.47% annualized volatility spread between extreme complexity gap groups provides a concrete economic magnitude for risk-adjusted position sizing. However, the modest incremental R² suggests it should be used as a complementary indicator rather than a standalone signal.

Moderate complexity. The core RMT eigenvalue decomposition and correlation matrix construction are standard linear algebra operations available in NumPy/SciPy. The complexity gap calculation is straightforward (difference of two scalars). Ordinal entropy computation requires permutation pattern extraction. The main implementation challenges are: (1) proper handling of rolling windows with missing data, (2) Monte Carlo portfolio simulation with 500 portfolios per window across multiple markets, (3) ensuring numerical stability with pseudo-inverse for MVP weights, and (4) the overall pipeline integrating multiple analytical components. The algorithm is well-specified in Algorithm 1, and all parameters are clearly defined. No specialized hardware or proprietary libraries are required.

The paper provides detailed mathematical formulations for all methods (RMT decomposition, complexity gap definition, ordinal entropy, portfolio optimization). Data is sourced from Yahoo Finance via the yfinance Python package, and stock tickers are listed in Appendix B. Rolling window parameters (T=60 days) and sensitivity analyses (L=30, L=90) are specified. However, no GitHub repository or code is explicitly provided, and the exact preprocessing steps for handling missing data are not fully detailed. The algorithm is summarized in Algorithm 1.