A Goodness-of-Fit Framework for Assessing Distributional Symmetry and Tail Asymmetry in Financial Equity Markets

The assumption that highly correlated financial assets share identical risk profiles often overlooks crucial distributional asymmetries. This study introduces a Goodness-of-Fit (GoF) framework to evaluate stochastic symmetry and structural alignment of equity returns. Moving beyond linear correlation, we apply non-parametric GoF tests—Kolmogorov–Smirnov, permutation-based Anderson–Darling, and Epps–Singleton—complemented by Energy Distance metrics, Extreme Value Theory (EVT) for 1% and 5% tail asymptotics, and robust L-moments to quantify tail asymmetry. We analyze major stocks against market indices and sectoral ETFs using ARMA-GARCH filtered innovations to isolate IID components. Our findings reveal a significant decoupling between correlation and stochastic symmetry; highly correlated assets frequently exhibit tail asymmetry and structural drift. Energy Distance decomposition isolates shape-driven deviations from scale-driven volatility. Furthermore, hierarchical clustering categorizes assets into distinct risk profiles, bridging structural divergence and left-tail risk. A 1000-iteration bootstrapped backtest shows that integrating our GoF framework with tail-risk penalties improves risk-adjusted performance, evidenced by superior Sharpe ratios (outperforming 80.3% of random allocations). In conclusion, high linear correlation does not guarantee distributional symmetry. The proposed framework offers deeper insights into asymmetric asset behavior than conventional second moment metrics, providing a robust tool for portfolio risk management under non-Gaussian market conditions.