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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.
Sevin et al. (Sat,) studied this question.