Copula Asymmetry Index (CAI++): Measuring Asymmetric Equity–Volatility Tail Dependence for Defensive Allocation

This paper introduces the Copula Asymmetry Index (CAI), a rolling, rank-based measure of asymmetric tail dependence between equity returns and implied-volatility proxies. CAI is defined as the difference between the empirical frequency of joint “equity-down & volatility-up” tail events and that of the mirror state (“equity-up & volatility-down”) within a rolling window. Building on this core asymmetry measure, we develop CAI++, an implementation framework that transforms CAI into an operational defensive allocation signal through smoothing, standardization, delayed execution, hysteresis, and cost-aware portfolio mapping. Using daily data from 2000 onward across a broad cross-section of 50 equity-volatility pairs, we evaluate the CAI++ strategy against buy-and-hold equity, a 60/40 benchmark, an inverse-volatility risk-parity portfolio, and a moving-average timing rule. Cross-sectional results indicate that CAI improves terminal outcomes relative to equity-only exposure for most pairs and shows particularly strong performance versus 60/40 in both final wealth and Sharpe. However, CAI does not dominate structurally diversified low-volatility allocations: risk parity retains a pronounced advantage in downside risk and risk-adjusted metrics. Overall, the findings support CAI as a tail-aware overlay for equity-centric and balanced portfolios rather than a substitute for institutional low-volatility baselines.