Tail-dependent lead-lag dynamics between fossil and sustainable assets: A Cross-Quantilogram approach

This study analyzed tail-dependent lead-lag linkages between fossil and sustainable assets using daily WTI crude oil futures, clean-energy equities, and the S&P Green Bond Index from August 3, 2015, to August 7, 2025. Unlike existing literature that typically studies oil-clean energy or green bond-equities in isolation, we embedded fossil fuel prices, clean-energy equities, and green bonds in a single tail-state lead-lag system and documented how transmission patterns reconfigure across downside and upside regimes. To condition the analysis on common uncertainty proxies, returns were regressed on the CBOE VIX and the (log) U.S. Economic Policy Uncertainty index, and the resulting residual-based series were examined with the cross-quantilogram (CQ) across target quantiles τ₁ ∈ {0.10, 0.50, 0.90}, conditional on source states τ₂ ∈ {0.10, 0.90}, with ~95% confidence bands. Heatmaps summarize average CQ signs (co-movement vs. stabilization) and the breadth of significance across lags. Two regularities emerged. First, dependence is state- and tail-contingent. In downside states (τ₂ = 0.10), patterns of strong downside co-movement and rally suppression are evident, particularly between oil and renewables, with modest but persistent linkages to green bonds. Second, in upside states (τ₂ = 0.90), the dominant pattern shifts toward stabilization and selective upside clustering, most visible within the "green block" and through lagged upside predictability from green bonds toward oil. Overall, conditional on controls for VIX and EPU, fossil and sustainable assets exhibit asymmetric, tail-driven interdependence: diversification weakens during distress, while stabilization and selective upside synchronization dominate in buoyant markets. These findings provide valuable insights for tail-aware portfolio design and state-contingent risk management.