Carbon Risk Without a Stable Premium: Nonlinear and State-Dependent Evidence from European ESG Leaders

Despite the economic relevance of climate-transition risk, firm-level carbon exposure often fails to appear as a robustly priced factor when ESG measures and sustainability shocks are conflated. This study examines whether carbon exposure is conditionally priced in European equity returns using a strongly balanced quarterly panel of 238 firms from the MSCI Europe ESG Leaders universe (2018–2024). Total greenhouse gas emissions act as a proxy for carbon exposure, mapped to within-year percentiles and standardized by sector-year. Regressions control for ESG scores and controversies and include firm and quarter fixed effects with firm-clustered, dependence-robust standard errors. The linear carbon coefficient is small and statistically indistinguishable from zero, indicating no stable return premium from within-firm changes in carbon exposure. Functional-form tests reject linearity: quadratic and quintile specifications reveal curvature and a non-monotonic pattern, with return differences concentrated in the middle of the carbon distribution. Conditioning on macro-financial stress, measured by the ECB Composite Indicator of Systemic Stress, yields limited evidence of a uniform carbon penalty. However, high-controversy states are associated with lower returns, while ESG scores show negative associations under dependence-robust inference. Overall, carbon-related pricing appears to be nonlinear and state-dependent, whereas controversy risk is the most robust sustainability predictor of returns.