Emissions-Robust Portfolios

TL;DR

The paper tackles portfolio design under noisy firm-level emissions data by embedding an emissions-penalty operator into robust optimization. The operator, uniquely characterized by axioms, yields the tractable form $P^{(m)}_j(r,\lambda) = \bigl(1 - \frac{\lambda}{\lambda_{\max,j}}\bigr)^m r$, enabling exact LP/SOCP reformulations under norm- or moment-based ambiguity sets. It develops robust mean-variance and CVaR programs, with dual variables interpretable as shadow carbon prices, and extends to dynamic and distributionally robust settings, producing a return--emissions Pareto frontier and Lipschitz bounds. Empirically, in a US large-cap universe with monthly rebalancing and transaction costs, EAPO delivers roughly a 92% reduction in portfolio Scope-1 emissions relative to equal-weight benchmarks while maintaining statistically indistinguishable Sharpe ratios, demonstrating practical implementability and policy relevance for financed-emissions mandates.

Abstract

We study portfolio choice when firm-level emissions intensities are measured with error. We introduce a scope-specific penalty operator that rescales asset payoffs as a smooth function of revenue-normalized emissions intensity. Under payoff homogeneity, unit-scale invariance, mixture linearity, and a curvature semigroup axiom, the operator is unique and has the closed form $P^{(m)}_j(r,λ)=\bigl(1-λ/λ_{\max,j}\bigr)^m r$. Combining this operator with norm- and moment-constrained ambiguity sets yields robust mean-variance and CVaR programs with exact linear and second-order cone reformulations and economically interpretable dual variables. In a U.S. large-cap equity universe with monthly rebalancing and uniform transaction costs, the resulting strategy reduces average Scope~1 emissions intensity by roughly 92\% relative to equal weight while exhibiting no statistically detectable reduction in the Sharpe ratio under block-bootstrap inference and no statistically detectable change in average returns under HAC inference. We report the return-emissions Pareto frontier, sensitivity to robustness and turnover constraints, and uncertainty propagation from multiple imputation of emissions disclosures.

Figures (9)

• Figure 1: From atmospheric accumulation to policy-relevant budgets. Panel (a) translates ppm growth into GtCO$_2$/yr and shows measurement uncertainty, panel (b) illustrates how non-linear emissions pathways induce different curvature in the remaining-budget trajectory. Values are illustrative and sensitive to methodological choices (e.g., non-CO$_2$ forcers and probability thresholds).
• Figure 2: Global and 2023 CO$_2$ emissions by source. Source: Our World in Data, "CO$_2$ and Greenhouse Gas Emissions" dataset.
• Figure 3: Workflow from data ingestion to optimization and evaluation.
• Figure 4: Distribution of reported emissions and concentration of revenue among the largest firms. Panels show (a) the cumulative distribution of reported emissions across firms and (b) the set of firms with the highest reported revenue over the sample period.
• Figure 5: Temporal dynamics and cross-sectional geometry of uncertainty sets. Panels show (a) the evolution of the uncertainty set area over time and (b) annual uncertainty sets represented as ellipses in the state space.

Theorems & Definitions (31)

• Definition 2.2: Emissions--penalty operator
• Lemma 2.3: Analytic properties
• proof
• Theorem 2.4: Exact conic reformulation
• proof
• Proposition 2.5: Sensitivity
• proof
• Theorem 2.6: $\phi$--divergence DRO reformulation
• proof
• Proposition 2.7: Convex Pareto frontier