Emissions-Robust Portfolios

Paper: arXiv 2601.06507

Authors: Khizar Qureshi, H. Oliver Gao

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.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a rigorous axiomatic foundation and robust optimization framework (LP/SOCP) for portfolio choice under emissions disclosure uncertainty. Empirically, it is highly thorough, using hierarchical Bayesian imputation, block-bootstrap, and HAC inference on US large-cap equities to demonstrate significant emissions reduction without sacrificing risk-adjusted returns.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Portfolio Choice Under Uncertain<br>Firm-Level Emissions Intensities"] --> B["Data Inputs:<br>U.S. Large-Cap Equity Universe<br>& Imputed Emissions Data"]
    
    B --> C["Core Methodology:<br>Construct Scope-Specific Penalty Operator<br>P_j^(m)(r, λ) = (1 - λ/λ_max,j)^m * r"]
    
    C --> D["Optimization Process:<br>Formulate Robust Mean-Variance & CVaR<br>Programs (Exact SOCP/Linear Reformulations)"]
    
    D --> E["Backtesting & Evaluation:<br>Monthly Rebalancing with Transaction Costs,<br>Block-Bootstrap & HAC Inference"]
    
    E --> F["Key Findings:<br>• ~92% Reduction in Avg Scope 1 Emissions<br>• No Statistically Significant Sharpe Ratio Loss<br>• Pareto Frontier of Return vs. Emissions"]

Cited References (95)

1. The Surveyor’s Area Formula (1986)
2. Optimal output-sensitive convex hull algorithms in two and three dimensions (1996)
3. The Eco-Efficiency Premium Puzzle (2004)
4. The Effect of Socially Responsible Investing on Portfolio Performance (2007)
5. The price of ethics and stakeholder governance: The performance of socially responsible mutual fund (2008)
6. Sin Stock Returns (2008)
7. Multi-objective probabilistically constrained programs with variable risk: Models for multi-portfolio financial optimization (2015)
8. Understanding Socially Responsible Investing: The Effect of Decision Frames and Trade-off Options (2008)

0 of 95 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.