Emissions-Robust Portfolios

Battle Count: 65

Highly relevant for institutional quantitative portfolio management. The EAPO framework provides a tractable, scalable method for integrating climate/emissions constraints into mean-variance and CVaR portfolio construction. The LP/SOCP reformulations ensure polynomial-time solvability for universes with thousands of securities. The projected-gradient implementation with warm-starting and turnover caps is directly deployable in production trading systems. The shadow carbon price interpretation provides actionable governance metrics. However, the paper focuses on monthly rebalancing long-only equity portfolios rather than high-frequency or intraday trading strategies. The robust optimization approach is more relevant for strategic asset allocation and index-plus mandates than for alpha-generating short-term trading.

The mathematical framework is sophisticated (axiomatic operator characterization, conic duality, distributionally robust extensions, dynamic programming). However, the actual implementation is well-structured: the core optimization reduces to LP/SOCP with O(n) constraints, solvable via standard conic solvers or the provided projected-gradient algorithm. Key complexity drivers include: (1) hierarchical Bayesian multiple imputation pipeline for missing emissions data, (2) Ledoit-Wolf covariance shrinkage, (3) proper timing conventions for forward-carry of emissions data, (4) hyper-parameter calibration via nested cross-validation, (5) HAC inference and block-bootstrap for statistical validation. The GitHub repository mitigates implementation burden. For a team with optimization and quantitative finance expertise, the system is implementable within a few months.

The paper provides a GitHub repository (https://github.com/stone-technologies/ERP/tree/main) with full implementation and scripts. Data sources are identified (CDP for emissions, Alpha-Vantage for prices, quarterly income statements for revenues). Hyper-parameter selection procedures (nested rolling cross-validation for m, profile-likelihood for Gamma) are described. However, CDP data access may require institutional subscription, and some preprocessing details (exact sector mappings, specific imputation priors) would need the code to fully replicate. The mathematical framework is fully specified with proofs in the appendix.