Optimizing ESG Portfolios

Jorge Hernandez and Enrique Villamor The Journal of Impact and ESG Investing, Spring 2026

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Overview

This paper develops a rolling-window portfolio optimization framework that incorporates ESG constraints into a unified Black-Litterman / MGARCH / quadratic-programming pipeline. Black-Litterman expected returns are formed from 64-day rolling average return differentials (tau = 0.025) combined with a market-cap-weighted equilibrium prior. A DCC-MGARCH(1,1) model provides the one-step-ahead covariance matrix at each rebalancing date. Three nested quadratic programs are then solved: a baseline model with no ESG filter (unconstrained Lagrangian), an ESG long-short model that enforces a mean deficiency ceiling via a closed-form two-multiplier Lagrangian, and an ESG long-only model solved numerically with sign and bound constraints. The framework is backtested over 16 out-of-sample trades (64-trading-day rebalancing intervals, July 2010 to May 2023) and shows monotonically increasing mean one-period returns as ESG constraints are tightened.

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Repository contents

Notebooks

File	Model	Description	Paper exhibits
Model 1.ipynb	Baseline (unconstrained)	Black-Litterman + MGARCH, no ESG constraint; closed-form Lagrangian weights	Exhibits 1–2
Model 2.ipynb	ESG long-short	Adds ESG deficiency ceiling; closed-form two-multiplier Lagrangian; short positions allowed	Exhibits 3–6
Model 3.ipynb	ESG long-only	Same ESG constraint; QP solved with qpsolvers/quadprog; weights bounded to [0.0001, 1]	Exhibits 7–9

Data files

File	Role
Stock Prices.xlsx	Daily adjusted closing prices (Bloomberg PX_LAST) for the 60-stock universe
ESG Scores.xlsx	S&P Global ESG Rank (RobecoSAM Total Sustainability Rank) for each stock; deficiency = 100 minus raw rank
Market Caps.xlsx	Daily market capitalisations used to construct the Black-Litterman equilibrium prior

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Data

• Universe: 60 US large-cap stocks
• Date range: July 2010 to May 2023
• ESG source: S&P Global ESG Rank (RobecoSAM Total Sustainability Rank); higher rank = higher ESG quality; the notebooks work with deficiency = 100 minus the raw rank so that lower values are better
• Price and market-cap source: Bloomberg Terminal

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Reproducing the results

Requirements

pip install -r requirements.txt

Execution

Open each notebook in Jupyter and run all cells top to bottom. Each notebook is self-contained. Runtime is dominated by the MGARCH fitting step (16 fits per notebook on a 60-asset covariance model).

Headline results

Notebook	Mean one-period return
Model 1.ipynb (baseline)	0.0024
Model 2.ipynb (ESG long-short)	0.0036
Model 3.ipynb (ESG long-only)	0.0066

Rolling 64-trading-day retraining window; 16 out-of-sample trades.

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Citation

@article{hernandez_villamor_2026_esg,
  author  = {Hernandez, Jorge and Villamor, Enrique},
  title   = {Optimizing {ESG} Portfolios},
  journal = {The Journal of Impact and {ESG} Investing},
  year    = {2026},
  season  = {Spring},
}

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Acknowledgements

The authors thank Daniel Bilsker for assistance with the Python implementation. This research was partially funded by the US Department of Defense under grant W911NF-25-1-0138. This is contribution #2000 from the Institute of Environment at Florida International University (FIU).