[Paper Review] Bayesian Optimization of ESG Financial Investments

Eduardo C. Garrido‐Merchán, Gabriel González Piris+1 more|arXiv (Cornell University)|Feb 10, 2023

Risk and Portfolio OptimizationDecision Sciences3 citations

TL;DR

This paper proposes a Bayesian optimization (BO) framework to simultaneously maximize portfolio Sharpe ratio and ESG compliance by treating ESG criteria as soft constraints in a black-box optimization setting. The method outperforms random search in both mean performance (1.662 vs. 1.538) and robustness, converging on an optimal portfolio allocation across 25 runs with varying ESG scores.

ABSTRACT

Financial experts and analysts seek to predict the variability of financial markets. In particular, the correct prediction of this variability ensures investors successful investments. However, there has been a big trend in finance in the last years, which are the ESG criteria. Concretely, ESG (Economic, Social and Governance) criteria have become more significant in finance due to the growing importance of investments being socially responsible, and because of the financial impact companies suffer when not complying with them. Consequently, creating a stock portfolio should not only take into account its performance but compliance with ESG criteria. Hence, this paper combines mathematical modelling, with ESG and finance. In more detail, we use Bayesian optimization (BO), a sequential state-of-the-art design strategy to optimize black-boxes with unknown analytical and costly-to compute expressions, to maximize the performance of a stock portfolio under the presence of ESG criteria soft constraints incorporated to the objective function. In an illustrative experiment, we use the Sharpe ratio, that takes into consideration the portfolio returns and its variance, in other words, it balances the trade-off between maximizing returns and minimizing risks. In the present work, ESG criteria have been divided into fourteen independent categories used in a linear combination to estimate a firm total ESG score. Most importantly, our presented approach would scale to alternative black-box methods of estimating the performance and ESG compliance of the stock portfolio. In particular, this research has opened the door to many new research lines, as it has proved that a portfolio can be optimized using a BO that takes into consideration financial performance and the accomplishment of ESG criteria.

Motivation & Objective

• To address the growing demand for socially responsible investing by integrating ESG criteria into portfolio optimization.
• To develop a scalable, data-driven method that optimizes financial performance while respecting ESG constraints.
• To evaluate the effectiveness of Bayesian optimization in handling black-box, costly-to-evaluate objective functions combining Sharpe ratio and ESG scores.
• To compare BO’s performance against random search under varying ESG score variability.
• To explore the feasibility of extending the framework to other ESG-related or ESG-related constraints.

Proposed method

• The objective function combines the Sharpe ratio (for risk-adjusted return) and a normalized ESG score (from 14 independent categories) into a single ESG-transformed Sharpe ratio.
• Bayesian optimization is applied using an upper confidence bound (UCB) acquisition function to sequentially select portfolio weights.
• The ESG score is normalized to a [0,10] scale, with higher values indicating better ESG performance.
• The optimization process treats the portfolio return and risk evaluation as a black-box function, requiring no analytical gradient or closed-form expression.
• The method is tested under two experimental settings: low-variability ESG scores (8.7, 8.97, 7.32) and high-variability scores (9, 5, 2).
• Performance is evaluated over 25 iterations with 25 independent runs per method, comparing mean performance and standard deviation.

Experimental results

Research questions

• RQ1 Can Bayesian optimization effectively optimize a portfolio under combined financial performance and ESG compliance objectives?
• RQ2 How does Bayesian optimization compare to random search in terms of mean performance and robustness when optimizing ESG-integrated portfolios?
• RQ3 Does the method converge to a consistent optimal portfolio allocation across multiple runs, even with varying ESG score inputs?
• RQ4 Can the framework be extended to incorporate additional ESG-related or non-financial constraints as black-box constraints?
• RQ5 How does the variability of ESG scores affect the optimization outcome and convergence behavior?

Key findings

• Bayesian optimization achieved a mean performance of 1.662, significantly outperforming random search’s mean of 1.538 in the low-variability ESG scenario.
• The standard deviation of performance was lower in Bayesian optimization (indicating higher robustness) compared to random search across all 25 runs.
• All 25 repetitions of Bayesian optimization converged on the same optimal portfolio: 57.6% Endesa, 21.2% Iberdrola, and 21.2% Repsol.
• In the high-variability ESG scenario (scores: 9, 5, 2), Bayesian optimization again outperformed random search in both mean performance and standard deviation.
• The optimal portfolio in the high-variability case had a lower ESG-transformed Sharpe ratio due to the reduced sum of ESG scores, confirming the method’s sensitivity to ESG input quality.
• The results demonstrate that Bayesian optimization is a viable and robust method for ESG-constrained portfolio optimization, even when ESG scores vary significantly.