Sustainable portfolio optimization with four objectives: Assessing the role of diversification
- 1Universitat Politècnica de València, Valencia, Spain; Corresponding author.
- 2Universitat Politècnica de València, Valencia, Spain
- 3Roma Tre University, Rome, Italy
Abstract
This study investigates the value of incorporating diversification as an explicit objective in sustainable portfolio optimization, alongside expected return, risk measured by Value-at-Risk (VaR), and sustainability performance. Since minimizing VaR and maximizing sustainability do not necessarily lead to well-diversified portfolios, we assess the incremental contribution of diversification, measured by the Diversification Ratio (DR). To this end, a four-objective Mean–VaR–ESG-diversification model is compared with a reduced three-objective Mean–VaR–ESG formulation. Given the non-convex nature of the resulting optimization problems, both formulations are solved using an adapted version of ev-MOGA. The study further incorporates investor preferences through a preference-direction framework. Instead of requiring predefined objective weights, this approach allows investors to specify their preferred direction in the objective space, facilitating the identification of portfolios that reflect different priorities across return, downside risk, and sustainability. The proposed methodology is evaluated through an extensive out-of-sample analysis of four equity datasets based on major stock indices: the Euro Stoxx 50, FTSE 100, S&P 100, and Nasdaq 100. The results show consistent improvements in diversification, volatility, and VaR, with generally modest reductions in ESG scores and trade-offs in return performance that vary across datasets and investor profiles.
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BibTeX
@article{garciabernabeu2026sustainable,
title = {{Sustainable portfolio optimization with four objectives: Assessing the role of diversification}},
author = {Ana Garcia-Bernabeu and Adolfo Hilario-Caballero and Francesca Luciani},
journal = {Operations Research Perspectives},
year = {2026},
month = oct,
doi = {10.1016/j.orp.2026.100420},
url = {https://doi.org/10.1016/j.orp.2026.100420},
note = {CC BY},
}
RIS
TY - JOUR
TI - Sustainable portfolio optimization with four objectives: Assessing the role of diversification
AU - Ana Garcia-Bernabeu
AU - Adolfo Hilario-Caballero
AU - Francesca Luciani
PY - 2026
DA - 2026/10/30
JO - Operations Research Perspectives
DO - 10.1016/j.orp.2026.100420
UR - https://doi.org/10.1016/j.orp.2026.100420
AB - This study investigates the value of incorporating diversification as an explicit objective in sustainable portfolio optimization, alongside expected return, risk measured by Value-at-Risk (VaR), and sustainability performance. Since minimizing VaR and maximizing sustainability do not necessarily lead to well-diversified portfolios, we assess the incremental contribution of diversification, measured by the Diversification Ratio (DR). To this end, a four-objective Mean–VaR–ESG-diversification model is compared with a reduced three-objective Mean–VaR–ESG formulation. Given the non-convex nature of the resulting optimization problems, both formulations are solved using an adapted version of ev-MOGA. The study further incorporates investor preferences through a preference-direction framework. Instead of requiring predefined objective weights, this approach allows investors to specify their preferred direction in the objective space, facilitating the identification of portfolios that reflect different priorities across return, downside risk, and sustainability. The proposed methodology is evaluated through an extensive out-of-sample analysis of four equity datasets based on major stock indices: the Euro Stoxx 50, FTSE 100, S&P 100, and Nasdaq 100. The results show consistent improvements in diversification, volatility, and VaR, with generally modest reductions in ESG scores and trade-offs in return performance that vary across datasets and investor profiles.
SN - 2214-7160
ER -