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Sustainable Investment: ESG Impacts on Large Portfolio

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  • Ruike Wu
  • Yonghe Lu
  • Yanrong Yang

Abstract

This paper investigates the impact of environmental, social, and governance (ESG) constraint on a regularized mean-variance (MV) portfolio optimization problem in a large-dimensional setting, in which a positive definite regularization matrix is imposed on the sample covariance matrix. We first derive the asymptotic results for the out-of-sample (OOS) Sharpe ratio (SR) of the proposed portfolio, which help quantify the impact of imposing an ESG-level constraint as well as the effect of estimation error arising from the sample mean estimation of the assets' ESG score. Furthermore, to study the influence of the choices of the regularization matrix, we develop an estimator for the OOS Sharpe ratio. The corresponding asymptotic properties of the Sharpe ratio estimator are established based on random matrix theory. Simulation results show that the proposed estimators perform close to the corresponding oracle level. Moreover, we numerically investigate the impact of various forms of regularization matrices on the OOS SR, which provides useful guidance for practical implementation. Finally, based on OOS SR estimator, we propose an adaptive regularized portfolio which uses the best regularization matrix yielding the highest estimated SR (among a set of candidates) at each decision node. Empirical evidence based on the S\&P 500 index demonstrates that the proposed adaptive ESG-constrained portfolio achieves a high OOS SR while satisfying the required ESG level, offering a practically effective approach for sustainable investment.

Suggested Citation

  • Ruike Wu & Yonghe Lu & Yanrong Yang, 2026. "Sustainable Investment: ESG Impacts on Large Portfolio," Papers 2602.14439, arXiv.org.
    • Handle: RePEc:arx:papers:2602.14439
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    References listed on IDEAS

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    1. Yonghe Lu & Yanrong Yang & Terry Zhang, 2024. "Double Descent in Portfolio Optimization: Dance between Theoretical Sharpe Ratio and Estimation Accuracy," Papers 2411.18830, arXiv.org.
    2. Kan, Raymond & Zhou, Guofu, 2007. "Optimal Portfolio Choice with Parameter Uncertainty," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 42(3), pages 621-656, September.
    3. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    4. Bodnar, Taras & Okhrin, Ostap & Parolya, Nestor, 2019. "Optimal shrinkage estimator for high-dimensional mean vector," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 63-79.
    5. Nathan Lassance & Alberto Martín-Utrera & Majeed Simaan, 2024. "The Risk of Expected Utility Under Parameter Uncertainty," Management Science, INFORMS, vol. 70(11), pages 7644-7663, November.
    6. Gasser, Stephan M. & Rammerstorfer, Margarethe & Weinmayer, Karl, 2017. "Markowitz revisited: Social portfolio engineering," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1181-1190.
    7. Wu, Ruike & Yang, Yanrong & Shang, Han Lin & Zhu, Huanjun, 2025. "Making distributionally robust portfolios feasible in high dimension," Journal of Econometrics, Elsevier, vol. 252(PA).
    8. Anatoly B. Schmidt, 2022. "Optimal ESG portfolios: an example for the Dow Jones Index," Journal of Sustainable Finance & Investment, Taylor & Francis Journals, vol. 12(2), pages 529-535, April.
    9. Jose Blanchet & Lin Chen & Xun Yu Zhou, 2022. "Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances," Management Science, INFORMS, vol. 68(9), pages 6382-6410, September.
    10. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    11. Hautsch, Nikolaus & Voigt, Stefan, 2019. "Large-scale portfolio allocation under transaction costs and model uncertainty," Journal of Econometrics, Elsevier, vol. 212(1), pages 221-240.
    12. Li, Hua & Bai, Zhidong & Wong, Wing-Keung & McAleer, Michael, 2022. "Spectrally-Corrected Estimation for High-Dimensional Markowitz Mean-Variance Optimization," Econometrics and Statistics, Elsevier, vol. 24(C), pages 133-150.
    13. Olivier Ledoit & Michael Wolf, 2017. "Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks," The Review of Financial Studies, Society for Financial Studies, vol. 30(12), pages 4349-4388.
    14. Davide Lauria & W. Brent Lindquist & Stefan Mittnik & Svetlozar T. Rachev, 2025. "Environmental, Social and Governance-Valued Portfolio Optimization and Dynamic Asset Pricing," JRFM, MDPI, vol. 18(3), pages 1-33, March.
    15. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    16. Andrew W. Lo & Ruixun Zhang, 2025. "Performance Attribution for Portfolio Constraints," Management Science, INFORMS, vol. 71(9), pages 7537-7559, September.
    17. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    18. Utz, Sebastian & Wimmer, Maximilian & Steuer, Ralph E., 2015. "Tri-criterion modeling for constructing more-sustainable mutual funds," European Journal of Operational Research, Elsevier, vol. 246(1), pages 331-338.
    19. Gaorong Li & Lei Huang & Jin Yang & Wenyang Zhang, 2022. "A Synthetic Regression Model for Large Portfolio Allocation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1665-1677, October.
    20. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    21. Zheng Tracy Ke & Bryan T. Kelly & Dacheng Xiu, 2019. "Predicting Returns With Text Data," NBER Working Papers 26186, National Bureau of Economic Research, Inc.
    22. Fan, Qingliang & Wu, Ruike & Yang, Yanrong & Zhong, Wei, 2024. "Time-varying minimum variance portfolio," Journal of Econometrics, Elsevier, vol. 239(2).
    23. Cai, Tony & Liu, Weidong, 2011. "Adaptive Thresholding for Sparse Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 672-684.
    24. Jan De Spiegeleer & Stephan Höcht & Daniel Jakubowski & Sofie Reyners & Wim Schoutens, 2023. "ESG: a new dimension in portfolio allocation," Journal of Sustainable Finance & Investment, Taylor & Francis Journals, vol. 13(2), pages 827-867, April.
    25. Andrew W. Lo & Ruixun Zhang, 2024. "Quantifying the Impact of Impact Investing," Management Science, INFORMS, vol. 70(10), pages 7161-7186, October.
    26. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    27. Ding, Yi & Li, Yingying & Zheng, Xinghua, 2021. "High dimensional minimum variance portfolio estimation under statistical factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 502-515.
    28. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    29. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev, 2025. "Sustainability-valued discrete option pricing in complete markets," Journal of Sustainable Finance & Investment, Taylor & Francis Journals, vol. 15(2), pages 403-437, April.
    30. Taras Bodnar & Yarema Okhrin & Nestor Parolya, 2022. "Optimal Shrinkage-Based Portfolio Selection in High Dimensions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 140-156, December.
    31. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
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