Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA

[EN] Despite the widespread use of the classical bicriteria Markowitz mean-variance framework, a broad consensus is emerging on the need to include more criteria for complex portfolio selection problems. Sustainable investing, also called socially responsible investment, is becoming a mainstream investment practice. In recent years, some scholars have attempted to include sustainability as a third criterion to better reflect the individual preferences of those ethical or green investors who are willing to combine strong financial performance with social benefits. For this purpose, new computational methods for optimizing this complex multiobjective problem are needed. Multiobjective evolutionary algorithms (MOEAs) have been recently used for portfolio selection, thus extending the mean-variance methodology to obtain a mean-variance-sustainability nondominated surface. In this paper, we apply a recent multiobjective genetic algorithm based on the concept of epsilon-dominance called ev-MOGA. This algorithm tries to ensure convergence towards the Pareto set in a smart distributed manner with limited memory resources. It also adjusts the limits of the Pareto front dynamically and prevents solutions belonging to the ends of the front from being lost. Moreover, the individual preferences of socially responsible investors could be visualised using a novel tool, known as level diagrams, which helps investors better understand the range of values attainable and the tradeoff between return, risk, and sustainability.This work was funded by "Ministerio de Economia y Competitividad" (Spain), research project RTI2018-096904B-I00, and "Conselleria de Educacion, Cultura y DeporteGeneralitat Valenciana" (Spain), research project AICO/2019/055Garcia-Bernabeu, A.; Salcedo-Romero-De-Ávila, J.; Hilario Caballero, A.; Pla Santamaría, D.; Herrero Durá, JM. (2019). Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA. Complexity. 2019:1-12. https://doi.org/10.1155/2019/6095712S1122019Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77. doi:10.2307/2975974Hirschberger, M., Steuer, R. E., Utz, S., Wimmer, M., & Qi, Y. (2013). Computing the Nondominated Surface in Tri-Criterion Portfolio Selection. Operations Research, 61(1), 169-183. doi:10.1287/opre.1120.1140Utz, S., Wimmer, M., Hirschberger, M., & Steuer, R. E. (2014). Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds. European Journal of Operational Research, 234(2), 491-498. doi:10.1016/j.ejor.2013.07.024Utz, S., Wimmer, M., & Steuer, R. E. (2015). Tri-criterion modeling for constructing more-sustainable mutual funds. European Journal of Operational Research, 246(1), 331-338. doi:10.1016/j.ejor.2015.04.035Qi, Y., Steuer, R. E., & Wimmer, M. (2015). An analytical derivation of the efficient surface in portfolio selection with three criteria. Annals of Operations Research, 251(1-2), 161-177. doi:10.1007/s10479-015-1900-yGasser, S. M., Rammerstorfer, M., & Weinmayer, K. (2017). Markowitz revisited: Social portfolio engineering. European Journal of Operational Research, 258(3), 1181-1190. doi:10.1016/j.ejor.2016.10.043Qi, Y. (2018). On outperforming social-screening-indexing by multiple-objective portfolio selection. Annals of Operations Research, 267(1-2), 493-513. doi:10.1007/s10479-018-2921-0Nathaphan, S., & Chunhachinda, P. (2010). Estimation Risk Modeling in Optimal Portfolio Selection: An Empirical Study from Emerging Markets. Economics Research International, 2010, 1-10. doi:10.1155/2010/340181DeMiguel, V., Garlappi, L., & Uppal, R. (2007). Optimal Versus Naive Diversification: How Inefficient is the 1/NPortfolio Strategy? Review of Financial Studies, 22(5), 1915-1953. doi:10.1093/rfs/hhm075Metaxiotis, K., & Liagkouras, K. (2012). Multiobjective Evolutionary Algorithms for Portfolio Management: A comprehensive literature review. Expert Systems with Applications, 39(14), 11685-11698. doi:10.1016/j.eswa.2012.04.053Bertsimas, D., & Shioda, R. (2007). Algorithm for cardinality-constrained quadratic optimization. Computational Optimization and Applications, 43(1), 1-22. doi:10.1007/s10589-007-9126-9Chang, T.-J., Yang, S.-C., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537. doi:10.1016/j.eswa.2009.02.062Woodside-Oriakhi, M., Lucas, C., & Beasley, J. E. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538-550. doi:10.1016/j.ejor.2011.03.030Chen, B., Lin, Y., Zeng, W., Xu, H., & Zhang, D. (2017). The mean-variance cardinality constrained portfolio optimization problem using a local search-based multi-objective evolutionary algorithm. Applied Intelligence, 47(2), 505-525. doi:10.1007/s10489-017-0898-zLiagkouras, K. (2019). A new three-dimensional encoding multiobjective evolutionary algorithm with application to the portfolio optimization problem. Knowledge-Based Systems, 163, 186-203. doi:10.1016/j.knosys.2018.08.025Kaucic, M., Moradi, M., & Mirzazadeh, M. (2019). Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures. Financial Innovation, 5(1). doi:10.1186/s40854-019-0140-6Silva, Y. L. T. V., Herthel, A. B., & Subramanian, A. (2019). A multi-objective evolutionary algorithm for a class of mean-variance portfolio selection problems. Expert Systems with Applications, 133, 225-241. doi:10.1016/j.eswa.2019.05.018Anagnostopoulos, K. P., & Mamanis, G. (2009). Multiobjective evolutionary algorithms for complex portfolio optimization problems. Computational Management Science, 8(3), 259-279. doi:10.1007/s10287-009-0113-8Ehrgott, M., Klamroth, K., & Schwehm, C. (2004). An MCDM approach to portfolio optimization. European Journal of Operational Research, 155(3), 752-770. doi:10.1016/s0377-2217(02)00881-0Steuer, R. E., Qi, Y., & Hirschberger, M. (2006). Suitable-portfolio investors, nondominated frontier sensitivity, and the effect of multiple objectives on standard portfolio selection. Annals of Operations Research, 152(1), 297-317. doi:10.1007/s10479-006-0137-1Anagnostopoulos, K. P., & Mamanis, G. (2010). A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37(7), 1285-1297. doi:10.1016/j.cor.2009.09.009Hallerbach, W. (2004). A framework for managing a portfolio of socially responsible investments. European Journal of Operational Research, 153(2), 517-529. doi:10.1016/s0377-2217(03)00172-3Ballestero, E., Bravo, M., Pérez-Gladish, B., Arenas-Parra, M., & Plà-Santamaria, D. (2012). Socially Responsible Investment: A multicriteria approach to portfolio selection combining ethical and financial objectives. European Journal of Operational Research, 216(2), 487-494. doi:10.1016/j.ejor.2011.07.011Cabello, J. M., Ruiz, F., Pérez-Gladish, B., & Méndez-Rodríguez, P. (2014). Synthetic indicators of mutual funds’ environmental responsibility: An application of the Reference Point Method. European Journal of Operational Research, 236(1), 313-325. doi:10.1016/j.ejor.2013.11.031Calvo, C., Ivorra, C., & Liern, V. (2014). Fuzzy portfolio selection with non-financial goals: exploring the efficient frontier. Annals of Operations Research, 245(1-2), 31-46. doi:10.1007/s10479-014-1561-2Laumanns, M., Thiele, L., Deb, K., & Zitzler, E. (2002). Combining Convergence and Diversity in Evolutionary Multiobjective Optimization. Evolutionary Computation, 10(3), 263-282. doi:10.1162/106365602760234108Blasco, X., Herrero, J. M., Sanchis, J., & Martínez, M. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences, 178(20), 3908-3924. doi:10.1016/j.ins.2008.06.01

Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach

[EN] Sustainable finance, which integrates environmental, social and governance criteria on financial decisions rests on the fact that money should be used for good purposes. Thus, the financial sector is also expected to play a more important role to decarbonise the global economy. To align financial flows with a pathway towards a low-carbon economy, investors should be able to integrate into their financial decisions additional criteria beyond return and risk to manage climate risk. We propose a tri-criterion portfolio selection model to extend the classical Markowitz's mean-variance approach to include investor's preferences on the portfolio carbon risk exposure as an additional criterion. To approximate the 3D Pareto front we apply an efficient multi-objective genetic algorithm called ev-MOGA which is based on the concept of epsilon-dominance. Furthermore, we introduce a-posteriori approach to incorporate the investor's preferences into the solution process regarding their climate-change related preferences measured by the carbon risk exposure and their loss-adverse attitude. We test the performance of the proposed algorithm in a cross-section of European socially responsible investments open-end funds to assess the extent to which climate-related risk could be embedded in the portfolio according to the investor's preferences.Hilario Caballero, A.; Garcia-Bernabeu, A.; Salcedo-Romero-De-Ávila, J.; Vercher, M. (2020). Tri-Criterion Model for Constructing Low-Carbon Mutual Fund Portfolios: A Preference-Based Multi-Objective Genetic Algorithm Approach. International Journal of Environmental research and Public Health. 17(17):1-15. https://doi.org/10.3390/ijerph17176324S1151717Morningstar Low Carbon Designationhttps://bit.ly/2SfAFUAKrueger, P., Sautner, Z., & Starks, L. T. (2020). 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Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market. Management Science, 37(5), 519-531. doi:10.1287/mnsc.37.5.519Rockafellar, R. T., & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking & Finance, 26(7), 1443-1471. doi:10.1016/s0378-4266(02)00271-6Mansini, R. (2003). LP solvable models for portfolio optimization: a classification and computational comparison. IMA Journal of Management Mathematics, 14(3), 187-220. doi:10.1093/imaman/14.3.187Hirschberger, M., Steuer, R. E., Utz, S., Wimmer, M., & Qi, Y. (2013). Computing the Nondominated Surface in Tri-Criterion Portfolio Selection. Operations Research, 61(1), 169-183. doi:10.1287/opre.1120.1140Utz, S., Wimmer, M., Hirschberger, M., & Steuer, R. E. (2014). Tri-criterion inverse portfolio optimization with application to socially responsible mutual funds. European Journal of Operational Research, 234(2), 491-498. doi:10.1016/j.ejor.2013.07.024Utz, S., Wimmer, M., & Steuer, R. E. (2015). Tri-criterion modeling for constructing more-sustainable mutual funds. European Journal of Operational Research, 246(1), 331-338. doi:10.1016/j.ejor.2015.04.035Chang, T.-J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271-1302. doi:10.1016/s0305-0548(99)00074-xMaringer, D., & Kellerer, H. (2003). Optimization of cardinality constrained portfolios with a hybrid local search algorithm. OR Spectrum, 25(4), 481-495. doi:10.1007/s00291-003-0139-1Shaw, D. X., Liu, S., & Kopman, L. (2008). Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optimization Methods and Software, 23(3), 411-420. doi:10.1080/10556780701722542Soleimani, H., Golmakani, H. R., & Salimi, M. H. (2009). Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Systems with Applications, 36(3), 5058-5063. doi:10.1016/j.eswa.2008.06.007Anagnostopoulos, K. P., & Mamanis, G. (2011). The mean–variance cardinality constrained portfolio optimization problem: An experimental evaluation of five multiobjective evolutionary algorithms. Expert Systems with Applications. doi:10.1016/j.eswa.2011.04.233Woodside-Oriakhi, M., Lucas, C., & Beasley, J. E. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538-550. doi:10.1016/j.ejor.2011.03.030Meghwani, S. S., & Thakur, M. (2017). Multi-criteria algorithms for portfolio optimization under practical constraints. Swarm and Evolutionary Computation, 37, 104-125. doi:10.1016/j.swevo.2017.06.005Liagkouras, K., & Metaxiotis, K. (2016). A new efficiently encoded multiobjective algorithm for the solution of the cardinality constrained portfolio optimization problem. Annals of Operations Research, 267(1-2), 281-319. doi:10.1007/s10479-016-2377-zMetaxiotis, K., & Liagkouras, K. (2012). Multiobjective Evolutionary Algorithms for Portfolio Management: A comprehensive literature review. Expert Systems with Applications, 39(14), 11685-11698. doi:10.1016/j.eswa.2012.04.053Silva, Y. L. T. V., Herthel, A. B., & Subramanian, A. (2019). A multi-objective evolutionary algorithm for a class of mean-variance portfolio selection problems. Expert Systems with Applications, 133, 225-241. doi:10.1016/j.eswa.2019.05.018Chang, T.-J., Yang, S.-C., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36(7), 10529-10537. doi:10.1016/j.eswa.2009.02.062Liagkouras, K. (2019). A new three-dimensional encoding multiobjective evolutionary algorithm with application to the portfolio optimization problem. Knowledge-Based Systems, 163, 186-203. doi:10.1016/j.knosys.2018.08.025Kaucic, M., Moradi, M., & Mirzazadeh, M. (2019). Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures. Financial Innovation, 5(1). doi:10.1186/s40854-019-0140-6Babaei, S., Sepehri, M. M., & Babaei, E. (2015). Multi-objective portfolio optimization considering the dependence structure of asset returns. European Journal of Operational Research, 244(2), 525-539. doi:10.1016/j.ejor.2015.01.025Ruiz, A. B., Saborido, R., Bermúdez, J. D., Luque, M., & Vercher, E. (2019). Preference-based evolutionary multi-objective optimization for portfolio selection: a new credibilistic model under investor preferences. Journal of Global Optimization, 76(2), 295-315. doi:10.1007/s10898-019-00782-1Anagnostopoulos, K. P., & Mamanis, G. (2010). A portfolio optimization model with three objectives and discrete variables. Computers & Operations Research, 37(7), 1285-1297. doi:10.1016/j.cor.2009.09.009Hu, Y., Chen, H., He, M., Sun, L., Liu, R., & Shen, H. (2019). Multi-Swarm Multi-Objective Optimizer Based on p-Optimality Criteria for Multi-Objective Portfolio Management. Mathematical Problems in Engineering, 2019, 1-22. doi:10.1155/2019/8418369Rangel-González, J. A., Fraire, H., Solís, J. F., Cruz-Reyes, L., Gomez-Santillan, C., Rangel-Valdez, N., & Carpio-Valadez, J. M. (2020). Fuzzy Multi-objective Particle Swarm Optimization Solving the Three-Objective Portfolio Optimization Problem. International Journal of Fuzzy Systems, 22(8), 2760-2768. doi:10.1007/s40815-020-00928-4Garcia-Bernabeu, A., Salcedo, J. V., Hilario, A., Pla-Santamaria, D., & Herrero, J. M. (2019). Computing the Mean-Variance-Sustainability Nondominated Surface by ev-MOGA. Complexity, 2019, 1-12. doi:10.1155/2019/6095712Laumanns, M., Thiele, L., Deb, K., & Zitzler, E. (2002). Combining Convergence and Diversity in Evolutionary Multiobjective Optimization. Evolutionary Computation, 10(3), 263-282. doi:10.1162/106365602760234108Matlab Central: ev-MOGA Multiobjective Evolutionary Algorithmhttps://bit.ly/3f2BYQMBlasco, X., Herrero, J. M., Sanchis, J., & Martínez, M. (2008). A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization. Information Sciences, 178(20), 3908-3924. doi:10.1016/j.ins.2008.06.01

ESG compliant optimal portfolios: The impact of ESG constraints on portfolio optimization in a sample of European stocks

The introduction of the Environmental, Social, Governance (ESG) dimensions in setting up optimal portfolios has been becoming of uttermost importance for the financial industry. Given the absence of consensus in empirical literature and the limited number of studies providing performance comparison of ESG strategies, the aim of this paper is to assess the impact of ESG on optimal portfolios and to compare different approaches to the construction of ESG compliant portfolios. Following Varmaz et al. (2022) optimization model, we minimize portfolio residual risk by imposing a desired level of portfolio average systemic risk and ESG (measured by Bloomberg ESG score) over both an unscreened and a screened sample based on the 586 stocks of the EURO STOXX Index in the period January 2007 – August 2022. Three are the main results. First, regardless of the level of portfolio systemic risk, the Sharpe ratio of the optimal portfolios worsens as the target ESG level increases. Second, the Sharpe ratio dynamics of portfolios with the highest average ESG scores follows market phases: it is very close to/higher than other portfolios in bull markets, whereas it underperforms in stable or bear markets suggesting that ESG portfolios do not seem to represent a safe haven. Third, negative screenings with medium low threshold reduce the performance of optimal portfolios with respect to optimization over an unscreened sample. However, when adopting a very severe screening we obtain a superior performance implying that very virtuous companies allows investors to do well by doing good

Selecting socially responsible portfolios: A fuzzy multicriteria approach

[EN] We propose a multi-objective approach for portfolio selection, which allows investors to consider not only return and downside risk criteria but also to include environmental, social and governance (ESG) scores in the investment decision-making process. Owing to the uncertain environment of portfolio selection, the return and ESG score of each asset are considered as independent L-R power fuzzy variables. To make the model more realistic, we take budget, floor ceiling and cardinality constraints into account. In order to select the optimal portfolio along the efficient frontier, we apply the Sortino ratio in a credibilistic environment. The subsequent empirical application uses a data set from Bloomberg's ESG Data in combination with US Dow Jones Industrial Average data. The experimental results show that the proposed model offers promising results for socially responsible investors seeking ethical and sustainability goals beyond the return-risk trade-off and its ability to beat the benchmarkGarcía García, F.; Gonzalez-Bueno, J.; Oliver-Muncharaz, J.; Riley, N. (2019). Selecting socially responsible portfolios: A fuzzy multicriteria approach. Sustainability. 11(9). https://doi.org/10.3390/su11092496S119Ballestero, E., Pérez-Gladish, B., & Garcia-Bernabeu, A. (2014). The Ethical Financial Question and the MCDM Framework. International Series in Operations Research & Management Science, 3-22. doi:10.1007/978-3-319-11836-9_1Zopounidis, C., & Doumpos, M. (2002). Multicriteria classification and sorting methods: A literature review. European Journal of Operational Research, 138(2), 229-246. doi:10.1016/s0377-2217(01)00243-0ARRIBAS, I., GARCÍA, F., GUIJARRO, F., OLIVER, J., & TAMOŠIŪNIENĖ, R. (2016). 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The Unresolved Problem of Negative Screening in Socially Responsible Investing. Journal of Business Ethics, 85(S1), 83-95. doi:10.1007/s10551-008-9949-zDerwall, J., & Koedijk, K. (2009). Socially Responsible Fixed-Income Funds. Journal of Business Finance & Accounting, 36(1-2), 210-229. doi:10.1111/j.1468-5957.2008.02119.xWu, J., Lodorfos, G., Dean, A., & Gioulmpaxiotis, G. (2015). The Market Performance of Socially Responsible Investment during Periods of the Economic Cycle - Illustrated Using the Case of FTSE. Managerial and Decision Economics, 38(2), 238-251. doi:10.1002/mde.2772Chang, C. E., & Doug Witte, H. (2010). Performance Evaluation of U.S. Socially Responsible Mutual Funds: Revisiting Doing Good and Doing Well. American Journal of Business, 25(1), 9-24. doi:10.1108/19355181201000001Cortez, M. C., Silva, F., & Areal, N. (2008). The Performance of European Socially Responsible Funds. 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Corporate social responsibility in portfolio selection: A "goal games" against nature approach

Nowadays, there is an uprising social pressure on big companies to incorporate into their decision-making process elements of the so-called social responsibility. Among the many implications of this fact, one relevant one is the need to include this new element in classic portfolio selection models. This paper meets this challenge by formulating a model that combines goal programming with "goal games" against nature in a scenario where the social responsibility is defined through the introduction of a battery of sustainability indicators amalgamated into a synthetic index. In this way, we have obtained an efficient model that only implies solving a small number of linear programming problems. The proposed approach has been tested and illustrated by using a case study related to the selection of securities in international markets

Socially responsible investment portfolios: does the optimization process matter?

This study investigates the impact of the choice of optimization technique when constructing Socially Responsible Investment (SRI) portfolios. Corporate Social Performance (CSP) scores are price sensitive information that is subject to considerable estimation risk. Therefore, uncertainty in the input parameters is greater for SRI portfolios than conventional portfolios, and this affects the selection of the appropriate optimization method. We form SRI portfolios based on six different approaches and compare their performance along the dimensions of risk, risk-return trade-off, diversification and stability. Our results for SRI portfolios contradict those of the conventional portfolio optimization literature. We find that the more “formal” optimization approaches (Black-Litterman, Markowitz and robust estimation) lead to SRI portfolios that are both less risky and have superior risk-return trade-offs than do more simplistic approaches; although they also have more unstable asset allocations and lower diversification. Our conclusions are robust to a series of tests, including the use of different estimation windows and stricter screening criteria

PERFORMANCE OF SOCIALLY RESPONSIBLE INDICES DURING MARKET CRISIS IN NORTH AMERICA AND EUROPE

This paper investigates whether socially responsible investment indices in the United States, Canada, the Eurozone and the United Kingdom provide downside protection during market crisis when compared to their respective market indices. Socially responsible investment indices in US and Canada perform similarly to their market indices during market crisis periods between 2000 and 2014, offering neither downside protection nor excess return in overall market conditions.   In Eurozone, the socially responsible investment index we selected performs worse than their market index during both the Financial Crisis and the Euro Crisis but not during the Tech Bubble. In the United Kingdom, socially responsible investment index underperforms its respective market index during all crisis periods, including the Tech Bubble, Financial Crisis and the Euro Crisis but outperforms during non-crisis periods. Overall, we do not find that SRI indices offer downmarket protection in North America and Europe