Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory

[EN] The present research proposes a novel methodology to solve the problems faced by investors who take into consideration different investment criteria in a fuzzy context. The approach extends the stochastic mean-variance model to a fuzzy multiobjective model where liquidity is considered to quantify portfolio's performance, apart from the usual metrics like return and risk. The uncertainty of the future returns and the future liquidity of the potential assets are modelled employing trapezoidal fuzzy numbers. The decision process of the proposed approach considers that portfolio selection is a multidimensional issue and also some realistic constraints applied by investors. Particularly, this approach optimizes the expected return, the risk and the expected liquidity of the portfolio, considering bound constraints and cardinality restrictions. As a result, an optimization problem for the constraint portfolio appears, which is solved by means of the NSGA-II algorithm. This study defines the credibilistic Sortino ratio and the credibilistic STARR ratio for selecting the optimal portfolio. An empirical study on the S&P100 index is included to show the performance of the model in practical applications. The results obtained demonstrate that the novel approach can beat the index in terms of return and risk in the analyzed period, from 2008 until 2018.García García, F.; González-Bueno, J.; Guijarro, F.; Oliver-Muncharaz, J.; Tamosiuniene, R. (2020). Multiobjective Approach to Portfolio Optimization in the Light of the Credibility Theory. Technological and Economic Development of Economy (Online). 26(6):1165-1186. https://doi.org/10.3846/tede.2020.13189S11651186266Acerbi, C., & Tasche, D. (2002). On the coherence of expected shortfall. Journal of Banking & Finance, 26(7), 1487-1503. doi:10.1016/s0378-4266(02)00283-2Ahmed, A., Ali, R., Ejaz, A., & Ahmad, I. (2018). Sectoral integration and investment diversification opportunities: evidence from Colombo Stock Exchange. Entrepreneurship and Sustainability Issues, 5(3), 514-527. doi:10.9770/jesi.2018.5.3(8)Arenas Parra, M., Bilbao Terol, A., & Rodrı́guez Urı́a, M. V. (2001). A fuzzy goal programming approach to portfolio selection. European Journal of Operational Research, 133(2), 287-297. doi:10.1016/s0377-2217(00)00298-8Arribas, I., Espinós-Vañó, M. D., García, F., & Tamošiūnienė, R. (2019). Negative screening and sustainable portfolio diversification. Entrepreneurship and Sustainability Issues, 6(4), 1566-1586. doi:10.9770/jesi.2019.6.4(2)Artzner, P., Delbaen, F., Eber, J.-M., & Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance, 9(3), 203-228. doi:10.1111/1467-9965.00068Bawa, V. S. (1975). Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2(1), 95-121. doi:10.1016/0304-405x(75)90025-2Bermúdez, J. D., Segura, J. V., & Vercher, E. (2012). A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection. Fuzzy Sets and Systems, 188(1), 16-26. doi:10.1016/j.fss.2011.05.013Bezoui, M., Moulaï, M., Bounceur, A., & Euler, R. (2018). An iterative method for solving a bi-objective constrained portfolio optimization problem. Computational Optimization and Applications, 72(2), 479-498. doi:10.1007/s10589-018-0052-9Bi, T., Zhang, B., & Wu, H. (2013). Measuring Downside Risk Using High-Frequency Data: Realized Downside Risk Measure. Communications in Statistics - Simulation and Computation, 42(4), 741-754. doi:10.1080/03610918.2012.655826Carlsson, C., Fullér, R., & Majlender, P. (2002). A possibilistic approach to selecting portfolios with highest utility score. Fuzzy Sets and Systems, 131(1), 13-21. doi:10.1016/s0165-0114(01)00251-2Chen, W., & Xu, W. (2018). A Hybrid Multiobjective Bat Algorithm for Fuzzy Portfolio Optimization with Real-World Constraints. International Journal of Fuzzy Systems, 21(1), 291-307. doi:10.1007/s40815-018-0533-0Choobineh, F., & Branting, D. (1986). A simple approximation for semivariance. European Journal of Operational Research, 27(3), 364-370. doi:10.1016/0377-2217(86)90332-2Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. doi:10.1109/4235.996017Fang, Y., Lai, K. K., & Wang, S.-Y. (2006). Portfolio rebalancing model with transaction costs based on fuzzy decision theory. European Journal of Operational Research, 175(2), 879-893. doi:10.1016/j.ejor.2005.05.020Favre, L., & Galeano, J.-A. (2002). Mean-Modified Value-at-Risk Optimization with Hedge Funds. The Journal of Alternative Investments, 5(2), 21-25. doi:10.3905/jai.2002.319052García, F., González-Bueno, J., Guijarro, F., & Oliver, J. (2020). Forecasting the Environmental, Social, and Governance Rating of Firms by Using Corporate Financial Performance Variables: A Rough Set Approach. Sustainability, 12(8), 3324. doi:10.3390/su12083324García, González-Bueno, Oliver, & Riley. (2019). Selecting Socially Responsible Portfolios: A Fuzzy Multicriteria Approach. Sustainability, 11(9), 2496. doi:10.3390/su11092496García, F., González-Bueno, J., Oliver, J., & Tamošiūnienė, R. (2019). A CREDIBILISTIC MEAN-SEMIVARIANCE-PER PORTFOLIO SELECTION MODEL FOR LATIN AMERICA. Journal of Business Economics and Management, 20(2), 225-243. doi:10.3846/jbem.2019.8317García, F., Guijarro, F., & Moya, I. (2013). A MULTIOBJECTIVE MODEL FOR PASSIVE PORTFOLIO MANAGEMENT: AN APPLICATION ON THE S&P 100 INDEX. Journal of Business Economics and Management, 14(4), 758-775. doi:10.3846/16111699.2012.668859García, F., Guijarro, F., & Oliver, J. (2017). Index tracking optimization with cardinality constraint: a performance comparison of genetic algorithms and tabu search heuristics. Neural Computing and Applications, 30(8), 2625-2641. doi:10.1007/s00521-017-2882-2García, F., Guijarro, F., Oliver, J., & Tamošiūnienė, R. (2018). HYBRID FUZZY NEURAL NETWORK TO PREDICT PRICE DIRECTION IN THE GERMAN DAX-30 INDEX. Technological and Economic Development of Economy, 24(6), 2161-2178. doi:10.3846/tede.2018.6394Goel, A., Sharma, A., & Mehra, A. (2018). Index tracking and enhanced indexing using mixed conditional value-at-risk. Journal of Computational and Applied Mathematics, 335, 361-380. doi:10.1016/j.cam.2017.12.015González-Bueno, J. (2019). Optimización multiobjetivo para la selección de carteras a la luz de la teoría de la credibilidad. Una aplicación en el mercado integrado latinoamericano. Editorial Universidad Pontificia Bolivariana.Gupta, P., Inuiguchi, M., & Mehlawat, M. K. (2011). A hybrid approach for constructing suitable and optimal portfolios. Expert Systems with Applications, 38(5), 5620-5632. doi:10.1016/j.eswa.2010.10.073Gupta, P., Inuiguchi, M., Mehlawat, M. K., & Mittal, G. (2013). Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints. Information Sciences, 229, 1-17. doi:10.1016/j.ins.2012.12.011Gupta, P., Mehlawat, M. K., Inuiguchi, M., & Chandra, S. (2014). Portfolio Optimization Using Credibility Theory. Studies in Fuzziness and Soft Computing, 127-160. doi:10.1007/978-3-642-54652-5_5Gupta, P., Mehlawat, M. K., Inuiguchi, M., & Chandra, S. (2014). Portfolio Optimization with Interval Coefficients. Studies in Fuzziness and Soft Computing, 33-59. doi:10.1007/978-3-642-54652-5_2Gupta, P., Mehlawat, M. K., Kumar, A., Yadav, S., & Aggarwal, A. (2020). A Credibilistic Fuzzy DEA Approach for Portfolio Efficiency Evaluation and Rebalancing Toward Benchmark Portfolios Using Positive and Negative Returns. International Journal of Fuzzy Systems, 22(3), 824-843. doi:10.1007/s40815-020-00801-4Gupta, P., Mehlawat, M. K., & Saxena, A. (2010). A hybrid approach to asset allocation with simultaneous consideration of suitability and optimality. Information Sciences, 180(11), 2264-2285. doi:10.1016/j.ins.2010.02.007Gupta, P., Mehlawat, M. K., Yadav, S., & Kumar, A. (2020). Intuitionistic fuzzy optimistic and pessimistic multi-period portfolio optimization models. Soft Computing, 24(16), 11931-11956. doi:10.1007/s00500-019-04639-3Gupta, P., Mittal, G., & Mehlawat, M. K. (2013). Expected value multiobjective portfolio rebalancing model with fuzzy parameters. Insurance: Mathematics and Economics, 52(2), 190-203. doi:10.1016/j.insmatheco.2012.12.002Heidari-Fathian, H., & Davari-Ardakani, H. (2019). Bi-objective optimization of a project selection and adjustment problem under risk controls. Journal of Modelling in Management, 15(1), 89-111. doi:10.1108/jm2-07-2018-0106Hilkevics, S., & Semakina, V. (2019). The classification and comparison of business ratios analysis methods. Insights into Regional Development, 1(1), 48-57. doi:10.9770/ird.2019.1.1(4)Huang, X. (2006). Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation, 177(2), 500-507. doi:10.1016/j.amc.2005.11.027Huang, X. (2008). Mean-semivariance models for fuzzy portfolio selection. Journal of Computational and Applied Mathematics, 217(1), 1-8. doi:10.1016/j.cam.2007.06.009Huang, X. (2009). A review of credibilistic portfolio selection. Fuzzy Optimization and Decision Making, 8(3), 263-281. doi:10.1007/s10700-009-9064-3Huang, X. (2010). Portfolio Analysis. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-642-11214-0Huang, X. (2017). A review of uncertain portfolio selection. Journal of Intelligent & Fuzzy Systems, 32(6), 4453-4465. doi:10.3233/jifs-169211Huang, X., & Di, H. (2016). Uncertain portfolio selection with background risk. Applied Mathematics and Computation, 276, 284-296. doi:10.1016/j.amc.2015.12.018Huang, X., & Wang, X. (2019). International portfolio optimization based on uncertainty theory. Optimization, 70(2), 225-249. doi:10.1080/02331934.2019.1705821Huang, X., & Yang, T. (2020). How does background risk affect portfolio choice: An analysis based on uncertain mean-variance model with background risk. Journal of Banking & Finance, 111, 105726. doi:10.1016/j.jbankfin.2019.105726Jalota, H., Thakur, M., & Mittal, G. (2017). Modelling and constructing membership function for uncertain portfolio parameters: A credibilistic framework. Expert Systems with Applications, 71, 40-56. doi:10.1016/j.eswa.2016.11.014Jalota, H., Thakur, M., & Mittal, G. (2017). A credibilistic decision support system for portfolio optimization. Applied Soft Computing, 59, 512-528. doi:10.1016/j.asoc.2017.05.054Kaplan, P. D., & Alldredge, R. H. (1997). Semivariance in Risk-Based Index Construction. The Journal of Investing, 6(2), 82-87. doi:10.3905/joi.1997.408419Konno, H., & Yamazaki, H. (1991). Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market. Management Science, 37(5), 519-531. doi:10.1287/mnsc.37.5.519Li, B., Zhu, Y., Sun, Y., Aw, G., & Teo, K. L. (2018). Multi-period portfolio selection problem under uncertain environment with bankruptcy constraint. Applied Mathematical Modelling, 56, 539-550. doi:10.1016/j.apm.2017.12.016Li, H.-Q., & Yi, Z.-H. (2019). Portfolio selection with coherent Investor’s expectations under uncertainty. Expert Systems with Applications, 133, 49-58. doi:10.1016/j.eswa.2019.05.008Li, X., & Qin, Z. (2014). Interval portfolio selection models within the framework of uncertainty theory. Economic Modelling, 41, 338-344. doi:10.1016/j.econmod.2014.05.036Liagkouras, K., & Metaxiotis, K. (2015). Efficient Portfolio Construction with the Use of Multiobjective Evolutionary Algorithms: Best Practices and Performance Metrics. International Journal of Information Technology & Decision Making, 14(03), 535-564. doi:10.1142/s0219622015300013Liu, B. (2004). Uncertainty Theory. Studies in Fuzziness and Soft Computing. doi:10.1007/978-3-540-39987-2Baoding Liu, & Yian-Kui Liu. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445-450. doi:10.1109/tfuzz.2002.800692Liu, N., Chen, Y., & Liu, Y. (2018). Optimizing portfolio selection problems under credibilistic CVaR criterion. Journal of Intelligent & Fuzzy Systems, 34(1), 335-347. doi:10.3233/jifs-171298Liu, Y.-J., & Zhang, W.-G. (2018). Multiperiod Fuzzy Portfolio Selection Optimization Model Based on Possibility Theory. International Journal of Information Technology & Decision Making, 17(03), 941-968. doi:10.1142/s0219622018500190Mansour, N., Cherif, M. S., & Abdelfattah, W. (2019). Multi-objective imprecise programming for financial portfolio selection with fuzzy returns. Expert Systems with Applications, 138, 112810. doi:10.1016/j.eswa.2019.07.027Markowitz, H. (1952). PORTFOLIO SELECTION*. The Journal of Finance, 7(1), 77-91. doi:10.1111/j.1540-6261.1952.tb01525.xMarkowitz, H., Todd, P., Xu, G., & Yamane, Y. (1993). Computation of mean-semivariance efficient sets by the Critical Line Algorithm. Annals of Operations Research, 45(1), 307-317. doi:10.1007/bf02282055Martin, R. D., Rachev, S. (Zari), & Siboulet, F. (2003). Phi-alpha optimal portfolios and extreme risk management. Wilmott, 2003(6), 70-83. doi:10.1002/wilm.42820030619Mehlawat, M. K. (2016). Credibilistic mean-entropy models for multi-period portfolio selection with multi-choice aspiration levels. Information Sciences, 345, 9-26. doi:10.1016/j.ins.2016.01.042Mehlawat, M. K., Gupta, P., Kumar, A., Yadav, S., & Aggarwal, A. (2020). Multiobjective Fuzzy Portfolio Performance Evaluation Using Data Envelopment Analysis Under Credibilistic Framework. IEEE Transactions on Fuzzy Systems, 28(11), 2726-2737. doi:10.1109/tfuzz.2020.2969406Mehralizade, R., Amini, M., Sadeghpour Gildeh, B., & Ahmadzade, H. (2020). Uncertain random portfolio selection based on risk curve. Soft Computing, 24(17), 13331-13345. doi:10.1007/s00500-020-04751-9Moeini, M. (2019). Solving the index tracking problem: a continuous optimization approach. Central European Journal of Operations Research. doi:10.1007/s10100-019-00633-0Narkunienė, J., & Ulbinaitė, A. (2018). Comparative analysis of company performance evaluation methods. Entrepreneurship and Sustainability Issues, 6(1), 125-138. doi:10.9770/jesi.2018.6.1(10)Palanikumar, K., Latha, B., Senthilkumar, V. S., & Karthikeyan, R. (2009). Multiple performance optimization in machining of GFRP composites by a PCD tool using non-dominated sorting genetic algorithm (NSGA-II). Metals and Materials International, 15(2), 249-258. doi:10.1007/s12540-009-0249-7Pflug, G. C. (2000). Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk. Probabilistic Constrained Optimization, 272-281. doi:10.1007/978-1-4757-3150-7_15Rockafellar, R. T., & Uryasev, S. (2000). Optimization of conditional value-at-risk. The Journal of Risk, 2(3), 21-41. doi:10.21314/jor.2000.038Rockafellar, 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)00271-6Rubio, A., Bermúdez, J. D., & Vercher, E. (2016). Forecasting portfolio returns using weighted fuzzy time series methods. International Journal of Approximate Reasoning, 75, 1-12. doi:10.1016/j.ijar.2016.03.007Saborido, R., Ruiz, A. B., Bermúdez, J. D., Vercher, E., & Luque, M. (2016). Evolutionary multi-objective optimization algorithms for fuzzy portfolio selection. Applied Soft Computing, 39, 48-63. doi:10.1016/j.asoc.2015.11.005Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(S1), 119. doi:10.1086/294846Sharpe, W. F. (1994). The Sharpe Ratio. The Journal of Portfolio Management, 21(1), 49-58. doi:10.3905/jpm.1994.409501Sortino, F. A., & Price, L. N. (1994). Performance Measurement in a Downside Risk Framework. The Journal of Investing, 3(3), 59-64. doi:10.3905/joi.3.3.59Srinivas, N., & Deb, K. (1994). Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms. Evolutionary Computation, 2(3), 221-248. doi:10.1162/evco.1994.2.3.221Vercher, E., & Bermúdez, J. D. (2012). Fuzzy Portfolio Selection Models: A Numerical Study. Financial Decision Making Using Computational Intelligence, 253-280. doi:10.1007/978-1-4614-3773-4_10Vercher, E., & Bermudez, J. D. (2013). A Possibilistic Mean-Downside Risk-Skewness Model for Efficient Portfolio Selection. IEEE Transactions on Fuzzy Systems, 21(3), 585-595. doi:10.1109/tfuzz.2012.2227487Vercher, E., & Bermúdez, J. D. (2015). Portfolio optimization using a credibility mean-absolute semi-deviation model. Expert Systems with Applications, 42(20), 7121-7131. doi:10.1016/j.eswa.2015.05.020Vercher, E., Bermúdez, J. D., & Segura, J. V. (2007). Fuzzy portfolio optimization under downside risk measures. Fuzzy Sets and Systems, 158(7), 769-782. doi:10.1016/j.fss.2006.10.026Wang, S., & Zhu, S. (2002). Fuzzy Optimization and Decision Making, 1(4), 361-377. doi:10.1023/a:1020907229361Yue, W., & Wang, Y. (2017). A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios. Physica A: Statistical Mechanics and its Applications, 465, 124-140. doi:10.1016/j.physa.2016.08.009Yue, W., Wang, Y., & Xuan, H. (2018). Fuzzy multi-objective portfolio model based on semi-variance–semi-absolute deviation risk measures. Soft Computing, 23(17), 8159-8179. doi:10.1007/s00500-018-3452-yZadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. doi:10.1016/s0019-9958(65)90241-xZhai, J., & Bai, M. (2018). Mean-risk model for uncertain portfolio selection with background risk. Journal of Computational and Applied Mathematics, 330, 59-69. doi:10.1016/j.cam.2017.07.038Zhao, Z., Wang, H., Yang, X., & Xu, F. (2020). CVaR-cardinality enhanced indexation optimization with tunable short-selling constraints. Applied Economics Letters, 28(3), 201-207. doi:10.1080/13504851.2020.174015

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). MASS APPRAISAL OF RESIDENTIAL REAL ESTATE USING MULTILEVEL MODELLING. International Journal of Strategic Property Management, 20(1), 77-87. doi:10.3846/1648715x.2015.1134702García, F., Guijarro, F., Oliver, J., & Tamošiūnienė, R. (2018). HYBRID FUZZY NEURAL NETWORK TO PREDICT PRICE DIRECTION IN THE GERMAN DAX-30 INDEX. Technological and Economic Development of Economy, 24(6), 2161-2178. doi:10.3846/tede.2018.6394Xidonas, P., Doukas, H., Mavrotas, G., & Pechak, O. (2015). Environmental corporate responsibility for investments evaluation: an alternative multi-objective programming model. Annals of Operations Research, 247(2), 395-413. doi:10.1007/s10479-015-1820-xMiralles-Quirós, M. del M., & Miralles-Quirós, J. L. (2015). Improving Diversification Opportunities for Socially Responsible Investors. Journal of Business Ethics, 140(2), 339-351. doi:10.1007/s10551-015-2691-4JERÓNIMO SILVESTRE, W., ANTUNES, P., & LEAL FILHO, W. (2016). THE CORPORATE SUSTAINABILITY TYPOLOGY: ANALYSING SUSTAINABILITY DRIVERS AND FOSTERING SUSTAINABILITY AT ENTERPRISES. Technological and Economic Development of Economy, 24(2), 513-533. doi:10.3846/20294913.2016.1213199Rahman, S., Lee, C.-F., & Xiao, Y. (2016). The investment performance, attributes, and investment behavior of ethical equity mutual funds in the US: an empirical investigation. Review of Quantitative Finance and Accounting, 49(1), 91-116. doi:10.1007/s11156-016-0581-1Bouslah, K., Kryzanowski, L., & M’Zali, B. (2013). The impact of the dimensions of social performance on firm risk. Journal of Banking & Finance, 37(4), 1258-1273. doi:10.1016/j.jbankfin.2012.12.004Petrillo, A., De Felice, F., García-Melón, M., & Pérez-Gladish, B. (2016). Investing in socially responsible mutual funds: Proposal of non-financial ranking in Italian market. Research in International Business and Finance, 37, 541-555. doi:10.1016/j.ribaf.2016.01.027Fowler, S. J., & Hope, C. (2007). A Critical Review of Sustainable Business Indices and their Impact. Journal of Business Ethics, 76(3), 243-252. doi:10.1007/s10551-007-9590-2Jankalová, M., & Jankal, R. (2017). The assessment of corporate social responsibility: approaches analysis. Entrepreneurship and Sustainability Issues, 4(4), 441-459. doi:10.9770/jesi.2017.4.4(4)Smaliukienė, R., & Monni, S. (2019). A step-by-step approach to social marketing in energy transition. Insights into Regional Development, 1(1), 19-32. doi:10.9770/ird.2019.1.1(2)Anagnostopoulos, T., Skouloudis, A., Khan, N., & Evangelinos, K. (2018). Incorporating Sustainability Considerations into Lending Decisions and the Management of Bad Loans: Evidence from Greece. Sustainability, 10(12), 4728. doi:10.3390/su10124728Charlo, M., Moya, I., & Muñoz, A. (2017). Financial Performance of Socially Responsible Firms: The Short- and Long-Term Impact. Sustainability, 9(9), 1622. doi:10.3390/su9091622De Colle, S., & York, J. G. (2008). Why Wine is not Glue? 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. Journal of Business Ethics, 87(4), 573-588. doi:10.1007/s10551-008-9959-xInvesting in Socially Responsible Mutual Fundshttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1444&context=fnce_papersJones, S., van der Laan, S., Frost, G., & Loftus, J. (2007). The Investment Performance of Socially Responsible Investment Funds in Australia. Journal of Business Ethics, 80(2), 181-203. doi:10.1007/s10551-007-9412-6Renneboog, L., Ter Horst, J., & Zhang, C. (2008). Socially responsible investments: Institutional aspects, performance, and investor behavior. Journal of Banking & Finance, 32(9), 1723-1742. doi:10.1016/j.jbankfin.2007.12.039Bauer, R., Koedijk, K., & Otten, R. (2005). International evidence on ethical mutual fund performance and investment style. Journal of Banking & Finance, 29(7), 1751-1767. doi:10.1016/j.jbankfin.2004.06.035Brzeszczyński, J., & McIntosh, G. (2013). Performance of Portfolios Composed of British SRI Stocks. Journal of Business Ethics, 120(3), 335-362. doi:10.1007/s10551-012-1541-xGoldreyer, E. F., & Diltz, J. D. (1999). The performance of socially responsible mutual funds: incorporating sociopolitical information in portfolio selection. Managerial Finance, 25(1), 23-36. doi:10.1108/03074359910765830Hamilton, S., Jo, H., & Statman, M. (1993). Doing Well While Doing Good? The Investment Performance of Socially Responsible Mutual Funds. Financial Analysts Journal, 49(6), 62-66. doi:10.2469/faj.v49.n6.62Revelli, C., & Viviani, J.-L. (2014). Financial performance of socially responsible investing (SRI): what have we learned? A meta-analysis. Business Ethics: A European Review, 24(2), 158-185. doi:10.1111/beer.12076McWilliams, A., & Siegel, D. (2001). Corporate Social Responsibility: a Theory of the Firm Perspective. Academy of Management Review, 26(1), 117-127. doi:10.5465/amr.2001.4011987El Ghoul, S., Guedhami, O., Kwok, C. C. Y., & Mishra, D. R. (2011). Does corporate social responsibility affect the cost of capital? Journal of Banking & Finance, 35(9), 2388-2406. doi:10.1016/j.jbankfin.2011.02.007Attig, N., El Ghoul, S., Guedhami, O., & Suh, J. (2013). Corporate Social Responsibility and Credit Ratings. Journal of Business Ethics, 117(4), 679-694. doi:10.1007/s10551-013-1714-2Cheng, B., Ioannou, I., & Serafeim, G. (2013). Corporate social responsibility and access to finance. Strategic Management Journal, 35(1), 1-23. doi:10.1002/smj.2131Hallerbach, 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)00172-3Steuer, 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/s10479-006-0137-1Bilbao-Terol, A., Arenas-Parra, M., & Cañal-Fernández, V. (2012). A fuzzy multi-objective approach for sustainable investments. Expert Systems with Applications, 39(12), 10904-10915. doi:10.1016/j.eswa.2012.03.034Calvo, 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/s10479-014-1561-2Li, Z. F., Minor, D., Wang, J., & Yu, C. (2018). A Learning Curve of the Market: Chasing Alpha of Socially Responsible Firms. SSRN Electronic Journal. doi:10.2139/ssrn.3224796Bilbao-Terol, A., Arenas-Parra, M., Cañal-Fernández, V., & Obam-Eyang, P. N. (2018). Multi-criteria analysis of the GRI sustainability reports: an application to Socially Responsible Investment. Journal of the Operational Research Society, 69(10), 1576-1598. doi:10.1057/s41274-017-0229-0Gasser, 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.2016.10.043Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. doi:10.1016/s0019-9958(65)90241-xGupta, P., Mehlawat, M. K., & Saxena, A. (2013). Hybrid optimization models of portfolio selection involving financial and ethical considerations. Knowledge-Based Systems, 37, 318-337. doi:10.1016/j.knosys.2012.08.014Baoding Liu, & Yian-Kui Liu. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445-450. doi:10.1109/tfuzz.2002.800692Barak, S., Abessi, M., & Modarres, M. (2013). Fuzzy turnover rate chance constraints portfolio model. European Journal of Operational Research, 228(1), 141-147. doi:10.1016/j.ejor.2013.01.036Huang, X. (2006). Fuzzy chance-constrained portfolio selection. Applied Mathematics and Computation, 177(2), 500-507. doi:10.1016/j.amc.2005.11.027Vercher, E., & Bermúdez, J. D. (2015). Portfolio optimization using a credibility mean-absolute semi-deviation model. Expert Systems with Applications, 42(20), 7121-7131. doi:10.1016/j.eswa.2015.05.020Gupta, P., Mittal, G., & Mehlawat, M. K. (2013). Expected value multiobjective portfolio rebalancing model with fuzzy parameters. Insurance: Mathematics and Economics, 52(2), 190-203. doi:10.1016/j.insmatheco.2012.12.002Mohebbi, N., & Najafi, A. A. (2018). Credibilistic multi-period portfolio optimization based on scenario tree. Physica A: Statistical Mechanics and its Applications, 492, 1302-1316. doi:10.1016/j.physa.2017.11.058Jalota, H., Thakur, M., & Mittal, G. (2017). Modelling and constructing membership function for uncertain portfolio parameters: A credibilistic framework. Expert Systems with Applications, 71, 40-56. doi:10.1016/j.eswa.2016.11.014García, F., González-Bueno, J., Oliver, J., & Tamošiūnienė, R. (2019). A CREDIBILISTIC MEAN-SEMIVARIANCE-PER PORTFOLIO SELECTION MODEL FOR LATIN AMERICA. Journal of Business Economics and Management, 20(2), 225-243. doi:10.3846/jbem.2019.8317Markowitz, H., Todd, P., Xu, G., & Yamane, Y. (1993). Computation of mean-semivariance efficient sets by the Critical Line Algorithm. Annals of Operations Research, 45(1), 307-317. doi:10.1007/bf02282055Sortino, F. A., & van der Meer, R. (1991). Downside risk. The Journal of Portfolio Management, 17(4), 27-31. doi:10.3905/jpm.1991.409343Vercher, E., & Bermúdez, J. D. (2012). Fuzzy Portfolio Selection Models: A Numerical Study. Financial Decision Making Using Computational Intelligence, 253-280. doi:10.1007/978-1-4614-3773-4_10Vercher, E., & Bermudez, J. D. (2013). A Possibilistic Mean-Downside Risk-Skewness Model for Efficient Portfolio Selection. IEEE Transactions on Fuzzy Systems, 21(3), 585-595. doi:10.1109/tfuzz.2012.2227487Liagkouras, K., & Metaxiotis, K. (2015). Efficient Portfolio Construction with the Use of Multiobjective Evolutionary Algorithms: Best Practices and Performance Metrics. International Journal of Information Technology & Decision Making, 14(03), 535-564. doi:10.1142/s0219622015300013Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182-197. doi:10.1109/4235.996017Gupta, P., Mehlawat, M. K., Inuiguchi, M., & Chandra, S. (2014). Portfolio Optimization with Interval Coefficients. Studies in Fuzziness and Soft Computing, 33-59. doi:10.1007/978-3-642-54652-5_2Sharpe, W. F. (1966). Mutual Fund Performance. The Journal of Business, 39(S1), 119. doi:10.1086/29484

Mean-Variance-Skewness Portfolio Selection Model Based on RBF-GA

The classical Markowitz’s mean-variance model in modern investment science uses variance as risk measure while it ignores the asymmetry of the return distribution. This article introduces skewness, V-type transaction costs, cardinality constraint and initial investment proportion, and builds a new class of nonlinear multi-objective portfolio model (mean-variance-skewness portfolio selection model). To solve the model, we develop a genetic algorithm(GA) which contains radial basis function(RBF) neural network, called RBF-GA. The experimental results show that the proposed model is more effective and more realistic than others

Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations

In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements

Uncertain Portfolio Selection with Background Risk and Liquidity Constraint

This paper discusses an uncertain portfolio selection problem with consideration of background risk and asset liquidity. In addition, the transaction costs are also considered. The security returns, background asset return, and asset liquidity are estimated by experienced experts instead of historical data. Regarding them as uncertain variables, a mean-risk model with background risk, liquidity, and transaction costs is proposed for portfolio selection and the crisp forms of the model are provided when security returns obey different uncertainty distributions. Moreover, for better understanding of the impact of background risk and liquidity on portfolio selection, some important theorems are proved. Finally, numerical experiments are presented to illustrate the modeling idea

Portfolio selection based on minmax rule and fuzzy set theory.

Yang, Fan.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (p. 100-106).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Literature review --- p.1Chapter 1.2 --- The main contribution of this thesis --- p.5Chapter 1.3 --- Relations between the above three models --- p.7Chapter 2 --- Model 1 --- p.9Chapter 2.1 --- Introduction --- p.9Chapter 2.2 --- Minimax rule risk function --- p.11Chapter 2.3 --- Fuzzy liquidity of asset --- p.12Chapter 2.4 --- Notations --- p.15Chapter 2.5 --- Model formulation --- p.16Chapter 2.6 --- Numerical example and result --- p.25Chapter 3 --- Model 2 --- p.36Chapter 3.1 --- Introduction --- p.36Chapter 3.2 --- Notations --- p.39Chapter 3.3 --- Model formulation --- p.41Chapter 3.4 --- Numerical example and result --- p.45Chapter 4 --- Model 3 --- p.51Chapter 4.1 --- Introduction --- p.51Chapter 4.2 --- Notations --- p.52Chapter 4.3 --- Model formulation --- p.54Chapter 4.4 --- Numerical example and result --- p.62Chapter 5 --- Conclusion --- p.68Chapter A --- Source Data for Model 1 --- p.71Chapter B --- Source Data for Model 2 --- p.80Chapter C --- Source Data for Model 3 --- p.90Bibliography --- p.10

Modelling Credit Risk for SMEs in Saudi Arabia

The Saudi Government’s 2030 Vision directs local banks to increase and improve credit for the Small and Medium Enterprises (SMEs) of the economy (Jadwa, 2017). Banks are, however, still finding it difficult to provide credit for small businesses that meet Basel’s capital requirements. Most of the current credit-risk models only apply to large corporations with little constructed for SMEs applications (Altman and Sabato, 2007). This study fills this gap by focusing on the Saudi SMEs perspective. My empirical work constructs a bankruptcy prediction model based on logistic regressions that cover 14,727 firm-year observations for an 11-year period between 2001 and 2011. I use the first eight years data (2001-2008) to build the model and use it to predict the last three years (2009-2011) of the sample, i.e. conducting an out-of-sample test. This approach yields a highly accurate model with great prediction power, though the results are partially influenced by the external economic and geopolitical volatilities that took place during the period of 2009-2010 (the world financial crisis). To avoid making predictions in such a volatile period, I rebuild the model based on 2003-2010 data, and use it to predict the default events for 2011. The new model is highly consistent and accurate. My model suggests that, from an academic perspective, some key quantitative variables, such as gross profit margin, days inventory, revenues, days payable and age of the entity, have a significant power in predicting the default probability of an entity. I further price the risks of the SMEs by using a credit-risk pricing model similar to Bauer and Agarwal (2014), which enables us to determine the risk-return tradeoffs on Saudi’s SMEs

Scaled and stable mean-variance-EVaR portfolio selection strategy with proportional transaction costs

This paper studies a portfolio optimization problem with variance and Entropic Value-at-Risk (evar) as risk measures. As the variance measures the deviation around the expected return, the introduction of evar in the mean-variance framework helps to control the downside risk of portfolio returns. This study utilized the squared l2-norm to alleviate estimation risk problems arising from the mean estimate of random returns. To adequately represent the variance-evar risk measure of the resulting portfolio, this study pursues rescaling by the capital accessible after payment of transaction costs. The results of this paper extend the classical Markowitz model to the case of proportional transaction costs and enhance the efficiency of portfolio selection by alleviating estimation risk and controlling the downside risk of portfolio returns. The model seeks to meet the requirements of regulators and fund managers as it represents a balance between short tails and variance. The practical implications of the findings of this study are that the model when applied, will increase the amount of capital for investment, lower transaction cost and minimize risk associated with the deviation around the expected return at the expense of a small additional risk in short tails