A multi-objective approach based on Markowitz and DEA cross-efficiency models for the intuitionistic fuzzy portfolio selection problem
Nowadays, the main concerns of investors are choosing the best portfolio in a way that the highest possible return of investment can be achieved by accepting the least risk. In this regard, the classical Markowitz model is one of the most widely used models which helps investors get closer to their goals. On the other hand, data envelopment analysis (DEA) is also a practical technique that can analyze the efficiency of enterprises. However, in real problems, we have faced with several uncertainty issues and the intuitionistic fuzzy set (IFS) is one of the best tools to handle these phenomena. Therefore, in this paper, we combine all these tools and with returns of intuitionistic fuzzy numbers, propose a new combined Markowitz and the cross DEA models. Furthermore, to get the best portfolio of assets, this model obtains the efficiency of all companies and at the same time, fully covers all constraints of the Markowitz model. To show the practicality of the model, we studied a case study based on information of 50 active enterprises in the Tehran Stock Exchange and solved the proposed model using the Non-Dominated Sorting Genetic Algorithm II (NSGA-II). The obtained results as well as the comparisons made with the existing approaches show the effectiveness of the proposed model.
Afshar, K. M., Khaliliaraghi, M., & Sadat, K. A. (2012). Stock selection of Tehran stock exchange investors with hybrid of data envelopment analysis (DEA) and goal programming (GP), 49-63.
Algarvio, H., Lopes, F., Sousa, J., & Lagarto, J. (2017). Multi-agent electricity markets: Retailer portfolio optimization using Markowitz theory. Electric Power Systems Research, 148, 282-294. DOI: https://doi.org/10.1016/j.epsr.2017.02.031
Amin, G. R., & Hajjami, M. (2021). Improving DEA cross-efficiency optimization in portfolio selection. Expert Systems with Applications, 168, 114280.
Aouni, B., Colapinto, C., & La Torre, D. (2014). Financial portfolio management through the goal programming model: Current state-of-the-art. European Journal of Operational Research, 234(2), 536-545. DOI: https://doi.org/10.1016/j.ejor.2013.09.040
Carlsson, C., & Fullér, R. (2001). On possibilistic mean value and variance of fuzzy numbers. Fuzzy sets and systems, 122(2), 315-326. DOI: https://doi.org/10.1016/S0165-0114(00)00043-9
Carlsson, C., Fuller, R., Heikkilä, M., & Majlender, P. (2007). A fuzzy approach to R&D project portfolio selection. International Journal of Approximate Reasoning, 44(2), 93-105. DOI: https://doi.org/10.1016/j.ijar.2006.07.003
Carlsson, 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: https://doi.org/10.1016/S0165-0114(01)00251-2
Chang, 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: https://doi.org/10.1016/S0305-0548(99)00074-X
Chang, T. S., Tone, K., & Wu, C. H. (2021). Nested dynamic network data envelopment analysis models with infinitely many decision making units for portfolio evaluation. European journal of operational research, 291(2), 766-781.
Chang, 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: https://doi.org/10.1016/j.eswa.2009.02.062
Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429-444. DOI: https://doi.org/10.1016/0377-2217(78)90138-8
Chen, W., Li, S. S., Zhang, J., & Mehlawat, M. K. (2020). A comprehensive model for fuzzy multi-objective portfolio selection based on DEA cross-efficiency model. Soft computing, 24(4), 2515-2526.
Chen, W., Li, S. S., Mehlawat, M. K., Jia, L., & Kumar, A. (2021). Portfolio Selection Using Data Envelopment Analysis Cross-Efficiency Evaluation with Undesirable Fuzzy Inputs and Outputs. International Journal of Fuzzy Systems, 23(5), 1478-1509.
Chen, W., Gai, Y., & Gupta, P. (2018). Efficiency evaluation of fuzzy portfolio in different risk measures via DEA. Annals of Operations Research, 269(1), 103-127. DOI: https://doi.org/10.1007/s10479-017-2411-9
Cooper, W. W., Park, K. S., & Pastor, J. T. (1999). RAM: a range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. Journal of Productivity analysis, 11(1), 5-42. DOI: https://doi.org/10.1023/A:1007701304281
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. A. M. T. (2002). A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE transactions on evolutionary computation, 6(2), 182-197. DOI: https://doi.org/10.1109/4235.996017
Edalatpanah, S. A. (2020). Data envelopment analysis based on triangular neutrosophic numbers. CAAI transactions on intelligence technology, 5(2), 94-98.
Edalatpanah, S. A. (2019). A data envelopment analysis model with triangular intuitionistic fuzzy numbers. International journal of data envelopment analysis, 7(4), 47-58.
Edalatpanah, S. A. (2018). Neutrosophic perspective on DEA. Journal of applied research on industrial engineering, 5(4), 339-345.
Edirisinghe, N. C. P., & Zhang, X. (2008). Portfolio selection under DEA-based relative financial strength indicators: case of US industries. Journal of the operational research society, 59(6), 842-856. DOI: https://doi.org/10.1057/palgrave.jors.2602442
Edirisinghe, N. C., & Zhang, X. (2007). Generalized DEA model of fundamental analysis and its application to portfolio optimization. Journal of banking & finance, 31(11), 3311-3335. DOI: https://doi.org/10.1016/j.jbankfin.2007.04.008
Eftekharian, S. E., Shojafar, M., & Shamshirband, S. (2017). 2-phase NSGA II: An optimized reward and risk measurements algorithm in portfolio optimization. Algorithms, 10(4), 130. DOI: https://doi.org/10.3390/a10040130
Fernández, A., & Gómez, S. (2007). Portfolio selection using neural networks. Computers & Operations Research, 34(4), 1177-1191. DOI: https://doi.org/10.1016/j.cor.2005.06.017
Goodarzi, M., Yakideh, K., & Mahfoozi, G. (2017). Portfolio optimization by combining data envelopment analysis and decision-making Hurwicz Method. Modern Research in Decision Making, 1(4), 143-165.
Grzegorzewski, P. (2003, September). Distances and orderings in a family of intuitionistic fuzzy numbers. In EUSFLAT Conf. (pp. 223-227).
Guo, H., Sun, B., Karimi, H. R., Ge, Y., & Jin, W. (2012). Fuzzy investment portfolio selection models based on interval analysis approach. Mathematical Problems in Engineering, 2012. DOI: https://doi.org/10.1155/2012/628295
Hajiagha, S. H. R., Akrami, H., Kazimieras Zavadskas, E., & Hashemi, S. S. (2013). An intuitionistic fuzzy data envelopment analysis for efficiency evaluation under ucertainty: case of a finance and credit institution.
Hoe, L. W., Siew, L. W., & Fai, L. K. (2017, November). Improvement on the efficiency of technology companies in Malaysia with data envelopment analysis model. In International Visual Informatics Conference (pp. 19-30). Springer, Cham. DOI: https://doi.org/10.1007/978-3-319-70010-6_2
Huang, C. Y., Chiou, C. C., Wu, T. H., & Yang, S. C. (2015). An integrated DEA-MODM methodology for portfolio optimization. Operational Research, 15(1), 115-136. DOI: https://doi.org/10.1007/s12351-014-0164-7
Huang, X. (2008). Risk curve and fuzzy portfolio selection. Computers & Mathematics with Applications, 55(6), 1102-1112. DOI: https://doi.org/10.1016/j.camwa.2007.06.019
Hunjra, A. I., Alawi, S. M., Colombage, S., Sahito, U., & Hanif, M. (2020). Portfolio Construction by Using Different Risk Models: A Comparison among Diverse Economic Scenarios. Risks, 8(4), 126.
Javaherian, N., Hamzehee, A., & Sayyadi Tooranloo, H. (2021). Designing an intuitionistic fuzzy network data envelopment analysis model for efficiency evaluation of decision-making units with two-stage structures. Advances in Fuzzy Systems, 2021.
Jin, F., Garg, H., Pei, L., Liu, J., & Chen, H. (2020). Multiplicative consistency adjustment model and data envelopment analysis-driven decision-making process with probabilistic hesitant fuzzy preference relations. International Journal of Fuzzy Systems, 22(7), 2319-2332.
Karimi, A. (2021). Stock portfolio optimization using multi-objective genetic algorithm (NSGA II) and maximum Sharp ratio, 389-410.
Kaucic, M., Moradi, M., & Mirzazadeh, M. (2019). Portfolio optimization by improved NSGA-II and SPEA 2 based on different risk measures. Financial Innovation, 5(1), 1-28. DOI: https://doi.org/10.1186/s40854-019-0140-6
Kellerer, H., Mansini, R., & Speranza, M. G. (2000). Selecting portfolios with fixed costs and minimum transaction lots. Annals of Operations Research, 99(1), 287-304. DOI: https://doi.org/10.1023/A:1019279918596
Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market. Management science, 37(5), 519-531. DOI: https://doi.org/10.1287/mnsc.37.5.519
Lamb, J. D., & Tee, K. H. (2012). Resampling DEA estimates of investment fund performance. European Journal of Operational Research, 223(3), 834-841. DOI: https://doi.org/10.1016/j.ejor.2012.07.015
Lim, S., Oh, K. W., & Zhu, J. (2014). Use of DEA cross-efficiency evaluation in portfolio selection: An application to Korean stock market. European Journal of Operational Research, 236(1), 361-368. DOI: https://doi.org/10.1016/j.ejor.2013.12.002
Mao, X., Guoxi, Z., Fallah, M., & Edalatpanah, S. A. (2020). A neutrosophic-based approach in data envelopment analysis with undesirable outputs. Mathematical problems in engineering, 2020.
Markowitz, H. (1952). Portfolio Selection in The Journal of Finance Vol. 7, 77-91. DOI: https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
Mashayekhi, Z., & Omrani, H. (2016). An integrated multi-objective Markowitz–DEA cross-efficiency model with fuzzy returns for portfolio selection problem. Applied Soft Computing, 38, 1-9. DOI: https://doi.org/10.1016/j.asoc.2015.09.018
Omrani, H., Mashayekhi, Z. (2017). Multi objective portfolio selection by combining markowitz and dea cross efficiency models. Sharif Journal of Industrial Engineering & Management, 33.1(1.1), 87-94. doi: 10.24200/j65.2017.5578. DOI: https://doi.org/10.24200/j65.2017.5578
Pal, R., Chaudhuri, T. D., & Mukhopadhyay, S. (2021). Portfolio formation and optimization with continuous realignment: A suggested method for choosing the best portfolio of stocks using variable length NSGA-II. Expert Systems with Applications, 186, 115732.
Pastor, J. T., & Ruiz, J. L. (2007). Variables with negative values in DEA. In Modeling data irregularities and structural complexities in data envelopment analysis (pp. 63-84). Springer, Boston, MA. DOI: https://doi.org/10.1007/978-0-387-71607-7_4
Puri, J., & Yadav, S. P. (2015). Intuitionistic fuzzy data envelopment analysis: An application to the banking sector in India. Expert Systems with Applications, 42(11), 4982-4998. DOI: https://doi.org/10.1016/j.eswa.2015.02.014
Puri, J., Yadav, S. P., & Garg, H. (2017). A new multi-component DEA approach using common set of weights methodology and imprecise data: an application to public sector banks in India with undesirable and shared resources. Annals of Operations Research, 259(1), 351-388. DOI: https://doi.org/10.1007/s10479-017-2540-1
Rasoulzadeh, M., & Fallah, M. (2020). An overview of portfolio optimization using fuzzy data envelopment analysis models. Journal of fuzzy extension and applications, 1(3), 180-188.
Sadjadi, S. J., Gharakhani, M., & Safari, E. (2012). Robust optimization framework for cardinality constrained portfolio problem. Applied Soft Computing, 12(1), 91-99. DOI: https://doi.org/10.1016/j.asoc.2011.09.006
Schaerf, A. (2002). Local search techniques for constrained portfolio selection problems. Computational Economics, 20(3), 177-190. DOI: https://doi.org/10.1023/A:1020920706534
Soleimani, 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: https://doi.org/10.1016/j.eswa.2008.06.007
Yang, W., Cai, L., Edalatpanah, S. A., & Smarandache, F. (2020). Triangular single valued neutrosophic data envelopment analysis: application to hospital performance measurement. Symmetry, 12(4), 588.
Yu, G. F., Li, D. F., Liang, D. C., & Li, G. X. (2021). An Intuitionistic Fuzzy Multi-Objective Goal Programming Approach to Portfolio Selection. International Journal of Information Technology & Decision Making, 20(05), 1477-1497.
Zhao, L., & Palomar, D. P. (2018). A markowitz portfolio approach to options trading. IEEE Transactions on Signal Processing, 66(16), 4223-4238.
Zhou, W., & Xu, Z. (2018). Portfolio selection and risk investment under the hesitant fuzzy environment. Knowledge-Based Systems, 144, 21-31. DOI: https://doi.org/10.1016/j.knosys.2017.12.020