عنوان مقاله [English]
Today, the portfolio optimization and its management is one of the most important areas in financial decision-making. Therefore, picking a portfolio of stocks that could bring the highest rate of return and the lowest risk investment for its holder simultaneously has become one of the main concerns of the economic actors. But in choosing the optimum portfolio just these factors are not decisive and according to the economic environment, many factors can affect this process which should be identified and considered. Therefore, in order to cover these matter multi-criteria decision-making approaches should be used. On the other hand, when the real-world conditions and restrictions, including restrictions on investment in any of the stocks and cardinality constraint are considered in portfolio optimization, the problem is not easily solvable by means of usual mathematical methods. Specially when there are a large number of assets in the portfolio evaluation process. Regarding this fact, the main purpose of this paper is to solve portfolio optimization problem by using the Data Envelopment Analysis (DEA) and Symbiotic Organisms Search (SOS). Finally, the model used in this study has been solved with real data and the results have been analyzed. The results of this paper demonstrate that the proposed approach has been successful in portfolio optimization and has been able to properly interact with the actual limitations and effective variables of the market.
 Markowitz, H. (1952) "Portfolio Selection," The journal of finance, vol. 7, pp. 77-91.
 Sharpe, W. F. (1963) "A Simplified Model for Portfolio Analysis," Management Science, vol. 9, pp. 277-293.
 Farrell, M. J. (1957) "The Measurement of Productive Efficiency," Journal of the Royal Statistical Society. Series A (General), vol. 120, pp. 253-290.
 Charnes, A., Cooper, W. W., and Rhodes, E. (1978) "Measuring the Efficiency of Decision Making Units," European Journal of Operational Research, vol. 2, pp. 429-444.
 Powers, J., and McMullen, P. (2000) "Using Data Envelopment Analysis to Select Efficient Large Market Cap Securities," Journal of Business and Management, vol. 7, pp. 31-42.
 Edirisinghe, N., and Zhang, X. (2007) "Generalized DEA Model of Fundamental Analysis and its Application to Portfolio Optimization," Journal of Banking & Finance, vol. 31, pp. 3311-3335.
 Lopes, A., Lanzer, E., Lima, M., and da Costa Jr, N. (2008) "DEA Investment Strategy in the Brazilian Stock Market," Economics Bulletin, vol. 13, pp. 1-10.
 Alinezhad, A., Zohrebandian, M., and Dehdar, F. (2010) "Portfolio Selection Using Data Envelopment Analysis with Common Weights," Iranian Journal of Optimization, vol. 2, pp. 323-333.
 Khajavi, Sh., Salimifard, A.R., and Rabie, M. (2005) " Application of Data Envelopment Analysis (DEA) in Determining the Most Efficient Portfolio of Companies Listed in the Tehran Stock Exchange," Journal of Humanities and Social Sciences, vol. 22, pp. 75-89. (in Persian)
 Afshar Kazemi, M.A., Khalili Araghi, M., and Sadat Kiyayi, A. (2012) "Stock Selection of Tehran Stock Exchange Investors with Hybrid of Data Envelopment Analysis (DEA) and Goal Programming (GP)," Financial Knowledge of Securities Analysis, vol. 13, pp. 49-63. (in Persian)
 Goodarzi, M., Yakideh, k., and Mahfoozi, G. (2016) "Portfolio Optimization by Combining Data Envelopment Analysis and Decision-Making Hurwicz Method," Modern Research in Decision Making, vol. 1, pp. 143-165. (in Persian)
 Azar, A., Khosravani, F., and Jalali, R. (2013) "The Application of DEA in Selecting a Portfolio Consisting of the Most Efficient and the Most Inefficient Companies Now Present in Tehran Stock Market," Management Researches in Iran, vol. 17, pp. 1-19. (in Persian)
 Sadjadi, S. J., Gharakhani, M., and Safari, E. (2012) "Robust Optimization Framework for Cardinality Constrained Portfolio Problem," Applied Soft Computing, vol. 12, pp. 91-99.
 Deng, G.-F., Lin, W.-T., and Lo, C.-C. (2012) "Markowitz-Based Portfolio Selection with Cardinality Constraints Using Improved Particle Swarm Optimization," Expert Systems with Applications, vol. 39, pp. 4558-4566.
 Najafi, A. A., and Mushakhian, S. (2015) "Multi-Stage Stochastic Mean–Semivariance–CVaR Portfolio Optimization Under Transaction Costs," Applied Mathematics and Computation, vol. 256, pp. 445-458.
 Afsar, A., and Helyel, F. (2017) " A Hybrid Approach to Portfolio Optimization Using Technical Analysis and Data Mining," Modern Research in Decision Making, vol. 2, pp. 1-22. (in Persian).
 Kiyani, M., Nabavi, S.A., and Memarian, E. (2015) " Optimizing Stock Portfolio with Regard to Minimum Level of Total Risk Using Genetic Algorithm," Journal of Investment Knowledge, vol. 3, pp. 125-164. (in Persian)
 Cheng, M.-Y., and Prayogo, D. (2014) "Symbiotic Organisms Search: A new Metaheuristic Optimization Algorithm," Computers & Structures, vol. 139, pp. 98-112.
 Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., and Nikoomaram, H. (2010) " Data Envelopment Analysis and Its Applications," Islamic Azad University Publication. (in Persian)
 Peykani, P., and Roghanian, E. (2015) "Using Data Envelopment Analysis and Robust Optimization in the Selection of Portfolio," Journal of Operational Research In Its Applications ( Applied Mathematics ) - Lahijan Azad University, vol. 44, pp. 61-78. (in Persian)
 Mehregan, M.R. (2012) " DEA: Quantitative Models in Evaluating the Performance of Organizations," Nashre Ketabe Daneshgahi. (in Persian)
 Zhu, J. (2014) Quantitative Models for Performance Evaluation and Benchmarking: Data Envelopment Analysis with Spreadsheets vol. 213: Springer.
 Beale, E. and Forrest, J. J. (1976) "Global Optimization Using Special Ordered Sets," Mathematical Programming, vol. 10, pp. 52-69.
 Fernández, A., and Gómez, S. (2007) "Portfolio Selection Using Neural Networks," Computers & Operations Research, vol. 34, pp. 1177-1191.
 Holland, J. H. (1975) Adaptation in Natural and Artificial Systems: an Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence: U Michigan Press.
 Eberhart, R. C., and Kennedy, J. (1995) "A New Optimizer Using Particle Swarm Theory," in Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39-43.