Portfolio Optimization in Tehran Stock Exchange by Water Cycle Algorithm

Document Type : Original Article

Author

Management Faculty, University of Tehran

Abstract

Portfolio selection is one of the vital financial challenges. This study seeks to apply the multi-objective water cycle algorithm (MOWCA) to find efficient frontiers associated with portfolio. This problem is non-linear multi-objective problem including maximiaing return and minimizing risk of portfolio. The inspired concept of WCA is based on the simulation of water cycle process in the nature. At the first time, it was applied by Moradi et al. (2017) for optimizating portfolio. Computational results are obtained for analyses of daily data for the period 2013 to 2015 including TSE 30. The performance of the MOWCA for solving portfolio optimization problems has been evaluated in comparison with other multi-objective optimizers including the MOGA and MOPSO. Four well-known performance metrics are used to compare the reported optimizers: GD, MS, S and ∆. Statistical optimization results indicate that the applied MOWCA is an efficient and practical optimizer compared with the other methods for handling portfolio optimization problems.

Keywords

References

  1. بیات، علی و اسدی، لیدا. (1396). بهینه سازی پرتفوی سهام: سودمندی الگوریتم پرندگان و مدل مارکویتز. مهندسی مالی و مدیریت اوراق بهادار، شماره سی و دوم : 64-85.
  2. عباسی، ابراهیم، ابوالی، مهدی وسربازی، مهدی. (1391). انتخاب سبد سهام بهینه با استفاده از الگوریتم ژنتیک. مهندسی مالی و مدیریت اوراق بهادار، شماره دهم : 23-38.
  3. Ali, M. M., & Kaelo, P. (2008). Improved particle swarm algorithms for global optimization. Applied Mathematics and Computation, 196, 578–593.
  4. Bermْdez, J. D., Segura, J. V., & Vercher, E. (2012). A multi-objective genetic algorithm for cardinality constrained fuzzy portfolio selection. Fuzzy Sets and Systems, 188, 16–26.
  5. Chang, T.-J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimization. Computers & Operations Research, 27, 1271–1302.
  6. Chang, T.-J., Sang-Chin, Y., & Chang, K.-J. (2009). Portfolio optimization problems in different risk measures using genetic algorithm. Expert Systems with Applications, 36, 10529–10537.
  7. Chen, W. (2015). Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem. Physica A, 429, 125–139.
  8. Coello, C. A. C. (2000). An updated survey of GA-based multi-objective optimization techniques. ACM Computing Surveys, 32, 109–143.
  9. Corazza, M., Fasano, G., & Gusso, R. (2013). Particle swarm optimization with non-smooth penalty reformulation, for a complex portfolio selection problem. Applied Mathematics Computing, 224, 611–624.
  10. Crama, Y., & Schyns, M. (2003). Simulated annealing for complex portfolio selection problems. European Journal of Operational Research, 150, 546–571.
  11. Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. Chichester: Wiley.
  12. Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multi objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6, 182–197.
  13. Deng, G.-F., Lin, W.-T., & Lo, C.-C. (2012). Markowitz-based portfolio selection with cardinality constraints using improved particle swarm optimization. Expert Systems with Applications, 39, 4558–4566.
  14. Eskandar, H., Sadollah, A., Bahreininejad, A., & Hamdi, M. (2012). Water cycle algorithm – A novel metaheuristic optimization method for solving constrained engineering optimization problems. Computers & Structures, 110-111, 151–166.
  15. Goldberg, D. (1989). Genetic algorithms in search, optimization and machine learning. Reading, MA: Addison-Wesley.
  16. Golmakani, H. R., & Fazel, M. (2011). Constrained portfolio selection using particle swarm optimization. Expert Systems with Applications, 38, 8327–8335.
  17. Haupt, R. L., & Haupt, S. E. (2004). Practical genetic algorithms (2nd ed.). USA: John Wiley & Sons Inc.
  18. Holland, J. H. (1975). Adaptation in natural and articial systems: An introductory analysis with applications to biology, control, and articial intelligence. Michigan: University of Michigan Press.
  19. Jiang, Y., Hu, T., Huang, C., & Wu, X. (2007). An improved particle swarm optimization algorithm. Applied Mathematics and Computation, 193, 231–239.
  20. Kaveh, A., & Laknejadi, K. (2011). A novel hybrid charge system search and particle swarm optimization method for multi-objective optimization. Expert Systems with Applications, 20, 1–14.
  21. Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization, in Proc. of the IEEE international conference on neural networks, Perth, Australia, 1942–1948.
  22. Kennedy, J., Eberhart, R. C., & Shi, Y. (2001). Swarm intelligence. San Francisco, CA: Kaufmann.
  23. Kolm, P. N., Tütüncü, R., & Fabozzi, F. J. (2013). 60 Years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 236, 258–267.
  24. Kyong, J. O., Tae, Y. K., & Sungky, M. (2005). Using genetic algorithm to support portfolio optimization for index fund management. Expert Systems with Applications, 28, 371–379.
  25. Li, X. (2003, July). A non-dominated sorting particle swarm optimizer for multiobjective optimization. In E. Cantu-Paz, J. A. Foster, K. Deb, L. D. Davis, R. Roy, U.-M. O’Reilly, … A. C. Schultz (Eds.), Proceedings of the Genetic and Evolutionary Computation Conference (GECCO'2003) (Vol. 2723, pp. 37–48). Madrid: Springer, Lecture Notes in Computer Science.
  26. Li, J., & Xu, J. (2007). A class of possibilistic portfolio selection model with interval coefficients and its application. Fuzzy Optimization and Decision Making, 6, 123–137.
  27. Lin, C.-C., & Liu, Y.-T. (2008). Genetic algorithms for portfolio selection problems with minimum transaction lots. European Journal of Operational Research, 185, 393–404.
  28. Lin, Chi-Ming, and Gen, M. (2007) “An Effective Decision-Based Genetic Algorithm Approach to Multiobjective Portfolio Optimization Problem”, Applied Mathematical sciences, 1(5); 201-210
  29. Liu, Y., Wu, X., & Hao, F. (2012). A new chance-variance optimization criterion for portfolio selection in uncertain decision systems. Expert Systems with Applications, 39, 6514–6526.
  30. Maringer, D., & Kellerer, H. (2003). Optimization of cardinality constrained portfolios with a hybrid local search algorithm. OR Spectrum, 25, 481–495.
  31. Markowitz, H. M. (1952). Portfolio selectionJournal of Finance, 7, 77–91.
  32. Markowitz, H. M. (1991). Portfolio selection: Efficient diversification of investments. New York, NY: Yale University Press, John Wiley.
  33. Melanie, M., (1999), “An Introduction to Genetic Algorithms”, A Bradford Book The MIT Press Cambridge, Massachusetts-London, England, Fifth Printing.
  34. Moradi, Mohammad, Sadollah, Ali, Eskandar, Hoda and Eskandar, Hadi. (2017). The application of water cycle algorithm to portfolio selection. Economic Research, 30(1): 1277–1299.
  35. Najafi, A. A., & Mushakhian, S. (2015). Multi-stage stochastic mean-semivariance-CVaR portfolio optimization under transaction costs. Applied Mathematics Computing, 256, 445–458.
  36. Ruiz-Torrubiano, R., & Suarez, A. (2010). Hybrid approaches and dimensionality reduction for portfolio selection with cardinality constraints. IEEE Computational Intelligence Magazine, 5, 92–107.
  37. Sadollah, A., Eskandar, H., Kim, J. H., & Bahreininejad, A. (2014). Water cycle algorithm for solving multi-objective optimization problems. Soft Computing, 19, 2587–2603. doi:10.1007/s00500-014-1424-4
  38. Sadollah, A., Eskandar, H., & Kim, J. H. (2015). Water cycle algorithm for solving constrained multiobjective optimization problems. Applied Soft Computing, 27, 279–298.
  39. Schott, J. R. (1995). Fault tolerant design using single and multicriteria genetic algorithm optimization (Master’s thesis), Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA.
  40. 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, 5058–5063.
  41. Tsai, S.-J., Sun, T.-Y., Liu, C.-C., Hsieh, S.-T., Wu, W.-C., & Chiu, S.-Y. (2010). An improved multiobjective particle swarm optimizer for multi-objective problems. Expert Systems with Applications, 37, 5872–5886.
  42. Veldhuizen, D. A. V., & Lamont, G. B. (1998). Multi-objective evolutionary algorithm research: A history and analysis. Technical Report TR-98-03, Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology, Wright-Patterson AFB, OH.
  43. Woodside-Oriakhi, M., Lucas, C., & Beasley, J. E. (2011). Heuristic algorithms for the cardinalityرconstrained efficient frontier. European Journal of Operational Research, 213, 538–550.
  44. Yang, X., Yuan, J., Yuan, J., & Mao, H. (2007). A modified particle swarm optimizer with dynamic adaptation. Applied Mathematics and Computation, 189, 1205–1213.
  45. Zhu, H., Wang, Y., Wang, K., & Chen, Y. (2011). Particle Swarm Optimization (PSO) for the constrained portfolio optimization problem. Expert Systems with Applications, 38, 10161–10169.

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