Portfolio Optimization Problem Considering Cardinality and Bounding Constraints Using a Metaheuristic Algorithm
Subject Areas : International Journal of Finance, Accounting and Economics StudiesShohreh Zakaei 1 , Mohammadreza Sanaei 2 , Akbar Mirzapour Babajan 3
1 - PhD student of Information Technology Management, Department of Information Technology Management, Faculty of Management and Accounting, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 - Department of Information Technology Management, Faculty of Management and Accounting, Qazvin Branch, Islamic Azad University, Qazvin, Iran
3 - Department of Economics, Faculty of Management and Accounting, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Keywords: Optimization, Metaheuristic algorithm, Portfolio, Cardinality constraint,
Abstract :
The optimal portfolio selection problem is one of the most important problems in finance investigated by many researchers and professors over the last few decades. Of the exact methods and effective approximate solution algorithms, metaheuristic methods have also been successfully proposed to solve some practical and large-scale problems with large numbers of assets and constraints. Hence, in this study, it is tried to optimize the portfolio selection problem by the metaheuristic cuckoo search algorithm (CSA) considering cardinality constraints and show that the mentioned algorithm is capable of achieving suitable solutions. Once the algorithm is designed and run in MATLAB software, the efficient frontier diagram obtained from CSA is close and similar to the efficient frontier diagram obtained from the basic Markowitz model confirming the accuracy and validity of the results obtained from CSA. However, it should be noted that the convergence of the solutions obtained according to CSA is better. Finally, a general comparison between the results obtained from the use of CSA in this study and bee and genetic algorithms in other studies is shown. Based on the results, the average risk return according to CSA is higher than the other two algorithms. Moreover, the portfolio risk according to CSA is lower compared to the other algorithms.
Aranha, C., & Iba, H. (2009). The memetic tree-based genetic algorithm and its application to portfolio optimization. Memetic Computing, 1(2), 139-151.
Fabozzi, F. J., Kolm, P. N., Pachamanova, D. A., & Focardi, S. M. (2007). Robust portfolio optimization and management. John Wiley & Sons.
Karaboga, D., & Gorkemli, B. (2014). A quick artificial bee colony (qABC) algorithm and its performance on optimization problems. Applied Soft Computing, 23, 227-238.
Markowitz, H. (1959). Portfolio selection.
Di Tollo, G., & Roli, A. (2008). Metaheuristics for the portfolio selection problem. International Journal of Operations Research, 5(1), 13-35.
Streichert, F., Ulmer, H., and Zell, A. (2004). “Comparing discrete and continuous genotypes on the constrained portfolio selection problem”. Proceedings of the Genetic and Evolutionary Computation Conference, Seattle, Washington, USA, pp. 1239-1250.
Armañanzas, R. and Lozano, J.A. (2005). “A multiobjective approach to the portfolio optimization problem”. Proceedings of the 2005 IEEE Congress on Evolutionary Computation, Edinburgh, UK, pp.1388-1395.
Ehrgott, M., Klamroth, K., and Schwehm, C. (2004). “An MCDM approach to portfolio optimization”. European Journal of Operational Research, 155(3), pp. 752-770.
Subbu, R., Bonissone, P., Eklund, N., Bollapragada, S., and Chalermkraivuth K. (2005). “Multiobjective financial portfolio design: A hybrid evolutionary approach”. Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2005), Munich, Germany, pp.1722-1729.
Ong, C.-S., Huang, J.-J., and Tzeng, G.-H. (2005). “A novel hybrid model for portfolio selection”. Applied Mathematics and Computation, 169, 1195-1210.
Konno, H. and Yamazaki, H. (1991). Mean absolute deviation portfolio optimization model and its applications to Tokyo stock market”. Management Science, 37, 519-531.
Speranza, M.-G. (1996). “A heuristic algorithm for a portfolio optimization model applied to the Milan stock market”. Computers & Operations Research, 23(5), 433-441.
Gilli, M., Këllezi, E., and Hysi, H. (2006). “A data-driven optimization heuristic for downside risk minimization”. The Journal of Risk, 3, 1-19.
Chang, T.-J., Meade, N., Beasley, J.-E., and Sharaiha Y.-M. (2000). “Heuristics for cardinality constrained portfolio optimization”. Computers & Operations Research, 27(13), 1271-1302.
Xia, Y.-S., Liu, B.-D., Wang, S., and Lai, K.-K. (2000). “A model for portfolio selection with order of expected returns”. Computers & Operations Research, 27(5), 409-422.
Kellerer, H. and Maringer, D. (2003). “Optimization of cardinality constrained portfolios with a hybrid local search algorithm”. OR Spectrum, 25(4), 481-495.
Rolland, E. (1997). “A tabu search method for constrained real number search: Applications to portfolio selection”. Technical report, Department of Accounting and Management Information Systems, Ohio State University, Columbus, Ohio.
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.
Ma, X., Gao, Y., & Wang, B. (2012). Portfolio optimization with cardinality constraints based on hybrid differential evolution. AASRI Procedia, 1, 311-317.
Chen, W. (2015). Artificial bee colony algorithm for constrained possibilistic portfolio optimization problem. Physica A: Statistical Mechanics and its Applications, 429, 125-139.
Ruiz-Torrubiano, R., & Suárez, A. (2015). A memetic algorithm for cardinality-constrained portfolio optimization with transaction costs. Applied Soft Computing, 36, 125-142.