Volume 2 Issue 2 pp. 249-262 Spring, 2011


A new IPSO-SA approach for cardinality constrained portfolio optimization


Marzieh Mozafari, Sajedeh Tafazzoli and Fariborz Jolai


The problem of portfolio optimization has always been a key concern for investors. This paper addresses a realistic portfolio optimization problem with floor, ceiling, and cardinality constraints. This problem is a mixed integer quadratic programming where traditional optimization methods fail to find the optimal solution, efficiently. The present paper develops a new hybrid approach based on an improved particle swarm optimization (PSO) and a modified simulated annealing (SA) methods to find the cardinality constrained efficient frontier. The proposed algorithm benefits simple and easy characteristics of PSO with an adaptation of inertia weights and constriction factor. In addition, incorporating an SA procedure into IPSO helps escaping from local optima and improves the precision of convergence. Computational results on benchmark problems with up to 225 assets signify that our proposed algorithm exceeds not only the standard PSO but also the other heuristic algorithms previously presented to solve the cardinality constrained portfolio problem.


DOI: 10.5267/j.ijiec.2011.01.004

Keywords: Portfolio optimization, Cardinality constraint, Hybrid solution approach, Improved particle swarm optimization, Simulated annealing
References

Armañanzas, R., & Lozano, J. A. (2005). A multiobjective approach to the portfolio optimization problem. Proceedings of the IEEE Congress on Evolutionary Computation, Edinburgh, UK, 2 1388-1395.

Arnone, S., Loraschi, A., & Tettamanzi, A. (1993). A genetic approach to portfolio selection. Neural Network World. International Journal on Neural and Mass-Parallel Computing and Information Systems, 3(6), 597-604.

Beasley, J.E. (1996). Obtaining test problems via Internet. Journal of Global Optimization, 8(4), 429-433.

Behnamian, J., Fatemi Ghomi, S. M. T. (2010) Development of a PSO-SA hybrid metaheuristic for a new comprehensive regression model to time-series forecasting. Expert Systems and Applications, 37(2), 974-984.

Blum, C., & Li, X. (2008). Swarm Intelligence in Optimization, in Blum, C. & Merkle, D. (eds.), Swarm Intelligence - Introduction and Applications, Springer, 43 – 85.

Cerny, V. (1985). Thermodynamical approach to the travelling salesman problem: an efficient simulation algorithm. Journal of Optimization Theory and Applications, 45(1), 41-51.

Chang, T. J., Meade, N., Beasley, J. E., & Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimization. Computers and Operational Research, 27, 1271-1302.

Chen, A. L., Yang, G. K., & Wu, Z. M. (2006). Hybrid Discrete Particle Swarm Optimization Algorithm for Capacitated Vehicle Routing Problem. Journal of Zhejiang University Science A, 7, 607-614.

Clerc, M., & Kennedy, J. (2002). The particle swarm-explosion, stability and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6, 58-73.

Coffin, M. & Saltzman, M. J. (2000). Statistical analysis of computational tests of algorithms and heuristics. INFORMS Journal on Computing, 12(1), 24-44.

Crama, Y., & Schyns, M. (2003). Simulated annealing for complex portfolio selection problems. European Journal of Operational Research, 150, 546-571.

Cura, T. (2009). Particle swarm optimization approach to portfolio optimization. Nonlinear Analysis: Real World Applications, 10(4), 2396-2406.

Di Tollo, G., & Roli, A. (2008). Metaheuristics for the Portfolio Selection Problem. International Journal of Operations Research, 5(1), 13-35.

Dueck, G., & Winker, P. (1992). New concepts and algorithms for portfolio choice. Applied Stochastic Models and Data Analysis, 8, 159-178.

Eberhart, R. C., & Kennedy, J. (1995b). A new optimizer using particle swarm theory. Proceeding of 6th International Symposium on Micromachine and Human Science. Nagoya, Japan, 39-43.

Fernandez, A., & Gomez, S. (2007) Portfolio selection using neural networks. Computers & Operations Research, 34(4), 1177-1191.

Gao, J., & Chu, Z. (2010). A new particle swarm optimisation based on MATLAB for portfolio selection problem. International Journal of Modelling, Identification and Control, 9(1-2), 206 - 211.

Gilli, M., Këllezi, E., & Hysi, H. (2006). A data-driven optimization heuristic for downside risk minimization. The Journal of Risk, 8(3), 1-19.

Glover, F., Mulvey, J. M., & Hoyland, K. (1995). Solving dynamic stochastic control problems in finance using tabu search with variable scaling. Proceedings of the Metaheuristics International Conference, Breckenridge, Colorado, 429-448.

Kennedy, J., & Eberhart, R.C. (1995a). Particle swarm optimization. IEEE International Conference on Neural Networks, 4, 1942-1948.

Kirkpatrick, S., Gelatt, C. D., & Vecchi, P. M. (1983). Optimization by simulated annealing. Science, 220, 671-680.

Konno, H., & Yamazaki, H. (1991). Mean-absolute deviation portfolio in optimization model and its application to Tokyo stock market. Management Science, 37(5), 519-531.

Koshino, M., Murata, H., & Kimura, H. (2007). Improved particle swarm optimization and application to portfolio selection. Electronics and Communications in Japan (Part 3), 90(3), 13-25.

Lee, S. M., & Chesser, D. L. (1980). Goal programming for portfolio selection. Journal of Portfolio Management, 6(3), 22-26.

Liu, B., Wang, L. & Jin, Y.H. (2007). An effective PSO-based memetic algorithm for flow shop scheduling. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 37, 18-27.

Maringer, D. G. (2001). Optimizing portfolios with ant systems. Proceedings of the International ICSC Congress on Computational Intelligence: Methods and Applications, Bangor, Wales, United Kingdom, 288-294.

Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.

Mishra, S. K., Panda, G., & Meher, S. (2009). Multi-objective particle swarm optimization approach to portfolio optimization, World Congress on Nature and Biologically Inspired Computing, Coimbatore, India, 1612 - 1615.

Mous, L., Dallagnol, V. A. F., Cheung, W., & van den Berg, J. (2006). A comparison of particle swarm optimization and genetic algorithms applied to portfolio selection. Proceedings of the Workshop on Nature Inspired Cooperative Strategies for Optimization NICSO, Granada, Spain, 109-121.

Peram, T., Veeramachaneni, K., & Mohan, C. K. (2003) Fitness-distance-ratio based particle swarm optimization. Swarm Intelligence Symposium, Indiana, USA, 174-181.

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.

Schaerf, A. (2002). Local search techniques for constrained portfolio selection problems. Computational Economics, 20, 177-190.

Shen Q., Shi, W. M., & Kong, W. (2008). Hybrid particle swarm optimization and tabu search approach for selecting genes for tumor classification using gene expression data. Computational Biology and Chemistry, 32, 53–60.

Shi, Y., & Eberhart, R C. (1998). A modified particle swarm optimizer. Proceedings IEEE Congress on Evolutionary Computation, pp. 69–73.

Simaan, Y. (1997). Estimation risk in portfolio selection: The mean variance model versus the mean absolute deviation model. Management Science, 43(10), 1437-1446.

Tang, J., Zhang, G., Lin, B., & Zhang, B. (2010). Power mutation embedded modified PSO for global optimization problems. Tan Y., Shi Y. Tan, K.C. (eds.) Advances in Swarm Intelligence, Lecture Notes in Computer Science, 6145, 566-573.

Tasgetiren M.F., Sevkli M., Liang Y.C., Gencyilmaz G. (2004). Particle swarm optimization algorithm for makespan and maximum lateness minimization in permutation flowshop sequencing problem. Proceedings of the fourth international symposium on intelligent manufacturing systems, Sakarya, Turkey, 431-41.

Xu, F., Chen, W., & Yang, L. (2007). Improved particle swarm optimization for realistic portfolio selection. Proceedings of Eighth ACIS International Conference on Software Engineering, Artificial Intelligence, Networking, and Parallel/Distributed Computing,1, 185-190.

Yang, X. (2006). Improving portfolio efficiency: A genetic algorithm approach. Computational Economics, 28, 1-14.

Young, M. R. (1998). A minimax portfolio selection rule with linear programming solution. Management Science, 44(5), 673-683.