CONSTRAINED PORTFOLIO SELECTION OPTIMIZATION USING CALIBRATED GENETIC ALGORITHM

Authors

Abstract

Portfolios are a proper collection of investments choosing by an organization or a person. Hence portfolio optimization is a very prominent problem by optimizing which we can attain more profit with the less risk. In this paper, we consider a portfolio optimization problem with some constraints such as boundary and cardinality constraints. Although adding these constraints makes the model more adapted to real world problems, it leads to disability of exact methods to find the optimal solutions in a reasonable time. In order to find optimal solutions, we use an improved genetic algorithm inspiring by natural evolution. We indicate that our proposed algorithm is more efficient and effective than many genetic algorithms which have been previously presented. Parameter setting of the proposed algorithm is done by means of a statistical method based on Taguchi technique. Finally, we perform some computational experiments which confirm the efficiency of our algorithm for portfolio optimization.

Keywords


[1] Markowitz, H. M. (1952) “Portfolio selection”, The Journal of Finance, 7(1); 77-91.
[2] Konno, H., and Yamazaki, H. (1991) “Mean-absolute deviation portfolio optimization model and its application to the Tokyo Stock Market”, Management Science, 37(5); 519-531.   
[3]Moon, Y., and Yao, T. (2011). “A robust mean absolute deviation model for portfolio optimization”, Computers & Operations Research, 38(9); 1251-1258.
[4] Simaan, Y. (1997) “Estimation Risk in Portfolio Selection: The Mean Variance Model Versus the Mean Absolute Deviation Model”, Management Science, 43(10); 1437-1446.
[5] Lee, S. M., and Chesser, D. L. (1980) “Goal programming for portfolio selection”, The journal of portfolio management, 6(3); 22-26.
[6] Young M. R. (1998) “A Minimax Portfolio Selection Rule with Linear Programming Solution” Management Science, 44(5); 673-683.
[7] Polak, G. G., Rogers, D. F., and Sweeney, D. J. (2010) “Risk management strategies via minimax portfolio optimization European Journal of Operational Research. 207(1); 409-419.
[8] Anagnostopoulos, K. P., and Mamanis, G. (2010) “A portfolio optimization model with three objectives and discrete variables”,Computers & Operations Research, 37(7); 1285-1297.
[9] 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.
[10] Yang, X. (2006) “Improving portfolio efficiency: a Genetic Algorithm Approach”, Computational Economics, 28(1); 1-14.
[11] 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.
[12] Lin, Chang-Chun, and Liu, Yi-Ting (2008) “Genetic algorithms for portfolio selection problems minimum transaction lots”, European Journal of Operational Research, 185(1); 393-404.
[13] Aranha, C., and Iba, H. (2009), “The Memetic Tree-based Genetic Algorithm and its application to Portfolio Optimization”, Memetic Computing 1(1); 139–151.
[14]  Hao, F.F., and Liu, Y.K. (2009) “Mean-variance models for portfolio selection with fuzzy random returns”, Journal of Applied Mathematics and Computing  30(1); 9–38
[15]  Chang, T. J., Yang, S. C., and Chang, K. J. (2009) “Portfolio optimization problems in different risk measures using genetic algorithm”, Expert Systems with Applications 36(1); 10529–10537.
[16] Chen, W., and Zhang, Wei-Guo (2010) “The admissible portfolio selection problem with transaction costs and an improved PSO algorithm”, Statistical Mechanics and its Applications, 389(10); 2070-2076.
[17] Pinto, D. D. D., Monteiro, J.G.M..S., and Nakao, E. H. (2011) “An approach to portfolio selection using an ARX predictor for securities’ risk and return”, Expert Systems with Applications, 38(12); 15009-15013.
[18] Naimi Sadigh, A., Mokhtari, H., Iranpoor, M., and Fatemi Ghomi S. M. T. (2012) “Cardinality Constrained Portfolio Optimization Using a Hybrid Approach based on Particle Swarm Optimization and Hopfield Neural Network”, Advanced Science Letters, 17(1) 11–20.
[19] Gupta, P., Inuiguchi, M., Mehlawat, M. K., and Mittal G. (2013) “Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints”, Information Sciences, 229(1); 1-17.
[20] Liu, Yong-Jun, and  Zhang, Wei-Guo  (2013) “ Fuzzy portfolio optimization model under real constraints”,   Mathematics and Economics, 53(3); 704-711.
[21] Zhang, X., Zhang, W., and  Xiao, W. (2013) “Multi-period portfolio optimization under possibility measures”. Economic Modelling, 35(1); 401-408.
[22] Cochran W. G., and Cox, G. M. (1992) “Experimental Design, 2nd edition”, Wiley, New York. John Wiley& Sons.
[23] Taguchi, G. (1986) “Introduction to quality engineering”, White Plains: Asian Productivity Organization/UNIPUB.             
[24] Mozafari, M., Tafazzoli, S., and Jolai, F. (2011) “A new IPSO-SA approach for cardinality constrained portfolio optimization”, International Journal of Industrial Engineering Computation, 2(2); 249-262.