Portfolio Selection Using Double GAs Searching for Cardinality and Integer Multiplied Optimal Weights

This paper studied cardinality constrained portfolio with integer weight. We suggested two optimization models and used two genetic algorithms to solve them. In this paper, after finding well matching stocks, according to investor’s target by using first genetic algorithm, we gave optimal integer weight of portfolio with well matching stocks by using second genetic algorithm. Through numerical comparisons with other feasible portfolios, we verified advantages of designed portfolio with two genetic algorithms. For a numerical comparison, we used a prepared data consisted of 18 stocks listed in S & P 500 and numerical example strongly supported the designed portfolio in this paper. Also, we made all comparisons visible through all feasible efficient frontiers.

Amenc, N., & Le Sourd, V. (2003). Portfolio theory and performance analysis. Chichester: John Wiley and Sons.

Black, F., & Litterman, R. (1992). Global portfolio optimization. Financial Analysts Journal, 48(5), 28-43.

Black, F., Jensen, M. C., & Scholes, M. (1972). The capital asset pricing model: Some empirical tests. New York: Praeger Publishers.

Bonami, P., & Lejeune, M. A. (2009). An exact solution approach for portfolio optimization problems under stochastic and integer constraints. Operations Research, 57(3), 650-670.

Chang, T. J., Meade, N., Beasley, J., & Sharaiha, Y. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers & Operations Research, 27(13), 1271-1302.

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

Gilli, M., & Këllezi, E. (2000). Heuristic approaches for portfolio optimization. The Sixth International Conference on Computing in Economics and Finance of the Society for Computational Economics, July 6-8, Barcelona, Spain.

Golmakani, H. R., & Fazel, M. (2011). Constrained portfolio selection using particle swarm optimization. Expert Systems with Applications, 38(7), 8327-8335.

Hajinezhad, E., Eatiy, S., & Ghanbariy, R. (2013). Mixed Tabu Machine for portfolio optimization problem. The 3rd Conference on Financial Mathematics & Applications, January 30-31, Semnan, Iran.

Jansen, R., & van Dijk, R. (2002). Optimal benchmark tracking with small portfolios. The Journal of Portfolio Management, 28(2), 33-39.

Jin, Y., Qu, R., & Atkin, J. (2014). A population-based incremental learning method for constrained portfolio optimisation. The 16th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), September 22-25, Timisoara, Romania.

Jobst, N., Horniman, M., Lucas, C., & Mitra, G. (2001). Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints. Quantitative Finance, 1(5), 489-501.

Kellerer, H., & Maringer, D. (2001). Optimization of cardinality constrained portfolios with a hybrid local search algorithm. The 4th Methaheuristics International Conference (MIC), July 16-20, Porto, Portugal.

Kellerer, H., Mansini, R., & Speranza, M. (2000). Selecting portfolios with fixed costs and minimum transaction lots. Annals of Operations Research, 99(1-4), 287-304.

Li, Y. B. (2015). Solving cardinality constrained portfolio optimisation problem using genetic algorithms and ant colony optimization (Ph.D. thesis, Brunel University, 2015).

Lin, C. C., & Liu, Y. T. (2008). Genetic algorithms for portfolio selection problems with minimum transaction lots. European Journal of Operational Research, 185(1), 393-404.

Loraschi, A., Tettamanzi, A., Tomassini, M., & Verda, P. (1995). Distributed genetic algorithms with an application to portfolio selection. In D. W. Pearson, N. C. Steele, R. F. Albrecht (Eds.), Artificial neural nets and genetic (pp. 384-387). Berlin: Springer.

Mangram, M. E. (2013). A simplified perspective of the Markowitz portfolio theory. Global Journal of Business Research, 7(1), 1-12.

Mansini, R., & Speranza, M. G. (1999). Heuristic algorithms for the portfolio selection problem with minimum transaction lots. European Journal of Operational Research, 114(2), 219-233.

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

Murray, W., & Shek, H. (2012). A local relaxation method for the cardinality constrained portfolio optimization problem. Springer. Retrieved from https://link.springer.com/article/10.1007/s10589-012-9471-1

Pedersen, K. G. (2014). Modern portfolio theory—A way to bridge the gap between strategy and risk? (Unpublished Master’s thesis, Copenhagen Business School, 2014).

Reilly, F. K., & Brown, K. C. (1997). Investment analysis and portfolio management. Chicago: Dryden Press.

Reilly, F. K. (1989). Investment analysis and portfolio management (3rd ed.). New York: Harcourt Brace Jovanovish College Publishers.

Ruiz-Torrubiano, R., & Suarez, A. (2010). Hybrid approaches and dimensionality reduction for portfolio selection with cardinality constraints. Computational Intelligence Magazine, 5(2), 92-107.

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

Skolpadungket, P. (2013). Portfolio management using computational intelligence approaches (Ph.D. thesis, Department of Computing, University of Bradford).

Skolpadungket, P., Dahal, K., & Harnpornchai, N. (2007). Portfolio optimization using multi-objective Genetic Algorithms. Congress on Evolutionary Computation (CEC) 2007, September 25-28, Singapore.

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.

Streichert, F., Ulmer, H., & Zell, A. (2004). Evaluating a hybrid encoding and three crossover operators on the constrained portfolio selection problem. Congress on Evolutionary Computation (CEC) 2004, June 19-23, Portland, OR, USA.

Thein, L. K. (2015). Evolutionary approaches to portfolio optimization (Ph.D. thesis, University of Nortingham, 2015).

Tobin, J. (1958). Liquidity preference as behavior toward risk. Review of Economic Studies, 25(2), 65-85.

Vercher, E. (2006). Optimization in Finance: Portfolio selection models. Iberian Conference in Optimization, November 16-18, Coimbra, Portugal.

Woodside-Oriakhi, M., Lucas, C., & Beasley, J. (2011). Heuristic algorithms for the cardinality constrained efficient frontier. European Journal of Operational Research, 213(3), 538-550.

Xu, R. T., Zhang, J., Liu, O., & Huang, R. Z. (2010). An estimation of distribution algorithm based portfolio selection approach. The 2010 International Conference on Technologies and Applications of Artificial Intelligence (TAAI), November 18-20, Hsinchu City, Taiwan.