Stock Portfolio Selection Using Chemical Reaction Optimization

Stock portfolio selection is a classic problem in finance, and it involves deciding how to allocate an institution-s or an individual-s wealth to a number of stocks, with certain investment objectives (return and risk). In this paper, we adopt the classical Markowitz mean-variance model and consider an additional common realistic constraint, namely, the cardinality constraint. Thus, stock portfolio optimization becomes a mixed-integer quadratic programming problem and it is difficult to be solved by exact optimization algorithms. Chemical Reaction Optimization (CRO), which mimics the molecular interactions in a chemical reaction process, is a population-based metaheuristic method. Two different types of CRO, named canonical CRO and Super Molecule-based CRO (S-CRO), are proposed to solve the stock portfolio selection problem. We test both canonical CRO and S-CRO on a benchmark and compare their performance under two criteria: Markowitz efficient frontier (Pareto frontier) and Sharpe ratio. Computational experiments suggest that S-CRO is promising in handling the stock portfolio optimization problem.

Authors:

• Jin Xu
• Albert Y.S. Lam
• Victor O.K. Li

Keywords:

• Stock portfolio selection
• Markowitz model
• Chemical Reaction Optimization
• Sharpe ratio

References:

[1] H. Markowitz, "Portfolio selection," Journal of Finance, vol. 7, no. 12,
pp. 77-91, 1952.
[2] H. Markowitz, "Portfolio selection: efficient diversification of investments,"
New York: Wiley, 1959.
[3] W. F. Sharpe, "Mutual fund performance," Journal of Business, vol. 39,
no. 1, pp. 119-138, 1966.
[4] J. K. Sengupta, "Portfolio decisions as games," International Journal of
Systems Science, vol. 20, no. 8, pp. 1323-1334, 1989.
[5] B. K. Stone, "A linear programming formulation of the general portfolio
selection problem," Journal of Financial and Quantitative Analysis, vol.
8, no. 4, pp. 621-636, 1973.
[6] G. D. Tollo, and A. Roli, "Metaheuristics for the portfolio selection
problem," International Journal of Operations Research, vol. 5, no. 1,
pp. 13-35, 2008.
[7] K. J. Oh, T. Y. Kim, S. H. Min and H. Y. Lee, "Portfolio algorithm
based on portfolio beta using genetic algorithm," Expert Systems with
Applications, vol. 30, no. 3, pp. 527-534, 2006.
[8] S. M. Wang, J. C. Chen, H. M. Wee, and K. J. Wang, "Non-linear
stochastic optimization using genetic algorithm for portfolio selection,"
International Journal of Operations Research, vol. 3, no. 1, pp. 16-22,
2006.
[9] Y. Crama, and M. Schyns, "Simulated annealing for complex portfolio
selection problem," European Journal of Operational Research, vol. 150,
no. 3, pp. 546-571, 2003.
[10] G. Kendall, and Y. Su, "A particle swarm optimization approach in
the construction of optimal risky portfolios," in Proc. of the 23rd
LASTED International Multi-Conference on Artificial Intelligence and
Applications, pp. 140-145, Innsbruck, Austria, 2005.
[11] R. Armananzas, and J. A. Lozano, "A multiobjective approach to
the portfolio optimization problem," in Proc. of IEEE Congress on
Evolutionary Computation (CEC), pp. 1388-1395, Edinburgh, UK, 2005.
[12] A. Y. S. Lam and V. O. K. Li, "Chemical-Reaction-Inspired Metaheuristic
for Optimization," IEEE Transactions on Evolutionary Computation,
vol. 14, no. 3, pp. 381-399, June 2010.
[13] J. Xu, A. Y.S. Lam, and V. O.K. Li, "Chemical reaction optimization
for task scheduling in grid computing," IEEE Transactions on Parallel
and Distributed Systems (TPDS), 18 Jan. 2011.
[14] J. Xu, A. Y. S. Lam, and V. O. K. Li, "Chemical reaction optimization for
the grid scheduling problem," in Proc. of IEEE Int-l Conf. on Commun.
(ICC2010), May 2010.
[15] A. Y. S. Lam, J. Xu, and V. O. K. Li, "Chemical reaction optimization
for population transition in peer-to-peer live streaming," in Proc. of IEEE
Congress on Evolutionary Computation, July 2010.
[16] http://people.brunel.ac.uk/ mastjjb/jeb/orlib/portinfo.html