Um Algoritmo Genético para Seleção de Portfólio de Investimentos com Restrições de Cardinalidade e Lotes-Padrão
Resumo
O modelo quadrático de Markowitz desempenhou um papel fundamental no problema da seleção de portfólio de investimentos, contudo, já não atende às necessidades da complexidade do mercado atual. A adição de restrições que aproximam o modelo à situação real enfrentada pelos investidores, tornam o problema NP-Completo. Assim, este artigo apresenta um Algoritmo Genético que busca maximizar o retorno de um investimento, dado um patamar aceitável de risco. Após a otimização do portfólio com base em dados históricos, faz-se uma previsão para o ano posterior. Os resultados superam a performance do íIndice Bovespa, destacando os efeitos da diversificação de acordo com o número de ativos e com o capital disponível para investimento.
Referências
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Bird, R. e Tippett, M. (1986). Näve diversication and portfolio risk: A note. Management Science.
Bovespa (2012). Índice bovespa. http://www.bmfbovespa.com.br.
Chang, T.-J., Meade, N., Beasley, J. E., e Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers and Operations Research, 27:1271– 1302.
Coley, D. A. (1999). Introduction to Genetic Algorithms for Scientists and Engineers. World Scientic.
Corazza, M. e Favaretto, D. (2007). On the existence of solutions to the quadratic mixedinteger mean-variance portfolio selection problem. European Journal of Operational Research, 176:1947–1960.
Cura, T. (2009). Particle swarm optimization approach to portfolio optimization. Nonlinear Analysis: Real World Applications, 10:2396–2406.
Derigs, U. e Nickel, N.-H. (2003). Meta-heuristic based decision support for portfolio optimisation with a case study on tracking error minimization in passive portfolio management. OR Spectrum, 25:345–378.
Evans, J. L. e Archer, S. H. (1968). Diversication and the reduction of dispersion: An empirical analysis. Journal of nance, pp 761–767.
Freitas, E. T. e Ribeiro, C. O. (2009). Abordagem robusta ao problema de seleção de portfólio. Simpósio Brasileiro de Pesquisa Operacional.
Gen, M. e Cheng, R. (1997). Genetic Algorithms and Engineering Design. New York: Wiley.
Holland, J. H. (1975). Adaptation in Natural and Articial Systems: An Introductory Analysis With Applications to Biology, Control, and Articial Intelligence. SpringerVerlag.
Junior, M. P. L., de Almeida, M. R., e Ferreira, R. J. P. (2011). Seleção de portfólios por meio de busca tabú híbrida: Modelo de média variância em lotes. Simpósio Brasileiro de Pesquisa Operacional.
Kellerer, H., Mansini, R., e Speranza, M. G. (1999). Selecting portfolios with xed costs and minimum transaction lots. Annals of Operations Research, 99:877–304.
Konno, H. e Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its application to tokyo stock market. Management Science, 37(3):519–531.
Li, D., Sun, X., e Wang, J. (2006). Optimal lot solution to cardinality constrained meanvariance formulation for portfolio selection. Mathematical Finance, 16:83–101.
Lin, C. C. e Liu, T. Y. (2007). Genetic algorithms for portfolio selection problems with minimum transaction lots. European Journal of Operational Research. O.R. Applications.
Maringer, D. (2005). Portfolio management with heuristic optimization. Springer, The Netherlands. New York: Wiley.
Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1):77–91.
Markowitz, H. M. (1959). Portfolio selection: Efcient diversication of investments.
Markowitz, H. M., Todd, P., Xu, G., e Yamane, Y. (1993). Computation of meansemivariance efcient sets by the critical line algorithm. Annals of Operations Research, 45:307–317.
Pham, D. T. e Karaboga, D. (2000). Intelligent Optimisation Techniques: Genetic Algorithms, Tabu Search, Simulated Annealing and Neural Networks. Springer.
Radcliffe, N. J. (1991). Forma analysis and random respectful recombination. Fourth International Conference on Genetic Algorithms, pp 222–229.
Raposo, R. C. T. (2010). Seleção de portfólios por meio de busca tabú híbrida: Modelo de média variância em lotes. Workshop de Inteligência Computacional Aplicada.
Sharpe, W. F. (1963). A simplied model for portfolio analysis. Management Science, pp 277–293.
Shaw, D. X., Liu, S., e Kopman, L. (2008). Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optimization Methods and Software, 23:411–420.
Torre, N. G. e Rudd, A. (2004). The portfolio management problem of individual investors: A quantitative perspective. Institutional Investor’s Guide to Integrated Wealth Management.
Bird, R. e Tippett, M. (1986). Näve diversication and portfolio risk: A note. Management Science.
Bovespa (2012). Índice bovespa. http://www.bmfbovespa.com.br.
Chang, T.-J., Meade, N., Beasley, J. E., e Sharaiha, Y. M. (2000). Heuristics for cardinality constrained portfolio optimisation. Computers and Operations Research, 27:1271– 1302.
Coley, D. A. (1999). Introduction to Genetic Algorithms for Scientists and Engineers. World Scientic.
Corazza, M. e Favaretto, D. (2007). On the existence of solutions to the quadratic mixedinteger mean-variance portfolio selection problem. European Journal of Operational Research, 176:1947–1960.
Cura, T. (2009). Particle swarm optimization approach to portfolio optimization. Nonlinear Analysis: Real World Applications, 10:2396–2406.
Derigs, U. e Nickel, N.-H. (2003). Meta-heuristic based decision support for portfolio optimisation with a case study on tracking error minimization in passive portfolio management. OR Spectrum, 25:345–378.
Evans, J. L. e Archer, S. H. (1968). Diversication and the reduction of dispersion: An empirical analysis. Journal of nance, pp 761–767.
Freitas, E. T. e Ribeiro, C. O. (2009). Abordagem robusta ao problema de seleção de portfólio. Simpósio Brasileiro de Pesquisa Operacional.
Gen, M. e Cheng, R. (1997). Genetic Algorithms and Engineering Design. New York: Wiley.
Holland, J. H. (1975). Adaptation in Natural and Articial Systems: An Introductory Analysis With Applications to Biology, Control, and Articial Intelligence. SpringerVerlag.
Junior, M. P. L., de Almeida, M. R., e Ferreira, R. J. P. (2011). Seleção de portfólios por meio de busca tabú híbrida: Modelo de média variância em lotes. Simpósio Brasileiro de Pesquisa Operacional.
Kellerer, H., Mansini, R., e Speranza, M. G. (1999). Selecting portfolios with xed costs and minimum transaction lots. Annals of Operations Research, 99:877–304.
Konno, H. e Yamazaki, H. (1991). Mean-absolute deviation portfolio optimization model and its application to tokyo stock market. Management Science, 37(3):519–531.
Li, D., Sun, X., e Wang, J. (2006). Optimal lot solution to cardinality constrained meanvariance formulation for portfolio selection. Mathematical Finance, 16:83–101.
Lin, C. C. e Liu, T. Y. (2007). Genetic algorithms for portfolio selection problems with minimum transaction lots. European Journal of Operational Research. O.R. Applications.
Maringer, D. (2005). Portfolio management with heuristic optimization. Springer, The Netherlands. New York: Wiley.
Markowitz, H. M. (1952). Portfolio selection. Journal of Finance, 7(1):77–91.
Markowitz, H. M. (1959). Portfolio selection: Efcient diversication of investments.
Markowitz, H. M., Todd, P., Xu, G., e Yamane, Y. (1993). Computation of meansemivariance efcient sets by the critical line algorithm. Annals of Operations Research, 45:307–317.
Pham, D. T. e Karaboga, D. (2000). Intelligent Optimisation Techniques: Genetic Algorithms, Tabu Search, Simulated Annealing and Neural Networks. Springer.
Radcliffe, N. J. (1991). Forma analysis and random respectful recombination. Fourth International Conference on Genetic Algorithms, pp 222–229.
Raposo, R. C. T. (2010). Seleção de portfólios por meio de busca tabú híbrida: Modelo de média variância em lotes. Workshop de Inteligência Computacional Aplicada.
Sharpe, W. F. (1963). A simplied model for portfolio analysis. Management Science, pp 277–293.
Shaw, D. X., Liu, S., e Kopman, L. (2008). Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optimization Methods and Software, 23:411–420.
Torre, N. G. e Rudd, A. (2004). The portfolio management problem of individual investors: A quantitative perspective. Institutional Investor’s Guide to Integrated Wealth Management.
Publicado
22/05/2013
Como Citar
TOURINHO, Renan Fortes; OLIVEIRA, Antônio Costa de; VERAS, Rodrigo de Melo Souza.
Um Algoritmo Genético para Seleção de Portfólio de Investimentos com Restrições de Cardinalidade e Lotes-Padrão. In: SIMPÓSIO BRASILEIRO DE SISTEMAS DE INFORMAÇÃO (SBSI), 9. , 2013, João Pessoa.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2013
.
p. 541-552.
DOI: https://doi.org/10.5753/sbsi.2013.5720.
