Article Contents
Article Contents

# Portfolio optimization and risk measurement based on non-dominated sorting genetic algorithm

• This paper introduces a multi-objective genetic algorithm (MOGA) in regard to the portfolio optimization issue in different risk measures, such as mean-variance, semi-variance, mean-variance-skewness, mean-absolute-deviation and lower-partial-moment to optimize risk of portfolio. This study introduces a PONSGA model by appling the non-dominated sorting genetic algorithm (NSGA-II) to maximize both the expected return and the skewness of portfolio as well as to simultaneously minimize different portfolio risks. The experimental results demonstrated that the PONSGA approach is significantly superior to the GA in all performances, examined such as the coefficient of variation, Sharpe index, Sortino index and portfolio performance index. The statistical significance tests also showed that the NSGA-II models outperformed the GA models in different risk measures.
Mathematics Subject Classification: Portfolio, risk measurement, multi-objective genetic algorithm, NSGA-II, GA.

 Citation:

•  [1] H. A. Abbass, S. Alam and A. Bender, MEBRA: Multiobjective evolutionary-based risk assessment, IEEE Computational Intelligence Magazine, 4 (2009), 29-36. [2] F. B. Abdelaziz, B. Aouni and R. E. Fayedh, Multi-objective stochastic programming for portfolio selection, European Journal of Operational Research, 177 (2007), 1811-1823.doi: 10.1016/j.ejor.2005.10.021. [3] E. E. Ammar, On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem, Information Sciences, 178 (2008), 468-484.doi: 10.1016/j.ins.2007.03.029. [4] V. S. Bawa and E. B. Lingenberg, Capital market equilibrium in a mean-lower partial moment framework, Journal of Financial Economics, 5 (1977), 189-200. [5] T. J. Chang, S. C. Yang and K. J. Chang, Portfolio optimization problems in different risk measures using genetic algorithm, Expert Systems with Applications, 36 (2009), 10529-10537.doi: 10.1016/j.eswa.2009.02.062. [6] P. Chunhachinda, K. Dandapani, S. Hamid and A. J. Prakash, Portfolio selection and skewness: Evidence from international stock markets, Journal of Banking & Finance, 21 (1997), 143-167.doi: 10.1016/S0378-4266(96)00032-5. [7] M. Corazza and D. Favaretto, On the existence of solutions to the quadratic mixed-integer mean-variance portfolio selection problem, European Journal of Operational Research, 176 (2007), 1947-1960.doi: 10.1016/j.ejor.2005.10.053. [8] X. Cui, X. Sun and D. Sha, An empirical study on discrete optimization models for portfolio selection, Journal of Industrial and Management Optimization, 5 (2009), 33-46. [9] K. Deb, "Multi-Objective Optimization using Evolutionary Algorithms," With a foreword by David E. Goldberg, Wiley-Interscience Series in Systems and Optimization, John Wiley & Sons, Ltd., Chichester, 2001. [10] K. Deb, A. Pratap, S. Agarwal and T. Meyarivan, A fast and elitist multiobjective genetic algorithm: NSGA-II, IEEE Transaction on Evolutionary Computation, 6 (2002), 182-197. [11] P. C. Fishburn, Mean-risk analysis with risk associated with below-target returns, The American Economic Review, 67 (1977), 116-126. [12] T. H. Goodwin, The information ratio, Financial Analysts Journal, 54 (1998), 34-43.doi: 10.2469/faj.v54.n4.2196. [13] B. Graham, "The Intelligent Investor: A Book of Practical Counsel," Harper & Row Publishers, 1986. [14] P. C. Ko and P. C. Lin, Resource allocation neural network in portfolio selection, Expert Systems With Applications, 35 (2008), 330-337.doi: 10.1016/j.eswa.2007.07.031. [15] A. Konak, D. W. Coit and A. E. Smith, Multi-objective optimization using genetic algorithms: A tutorial, Reliability Engineering and System Safety, 91 (2006), 992-1007.doi: 10.1016/j.ress.2005.11.018. [16] H. Konno and H. Yamazaki, Mean-absolute deviation portfolio optimization model and its application to the Tokyo stock market, Management Science, 37 (1990), 519-531.doi: 10.1287/mnsc.37.5.519. [17] M. T. Leung, H. Daouk and A. S. Chen, Theory and Methodology using investment portfolio return to combine forecasts: A multiobjective approach, European Journal of Operational Research, 134 (2001), 84-102.doi: 10.1016/S0377-2217(00)00241-1. [18] P. C. Lin and P. C. Ko, Portfolio value-at-risk forecasting with GA-based extreme value theory, Expert Systems with Applications, 36 (2009), 2503-2512.doi: 10.1016/j.eswa.2008.01.086. [19] C. Marchdo-Santos and A. C. Fernandes, Skewness in financial returns: Evidence from the Portuguese stock market, Journal of Economics and Finance, 55 (2005), 460-470. [20] H. Markowitz, Portfolio selection, Journal of Finance, 7 (1952), 77-91. [21] H. Markowitz, "Portfolio Selection: Efficient Diversification of Investments," Cowles Foundation for Research in Economics at Yale University, Monograph 16, John Wiley & Sons, Inc., New York, Chapman & Hall, Ltd., London, 1959. [22] 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, 30 (2006), 527-534.doi: 10.1016/j.eswa.2005.10.010. [23] P. Samuelson, The fundamental approximation theorem of portfolio analysis in terms of means variances and higher moments, Review of Economic Studies, 37 (1970), 537-542.doi: 10.2307/2296483. [24] F. A. Sortino and R. Meer, Downside risk, The Journal of Portfolio Management, 17 (1991), 27-31.doi: 10.3905/jpm.1991.409343. [25] M. Stutzer, A portfolio performance index, Financial Analysts Journal, 56 (2000), 52-61.doi: 10.2469/faj.v56.n3.2360. [26] Q. Sun and Y. Yan, Skewness persistence with optimal portfolio selection, Journal of Banking & Finance, 27 (2003), 1111-1121.doi: 10.1016/S0378-4266(02)00247-9. [27] N. Topaloglou, H. Vladimirou and S. A. Zenios, A dynamic stochastic programming model for international portfolio management, European Journal of Operational Research, 185 (2008), 1501-1524.doi: 10.1016/j.ejor.2005.07.035. [28] T. Wilding, Using genetic algorithms to construct portfolios, in "Advances in Portfolio Construction and Implementation," Butterworth-Heinemann, (2003), 135-160. [29] Y. Xia, B. Liu, S. Wang and K. K. Lai, A model for portfolio selection with order of expected returns, Computers and Operations Research, 27 (2000), 409-422.doi: 10.1016/S0305-0548(99)00059-3.