July  2012, 8(3): 549-564. doi: 10.3934/jimo.2012.8.549

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

1. 

National Kaohsiung University of Applied Sciences, Institute of Finance and Information, No. 415, Jiangung Rd., Sanmin Chiu, Kaohsiung, 807, Taiwan

Received  May 2011 Revised  November 2011 Published  June 2012

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.
Citation: Ping-Chen Lin. Portfolio optimization and risk measurement based on non-dominated sorting genetic algorithm. Journal of Industrial & Management Optimization, 2012, 8 (3) : 549-564. doi: 10.3934/jimo.2012.8.549
References:
[1]

H. A. Abbass, S. Alam and A. Bender, MEBRA: Multiobjective evolutionary-based risk assessment,, IEEE Computational Intelligence Magazine, 4 (2009), 29.   Google Scholar

[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.  doi: 10.1016/j.ejor.2005.10.021.  Google Scholar

[3]

E. E. Ammar, On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem,, Information Sciences, 178 (2008), 468.  doi: 10.1016/j.ins.2007.03.029.  Google Scholar

[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.   Google Scholar

[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.  doi: 10.1016/j.eswa.2009.02.062.  Google Scholar

[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.  doi: 10.1016/S0378-4266(96)00032-5.  Google Scholar

[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.  doi: 10.1016/j.ejor.2005.10.053.  Google Scholar

[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.   Google Scholar

[9]

K. Deb, "Multi-Objective Optimization using Evolutionary Algorithms,", With a foreword by David E. Goldberg, (2001).   Google Scholar

[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.   Google Scholar

[11]

P. C. Fishburn, Mean-risk analysis with risk associated with below-target returns,, The American Economic Review, 67 (1977), 116.   Google Scholar

[12]

T. H. Goodwin, The information ratio,, Financial Analysts Journal, 54 (1998), 34.  doi: 10.2469/faj.v54.n4.2196.  Google Scholar

[13]

B. Graham, "The Intelligent Investor: A Book of Practical Counsel,", Harper & Row Publishers, (1986).   Google Scholar

[14]

P. C. Ko and P. C. Lin, Resource allocation neural network in portfolio selection,, Expert Systems With Applications, 35 (2008), 330.  doi: 10.1016/j.eswa.2007.07.031.  Google Scholar

[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.  doi: 10.1016/j.ress.2005.11.018.  Google Scholar

[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.  doi: 10.1287/mnsc.37.5.519.  Google Scholar

[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.  doi: 10.1016/S0377-2217(00)00241-1.  Google Scholar

[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.  doi: 10.1016/j.eswa.2008.01.086.  Google Scholar

[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.   Google Scholar

[20]

H. Markowitz, Portfolio selection,, Journal of Finance, 7 (1952), 77.   Google Scholar

[21]

H. Markowitz, "Portfolio Selection: Efficient Diversification of Investments,", Cowles Foundation for Research in Economics at Yale University, (1959).   Google Scholar

[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.  doi: 10.1016/j.eswa.2005.10.010.  Google Scholar

[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.  doi: 10.2307/2296483.  Google Scholar

[24]

F. A. Sortino and R. Meer, Downside risk,, The Journal of Portfolio Management, 17 (1991), 27.  doi: 10.3905/jpm.1991.409343.  Google Scholar

[25]

M. Stutzer, A portfolio performance index,, Financial Analysts Journal, 56 (2000), 52.  doi: 10.2469/faj.v56.n3.2360.  Google Scholar

[26]

Q. Sun and Y. Yan, Skewness persistence with optimal portfolio selection,, Journal of Banking & Finance, 27 (2003), 1111.  doi: 10.1016/S0378-4266(02)00247-9.  Google Scholar

[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.  doi: 10.1016/j.ejor.2005.07.035.  Google Scholar

[28]

T. Wilding, Using genetic algorithms to construct portfolios,, in, (2003), 135.   Google Scholar

[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.  doi: 10.1016/S0305-0548(99)00059-3.  Google Scholar

show all references

References:
[1]

H. A. Abbass, S. Alam and A. Bender, MEBRA: Multiobjective evolutionary-based risk assessment,, IEEE Computational Intelligence Magazine, 4 (2009), 29.   Google Scholar

[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.  doi: 10.1016/j.ejor.2005.10.021.  Google Scholar

[3]

E. E. Ammar, On solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem,, Information Sciences, 178 (2008), 468.  doi: 10.1016/j.ins.2007.03.029.  Google Scholar

[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.   Google Scholar

[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.  doi: 10.1016/j.eswa.2009.02.062.  Google Scholar

[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.  doi: 10.1016/S0378-4266(96)00032-5.  Google Scholar

[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.  doi: 10.1016/j.ejor.2005.10.053.  Google Scholar

[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.   Google Scholar

[9]

K. Deb, "Multi-Objective Optimization using Evolutionary Algorithms,", With a foreword by David E. Goldberg, (2001).   Google Scholar

[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.   Google Scholar

[11]

P. C. Fishburn, Mean-risk analysis with risk associated with below-target returns,, The American Economic Review, 67 (1977), 116.   Google Scholar

[12]

T. H. Goodwin, The information ratio,, Financial Analysts Journal, 54 (1998), 34.  doi: 10.2469/faj.v54.n4.2196.  Google Scholar

[13]

B. Graham, "The Intelligent Investor: A Book of Practical Counsel,", Harper & Row Publishers, (1986).   Google Scholar

[14]

P. C. Ko and P. C. Lin, Resource allocation neural network in portfolio selection,, Expert Systems With Applications, 35 (2008), 330.  doi: 10.1016/j.eswa.2007.07.031.  Google Scholar

[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.  doi: 10.1016/j.ress.2005.11.018.  Google Scholar

[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.  doi: 10.1287/mnsc.37.5.519.  Google Scholar

[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.  doi: 10.1016/S0377-2217(00)00241-1.  Google Scholar

[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.  doi: 10.1016/j.eswa.2008.01.086.  Google Scholar

[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.   Google Scholar

[20]

H. Markowitz, Portfolio selection,, Journal of Finance, 7 (1952), 77.   Google Scholar

[21]

H. Markowitz, "Portfolio Selection: Efficient Diversification of Investments,", Cowles Foundation for Research in Economics at Yale University, (1959).   Google Scholar

[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.  doi: 10.1016/j.eswa.2005.10.010.  Google Scholar

[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.  doi: 10.2307/2296483.  Google Scholar

[24]

F. A. Sortino and R. Meer, Downside risk,, The Journal of Portfolio Management, 17 (1991), 27.  doi: 10.3905/jpm.1991.409343.  Google Scholar

[25]

M. Stutzer, A portfolio performance index,, Financial Analysts Journal, 56 (2000), 52.  doi: 10.2469/faj.v56.n3.2360.  Google Scholar

[26]

Q. Sun and Y. Yan, Skewness persistence with optimal portfolio selection,, Journal of Banking & Finance, 27 (2003), 1111.  doi: 10.1016/S0378-4266(02)00247-9.  Google Scholar

[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.  doi: 10.1016/j.ejor.2005.07.035.  Google Scholar

[28]

T. Wilding, Using genetic algorithms to construct portfolios,, in, (2003), 135.   Google Scholar

[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.  doi: 10.1016/S0305-0548(99)00059-3.  Google Scholar

2018 Impact Factor: 1.025

Metrics

  • PDF downloads (13)
  • HTML views (0)
  • Cited by (7)

Other articles
by authors

[Back to Top]