Skip to main content
SpringerLink
Log in

A hybrid algorithm for constrained portfolio selection problems

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Since Markowitz’s seminal work on the mean-variance model in modern portfolio theory, many studies have been conducted on computational techniques and recently meta-heuristics for portfolio selection problems. In this work, we propose and investigate a new hybrid algorithm integrating the population based incremental learning and differential evolution algorithms for the portfolio selection problem. We consider the extended mean-variance model with practical trading constraints including the cardinality, floor and ceiling constraints. The proposed hybrid algorithm adopts a partially guided mutation and an elitist strategy to promote the quality of solution. The performance of the proposed hybrid algorithm has been evaluated on the extended benchmark datasets in the OR Library. The computational results demonstrate that the proposed hybrid algorithm is not only effective but also efficient in solving the mean-variance model with real world constraints.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Notes

  1. For an analytic derivation of the efficient frontier, see [35].

  2. In some literature, it is also known as quantity constraints or buy-in threshold constraints.

References

  1. Anagnostopoulos K, Mamanis G (2011) The mean-variance cardinality constrained portfolio optimization problem: an experimental evaluation of five multiobjective evolutionary algorithms. Expert Syst Appl 38(11):14. 208–14, 217

    Google Scholar 

  2. Arriaga J, Valenzuela-Rendón M (2012) Steepest ascent hill climbing for portfolio selection. In: Applications of evolutionary computation. Lecture notes in computer science, vol 7248. Springer, Berlin, pp 145–154. doi:10.1007/978-3-642-29178-4_15

    Chapter  Google Scholar 

  3. Baluja S (1994) Population-based incremental learning. Tech Rep CMU-CS-94-163, Carnegie Mellon University, Pittsburgh, Pa

  4. Baluja S, Caruana R (1995) Removing the genetics from the standard genetic algorithm. In: Machine learning: proceedings of the twelfth international conference on machine learning, Tahoe City, California, July 9–12, 1995. Morgan Kaufmann, San Mateo, pp 38–46

    Google Scholar 

  5. Beasley J (1990) Or-library: distributing test problems by electronic mail. J Oper Res Soc 41(11):1069–1072

    Google Scholar 

  6. Beasley JE (1999) Or library dataset. Available from: http://people.brunel.ac.uk/~mastjjb/jeb/orlib/portinfo.html, [Online; accessed 02-Oct-2011]

  7. Bertsimas D, Shioda R (2009) Algorithm for cardinality-constrained quadratic optimization. Comput Optim Appl 43(1):1–22

    Article  MathSciNet  MATH  Google Scholar 

  8. Best M, Hlouskova J (2000) The efficient frontier for bounded assets. Math Methods Oper Res 52(2):195–212

    Article  MathSciNet  MATH  Google Scholar 

  9. Bienstock D (1996) Computational study of a family of mixed-integer quadratic programming problems. Math Program 74(2):121–140

    Article  MathSciNet  MATH  Google Scholar 

  10. Busetti F (2005) Metaheuristic approaches to realistic portfolio optimization. Master’s thesis, University of South Aferica. http://arxiv.org/ftp/cond-mat/papers/0501/0501057.pdf

  11. Chang T, Meade N, Beasley J, Sharaiha Y (2000) Heuristics for cardinality constrained portfolio optimisation. Comput Oper Res 27(13):1271–1302

    Article  MATH  Google Scholar 

  12. Crama Y, Schyns M (2003) Simulated annealing for complex portfolio selection problems. Eur J Oper Res 150(3):546–571

    Article  MATH  Google Scholar 

  13. Cura T (2009) Particle swarm optimization approach to portfolio optimization. Nonlinear Anal, Real World Appl 10(4):2396–2406

    Article  MathSciNet  MATH  Google Scholar 

  14. Das S, Suganthan P (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31. doi:10.1109/TEVC.2010.2059031

    Article  Google Scholar 

  15. Di Tollo G, Roli A (2006) Metaheuristics for the portfolio selection problem. Technical Report R-2006-005, Dipartimento di Scienze, Universita Chieti–Pescara 200

  16. Ehrgott M, Klamroth K, Schwehm C (2004) An mcdm approach to portfolio optimization. Eur J Oper Res 155(3):752–770

    Article  MathSciNet  MATH  Google Scholar 

  17. Ellison EDF, Hajian M, Levkovitz R, Maros I, Mitra G (1999) A Fortran based mathematical programming system. FortMP. Brunel University, UK and NAG Ltd., Oxford, UK

  18. Feoktistov V (2006) Differential evolution: in search of solutions, vol 5. Springer, New York

    MATH  Google Scholar 

  19. Fernández A, Gómez S (2007) Portfolio selection using neural networks. Comput Oper Res 34(4):1177–1191

    Article  MATH  Google Scholar 

  20. Folly K, Venayagamoorthy G (2009) Effects of learning rate on the performance of the population based incremental learning algorithm. In: IEEE international joint conference on neural networks 2009, pp 861–868

    Chapter  Google Scholar 

  21. Fonseca C, Fleming P (1995) An overview of evolutionary algorithms in multiobjective optimization. Evol Comput 3(1):1–16

    Article  Google Scholar 

  22. Gaspero L, Tollo G, Roli A, Schaerf A (2011) Hybrid metaheuristics for constrained portfolio selection problems. Quant Finance 11(10):1473–1487

    Article  MathSciNet  MATH  Google Scholar 

  23. Glover F, Laguna M (1998) Tabu search, vol 1. Springer, Berlin

    Google Scholar 

  24. Golmakani H, Fazel M (2011) Constrained portfolio selection using particle swarm optimization. Expert Syst Appl 38(7):8327–8335

    Article  Google Scholar 

  25. Gosling JN T, Tsang E (2004) Population-based incremental learning versus genetic algorithms: iterated prisoners dilemma. Tech Rep CSM-401, University of Essex, England. http://dces.essex.ac.uk/research/CSP/finance/papers/GoJiTs-Pbil_vs_GA-csm401_2004.pdf

  26. Jobst N, Horniman M, Lucas C, Mitra G (2001) Computational aspects of alternative portfolio selection models in the presence of discrete asset choice constraints. Quant Finance 1:1–13

    Article  MathSciNet  Google Scholar 

  27. Krink T, Paterlini S (2008) Differential evolution for multiobjective portfolio optimization. Center for Economic Research (RECent) 21. See http://ideas.repec.org/p/mod/wcefin/08012.html

  28. Krink T, Paterlini S (2011) Multiobjective optimization using differential evolution for real-world portfolio optimization. Comput Manag Sci 8(1–2):157–179

    Article  MathSciNet  Google Scholar 

  29. Li D, Sun X, Wang J (2006) Optimal lot solution to cardinality constrained mean–variance formulation for portfolio selection. Math Finance 16(1):83–101

    Article  MathSciNet  MATH  Google Scholar 

  30. Maringer D (2005) Portfolio management with heuristic optimization, vol 8. Springer, Berlin

    MATH  Google Scholar 

  31. Maringer D (2008) Risk preferences and loss aversion in portfolio optimization. In: Computational methods in financial engineering, pp 27–45

  32. Markowitz H (1952) Portfolio selection. J Finance 7(1):77–91

    Google Scholar 

  33. Markowitz H (1956) The optimization of a quadratic function subject to linear constraints. Nav Res Logist Q 3(1–2):111–133

    Article  MathSciNet  Google Scholar 

  34. Markowitz H, Todd G, Sharpe W (2000) Mean-variance analysis in portfolio choice and capital markets, vol 66. Wiley, New York

    Google Scholar 

  35. Merton R (1972) An analytic derivation of the efficient portfolio frontier. J Financ Quant Anal 7(4):1851–1872

    Article  Google Scholar 

  36. Moral-Escudero R, Ruiz-Torrubiano R, Suarez A (2006) Selection of optimal investment portfolios with cardinality constraints. In: Evolutionary computation. IEEE congress on CEC 2006, pp 2382–2388

    Google Scholar 

  37. Pang J (1980) A new and efficient algorithm for a class of portfolio selection problems. Oper Res 28(3):754–767

    Article  MathSciNet  MATH  Google Scholar 

  38. Perold A (1984) Large-scale portfolio optimization. Manag Sci 30(10):1143–1160

    Article  MathSciNet  MATH  Google Scholar 

  39. Schaerf A (2002) Local search techniques for constrained portfolio selection problems. Comput Econ 20(3):177–190

    Article  MATH  Google Scholar 

  40. Schyns M, Crama P (2001) Modelling financial data and portfolio optimization problems. PhD thesis, Doctoral Thesis, University of Liège. http://orbi.ulg.ac.be/bitstream/2268/11831/1/MSthese.pdf

  41. Sebag M, Ducoulombier A (1998) Extending population-based incremental learning to continuous search spaces. In: Parallel problem solving from nature----PPSN V. Berlin, Germany, pp 418–427

    Chapter  Google Scholar 

  42. Shapiro J (2003) The sensitivity of pbil to its learning rate and how detailed balance can remove it. In: Foundations of genetic algorithms, vol 7, pp 115–132

    Google Scholar 

  43. Shaw D, Liu S, Kopman L (2008) Lagrangian relaxation procedure for cardinality-constrained portfolio optimization. Optim Methods Softw 23(3):411–420

    Article  MathSciNet  MATH  Google Scholar 

  44. Skolpadungket P, Dahal K, Harnpornchai N (2007) Portfolio optimization using multi-objective genetic algorithms. In: Evolutionary computation. IEEE congress on CEC 2007, pp 516–523

    Google Scholar 

  45. Soleimani H, Golmakani H, Salimi M (2009) Markowitz-based portfolio selection with minimum transaction lots, cardinality constraints and regarding sector capitalization using genetic algorithm. Expert Syst Appl 36(3):5058–5063

    Article  Google Scholar 

  46. Storn R, Price K (1995) Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. Tech Rep TR-95-012, Berkeley, CA. See http://www.icsi.berkeley.edu/ftp/global/global/pub/techreports/1995/tr-95-012.pdf

  47. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    Article  MathSciNet  MATH  Google Scholar 

  48. Streichert F, Ulmer H, Zell A (2003) Evolutionary algorithms and the cardinality constrained portfolio optimization problem. In: Operations research proceedings 2003, Selected papers of the international conference on operations research (OR 2003). Springer, Berlin, pp 3–5

    Google Scholar 

  49. Streichert F, Ulmer H, Zell A (2004) Evaluating a hybrid encoding and three crossover operators on the constrained portfolio selection problem. In: Congress on evolutionary computation, CEC2004, vol 1, pp 932–939

    Google Scholar 

  50. Sun J, Zhang Q, Tsang E (2005) De/eda: a new evolutionary algorithm for global optimization. Inf Sci 169(3):249–262

    Article  MathSciNet  Google Scholar 

  51. Vafashoar R, Meybodi MR, Momeni Âzandaryani AH (2012) Cla-de: a hybrid model based on cellular learning automata for numerical optimization. Appl Intell 36:735–748. doi:10.1007/s10489-011-0292-1

    Article  Google Scholar 

  52. Varian H (1993) A portfolio of Nobel laureates: Markowitz, Miller and Sharpe. J Econ Perspect 7(1):159–169

    Article  Google Scholar 

  53. Vesterstrom J, Thomsen R (2004) A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In: Congress on evolutionary computation, CEC2004, vol 2, pp 1980–1987

    Google Scholar 

  54. Vielma J, Ahmed S, Nemhauser G (2007) A lifted linear programming branch-and-bound algorithm for mixed integer conic quadratic programs. Manuscript, Georgia Institute of Technology

  55. Winker P, Lyra M, Sharpe C (2011) Least median of squares estimation by optimization heuristics with an application to the capm and a multi-factor model. Comput Manag Sci 8(1):103–123

    Article  MathSciNet  Google Scholar 

  56. Woodside-Oriakhi M, Lucas C, Beasley J (2011) Heuristic algorithms for the cardinality constrained efficient frontier. Eur J Oper Res 213(3):538–550

    Article  MathSciNet  MATH  Google Scholar 

  57. Xu F, Chen W, Yang L (2007) Improved particle swarm optimization for realistic portfolio selection. In: Software engineering, artificial intelligence, networking, and parallel/distributed computing. Eighth ACIS international conference on SNPD 2007, vol 1, pp 185–190

    Chapter  Google Scholar 

  58. Xu R, Zhang J, Liu O, Huang R (2010) An estimation of distribution algorithm based portfolio selection approach. In: 2010 International conference on technologies and applications of artificial intelligence. IEEE, New York, pp 305–313

    Chapter  Google Scholar 

  59. Zhang Q, Sun J, Tsang E (2005) An evolutionary algorithm with guided mutation for the maximum clique problem. IEEE Trans Evol Comput 9(2):192–200

    Article  Google Scholar 

Download references

Acknowledgements

This research was support by the School of Computer Science, The University of Nottingham.

Author information

Authors and Affiliations

  1. Automated Scheduling, Optimization and Planning Group, School of Computer Science, University of Nottingham, Nottingham, NG8 1BB, UK

    Khin Lwin & Rong Qu

Authors
  1. Khin Lwin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rong Qu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Khin Lwin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lwin, K., Qu, R. A hybrid algorithm for constrained portfolio selection problems. Appl Intell 39, 251–266 (2013). https://doi.org/10.1007/s10489-012-0411-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-012-0411-7

Keywords

Search

Navigation