Optimization Letters

, Volume 8, Issue 1, pp 61–80 | Cite as

Index tracking with fixed and variable transaction costs

Original Paper


Index tracking is a form of passive portfolio (fund) management that attempts to mirror the performance of a specific index and generate returns that are equal to those of the index, but without purchasing all of the stocks that make up the index. We present two mixed-integer linear programming formulations of this problem. In particular we explicitly consider both fixed and variable transaction costs. Computational results are presented for data sets drawn from major world markets.


Index tracking Transaction cost 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Angelelli E., Mansini R., Speranza M.G.: Kernel search: a general heuristic for the multi-dimensional knapsack problem. Comput. Oper. Res. 37, 2017–2026 (2010)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Angelelli E., Mansini R., Speranza M.G.: Kernel search: a new heuristic framework for portfolio selection. Comput. Optim. Appl. 51, 345–361 (2012)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Beasley J.E.: OR-Library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41, 1069–1072 (1990)Google Scholar
  4. 4.
    Beasley J.E., Meade N., Chang T.-J.: An evolutionary heuristic for the index tracking problem. Eur. J. Oper. Res. 148, 621–643 (2003)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Canakgoz N.A., Beasley J.E.: Mixed-integer programming approaches for index tracking and enhanced indexation. Eur. J. Oper. Res. 196, 384–399 (2009)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Chen C., Kwon R.H.: Robust portfolio selection for index tracking. Comput. Oper. Res. 39, 829–837 (2012)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    di Tollo, G., Maringer, D.: Metaheuristics for the index tracking problem. In: Geiger, M.J., Habenicht, W., Sevaux, M., Sorensen, K. (eds.) Metaheuristics in the Service Industry, Lecture Notes in Economics and Mathematical Systems, vol. 624, pp. 127–154 (2009)Google Scholar
  8. 8.
    Garcia F., Guijarro F., Moya I.: The curvature of the tracking frontier: a new criterion for the partial index tracking problem. Math. Comput. Modell. 54, 1781–1784 (2011)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Ghandar, A., Michalewicz, Z., Zurbruegg, R., Cheong, C.: Index tracking fund enhancement using evolving multi-criteria fuzzy decision models. In: 2010 IEEE Congress On Evolutionary Computation, pp. 1–8. IEEE, New York (2010)Google Scholar
  10. 10.
    Guastaroba G., Speranza M.G.: Kernel search: an application to the index tracking problem. Eur. J. Oper. Res. 217, 54–68 (2012)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    ILOG Cplex Solver http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/ (last accessed September 29th 2011)
  12. 12.
    Jeurissen, R., van den Berg, J.: Optimized index tracking using a hybrid genetic algorithm. In: 2008 IEEE Congress on Evolutionary Computation, pp. 2327–2334. IEEE, New York (2008)Google Scholar
  13. 13.
    Krink T., Mittnik S., Paterlini S.: Differential evolution and combinatorial search for constrained index-tracking. Ann. Oper. Res. 172, 153–176 (2009)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Li Q., Sun L., Bao L.: Enhanced index tracking based on multi-objective immune algorithm. Expert Syst. Appl. 38, 6101–6106 (2011)CrossRefGoogle Scholar
  15. 15.
    Maringer D.: Constrained index tracking under loss aversion using differential evolution. Stud. Comput. Intell. 100, 7–24 (2008)CrossRefGoogle Scholar
  16. 16.
    Maringer D., Oyewumi O.: Index tracking with constrained portfolios. Intell. Syst. Account. Finance Manag. 15, 57–71 (2007)CrossRefGoogle Scholar
  17. 17.
    Ruiz-Torrubiano R., Suarez A.: A hybrid optimization approach to index tracking. Ann. Oper. Res. 166, 57–71 (2009)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Storn R., Price K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11, 341–359 (1997)CrossRefMATHMathSciNetGoogle Scholar
  19. 19.
    Tabata Y., Takeda E.: Bicriteria optimization problem of designing an index fund. J. Oper. Res. Soc. 46, 1023–1032 (1995)MATHGoogle Scholar
  20. 20.
    van Montfort K., Visser E., van Draat L.F.: Index tracking by means of optimized sampling. J. Portfolio Manag. 34(2), 143–151 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Mathematical SciencesBrunel UniversityUxbridgeUK

Personalised recommendations