IDEAS home Printed from
   My bibliography  Save this paper

Cardinality versus q-Norm Constraints for Index Tracking


  • Bjöern Fastrich


  • Sandra Paterlini


  • Peter Winker



Index tracking aims at replicating a given benchmark with a smaller number of its constituents. Different quantitative models cam be set up to determine the optimal index replicating portfolio.In this paper, we propose an alternative based on imposing a constraint on the q-norm, 0

Suggested Citation

  • Bjöern Fastrich & Sandra Paterlini & Peter Winker, 2011. "Cardinality versus q-Norm Constraints for Index Tracking," Department of Economics 0642, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
  • Handle: RePEc:mod:depeco:0642

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Brodie, Joshua & Daubechies, Ingrid & De Mol, Christine & Giannone, Domenico, 2007. "Sparse and Stable Markowitz Portfolios," CEPR Discussion Papers 6474, C.E.P.R. Discussion Papers.
    2. Gunter Dueck & Peter Winker, 1992. "New concepts and algorithms for portfolio choice," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 8(3), pages 159-178, September.
    3. Manfred Gilli & Peter Winker, 2008. "Review of Heuristic Optimization Methods in Econometrics," Working Papers 001, COMISEF.
    4. Murat, Marina & Pirotti, Tommaso, 2010. "The attractiveness of countries for FDI. A fuzzy approach," Fuzzy Economic Review, International Association for Fuzzy-set Management and Economy (SIGEF), vol. 0(2), pages 43-61, November.
    5. Beasley, J. E. & Meade, N. & Chang, T. -J., 2003. "An evolutionary heuristic for the index tracking problem," European Journal of Operational Research, Elsevier, vol. 148(3), pages 621-643, August.
    6. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    7. Thiemo Krink & Stefan Mittnik & Sandra Paterlini, 2009. "Differential evolution and combinatorial search for constrained index-tracking," Annals of Operations Research, Springer, vol. 172(1), pages 153-176, November.
    8. Manfred Gilli & Enrico Schumann, 2009. "Optimal enough?," Working Papers 010, COMISEF.
    9. Marina Murat & Barbara Pistoresi, 2009. "Emigrant and immigrant networks in FDI," Applied Economics Letters, Taylor & Francis Journals, vol. 16(12), pages 1261-1264.
    10. Giuseppe Marotta, 1997. "Does trade credit redistribution thwart monetary policy? Evidence from Italy," Applied Economics, Taylor & Francis Journals, vol. 29(12), pages 1619-1629.
    11. Björn Fastrich & Peter Winker, 2012. "Robust portfolio optimization with a hybrid heuristic algorithm," Computational Management Science, Springer, vol. 9(1), pages 63-88, February.
    12. Thiemo Krink & Stefan Mittnik & Sandra Paterlini, 2009. "Differential evolution and combinatorial search for constrained index-tracking," Annals of Operations Research, Springer, vol. 172(1), pages 153-176, November.
    13. Canakgoz, N.A. & Beasley, J.E., 2009. "Mixed-integer programming approaches for index tracking and enhanced indexation," European Journal of Operational Research, Elsevier, vol. 196(1), pages 384-399, July.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    2. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2019. "Sparsity and Stability for Minimum-Variance Portfolios," Papers 1910.11840,
    3. de Paulo, Wanderlei Lima & de Oliveira, Estela Mara & do Valle Costa, Oswaldo Luiz, 2016. "Enhanced index tracking optimal portfolio selection," Finance Research Letters, Elsevier, vol. 16(C), pages 93-102.
    4. Andrea Scozzari & Fabio Tardella & Sandra Paterlini & Thiemo Krink, 2013. "Exact and heuristic approaches for the index tracking problem with UCITS constraints," Annals of Operations Research, Springer, vol. 205(1), pages 235-250, May.
    5. Yu Zheng & Bowei Chen & Timothy M. Hospedales & Yongxin Yang, 2019. "Index Tracking with Cardinality Constraints: A Stochastic Neural Networks Approach," Papers 1911.05052,, revised Nov 2019.
    6. B. Fastrich & S. Paterlini & P. Winker, 2015. "Constructing optimal sparse portfolios using regularization methods," Computational Management Science, Springer, vol. 12(3), pages 417-434, July.
    7. Margherita Giuzio & Sandra Paterlini, 2019. "Un-diversifying during crises: Is it a good idea?," Computational Management Science, Springer, vol. 16(3), pages 401-432, July.
    8. Philipp J. Kremer & Sangkyun Lee & Malgorzata Bogdan & Sandra Paterlini, 2017. "Sparse Portfolio Selection via the sorted $\ell_{1}$-Norm," Papers 1710.02435,
    9. Margherita Giuzio & Kay Eichhorn-Schott & Sandra Paterlini & Vincent Weber, 2018. "Tracking hedge funds returns using sparse clones," Annals of Operations Research, Springer, vol. 266(1), pages 349-371, July.
    10. Yu Zheng & Timothy M. Hospedales & Yongxin Yang, 2018. "Diversity and Sparsity: A New Perspective on Index Tracking," Papers 1809.01989,, revised Feb 2020.
    11. Kremer, Philipp J. & Lee, Sangkyun & Bogdan, Małgorzata & Paterlini, Sandra, 2020. "Sparse portfolio selection via the sorted ℓ1-Norm," Journal of Banking & Finance, Elsevier, vol. 110(C).
    12. Michele Bruni, 2011. "China’s New Demographic Challenge: From Unlimited Supply of Labour to Structural Lack of Labour Supply. Labour market and demographic scenarios: 2008-2048," Department of Economics 0643, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".

    More about this item


    Index tracking; Cardinality constraint; q-Norms; regularization methods; Heuristicalgorithms;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mod:depeco:0642. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sara Colombini). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.