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Cardinality versus q-Norm Constraints for Index Tracking

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  • Bjoern Fastrich
  • Sandra Paterlini
  • Peter Winker

Abstract

Index tracking aims at replicating a given benchmark with a smaller number of its constituents. Different quantitative models can 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

  • Bjoern Fastrich & Sandra Paterlini & Peter Winker, 2011. "Cardinality versus q-Norm Constraints for Index Tracking," Center for Economic Research (RECent) 056, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    • Handle: RePEc:mod:recent:056
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    Citations

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    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. Boudt, Kris & Dragun, Kirill & Sauri, Orimar & Vanduffel, Steven, 2023. "ETF Basket-Adjusted Covariance estimation," Journal of Econometrics, Elsevier, vol. 235(2), pages 1144-1171.
    3. Nakagawa, Kei & Suimon, Yoshiyuki, 2022. "Inflation rate tracking portfolio optimization method: Evidence from Japan," Finance Research Letters, Elsevier, vol. 49(C).
    4. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2019. "Sparsity and Stability for Minimum-Variance Portfolios," Papers 1910.11840, arXiv.org.
    5. 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.
    6. 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.
    7. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2022. "Sparsity and stability for minimum-variance portfolios," Risk Management, Palgrave Macmillan, vol. 24(3), pages 214-235, September.
    8. Zhiping Chen & Shen Peng & Abdel Lisser, 2020. "A sparse chance constrained portfolio selection model with multiple constraints," Journal of Global Optimization, Springer, vol. 77(4), pages 825-852, August.
    9. Yen, Yu-Min & Yen, Tso-Jung, 2014. "Solving norm constrained portfolio optimization via coordinate-wise descent algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 737-759.
    10. Yu Zheng & Bowei Chen & Timothy M. Hospedales & Yongxin Yang, 2019. "Index Tracking with Cardinality Constraints: A Stochastic Neural Networks Approach," Papers 1911.05052, arXiv.org, revised Nov 2019.
    11. 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.
    12. 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.
    13. Philipp J. Kremer & Sangkyun Lee & Malgorzata Bogdan & Sandra Paterlini, 2017. "Sparse Portfolio Selection via the sorted $\ell_{1}$-Norm," Papers 1710.02435, arXiv.org.
    14. Anubha Goel & Damir Filipovi'c & Puneet Pasricha, 2024. "Sparse Portfolio Selection via Topological Data Analysis based Clustering," Papers 2401.16920, arXiv.org, revised Dec 2024.
    15. Giuzio, Margherita & Ferrari, Davide & Paterlini, Sandra, 2016. "Sparse and robust normal and t- portfolios by penalized Lq-likelihood minimization," European Journal of Operational Research, Elsevier, vol. 250(1), pages 251-261.
    16. 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.
    17. Yu Zheng & Timothy M. Hospedales & Yongxin Yang, 2018. "Diversity and Sparsity: A New Perspective on Index Tracking," Papers 1809.01989, arXiv.org, revised Feb 2020.
    18. Julio Cezar Soares Silva & Adiel Teixeira de Almeida Filho, 2023. "A systematic literature review on solution approaches for the index tracking problem in the last decade," Papers 2306.01660, arXiv.org, revised Jun 2023.
    19. 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).
    20. 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".

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    More about this item

    Keywords

    index tracking; cardinality constraint; q-norm; regularization methods; heuristic algorithms;
    All these keywords.

    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

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