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Exact and Heuristic Approaches for the Index Tracking Problem with UCITS Constraints


Author Info

  • Andrea Scozzari


  • Fabio Tardella


  • Sandra Paterlini


  • Thiemo Krink



Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions in few assets, as required by the European Union Directive UCITS (Undertaking for Collective Investments in Transferable Securities) rules. The UCITS rules make the problem hard to be satisfactorily modeled and solved to optimality: no exact methods but only heuristics have been proposed so far. The aim of this paper is twofold. First, we present the first Mixed Integer Quadratic Programming (MIQP) formulation for the constrained index tracking problem with the UCITS rules compliance. This allows us to obtain exact solutions for small- and medium-size problems based on real-world datasets. Second, we compare these solutions with the ones provided by the state-of-art heuristic Di_erential Evolution and Combinatorial Search for Index Tracking (DECS-IT), obtaining information about the heuristic performance and its reliability for the solution of large-size problems that cannot be solved with the exact approach. Empirical results show that DECS-IT is indeed appropriate to tackle the index tracking problem in such cases. Furthermore, we propose a method that combines the good characteristics of the exact and of the heuristic approaches.

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Bibliographic Info

Paper provided by University of Modena and Reggio E., Faculty of Economics "Marco Biagi" in its series Department of Economics with number 0685.

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Length: pages 22
Date of creation: Jun 2012
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Handle: RePEc:mod:depeco:0685

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Keywords: Index tracking; mixed integer quadratic programming; stochastic search heuristics; differential evolution; cardinality constraints;

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  1. 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.
  2. 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.
  3. Diana Barro & Elio Canestrelli, 2005. "Tracking Error: a multistage portfolio model," GE, Growth, Math methods 0510012, EconWPA.
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Cited by:
  1. Renato Bruni & Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2012. "A new stochastic dominance approach to enhanced index tracking problems," Economics Bulletin, AccessEcon, vol. 32(4), pages 3460-3470.
  2. Renato Bruni & Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2012. "A New Lp Model For Enhanced Indexation," Departmental Working Papers of Economics - University 'Roma Tre' 0168, Department of Economics - University Roma Tre.
  3. Andriosopoulos, Kostas & Doumpos, Michael & Papapostolou, Nikos C. & Pouliasis, Panos K., 2013. "Portfolio optimization and index tracking for the shipping stock and freight markets using evolutionary algorithms," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 52(C), pages 16-34.
  4. Renato Bruni & Francesco Cesarone & Andrea Scozzari & Fabio Tardella, 2013. "No arbitrage and a linear portfolio selection model," Economics Bulletin, AccessEcon, vol. 33(2), pages 1247-1258.


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