Exact and heuristic approaches for the index tracking problem with UCITS constraints

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,...

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Vydané v:	Annals of operations research Ročník 205; číslo 1; s. 235 - 250
Hlavní autori:	Scozzari, Andrea, Tardella, Fabio, Paterlini, Sandra, Krink, Thiemo
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Boston Springer US 01.05.2013 Springer Springer Nature B.V
Predmet:	Algorithms Benchmarks Business and Management Combinatorial analysis Combinatorics Constituents Costs Datasets Heuristic Heuristic methods Heuristic programming Investments Investors Linear programming Mathematical economics Mathematical models Operations research Operations Research/Decision Theory Performance indices Portfolio management Quadratic programming Securities markets Stock exchanges Studies Theory of Computation Tracking Tracking problem Italy Differential evolution Mixed integer quadratic programming Index tracking Cardinality constraints Stochastic search heuristics
ISSN:	0254-5330, 1572-9338
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Abstract	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 Differential 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.
AbstractList	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. 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 Differential 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.[PUBLICATION ABSTRACT] 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 Differential 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. 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 Differential 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. Keywords Index tracking * Mixed integer quadratic programming * Stochastic search heuristics * Differential evolution * Cardinality constraints 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 Differential 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.
Audience	Academic
Author	Paterlini, Sandra Krink, Thiemo Tardella, Fabio Scozzari, Andrea
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Cites_doi	10.1016/0021-9991(90)90201-B 10.1007/s10479-006-0145-1 10.1287/mnsc.37.5.519 10.1007/s10479-009-0552-1 10.1007/s00291-003-0139-1 10.1126/science.220.4598.671 10.1088/1469-7688/1/5/301 10.3905/jpm.2002.319830 10.1007/0-387-28359-5_8 10.1007/11428862_76 10.1023/A:1008202821328 10.1016/0305-0548(95)00030-5 10.1080/1350485032000158636 10.1016/j.csda.2004.12.004 10.1023/B:ANOR.0000039512.98833.5a 10.1007/s10479-008-0404-4 10.1016/j.ejor.2008.03.015 10.1002/9780470748916.ch3 10.1002/asm.3150080306 10.1002/isaf.285 10.1007/s10479-007-0308-8 10.1016/S0377-2217(02)00425-3 10.1007/s10479-011-0862-y 10.21314/JOR.2006.134 10.1080/14697688.2012.691986 10.1007/s00291-003-0127-5
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Keywords	Differential evolution Mixed integer quadratic programming Index tracking Cardinality constraints Stochastic search heuristics
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SubjectTerms	Algorithms Benchmarks Business and Management Combinatorial analysis Combinatorics Constituents Costs Datasets Heuristic Heuristic methods Heuristic programming Investments Investors Linear programming Mathematical economics Mathematical models Operations research Operations Research/Decision Theory Performance indices Portfolio management Quadratic programming Securities markets Stock exchanges Studies Theory of Computation Tracking Tracking problem
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Title	Exact and heuristic approaches for the index tracking problem with UCITS constraints
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