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 < q < 1, of the replicating portfolios’ asset weights: the q-norm constraint regularises the problem and identifies a sparse model. Both approaches are challenging from an optimisation viewpoint due to either the presence of the cardinality constraint or a non-convex constraint on the q-norm. The problem can become even more complex when non-convex distance measures or other real-world constraints are considered. We employ a hybrid heuristic as a flexible tool to tackle both optimisation problems. The empirical analysis on real-world financial data allows to compare the two index tracking approaches. Moreover, we propose a strategy to determine the optimal number of constituents and the corresponding optimal portfolio asset weights.

Fastrich, B., S., Paterlini e P., Winker. "Cardinality versus q-Norm Constraints for Index Tracking" Working paper, RECENT WORKING PAPER SERIES, Dipartimento di Economia Marco Biagi – Università di Modena e Reggio Emilia, 2011.

Cardinality versus q-Norm Constraints for Index Tracking

Paterlini, S.;
2011

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 < q < 1, of the replicating portfolios’ asset weights: the q-norm constraint regularises the problem and identifies a sparse model. Both approaches are challenging from an optimisation viewpoint due to either the presence of the cardinality constraint or a non-convex constraint on the q-norm. The problem can become even more complex when non-convex distance measures or other real-world constraints are considered. We employ a hybrid heuristic as a flexible tool to tackle both optimisation problems. The empirical analysis on real-world financial data allows to compare the two index tracking approaches. Moreover, we propose a strategy to determine the optimal number of constituents and the corresponding optimal portfolio asset weights.
2011
Gennaio
Fastrich, B.; Paterlini, S.; Winker, P.
Fastrich, B., S., Paterlini e P., Winker. "Cardinality versus q-Norm Constraints for Index Tracking" Working paper, RECENT WORKING PAPER SERIES, Dipartimento di Economia Marco Biagi – Università di Modena e Reggio Emilia, 2011.
File in questo prodotto:
File Dimensione Formato  
RECent-wp56.pdf

Open access

Tipologia: Versione pubblicata dall'editore
Dimensione 2.23 MB
Formato Adobe PDF
2.23 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1292505
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact