Cardinality versus q-Norm Constraints for Index Tracking

21 Pages Posted: 21 Sep 2010

See all articles by Bjoern Fastrich

Bjoern Fastrich

University of Giessen - Department of Economics

Sandra Paterlini

University of Trento - Department of Economics and Management

Peter Winker

University of Giessen - Department of Economics

Date Written: July 22, 2010

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.

Keywords: Index tracking, Cardinality constraint, q-Norm, Regularization methods, Heuristic algorithms

JEL Classification: C15, C61, G11

Suggested Citation

Fastrich, Bjoern and Paterlini, Sandra and Winker, Peter, Cardinality versus q-Norm Constraints for Index Tracking (July 22, 2010). Available at SSRN: https://ssrn.com/abstract=1679690 or http://dx.doi.org/10.2139/ssrn.1679690

Bjoern Fastrich (Contact Author)

University of Giessen - Department of Economics ( email )

Licher Str. 64
D-35394, Giessen
Germany

Sandra Paterlini

University of Trento - Department of Economics and Management ( email )

Via Inama 5
Trento, I-38100
Italy

Peter Winker

University of Giessen - Department of Economics ( email )

Licher Str. 62
D-35394 Giessen, DE
Germany

HOME PAGE: http://wiwi.uni-giessen.de/home/oekonometrie/

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