Journal article

Publication year: 2014

Pages: 2019-2032

Journal: Quantitative Finance

Volume number: 14

Issue number: 11

ISSN: 1469-7688

eISSN: 1469-7696

DOI Link: https://doi.org/10.1080/14697688.2012.691986

Publisher: Taylor and Francis Group

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 optimization 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 optimization problems. The empirical analysis of real-world financial data allows us 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.

Harvard Citation style: Fastrich, B., Paterlini, S. and Winker, P. (2014) Cardinality versus q-norm constraints for index tracking, Quantitative Finance, 14(11), pp. 2019-2032. https://doi.org/10.1080/14697688.2012.691986

APA Citation style: Fastrich, B., Paterlini, S., & Winker, P. (2014). Cardinality versus q-norm constraints for index tracking. Quantitative Finance. 14(11), 2019-2032. https://doi.org/10.1080/14697688.2012.691986