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Cardinality versus q -norm constraints for index tracking

Björn Fastrich, Sandra Paterlini and Peter Winker ()

Quantitative Finance, 2014, vol. 14, issue 11, 2019-2032

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.

Date: 2014
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Working Paper: Cardinality versus q-Norm Constraints for Index Tracking (2011) Downloads
Working Paper: Cardinality versus q-Norm Constraints for Index Tracking (2011) Downloads
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