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.;
2011-01-01

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.
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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1292505
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