Cardinality versus q-norm constraints for index tracking |
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Authors: | Björn Fastrich Sandra Paterlini |
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Institution: | 1. Department of Economics, Justus-Liebig-University, D-35394 Giessen, Germany.;2. Department of Economics, CEFIN and RECent, University of Modena and Reggio E., Italy. |
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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. |
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Keywords: | Index tracking Portfolio optimization Finance Statistics |
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