Sparse Index Clones via the Sorted L1-Norm

30 Pages Posted: 2 Jul 2019

See all articles by Philipp Kremer

Philipp Kremer

EBS Universität für Wirtschaft und Recht; Prime Capital AG

Damian Brzyski

Wroclaw University of Technology

Malgorzata Bogdan

University of Wroclaw

Sandra Paterlini

University of Trento - Department of Economics and Management

Date Written: June 29, 2019

Abstract

Index tracking and hedge fund replication aim at cloning the return time series properties of a given benchmark, by either using only a subset of its original constituents or by a set of risk factors. In this paper, we propose a model that relies on the Sorted L1 Penalized Estimator, called SLOPE, for index tracking and hedge fund replication. SLOPE is capable of not only providing sparsity but also to form groups among assets depending on their partial correlation with the index or the hedge fund return times series. The grouping structure can then be exploited to create individual investment strategies that allow building portfolios with a smaller number of active positions, but still comparable tracking properties. Considering equity index data over the period from December 2004 to January 2016 and hedge fund returns from June 1994 to July 2017, we show that the SLOPE based approaches can often outperform state-of-the-art non-convex approaches.

Keywords: Index Tracking, Hedge Fund Clones, Regularization, SLOPE

JEL Classification: C01, C44, C58, G11

Suggested Citation

Kremer, Philipp and Brzyski, Damian and Bogdan, Malgorzata and Paterlini, Sandra, Sparse Index Clones via the Sorted L1-Norm (June 29, 2019). Available at SSRN: https://ssrn.com/abstract=3412061 or http://dx.doi.org/10.2139/ssrn.3412061

Philipp Kremer (Contact Author)

EBS Universität für Wirtschaft und Recht ( email )

Gustav-Stresemann-Ring 3
Wiesbaden, Hessen 65195
Germany

Prime Capital AG ( email )

Frankfurt
Germany

Damian Brzyski

Wroclaw University of Technology ( email )

ul. Smoluchowskiego 25
Wroclaw, 50-372
Poland

Malgorzata Bogdan

University of Wroclaw ( email )

50-384 Wroclaw
Grunwaldzki 2/4, Lower Silesia Province 50-137
Poland

Sandra Paterlini

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

Via Inama 5
Trento, I-38100
Italy

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