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Title: Sparse index tracking via the sorted $\ell_{1}$ - norm Authors:  Philipp Johannes Kremer - EBS Universitaet fuer Wirtschaft und Recht (Germany)
Damian Brzyski - Wroclaw University of Science and Technology (Poland)
Malgorzata Bogdan - University of Wroclaw (Poland)
Sandra Paterlini - University of Trento (Italy) [presenting]
Abstract: Index tracking and hedge fund replication aims at replicating or cloning the risk-return properties of a given benchmark, by either using only a subset of its original constituents or by a set of risk factors. We propose a new statistical model for index tracking and hedge fund replication, that relies on the convex \textit{Sorted $\ell_{1}$ Penalized Estimator} (SLOPE). SLOPE is capable not only to provide sparse clones but also to automatically group assets sharing similar statistical properties with respect to the benchmark, and thereby allowing to develop further investment strategies.