Sparse Index Clones via the Sorted L1-Norm

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