• The authors thank Joop Huij (referee) for his detailed and constructive advice. Alessio Matteuzzi from Citi is acknowledged for his many valuable comments on practical issues. This article has benefited from the suggestions of Andrea Resti and one referee, both from Carefin-Bocconi, Lionel Martelini, and Dimitris Flamouris, as well as from the comments of seminar participants at: the Financial Mathematics Seminar Series at the University of Minnesota School of Mathematics, the Tinbergen Institute Seminar Series at the VU University of Amsterdam, and the 2009 European Financial Management annual meeting. Financial support from Carefin-Bocconi Centre for Applied Research in Finance is greatly appreciated. Sandra Paterlini conducted part of this research while visiting the School of Mathematics, University of Minnesota. Sandra Paterlini acknowledges financial support from MIU RPRIN 20077P5AWA005 and from Fondazione Cassa di Risparmio di Modena for ASBE Project 36. Any remaining errors are our own.


This article addresses the problem of portfolio construction in the context of efficient hedge fund investments replication. We propose a modification to the standard Sharpe “style analysis” by introducing a constraint on the asset weights 1-norm and 2-norm. This constraint regularizes the optimization problem, allows efficient selection of relevant factor's and has significant effects on the stability of the resulting asset mix and the risk–return characteristics of the replicating portfolio. The empirical results suggest that the norm-constrained replicating portfolios exhibit significant correlations with their benchmarks, often higher than 0.9; have a fraction, which is about half to two-thirds, of active positions relative to those determined through the standard method; and are obtained with turnover, which is in some instances about one-fourth of that for the standard method.