Tracking hedge funds returns using sparse clones

Whether hedge fund returns could be attributed to systematic risk exposures rather than managerial skills is an interesting debate among academics and practitioners. Academic literature suggests that hedge fund performance is mostly determined by alternative betas, which justifies the construction of investable hedge fund clones or replicators. Practitioners often claim that management skills are instrumental for successful performance. In this paper, we study the risk exposure of different hedge fund indices to a set of liquid asset class factors by means of style analysis. We extend the classical style analysis framework by including a penalty that allows to retain only relevant factors, dealing effectively with collinearity, and to capture the out-of-sample properties of hedge fund indices by closely mimicking their returns. In particular, we introduce a Log-penalty and discuss its statistical properties, showing then that Log-clones are able to closely track the returns of hedge fund indices with a smaller number of factors and lower turnover than the clones built from state-of-art methods.