Tracking Problems, Hedge Fund Replication, and Alternative Beta

As hedge fund replication based on factor models has encountered growing interest among professionals and academics, and despite the launch of numerous products (indexes and mutual funds) in the past year, it has faced many critics. In this paper, we consider two of the main critiques, namely the lack of reactivity of hedge fund replication, its deficiency in capturing tactical allocations, and the lack of access to the alpha of hedge funds. To address these problems, we consider hedge fund replication as a general tracking problem which may be solved by means of Bayesian filters. Using the example provided by Roncalli and Teiletche (2008), we detail how the Kalman filter tracks changes in exposures, and show that it provides a replication methodology with a satisfying economic interpretation. Finally, we address the problem of accessing the pure alpha by proposing a core/satellite approach of alternative investments between high-liquid alternative beta and less liquid investments. Non-normality and non-linearities documented on hedge fund returns are investigated using the same framework in a companion paper [Roncalli and Weisang (2009)].