Factor Selection in Hedge Fund Replication Dynamic Models

Abstract

While the use of dynamic factor models for Hedge Fund Replication (HFR) has proven to be superior to standard OLS methodologies (e.g., Roncalli and Weisang, 2009a,b), current factor selection methodology in these dynamic settings by means of direct PCA-based estimation of the factors (e.g., Darolles and Mero, 2008) provides results having poor interpretability and small, yet significant, improvement over more naive selection methodologies. In this paper, I contend on the one hand that this type of direct factor estimation is doomed to be at best biased and unreliable in finite samples as indicated by results from random matrix theory (Harding, 2008). On the other hand, forward filtering-backward sampling (FFBS) algorithm and reversible-jump MCMC allow considering a factor selection methodology using observable instruments as potential factors hence solving both problems of identification and interpretability. I provide here a detailed algorithm and the results of its application to a simple and classic replication example.