A Learning-Based Linear Replicator for Hedge Fund Indexes

There has been great interest in creating portfolios using common liquid instruments to replicate hedge fund returns. In a recent article, Hasanhodzic and Lo (2007) demonstrate that a factor-based approach based on a linear regression model with 5 tradable risk factors can adequately replicate monthly returns of 1,610 hedge funds in 1986 to 2005. We propose a learning-based linear replication algorithm to enhance the linear model. Results show that our approach can improve the replicating capability of linear replicator, especially for some nonlinear and dynamic strategies, e.g., Event-driven and Emerging Markets. The annualized root mean squared error is improved by 40% and 34%, respectively. The new method can automatically detect the market changes and separate return points into different polyhedral regions, even high dimensions (multiple risk factors). By using 12 major strategy indexes' monthly returns compiled by 7 data vendors from their inception date until December 2008, we examine our method with six common risk factors and find that our algorithm can improve explanatory of hedge fund index returns. The performance of our new replicator is also tested by cloning out-of-sample monthly returns through using five out of these six factors