Replicating Hedge Fund Indices with Optimization Heuristics

Hedge funds offer desirable risk-return profiles; but we also find high management fees, lack of transparency and worse, very limited liquidity (they are often closed to new investors and disinvestment fees can be prohibitive). This creates an incentive to replicate the attractive features of hedge funds using liquid assets. We investigate this replication problem using monthly data of CS Tremont for the period of 1999 to 2009. Our model uses historical observations and combines tracking accuracy, excess return, and portfolio correlation with the index and the market. Performance is evaluated considering empirical distributions of excess return, final wealth and correlations of the portfolio with the index and the market. The distributions are compiled from a set of portfolio trajectories computed by a resampling procedure. The nonconvex optimization problem arising from our model specification is solved with a heuristic optimization technique. Our preliminary results are encouraging as we can track the indices accurately and enhance performance (e.g. have lower correlation with equity markets).