Funds of hedge funds: A comparison among different portfolio optimization models implementing the zero-investment strategy

Hedge funds are alternative investment vehicles where the fund manager's task is to generate positive returns regardless of the market conditions. A fund of hedge funds is a portfolio of hedge funds generally characterized by positive return and a high degree of diversification. In this paper, we analyze two portfolio optimization models for constructing a fund of hedge funds. Both models, which we refer to as the two-step model and the single-step model, are based on a zero-value strategy, a strategy which combines long and short selling in order to attain (ignoring margin and the cost of short selling) a zero initial investment. The principal difference between the two models is the selection techniques of the funds included in the long/short portfolio. The two-step model requires, as the first step, the classification of the funds into winner and loser groups according to their historical performance as is done in the literature on momentum strategies. After the pre-selection step, the model is solved via linear programming, the model's second step. The single- step model avoids the pre-selection of hedge funds at the cost of introducing binary variables to exclude the possibility that a hedge fund is present in both the short and long portfolios. Both models are solved with respect to a set of scenarios, based either on historical, or forecasted scenarios generated by GARCH modeling. Combining the two models and the two sets of scenarios, we end up with four strategies. Finally, we evaluate the ex post one-year performance of the four strategies with monthly portfolio rebalancing using hedge fund data that encompass the sub-prime crisis.