Dynamic Versus Static Optimization of Hedge Fund Portfolios : The Relevance of Performance Measures

This paper analyzes the relevance of a set of some performance measures for optimal portfolios including hedge funds. Four criteria are considered: the Sharpe Ratio, the Returns on VaR and on CVaR, and the Omega performance measure. The results are illustrated by an allocation on several indices: HFR (Global Hedge Fund Index), JPM Government Bond Index, S&P GSCI, MSCI World and the UBS Global Convertible. Both static and dynamic optimizations are considered. Due to the non-convexity of some of the criteria, we use the “threshold accepting algorithm” to solve numerically the optimization problems. The time period of the analysis is September 1997 to August 2007. Our results suggest that, for the dynamic optimization, the portfolio which maximizes the Omega measure has the more stable performances, in particular when compared to the Return-on-CVaR portfolio. As a by-product, we prove that all the optimal portfolios had to contain hedge funds for the time period 1997-2007