Dynamic Hedge Fund Portfolio Construction: A Semi-Parametric Approach

Abstract

In this paper, we evaluate alternative optimization frameworks for constructing portfolios of hedge funds. Using monthly hedge fund index returns for the period 1990 to 2011, we compare the standard mean-variance optimization model with models based on CVaR, CDaR and Omega, for both conservative and aggressive hedge fund investment strategies. In order to implement the CVaR, CDaR and Omega optimization models, we propose a semi-parametric methodology, in which we first model the marginal density of each hedge fund index using extreme value theory and construct the joint density of hedge fund index returns using a copula-based approach. We then simulate hedge fund returns from this joint density in order to compute CVaR, CDaR and Omega, which are used in the optimization process. We compare the semi-parametric approach with the standard, non-parametric approach, in which the quantiles of the marginal density of portfolio returns are estimated empirically and used to compute CVaR, CDaR and Omega. We report two main findings. The first is that the CVaR, CDaR and Omega models offer a significant improvement in terms of risk-adjusted portfolio performance over the mean-variance model. The second is that semi-parametric estimation of the CVaR, CDaR and Omega models offers a very substantial improvement over non-parametric estimation. Our results are robust to the choice of target return, risk limit and estimation sample size.