Modeling extreme returns and asymmetric dependence structures of hedge fund strategies using extreme value theory and copula theory

Jan Viebig and Thorsten Poddig

Journal of Risk

Abstract: ABSTRACT We use extreme value theory and copula theory to model multivariate daily return distributions of hedge fund strategy indexes. Multivariate outliers in time series of hedge fund strategies are clustered when volatilities and credit spreads increase and investors take a "flight to quality" and seek liquidity. In light of the strong "domino effect" in daily return series of hedge fund strategy indexes during the financial crisis 2008-9, the generalized Pareto distribution copula approach is an appropriate modeling choice for approximating multivariate hedge fund distributions exhibiting extreme return observations and asymmetric dependence structures. Generalized Pareto distributions are efficient approximations for the fat-tailed distributions of returns on hedge funds exceeding high thresholds. Tests for correlation symmetry show that dependence structures between several hedge fund strategies are often asymmetric. Copulas can be used to model symmetric and asymmetric dependence structures between different hedge fund strategies.

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