Tail-Dependence in Stock-Return Pairs

The empirical joint distribution of return-pairs on stock indices displays high tail-dependence in the lower tail and low tail-dependence in the upper tail. The presence of tail-dependence is not compatible with the assumption of (conditional) joint normality. The presence of asymmetric-tail dependence is not compatible with the assumption of a joint student-t distribution. A general test for one dependence structure versus another via the profile-likelihood is described and employed in a bivariate GARCH model, where the joint distribution of the disturbances is split into its marginals and its copula. The copula used is such that it allows for the presence of lower tail-dependence and for asymmetric tail-dependence, and that it encompasses the normal or t-copula. The model is estimated using bivariate data on a set of European stock indices. We find that the assumption of normal or student-t dependence is easily rejected in favour of an asymmetrically tail-dependent distribution.