We consider the problem of calcu-lating tail probabilities of the
returns of linear asset portfolios. As a flexible and accurate model for the logarithmic returns we use the t-copula dependence structure and marginals following the generalized hyperbolic distribution. Exact calcu- lation of the tail-loss probabilities is not possible and even simulation leads to challenging numerical problems. Applying a new numerical inversion method for the generation of the marginals and importance sampling with carefully selected mean shift we develop an efficient simulation algorithm. Numerical results for a variety of realistic portfolio examples show an impressive performance gain.