The stability of the financial system at higher loss levels is either characterized by asymptotic dependence or asymptotic independence. If asymptotically independent, the dependency, when present, eventually dies out completely at the more extreme quantiles, as in case of the multivariate normal distribution. Given that financial service firms' equity returns depend linearly on the risk drivers, we show that the marginals' distributions maximum domain of attraction determines the type of systemic (in-)stability. A scale for the amount of dependency at high loss lovels is designed. This permits a characterization of systemic risk inherent to different financial network structures. The theory also suggests the functional form of the economically relevant limit copulas
