We consider three measures on the systemic importance of a financial institution within a interconnected financial system. Based on the measures, we study the relation between the size of a financial institution and its systemic importance. From both theoretical model and empirical analysis, we find that in analyzing the systemic risk posed by one financial institution to the system, size should not be considered as a proxy of systemic importance. In other words, the "too big to fail" argument is not always valid, and alternative measures on systemic importance should be considered. We provide the estimation methodology of systemic importance measures under the multivariate Extreme Value Theory (EVT) framework.
Keywords: Too big to fail, systemic risk, systemic importance, multivariate extreme value theory.
JEL Classification: G21, C14.