In this paper, we decompose banks' systemic risk into two dimensions: the risk of a bank (“bank tail risk”) and the link of the bank to the system in financial distress (“systemic linkage”). Based on extreme value theory, we estimate a systemic risk measure that can be decomposed into two subcomponents reflecting these dimensions. Empirically, we assess the relationships of bank business models to the two dimensions of systemic risk. The observed differences in these relationships partly explain why micro- and macroprudential perspectives sometimes have different implications for banking regulation.