We analyze the emergence of systemic risk in a network model of interconnected bank balance sheets. The model incorporates multiple sources of systemic risk, including size of financial institutions, direct exposure from interbank lendings, and asset fire sales. We suggest a new macroprudential risk management approach building on a system wide value at risk (SVaR). Under the SVaR metric, the contribution of individual banks to systemic risk is well defined and can be approximated by a Shapley value-type measure. We show that, in a SVaR regime, a fair systemic risk charge which is proportional to a bank’s individual contribution to systemic risk diverges from the optimal macroprudential capitalization of the banks from a planner’s perspective. The results have implications for the design of macroprudential capital surcharges.