We propose a quantitative approach for assessing the systemic impact of the failure of a financial institution, based on a simple model of default contagion in a banking system. Our approach takes into account both volatility and correlation of market factors and contagion effects due to counterparty exposures: we argue that neglecting either of these aspects leads to a severe underestimation of systemic risk. By contrast to "backward-looking" indicators of systemic risk, our approach, based on exposures, is a forward-looking approach based on the simulation of future contagion scenarios. We discuss some theoretical properties of our proposed measure of systemic risk and show how it can be estimated in practice using a database of interbank exposures obtained from the Brazilian central bank. The analysis reveals the importance of network properties when modeling contagion and systemic risk and leads to some recommendations for the macro-prudential regulation of systemic risk.