The last financial crisis has shown that large banking crises not only pose a highly dangerous risk to financial systems, but also to both the real economy and public finances. Reducing that risk has become a priority for regulators and governments. Still, the debate is open on what the systemic risk is, and how to measure the contribution of each single bank.Market based measures have almost partially failed this goal, as the markets were not able to adequately signal the system riskiness before the crisis start.In this paper we propose an alternative approach for measuring risk contributions, based on balance sheet data, developed on the idea that the contribution of each bank to the system can be captured by the variation of the expected shortfall of the banking system when excluding the considered bank. We thus refer to it as the Leave-One-Out contribution to systemic risk.This measure can be split as the sum of two components, namely the idiosyncratic bank risk (the value of expected losses of the bank when not linked to the system), and the systemic component, defined as the system expected loss variation due to the bank linkages to the system.Results show that the distinction in idiosyncratic and systemic contribution is relevant, as the two components affects the bank riskiness in different ways, and the balance sheet variables related to each component are different. This consciousness of how linkages affect the system riskiness can relevantly contribute to macroprudential regulation.Moreover, we proof that thresholds set for computing the ES relevantly affect results, so that some banks can have a barrier effect in small crises while having a positive contribution in larger crises.Analyzing the evolution of the European financial system riskiness from 2007 to 2013, differently from the market based measures, we find a huge drop in the systemic component between 2011 and 2013, when the system experienced a strong recapitalization, leading the system to a much more reliable stability than what registered for 2007.Finally, comparing the Leave-One-Out outcome to the Shapley values on a small sample of nine French banks, we proof that the two measures are really highly correlated (more than 99.9%), but as LOO doesn't suffer the computational limits, it is also feasible
