We propose two indicators for quantifying the potential exposure of financial institutions to indirect contagion arising from deleveraging of assets in stress scenarios. The first indicator, the Endogenous Risk Index (ERI) captures spillovers across portfolios arising from deleveraging in stress scenarios. The second indicator, the Indirect Contagion Index (ICI) measures the systemic importance of a bank by quantifying the loss its distressed liquidation would inflict on other institutions. Both are computable from portfolio holdings of financial institutions and measures of market depth for the assets held in the portfolio. We discuss the micro-foundation of these indicators and apply them to the analysis of the vulnerability of the European banking system to indirect contagion. Using data on portfolio holdings of European banks, we show that our indicators correlate to the magnitude of fire-sales losses in simulated stress scenarios, thus providing a simple to compute proxy for the outcome of stress tests. We also show that the information provided by our indicators on the systemic importance of banks is different from indicators based on size, thereby providing a measure of interconnectedness complementary to those currently used by supervisors.

The traditional approach to the stress testing of financial institutions focuses on capital adequacy and solvency. Liquidity stress tests have been applied in parallel to and independently from solvency stress tests, based on scenarios which may not be consistent with those used in solvency stress tests. We propose a structural framework for the joint stress testing of solvency and liquidity: our approach exploits the mechanisms underlying the solvency-liquidity nexus to derive relations between solvency shocks and liquidity shocks. These relations are then used to model liquidity and solvency risk in a coherent framework, involving external shocks to solvency and endogenous liquidity shocks arising from these solvency shocks. We define the concept of “Liquidity at Risk”, which quantifies the liquidity resources required for a financial institution facing a stress scenario. Finally, we show that the interaction of liquidity and solvency may lead to the amplification of equity losses due to funding costs which arise from liquidity needs.