Financial stress tests that capture multiple interactions between contagion channels are conditional on specific, subjectively-imposed stress scenarios. Eigenvalue-based approaches, in contrast, provide a scenario-independent measure of systemic stability, but so far only handle a single contagion mechanism. We develop an eigenvalue-based approach that brings the best of both worlds, enabling the analysis of multiple interacting contagion channels without the need to impose a subjective stress scenario. Our model captures the solvency-liquidity nexus, which allows us to demonstrate that the instability due to interacting channels can far exceed that of the sum of the individual channels acting in isolation. The framework we develop is flexible and allows for calibration to the microstructure and contagion channels of real financial systems. Building on this framework, we derive an analytic stability criterion in the limit of a large number of institutions that gives the instability threshold as a function of the relative size and intensity of contagion channels. This analytical formula requires comparatively little data to elucidate the mechanisms that drive instability in real financial systems and thus complements the insights gained from traditional stress tests.

We investigate a simple dynamical model for the systemic risk caused by the use of Value-at-Risk, as mandated by Basel II. The model consists of a bank with a leverage target and an unleveraged fundamentalist investor subject to exogenous noise with clustered volatility. The parameter space has three regions: (i) a stable region, where the system has a fixed point equilibrium; (ii) a locally unstable region, characterized by cycles with chaotic behavior; and (iii) a globally unstable region. A calibration of parameters to data puts the model in region (ii). In this region there is a slowly building price bubble, resembling the period prior to the Global Financial Crisis, followed by a crash resembling the crisis, with a period of approximately 10–15 years. We dub this the Basel leverage cycle. To search for an optimal leverage control policy we propose a criterion based on the ability to minimize risk for a given average leverage. Our model allows us to vary from the procyclical policies of Basel II or III, in which leverage decreases when volatility increases, to countercyclical policies in which leverage increases when volatility increases. We find the best policy depends on the market impact of the bank. Basel II is optimal when the exogenous noise is high, the bank is small and leverage is low; in the opposite limit where the bank is large and leverage is high the optimal policy is closer to constant leverage. In the latter regime systemic risk can be dramatically decreased by lowering the leverage target adjustment speed of the banks. While our model does not show that the financial crisis and the period leading up to it were due to VaR risk management policies, it does suggest that it could have been caused by VaR risk management, and that the housing bubble may have just been the spark that triggered the crisis.

We use a simple agent based model of value investors in financial markets to test three credit regulation policies. The first is the unregulated case, which only imposes limits on maximum leverage. The second is Basle II and the third is a hypothetical alternative in which banks perfectly hedge all of their leverage-induced risk with options. When compared to the unregulated case both Basle II and the perfect hedge policy reduce the risk of default when leverage is low but increase it when leverage is high. This is because both regulation policies increase the amount of synchronized buying and selling needed to achieve deleveraging, which can destabilize the market. None of these policies are optimal for everyone: risk neutral investors prefer the unregulated case with low maximum leverage, banks prefer the perfect hedge policy, and fund managers prefer the unregulated case with high maximum leverage. No one prefers Basle II.