Contagious Synchronization and Endogenous Network Formation in Financial Networks

When banks choose similar investment strategies the financial system becomes vulnerable to common shocks. We model a simple financial system in which banks decide about their investment strategy based on a private belief about the state of the world and a social belief formed from observing the actions of peers. Observing a larger group of peers conveys more information and thus leads to a stronger social belief. Extending the standard model of Bayesian updating in social networks, we show that the probability that banks synchronize their investment strategy on a state non-matching action critically depends on the weighting between private and social belief. This effect is alleviated when banks choose their peers endogenously in a network formation process, internalizing the externalities arising from social learning.Comment: 41 pages, 10 figures, Journal of Banking & Finance 201

The dynamics of the leverage cycle

We present a simple agent-based model of a financial system composed of leveraged investors such as banks that invest in stocks and manage their risk using a Value-at-Risk constraint, based on historical observations of asset prices. The Value-at-Risk constraint implies that when perceived risk is low, leverage is high and vice versa, a phenomenon that has been dubbed pro-cyclical leverage. We show that this leads to endogenous irregular oscillations, in which gradual increases in stock prices and leverage are followed by drastic market collapses, i.e. a leverage cycle. This phenomenon is studied using simplified models that give a deeper understanding of the dynamics and the nature of the feedback loops and instabilities underlying the leverage cycle. We introduce a flexible leverage regulation policy in which it is possible to continuously tune from pro-cyclical to countercyclical leverage. When the policy is sufficiently countercyclical and bank risk is sufficiently low the endogenous oscillation disappears and prices go to a fixed point. While there is always a leverage ceiling above which the dynamics are unstable, countercyclical leverage can be used to raise the ceiling. We also study the impact on leverage cycles of direct, temporal control of the bank's riskiness via the bank's required Value-at-Risk quantile. Under such a rule the regulator relaxes the Value-at-Risk quantile following a negative stock price shock and tightens it following a positive shock. While such a policy rule can reduce the amplitude of leverage cycles, its effectiveness is highly dependent on the choice of parameters. Finally, we investigate fixed limits on leverage and show how they can control the leverage cycle.Comment: 35 pages, 9 figure

Taming the Basel leverage cycle

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

Models of systemic risk in financial markets

This thesis studies systemic risk in financial markets and how it emerges through dynamical and structural amplification mechanisms. In part (1) I study the dynamics and control of Basel leverage cycles. For this I develop a simple model of a financial system consisting of leveraged banks and an unleveraged fundamentalist investor (fund). Banks trade a risky asset with the fund and rely on historical information to estimate their portfolio risk. This risk estimate determines the banks' leverage limit. I show that these simple ingredients can lead to endogenous, irregular oscillations, which I call Basel leverage cycles. I then proceed to evaluate alternative regulatory capital requirements based on their impact on endogenous risk. I find that in the microprudential limit, when the bank is small and exogenous volatility is high, the optimal policy is simply given by a Value-at-Risk constraint. However, when the bank is large, the optimal policy is constant leverage. In part (2) I study contagion in financial networks for two examples. First, I study how intra-institutional linkages can amplify financial contagion when financial institutions are active in multiple over-the-counter markets. In particular, spillover within a diversified financial institution allows for contagion from one over-the-counter market to another. Using recent methods for coupled networks I illustrate that under certain circumstances, the presence of intra-institutional spillover can lead to the amplification of small shocks to the extent that trading across all markets collapses abruptly. Finally, I develop a simple model of social learning in the context of a financial network. I study how banks' portfolio decisions can synchronize if banks rely both on outside information and information from their social network to compute the expected payoff of an investment opportunity. In the same model, I propose a simple boundedly rational decision mechanism for endogenous network formation based on the information content of a bank’s neighbors' decisions.</p