Abstract

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. 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 further simplified models. We introduce a flexible leverage regulation policy in which it is possible to continuously tune from pro-cyclical to countercyclical leverage. In order to identify the optimal parameters of this leverage policy we study the trade off between risk in the financial sector and bank leverage. Our results suggest that the optimal leverage policy is close to constant leverage while slightly countercyclical.