We investigate the leverage cycle in the context of several different models, ranging from more realistic agent-based models to simple reduced form models with minimal assumptions. These models build on earlier work on the leverage cycle but in a more explicit dynamic context. They make it clear how managing a portfolio with a leverage target automatically gives rise to endogenous dynamics, coupling leverage and volatility and inducing chaotic oscillations driving clustered volatility and heavy tailed risk. As one moves from countercyclical to procyclical leverage, or from longer time horizons to shorter time horizons, volatility increases and stability decreases. Policies such as Basel II and III can have unintended consequences; while they can be effective for a single investor acting alone, when all investors use them they can be destabilizing. I will also discuss the relationship to the problem in the network context, where the same principle applies, i.e., diversification of risk by individuals often creates systemic risk. Finally, I will discuss possible stabilizing policies, such as impact-adjusted accounting.
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