Before revision: This paper documents a new stylized fact about the leverage cycle and proposes a model of risk preference heterogeneity to explain this fact. In particular, leverage cyclicality depends on the preferences of the marginal agent in the economy, as this determines financial variables. I propose a model of risk preference heterogeneity to explain this fact and prove existence of a new, low dimensional Markovian equilibrium which may exist in other heterogeneous agent models. This equilibrium is studied in an application to margin constraints  .
After revision: This paper solves an open problem in financial mathematics by characterizing the equilibrium in a continuous time financial market populated by heterogeneous agents who differ in their rate of relative risk aversion and face convex portfolio constraints. The model is studied in an application to margin constraints .