Heterogeneous Preferences, Constraints, and the Cyclicality of Leverage

Abstract

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. It is shown how this type of constraint increases the market price of risk and decreases the interest rate, producing a higher equity risk premium and asset price bubbles. In addition, heterogeneity and margin constraints are shown to produce both pro- and counter-cyclical leverage cycles as seen in the data. Finally, more preference types causes a reduction in the severity of crisis and a lower relative deviation from complete markets in all variables. At the same time expected returns on the stock must remain high to compensate risk averse agents to hold a larger share.