COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1800 Endogenous Leverage: VaR and Beyond Ana Fostel and John Geanakoplos May 2011 We study endogenous leverage in a general equilibrium model with
incomplete markets. We prove that in any binary tree leverage emerges in equilibrium at
the maximum level such that VaR = 0, so there is no default in equilibrium,
provided that agents get no utility from holding the collateral. When the collateral does
affect utility (as with housing) or when agents have sufficiently heterogenous beliefs
over three or more states, VaR = 0 fails to hold in equilibrium. We study
commonly used examples: an economy in which investors have heterogenous beliefs and a CAPM
economy consisting of investors with different risk aversion. We find two main departures
from VaR = 0. First, both examples show that with enough heterogeneity among the
investors, equilibrium default is normal. Second, we find that more than one contract is
actively traded in equilibrium on the same collateral, that is, the same asset is bought
at different margin requirements by different agents. Finally, we study the relationship
between leverage and asset prices. We provide an example that shows that as the regulatory
authority gradually relaxes leverage restrictions from low levels and permits leverage to
rise, asset prices start to rise, but eventually increased leverage paradoxically tends to
reduce asset prices because the risky bonds become substitutes for the asset used as
collateral. |
