COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1877 Endogenous Leverage in a Binomial Economy: Ana Fostel and John Geanakoplos September, 2012 We show that binomial economies with financial assets are an
informative and tractable model to study endogenous leverage and collateral equilibrium:
endogenous leverage can be highly volatile, but it is always easy to compute. The
possibility of default can have a dramatic effect on equilibrium, if collateral is scarce,
yet we prove the No-Default Theorem asserting that, without loss of generality, there is
no default in equilibrium. Thus potential default has a dramatic effect on equilibrium,
but actual default does not. This result is valid with arbitrary preferences, contingent
promises, many assets and consumption goods, production, and multiple periods. On the
other hand, we show that the theorem fails in trinomial models. For example, in a CAPM
model, we find that default is robust. In a model with heterogeneous beliefs, we find that
different agents might borrow on the same asset with different LTVs. |
