COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1877R Leverage and Default in Binomial Economies: Ana Fostel and John Geanakoplos September 2012 Our paper provides a complete characterization of leverage and default
in binomial economies with financial assets serving as collateral. First, our Binomial
No-Default Theorem states that any equilibrium is equivalent (in real allocations and
prices) to another equilibrium in which there is no default. Thus actual default is
irrelevant, though the potential for default drives the equilibrium and limits borrowing.
This result is valid with arbitrary preferences and endowments, arbitrary promises, many
assets and consumption goods, production, and multiple periods. We also show that the
no-default equilibrium would be selected if there were the slightest cost of using
collateral or handling default. Second, our Binomial Leverage Theorem shows that
equilibrium LTV for non-contingent debt contracts is the ratio of the worst-case
return of the asset to the riskless rate of interest. Finally, our Binomial
Leverage-Volatility theorem provides a precise link between leverage and volatility. |
