Leverage and Default in Binomial Economies: A Complete Characterization
Abstract
Our paper provides a complete characterization of leverage and default in binomial economies with financial assets serving as collateral. 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, contingent or non-contingent promises, many assets and consumption goods, production, and multiple periods. We also show that no-default equilibria would be selected if there were the slightest cost of using collateral or handling default. Our Binomial Leverage Theorem shows that equilibrium Loan to Value (LTV) for non-contingent debt contracts is the ratio of the worst-case return of the asset to the riskless gross rate of interest. In binomial economies leverage is determined by down risk and not by volatility.
Keywords: Endogenous leverage, Default, Collateral equilibrium, Financial asset, Binomial economy, VaR, Diluted leverage, Down risk