Leverage and Default in Binomial Economies: A Complete Characterization

47 Pages Posted: 10 Mar 2015

See all articles by Ana Fostel

Ana Fostel

University of Virginia

John Geanakoplos

Yale University; Santa Fe Institute

Multiple version iconThere are 3 versions of this paper

Date Written: March 9, 2015

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, LTV, Diluted leverage, Down risk

JEL Classification: D52, D53, E44, G01, G11, G12

Suggested Citation

Fostel, Ana and Geanakoplos, John D, Leverage and Default in Binomial Economies: A Complete Characterization (March 9, 2015). Cowles Foundation Discussion Paper No. 1877RRR, Available at SSRN: https://ssrn.com/abstract=2575750 or http://dx.doi.org/10.2139/ssrn.2575750

Ana Fostel

University of Virginia ( email )

1400 University Ave
Charlottesville, VA 22903
United States

John D Geanakoplos (Contact Author)

Yale University ( email )

30 Hillhouse Avenue
New Haven, CT 06511
United States
203-432-3397 (Phone)

HOME PAGE: http://https://economics.yale.edu/people/faculty/john-geanakoplos

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States

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