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Endogenous Leverage in a Binomial Economy: The Irrelevance of Actual Default

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Abstract

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.

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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1877.

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Length: 43 pages
Date of creation: Sep 2012
Date of revision:
Handle: RePEc:cwl:cwldpp:1877

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Endogenous leverage; Collateral equilibrium; Default; Financial asset; Binomial economy; VaR;

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  1. Acemoglu, Daron & Rogoff, Kenneth & Woodford, Michael (ed.), 2010. "NBER Macroeconomics Annual 2009," National Bureau of Economic Research Books, University of Chicago Press, number 9780226002095.
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