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Leverage and Default in Binomial Economies: A Complete Characterization

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  • Ana Fostel
  • John Geanakoplos

Abstract

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 LT V 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.

Suggested Citation

  • Ana Fostel & John Geanakoplos, 2013. "Leverage and Default in Binomial Economies: A Complete Characterization," Working Papers 2013-16, The George Washington University, Institute for International Economic Policy.
  • Handle: RePEc:gwi:wpaper:2013-16
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    File URL: http://www.gwu.edu/~iiep/assets/docs/papers/FostelIIEPWP201316.pdf
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    References listed on IDEAS

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    Cited by:

    1. John Geanakoplos & William Zame, 2014. "Collateral equilibrium, I: a basic framework," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 443-492, August.
    2. Gregory Phelan, 2017. "Collateralized borrowing and increasing risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 471-502, February.
    3. Aloísio Araújo & Susan Schommer & Michael Woodford, 2015. "Conventional and Unconventional Monetary Policy with Endogenous Collateral Constraints," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(1), pages 1-43, January.
    4. Ana Fostel & John Geanakoplos, 2013. "Reviewing the Leverage Cycle," Cowles Foundation Discussion Papers 1918, Cowles Foundation for Research in Economics, Yale University.
    5. Theodore Bogusz & Theodore Bogusz, 2013. "Bubbles and Leverage: A Simple and Unified Approach," Working Paper Series WP-2013-21, Federal Reserve Bank of Chicago.
    6. Geanakoplos, John, 2014. "Leverage, Default, and Forgiveness: Lessons from the American and European Crises," Journal of Macroeconomics, Elsevier, vol. 39(PB), pages 313-333.

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    More about this item

    Keywords

    Endogenous Leverage; Default; Collateral Equilibrium; Financial Asset; Binomial Economy; VaR; Diluted Leverage; Volatility;
    All these keywords.

    JEL classification:

    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G01 - Financial Economics - - General - - - Financial Crises
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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