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Leverage and Default in Binomial Economies: A Complete Characterization

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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 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.

Suggested Citation

  • Ana Fostel & John Geanakoplos, 2012. "Leverage and Default in Binomial Economies: A Complete Characterization," Cowles Foundation Discussion Papers 1877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2013.
  • Handle: RePEc:cwl:cwldpp:1877r
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d18/d1877-r.pdf
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    References listed on IDEAS

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    1. Adrian, Tobias & Boyarchenko, Nina, 2012. "Intermediary leverage cycles and financial stability," Staff Reports 567, Federal Reserve Bank of New York, revised 01 Feb 2015.
    2. Ana Fostel & John Geanakoplos, 2012. "Tranching, CDS, and Asset Prices: How Financial Innovation Can Cause Bubbles and Crashes," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(1), pages 190-225, January.
    3. Nicolae Gârleanu & Lasse Heje Pedersen, 2011. "Margin-based Asset Pricing and Deviations from the Law of One Price," Review of Financial Studies, Society for Financial Studies, vol. 24(6), pages 1980-2022.
    4. Fostel, Ana & Geanakoplos, John, 2012. "Why does bad news increase volatility and decrease leverage?," Journal of Economic Theory, Elsevier, vol. 147(2), pages 501-525.
    5. Araújo, Aloísio & Kubler, Felix & Schommer, Susan, 2012. "Regulating collateral-requirements when markets are incomplete," Journal of Economic Theory, Elsevier, vol. 147(2), pages 450-476.
    6. Viral V. Acharya & S. Viswanathan, 2011. "Leverage, Moral Hazard, and Liquidity," Journal of Finance, American Finance Association, vol. 66(1), pages 99-138, February.
    7. Bernanke, Ben & Gertler, Mark, 1989. "Agency Costs, Net Worth, and Business Fluctuations," American Economic Review, American Economic Association, vol. 79(1), pages 14-31, March.
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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. Geanakoplos, John, 2014. "Leverage, Default, and Forgiveness: Lessons from the American and European Crises," Journal of Macroeconomics, Elsevier, vol. 39(PB), pages 313-333.

    More about this item

    Keywords

    Endogenous leverage; Default; Collateral equilibrium; Financial asset; Binomial economy; VaR; Diluted leverage; Volatility;

    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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