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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.

Suggested Citation

  • Ana Fostel & John Geanakoplos, 2012. "Endogenous Leverage in a Binomial Economy: The Irrelevance of Actual Default," Cowles Foundation Discussion Papers 1877, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1877
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d18/d1877.pdf
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    References listed on IDEAS

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    1. 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.
    2. Acemoglu, Daron & Rogoff, Kenneth & Woodford, Michael (ed.), 2010. "NBER Macroeconomics Annual 2009," National Bureau of Economic Research Books, University of Chicago Press, number 9780226002095.
    3. 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.
    4. John Geanakoplos & Ana Fostel, 2008. "Leverage Cycles and the Anxious Economy," American Economic Review, American Economic Association, vol. 98(4), pages 1211-1244, September.
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    Cited by:

    1. Valentina Bruno & Hyun Song Shin, 2013. "Capital Flows, Cross-Border Banking and Global Liquidity," NBER Working Papers 19038, National Bureau of Economic Research, Inc.
    2. Shengxing Zhang, 2014. "Collateral Risk, Repo Rollover and Shadow Banking," 2014 Meeting Papers 562, Society for Economic Dynamics.
    3. Adrian, Tobias & Moench, Emanuel & Shin, Hyun Song, 2013. "Dynamic leverage asset pricing," Staff Reports 625, Federal Reserve Bank of New York, revised 01 Dec 2014.

    More about this item

    Keywords

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

    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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