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Endogenous Leverage: VaR and Beyond




We study endogenous leverage in a general equilibrium model with incomplete markets. We prove that in any binary tree leverage emerges in equilibrium at the maximum level such that VaR = 0, so there is no default in equilibrium, provided that agents get no utility from holding the collateral. When the collateral does affect utility (as with housing) or when agents have sufficiently heterogenous beliefs over three or more states, VaR = 0 fails to hold in equilibrium. We study commonly used examples: an economy in which investors have heterogenous beliefs and a CAPM economy consisting of investors with different risk aversion. We find two main departures from VaR = 0. First, both examples show that with enough heterogeneity among the investors, equilibrium default is normal. Second, we find that more than one contract is actively traded in equilibrium on the same collateral, that is, the same asset is bought at different margin requirements by different agents. Finally, we study the relationship between leverage and asset prices. We provide an example that shows that as the regulatory authority gradually relaxes leverage restrictions from low levels and permits leverage to rise, asset prices start to rise, but eventually increased leverage paradoxically tends to reduce asset prices because the risky bonds become substitutes for the asset used as collateral.

Suggested Citation

  • Ana Fostel & John Geanakoplos, 2011. "Endogenous Leverage: VaR and Beyond," Cowles Foundation Discussion Papers 1800, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1800

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    References listed on IDEAS

    1. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(03), pages 460-471, June.
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    Cited by:

    1. Sebastian Infante, 2013. "Repo collateral fire sales: the effects of exemption from automatic stay," Finance and Economics Discussion Series 2013-83, Board of Governors of the Federal Reserve System (U.S.).
    2. 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.
    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. Breuer, Thomas & Jandačka, Martin & Summer, Martin & Vollbrecht, Hans-Joachim, 2015. "Endogenous leverage and asset pricing in double auctions," Journal of Economic Dynamics and Control, Elsevier, vol. 53(C), pages 144-160.
    5. Ana Fostel, 2012. "Leverage and Asset Prices: An Experiment," Working Papers 2012-1, The George Washington University, Institute for International Economic Policy.
    6. Tomura, Hajime, 2013. "Heterogeneous beliefs and housing-market boom-bust cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 37(4), pages 735-755.

    More about this item


    Endogenous leverage; Collateral equilibrium; VaR; Asset prices;

    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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