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Leverage causes fat tails and clustered volatility

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  • Stefan Thurner
  • J. Doyne Farmer
  • John Geanakoplos

Abstract

We build a simple model of leveraged asset purchases with margin calls. Investment funds use what is perhaps the most basic financial strategy, called ‘value investing’, i.e. systematically attempting to buy underpriced assets. When funds do not borrow, the price fluctuations of the asset are approximately normally distributed and uncorrelated across time. This changes when the funds are allowed to leverage , i.e. borrow from a bank, which allows them to purchase more assets than their wealth would otherwise permit. During good times, funds that use more leverage have higher profits, increasing their wealth and making them dominant in the market. However, if a downward price fluctuation occurs while one or more funds is fully leveraged, the resulting margin call causes them to sell into an already falling market, amplifying the downward price movement. If the funds hold large positions in the asset, this can cause substantial losses. This in turn leads to clustered volatility: before a crash, when the value funds are dominant, they damp volatility, and after the crash, when they suffer severe losses, volatility is high. This leads to power-law tails, which are both due to the leverage-induced crashes and due to the clustered volatility induced by the wealth dynamics. This is in contrast to previous explanations of fat tails and clustered volatility, which depended on ‘irrational behavior’, such as trend following. A standard (supposedly more sophisticated) risk control policy in which individual banks base leverage limits on volatility causes leverage to rise during periods of low volatility, and to contract more quickly when volatility becomes high, making these extreme fluctuations even worse.

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File URL: http://hdl.handle.net/10.1080/14697688.2012.674301
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Quantitative Finance.

Volume (Year): 12 (2012)
Issue (Month): 5 (February)
Pages: 695-707

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Handle: RePEc:taf:quantf:v:12:y:2012:i:5:p:695-707

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Cited by:
  1. Mark Setterfield & Bill Gibson, 2013. "Real and financial crises: A multi-agent approach," Working Papers 1309, Trinity College, Department of Economics, revised Jul 2014.
  2. Doris Neuberger & Roger Rissi, 2014. "Macroprudential Banking Regulation: Does One Size Fit All?," Journal of Banking and Financial Economics, University of Warsaw, Faculty of Management, vol. 1(1), pages 5-28, May.
  3. Jean-Philippe Bouchaud, 2011. "Panel Statement: The endogenous dynamics of markets: price impact and feedback loops," Chapters, European Central Bank.
  4. Dospinescu, Andrei Silviu, 2012. "Local Environment Analysis and Rules Inferring Procedure in an Agent-Based Model – Applications in Economics," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 128-143, March.
  5. Zhang, Ting & Li, Honggang, 2013. "Buying on margin, selling short in an agent-based market model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4075-4082.
  6. Fischer, Thomas & Riedler, Jesper, 2013. "Prices, debt and market structure in an agent-based model of the financial market," ZEW Discussion Papers 12-045 [rev.], ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  7. Blake LeBaron, 2010. "Heterogeneous Gain Learning and the Dynamics of Asset Prices," Working Papers 29, Brandeis University, Department of Economics and International Businesss School, revised Dec 2010.
  8. Poledna, Sebastian & Thurner, Stefan & Farmer, J. Doyne & Geanakoplos, John, 2014. "Leverage-induced systemic risk under Basle II and other credit risk policies," Journal of Banking & Finance, Elsevier, vol. 42(C), pages 199-212.
  9. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics: agent-based models," Post-Print hal-00621059, HAL.
  10. David Morton de Lachapelle & Damien Challet, 2009. "Turnover, account value and diversification of real traders: evidence of collective portfolio optimizing behavior," Papers 0912.4723, arXiv.org, revised Jun 2010.
  11. Al-Suwailem, Sami, 2014. "Complexity and endogenous instability," Research in International Business and Finance, Elsevier, vol. 30(C), pages 393-410.
  12. Silvio M. Duarte Queiros & Evaldo M. F. Curado & Fernando D. Nobre, 2011. "Minding impacting events in a model of stochastic variance," Papers 1102.4819, arXiv.org, revised Feb 2011.
  13. Li-Xin Wang, 2014. "Gaussian-Chain Filters for Heavy-Tailed Noise with Application to Detecting Big Buyers and Big Sellers in Stock Market," Papers 1405.2220, arXiv.org.

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