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Leverage Causes Fat Tails and Clustered Volatility

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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 normally distributed and uncorrelated across time. All this changes when the funds are allowed to leverage, i.e. borrow from a bank, to purchase more assets than their wealth would otherwise permit. During good times competition drives investors to funds that use more leverage, because they have higher profits. As leverage increases price fluctuations become heavy tailed and display clustered volatility, similar to what is observed in real markets. Previous explanations of fat tails and clustered volatility depended on "irrational behavior," such as trend fol­lowing. Here instead this comes from the fact that leverage limits cause funds to sell into a falling market: A prudent bank makes itself locally safer by putting a limit to leverage, so when a fund exceeds its leverage limit, it must partially repay its loan by selling the asset. Unfortunately this sometimes happens to all the funds simultaneously when the price is already falling. The resulting nonlinear feedback amplifies large downward price movements. At the extreme this causes crashes, but the effect is seen at every time scale, producing a power law of price disturbances. 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 gets high, making these extreme fluctuations even worse.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1745.

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Length: 19 pages
Date of creation: Jan 2010
Date of revision:
Publication status: Published in Quantitative Finance (May 2012), 12(5): 695-707
Handle: RePEc:cwl:cwldpp:1745

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Keywords: Systemic risk; Clustered volatility; Fat tails; Crash; Margin calls; Leverage;

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References

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Cited by:
  1. Jean-Philippe Bouchaud, 2011. "Panel Statement: The endogenous dynamics of markets: price impact and feedback loops," Chapters, European Central Bank.
  2. 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.
  3. 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.
  4. Fischer, Thomas & Riedler, Jesper, 2012. "Prices, debt and market structure in an agent-based model of the financial market," ZEW Discussion Papers 12-045, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  5. 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.
  6. 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.
  7. 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.
  8. Neuberger, Doris & Rissi, Roger, 2012. "Macroprudential banking regulation: Does one size fit all?," Thuenen-Series of Applied Economic Theory 124, University of Rostock, Institute of Economics.
  9. Mark Setterfield & Bill Gibson, 2013. "Real and financial crises," Working Papers 1309, Trinity College, Department of Economics, revised Sep 2013.
  10. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics: agent-based models," Post-Print hal-00621059, HAL.
  11. 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.
  12. 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.
  13. Al-Suwailem, Sami, 2014. "Complexity and endogenous instability," Research in International Business and Finance, Elsevier, vol. 30(C), pages 393-410.
  14. 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.

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