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Leverage Causes Fat Tails and Clustered Volatility

  • Stefan Thurner
  • J. Doyne Farmer
  • John Geanakoplos

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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Paper provided by in its series Papers with number 0908.1555.

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Date of creation: Aug 2009
Date of revision: Jan 2010
Handle: RePEc:arx:papers:0908.1555
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  1. John Geanakoplos, 2009. "The Leverage Cycle," Cowles Foundation Discussion Papers 1715, Cowles Foundation for Research in Economics, Yale University.
  2. John Geanakoplos & Ana Fostel, 2008. "Leverage Cycles and the Anxious Economy," American Economic Review, American Economic Association, vol. 98(4), pages 1211-44, September.
  3. Tobias Adrian & Hyun Song Shin, 2008. "Liquidity and leverage," Staff Reports 328, Federal Reserve Bank of New York.
  4. Guercio, Diane Del & Tkac, Paula A., 2002. "The Determinants of the Flow of Funds of Managed Portfolios: Mutual Funds vs. Pension Funds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(04), pages 523-557, December.
  5. Erik R. Sirri & Peter Tufano, 1998. "Costly Search and Mutual Fund Flows," Journal of Finance, American Finance Association, vol. 53(5), pages 1589-1622, October.
  6. G. Caldarelli & M. Marsili & Y. -C. Zhang, 1997. "A Prototype Model of Stock Exchange," Papers cond-mat/9709118,
  7. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
  8. Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
  9. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, Oxford University Press, vol. 121(2), pages 461-504.
  10. Busse, Jeffrey A., 2001. "Another Look at Mutual Fund Tournaments," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 36(01), pages 53-73, March.
  11. Markus K. Brunnermeier & Lasse Heje Pedersen, 2007. "Market Liquidity and Funding Liquidity," NBER Working Papers 12939, National Bureau of Economic Research, Inc.
  12. repec:att:wimass:9621 is not listed on IDEAS
  13. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
  14. Eli M. Remolona & Paul Kleiman & Debbie Gruenstein, 1997. "Market returns and mutual fund flows," Economic Policy Review, Federal Reserve Bank of New York, issue Jul, pages 33-52.
  15. Chevalier, J. & Ellison, G., 1996. "Risk Taking by Mutual Funds as a Response to Incentives," Working papers 96-3, Massachusetts Institute of Technology (MIT), Department of Economics.
  16. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  17. repec:att:wimass:9706 is not listed on IDEAS
  18. W. Brian Arthur & John H. Holland & Blake LeBaron & Richard Palmer & Paul Taylor, 1996. "Asset Pricing Under Endogenous Expectation in an Artificial Stock Market," Working Papers 96-12-093, Santa Fe Institute.
  19. Ole Peters, 2009. "Optimal leverage from non-ergodicity," Papers 0902.2965,, revised Aug 2010.
  20. V. Plerou & P. Gopikrishnan & L. A. N. Amaral & M. Meyer & H. E. Stanley, 1999. "Scaling of the distribution of price fluctuations of individual companies," Papers cond-mat/9907161,
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