Leverage Causes Fat Tails and Clustered Volatility
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.
|Date of creation:||Jan 2010|
|Publication status:||Published in Quantitative Finance (May 2012), 12(5): 695-707|
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- 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.
- Brock, W.A. & Hommes, C.H., 1996. "Hetergeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model," Working papers 9621, Wisconsin Madison - Social Systems.
- 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.
- Adrian, Tobias & Shin, Hyun Song, 2010. "Liquidity and leverage," Journal of Financial Intermediation, Elsevier, vol. 19(3), pages 418-437, July.
- Tobias Adrian & Hyun Song Shin, 2008. "Liquidity and leverage," Staff Reports 328, Federal Reserve Bank of New York.
- Markus K. Brunnermeier & Lasse Heje Pedersen, 2009. "Market Liquidity and Funding Liquidity," Review of Financial Studies, Society for Financial Studies, vol. 22(6), pages 2201-2238, June.
- Brunnermeier, Markus K & Pedersen, Lasse Heje, 2007. "Market Liquidity and Funding Liquidity," CEPR Discussion Papers 6179, C.E.P.R. Discussion Papers.
- Lasse Heje Pederson & Markus K Brunnermeier, 2007. "Market Liquidity and Funding Liquidity," FMG Discussion Papers dp580, Financial Markets Group.
- Brunnermeier, Markus K. & Pedersen, Lasse Heje, 2007. "Market liquidity and funding liquidity," LSE Research Online Documents on Economics 24478, London School of Economics and Political Science, LSE Library.
- Markus K. Brunnermeier & Lasse Heje Pedersen, 2007. "Market Liquidity and Funding Liquidity," NBER Working Papers 12939, National Bureau of Economic Research, Inc.
- 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.
- Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
- Lux, T. & M. Marchesi, "undated". "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.
- 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, arXiv.org.
- Arthur, W.B. & Holland, J.H. & LeBaron, B. & Palmer, R. & Tayler, P., 1996. "Asset Pricing Under Endogenous Expectations in an Artificial Stock Market," Working papers 9625, Wisconsin Madison - Social Systems.
- 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.
- Chevalier, Judith & Ellison, Glenn, 1997. "Risk Taking by Mutual Funds as a Response to Incentives," Journal of Political Economy, University of Chicago Press, vol. 105(6), pages 1167-1200, December.
- Judith A. Chevalier & Glenn D. Ellison, 1995. "Risk Taking by Mutual Funds as a Response to Incentives," NBER Working Papers 5234, National Bureau of Economic Research, Inc.
- 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.
- Ole Peters, 2009. "Optimal leverage from non-ergodicity," Papers 0902.2965, arXiv.org, revised Aug 2010.
- 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.
- G. Caldarelli & M. Marsili & Y. -C. Zhang, 1997. "A Prototype Model of Stock Exchange," Papers cond-mat/9709118, arXiv.org.
- 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.
- 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.
- Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394-394.
- John Geanakoplos, 2009. "The Leverage Cycle," Cowles Foundation Discussion Papers 1715, Cowles Foundation for Research in Economics, Yale University.
- Brock, W.A. & Hommes, C.H., 1997. "Models of Compelxity in Economics and Finance," Working papers 9706, Wisconsin Madison - Social Systems.
- 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.
- John Geanakoplos & Ana Fostel, 2008. "Leverage Cycles and the Anxious Economy," American Economic Review, American Economic Association, vol. 98(4), pages 1211-1244, September. Full references (including those not matched with items on IDEAS)
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