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.
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- G. Caldarelli & M. Marsili & Y. -C. Zhang, 1997. "A Prototype Model of Stock Exchange," Papers cond-mat/9709118, arXiv.org.
- repec:att:wimass:9706 is not listed on IDEAS
- Brunnermeier, Markus K & Pedersen, Lasse Heje, 2007.
"Market Liquidity and Funding Liquidity,"
CEPR Discussion Papers
6179, C.E.P.R. Discussion Papers.
- Markus K. Brunnermeier & Lasse Heje Pedersen, 2007. "Market liquidity and funding liquidity," LSE Research Online Documents on Economics 24478, London School of Economics and Political Science, LSE Library.
- Lasse Heje Pederson & Markus K Brunnermeier, 2007. "Market Liquidity and Funding Liquidity," FMG Discussion Papers dp580, Financial Markets Group.
- Markus K. Brunnermeier & Lasse Heje Pedersen, 2007. "Market Liquidity and Funding Liquidity," NBER Working Papers 12939, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2006. "Institutional Investors and Stock Market Volatility," The Quarterly Journal of Economics, MIT Press, vol. 121(2), pages 461-504, May.
- W. Brian Arthur & John H. Holland & Blake LeBaron & Richard Palmer & Paul Taylor, 1996.
"Asset Pricing Under Endogenous Expectation in an Artificial Stock Market,"
96-12-093, Santa Fe Institute.
- 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.
- 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.
- Chevalier, J. & Ellison, G., 1996.
"Risk Taking by Mutual Funds as a Response to Incentives,"
96-3, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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.
- Adrian, Tobias & Shin, Hyun Song, 2010.
"Liquidity and leverage,"
Journal of Financial Intermediation,
Elsevier, vol. 19(3), pages 418-437, July.
- 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.
- 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.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- 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.
- 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.
- Ole Peters, 2009. "Optimal leverage from non-ergodicity," Papers 0902.2965, arXiv.org, revised Aug 2010.
- John Geanakoplos & Ana Fostel, 2008. "Leverage Cycles and the Anxious Economy," American Economic Review, American Economic Association, vol. 98(4), pages 1211-44, September.
- repec:att:wimass:9621 is not listed on IDEAS
- 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.
- John Geanakoplos, 2009. "The Leverage Cycle," Cowles Foundation Discussion Papers 1715, Cowles Foundation for Research in Economics, Yale University.
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