Leverage Causes Fat Tails and Clustered Volatility

20 Pages Posted: 11 Jan 2010 Last revised: 18 Mar 2010

See all articles by Stefan Thurner

Stefan Thurner

Institute for Science of Complex Systems, Medical University of Vienna; Santa Fe Institute

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; Santa Fe Institute

John Geanakoplos

Yale University - Cowles Foundation

Multiple version iconThere are 2 versions of this paper

Date Written: January 11, 2010

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.

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

JEL Classification: E32, E37, G01, G12, G14

Suggested Citation

Thurner, Stefan and Farmer, J. Doyne and Geanakoplos, John D, Leverage Causes Fat Tails and Clustered Volatility (January 11, 2010). Cowles Foundation Discussion Paper No. 1745. Available at SSRN: https://ssrn.com/abstract=1534648 or http://dx.doi.org/10.2139/ssrn.1534648

Stefan Thurner

Institute for Science of Complex Systems, Medical University of Vienna ( email )

Spitalgasse 23
Vienna, A-1090
Austria

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

HOME PAGE: http://www.inet.ox.ac.uk/people/view/4

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States
505-984-8800 (Phone)
505-982-0565 (Fax)

HOME PAGE: http://www.santafe.edu/~jdf/

John D Geanakoplos (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3397 (Phone)
203-432-6167 (Fax)

HOME PAGE: http://cowles.econ.yale.edu/P/au/d_gean.htm

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