Leverage Causes Fat Tails and Clustered Volatility

15 Pages Posted: 23 Nov 2011

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: November 22, 2011

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 approximately normally distributed and uncorrelated across time. This changes when the funds are allowed to leverage, i.e., borrow from a bank, which allows them to purchase more assets than their wealth would otherwise permit. During good times funds that use more leverage have higher profits, increasing their wealth and making them dominant in the market. However, if a downward price fluctuation occurs while one or more funds are fully leveraged, the resulting margin call causes them to sell into an already falling market, amplifying the downward price movement. If the funds hold large positions in the asset this can cause substantial losses. This in turns leads to clustered volatility: Before a crash, when the value funds are dominant, they damp volatility, and after the crash, when they suffer severe losses, volatility is high. This leads to power law tails which are both due to the leverage-induced crashes and due to the clustered volatility induced by the wealth dynamics. This is in contrast to previous explanations of fat tails and clustered volatility, which depended on "irrational behavior," such as trend following. 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 (November 22, 2011). Cowles Foundation Discussion Paper No. 1745R. Available at SSRN: https://ssrn.com/abstract=1963337

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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