COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1745R "Leverage Causes Fat Tails and Clustered Volatility" Stefan Thurner, J. Doyne Farmer, and John Geanakoplos January 2010 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. |
