COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1745 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 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. |
