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.