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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 normallydistributed and uncorrelated across time. All this changes when the funds areallowed to leverage, i.e. borrow from a bank, to purchase more assets thantheir wealth would otherwise permit. During good times competition drivesinvestors to funds that use more leverage, because they have higher profits. Asleverage increases price fluctuations become heavy tailed and display clusteredvolatility, similar to what is observed in real markets. Previous explanationsof fat tails and clustered volatility depended on "irrational behavior", suchas trend following. Here instead this comes from the fact that leverage limitscause funds to sell into a falling market: A prudent bank makes itself locallysafer by putting a limit to leverage, so when a fund exceeds its leveragelimit, it must partially repay its loan by selling the asset. Unfortunatelythis sometimes happens to all the funds simultaneously when the price isalready falling. The resulting nonlinear feedback amplifies large downwardprice movements. At the extreme this causes crashes, but the effect is seen atevery time scale, producing a power law of price disturbances. A standard(supposedly more sophisticated) risk control policy in which individual banksbase leverage limits on volatility causes leverage to rise during periods oflow volatility, and to contract more quickly when volatility gets high, makingthese extreme fluctuations even worse.

Leverage Causes Fat Tails and Clustered Volatility