Leverage Causes Fat Tails and Clustered Volatility

We build a very 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. When funds use leverage, 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. We show that the immediate cause of the increase in extreme risks in our model is the risk control policy of the banks: 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 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 by individual banks makes these extreme fluctuations even worse. Thus it is the very effort to control risk at the local level that creates excessive risk at the aggregate level, which shows up as fat tails and clustered volatility.