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 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.