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Michael Mauboussin: Fat Tails and Nonlinearity

Food for thought (PDF) from Michael Mauboussin:

If you are involved in financial markets, you have gotten the memo about fat tails by now.

But awareness of extreme events is not enough. Thoughtful investors must understand two interrelated aspects of the market. The first is the statistical properties of price movements, including important deviations from the bell-shaped distribution. Academics, risk managers, and quantitative investors have explored this aspect extensively. Researchers recognized decades ago that the distribution of price changes includes fat tails.

The second aspect, and one often overlooked or misunderstood, is the mechanism that leads to the statistical imprint. Much of the work on the market’s statistical properties is divorced from the propagating mechanism, while traditional theories of market efficiency assume the mechanisms. Crucially, understanding the mechanism provides insight into how and why markets fail.

Our focus here is on nonlinearity. Many complex systems, including markets, have critical points where small incremental condition changes lead to large-scale effects. Researchers in both the physical and social sciences have known about these critical points for a long time; so much so that terms like phase transition and tipping point have slipped into our day-to-day language. Still, critical points throw a monkey wrench into our mostly linear cause-and-effect thinking.

Critical points help explain our perpetual surprise at fat-tail events: We don’t see them coming because the state change is much greater than the perturbation suggests. Water does not undergo a dramatic change as it drops from 35 to 33 degrees Fahrenheit, but two degrees of additional cooling changes its state from liquid to solid. Likewise, large changes can occur in markets without visible manifestation in asset price change, while small additional changes can flip the price switch.

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