Fat Tails & Nonlinearity, Dec 2007
Diversity Breakdowns and Invisible Vulnerability
For he who is acquainted with the paths of nature, will more readily observe her deviations; and, vice versa, he who has learned her deviations will be able more accurately to describe her paths.
Novum Organum 1
The Memo Went Out
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.
Critical points are also important for proper counterfactual thinking. For every critical point we do see, how many were lurking but never triggered? Like water temperature dropping to 33 degrees and again rising, there are likely many nearmisses in the markets that elude our detection.
We survey three ideas: black swans and why patterns set us up for surprise; the conditions for crowds to be wise and the role of nonlinearity; and, finally, three examples of nonlinearity, including a physical system, an agent-based model, and a recent market dislocation.
Don't Feed the Turkey
Nassim Taleb uses the black swan metaphor to help popularize the fat-tail idea. He defines a black swan as an outlier event that has an extreme impact and that humans seek to explain after the fact. Recent market turmoil fits the definition well.
The black swan reference reflects Karl Popper’s criticism of induction. Popper’s point is that to understand a phenomenon, we’re better off focusing on falsification than on verification. Seeing lots of white swans doesn’t prove the theory that all swans are white, but seeing one black swan does disprove it.
Taleb relates the story of a turkey that is fed 1,000 days in a row. The feedings reinforce the turkey’s sense of security and well-being, until one day before Thanksgiving an unexpected and uninvited bad event occurs. All of the turkey’s experience and feedback is positive until fortune takes a turn for the worse. Recent comments by a senior executive at one of the world’s largest banks evoke the turkey story: “Our losses [from instruments based on U.S. subprime mortgages] greatly exceeded the profits we made in this field over several years.”
Here’s the point: rising asset prices provide investors confirming evidence that their strategy is good and everything is fine. This induction problem lulls investors into a sense of confidence, and sets the stage for the shock when events turn down. That nonlinearity causes sudden change only adds to the confusion.