Sornette, Why Stock Markets Crash, part 1—Drawdowns as Outliers

In 2001 Didier Sornette, a scientist who taught geophysics at UCLA and today wears many hats (among them, professor of entrepreneurial risks at ETH Zurich, professor of physics at ETH Zurich, professor of geophysics at ETH Zurich, and visiting professor of geophysics at UCLA), finished his book Why Stock Markets Crash: Critical Events in Complex Financial Systems. It was published by Princeton University Press in 2003. Some of the themes of his book have been expressed by other thinkers, but Sornette’s analysis is both extensive (the text alone is just shy of 400 pages) and accessible to the layman.

Sornette contends that financial markets are complex systems that cannot be explained reductionistically by decomposing them into their elements and then studying these elements. Complex systems often exhibit “coherent large-scale collective behaviors with a very rich structure, resulting from the repeated nonlinear interactions among its constituents: the whole turns out to be much more than the sum of its parts.” (p. 16) Moreover, says Sornette, “it is widely believed that most complex systems are not amenable to mathematical, analytic descriptions” and that “many complex systems are said to be computationally irreducible; that is, the only way to decide about their evolution is to actually let them evolve in time. Accordingly, the ‘dynamical’ future time evolution of complex systems would be inherently unpredictable.” (p. 17)

Sornette is dissatisfied with the hypothesis that the prediction of complex systems is impossible and sets out to find patterns that can be compared “simultaneously and iteratively, at multiple scales in hierarchical systems.” (p. 20) These patterns can then be used to compare the dynamical state of systems before and after a financial crash. Sornette’s hypothesis is that “stock market crashes are caused by the slow build-up of long-range correlations leading to a global cooperative behavior of the market and eventually ending in a collapse in a short, critical time interval.” (p. 23) With very few exceptions, he argues, “log-periodic power-laws adequately describe speculative bubbles on the Western markets as well as on the emerging markets.” (p. 25)

How does Sornette reach this conclusion? After rejecting the frequency distribution model as inadequate for characterizing anomalous events, Sornette turns to the familiar concept of drawdowns. Drawdowns, he argues, “embody a rather subtle dependence since they are constructed from runs of the same sign variations.” (p. 52) For instance, consider a drawdown of 10% a day over three days. There is a persistence here that is not captured in the distribution of returns that counts only (uncorrelated) frequency and minimizes the chance of an outlier occurring. The sequence of four drops marking the largest drawdown in the DJIA (Black Monday, October 1987) would occur, according to distribution theory, once in about 4 thousands of billions of billions of years. Oops!

The very largest drawdowns, Sornette shows, are outliers even though, with the exception of Black Monday, the very largest daily drops are not outliers. What accounts for the persistence that creates outliers? What mechanisms in the stock market and in the behavior of investors can lead to positive feedback? That’s the subject for part 2 of this post.