Why Stock Markets Crash: Critical Events in Complex Financial Systems

Published by EH.NET (April 2003)

Didier Sornette, Why Stock Markets Crash: Critical Events in Complex

Financial Systems. Princeton, NJ: Princeton University Press, 2002. xx +

421 pp. $29.95 (hardcover), ISBN: 0-691-09630-9.

Reviewed for EH.NET by Gary Santoni, Department of Economics, Ball State

University.

Why Stock Markets Crash by Didier Sornette is an interesting and

thought-provoking book. Sornette is a professor of geophysics at the University

of California, Los Angeles who specializes in the scientific prediction of

catastrophes. Since stock market crashes are, without question, catastrophes,

the reader might expect an informative treatment of the relationship between

catastrophes that occur in the natural world and those that occur in financial

markets. Sornette’s discussion of the science of earthquakes, volcanic

eruptions, hurricanes, tornadoes and meteorite impacts is riveting. In

addition, the reader learns about how such notions as finite-time

singularities, log periodic oscillations, Cantor sets, fractal dimensions,

Schrodinger’s equation and log-quasi-periodicity, are used to characterize and

predict these natural disasters. Readers interested in why stock markets crash

and the relationship between these events and natural catastrophes will be

disappointed, however.

Clearly, natural and financial phenomena are similar in that catastrophes occur

in both. It is something else to argue that the processes leading to these

events and the relevant tools of analysis are the same or even similar. George

Stigler once noted that the economist faces a level of difficulty not shared by

the physical scientist. The economist’s “main elements of analysis are people.

… Imagine the problems of a chemist if he had to deal with molecules of

oxygen, each of which was somewhat interested in whether it was joined in

chemical bond to hydrogen. Some would hurry him along; others would cry shrilly

for a federal program to drill wells for water instead; and several would

blandly assure him that they were molecules of argon.”1 None of this is meant

to suggest that the scientific method has no place in the study of economics.

Few economists did more than Stigler to promote the application of science in

economics but he warns that the economist can expect to encounter some special

problems.

Sornette bumps up against one of these special problems in his discussion of

the fundamentals of stock prices. He argues that, “These considerations make it

clear that it is the expectation of future earnings and future capital

gains rather than present economic reality that motivates the average investor,

thus creating a speculative bubble” (p. 270). Sornette fails to recognize that

stock prices (or, more precisely, the choices people make in determining these

prices) are always based on expectations regarding the future — and

this implies nothing about whether or not they contain a speculative bubble.

Irving Fisher said it best when he noted that, “Our present acts must be

controlled by the future, not as it actually is, but as it appears to us

through the veil of chance.”2 Decisions regarding stocks are no exception.

Expected future cash flows (dividends, capital gains, etc.) are the

important fundamentals of prices — they are the economic reality. Present

earnings, Sornette’s reality, are only relevant in so far as they contain

information about the future. The behavior of people, unlike molecules of

oxygen, is driven by expectations.

The most enlightening discussion in Sornette’s book is his treatment of the

efficient markets hypothesis in Chapters 2 and 3. This hypothesis implies that

stock prices move at a random walk so that changes in the price are

unpredictable. Since crashes are simply large negative changes in price, the

hypothesis implies that crashes cannot be predicted. While the evidence that

has accumulated over the years is largely consistent with this idea, an

interesting exception to this general result is noted in Chapter 3. Examining

daily data on the Dow Jones Industrial Average over the last century, Sornette

finds 14 episodes — a total of 64 trading days out of a sample of about 25,000

— that violate the implications of the hypothesis. These unusual observations

are all associated with large declines in stock prices ranging from -12.4% to

-30.7% (p. 61). The conclusion to be drawn from this is that stock prices

behave unusually (in the sense that successive changes in them may be related

and, hence, predictable) during episodes of large price declines.

There are several points that are important here. These unusual episodes only

occur during periods of large price declines. Second, there are relatively few

of them — 64 of 25,000 trading days. Third, the average length of these 14

episodes is only 4.5 days so the period over which prediction may be possible

is of short duration. Finally, these periods are only detectable after

prices have begun to decline. For the vast bulk of the evidence Sornette

analyzes (particularly, when prices are generally rising), changes in stock

prices behave randomly and, thus, are unpredictable.

Perhaps because of the confusion regarding the role of expectations in economic

decision-making, Sornette ignores the efficient market hypothesis and the

evidence regarding it in the remainder of his book and focuses instead on

various bubble models of stock prices all of which imply that prices behave

unusually before a crash, i.e., while prices are generally rising. In

this regard, the reader is treated to discussions of the Ising Model of

Cooperative Behavior, El-Farol’s Bar Problem, Mimetic Contagion and the Urn

Model, and Herd Behavior and Crowd Effects to name a few. Sornette models the

bubble with an equation containing a log-periodic correction to a power law for

a variable (stock prices) exhibiting a finite-time singularity. In short,

Sornette attempts to fit a trend to stock prices for periods prior to crashes

even though the data analyzed in Chapter 3 suggest that no such trend exists.

As might be expected, the results are disappointing even though the test

periods selected are those immediately preceding 1929 and 1987, the two largest

crashes on record. The statistic measuring the equation’s goodness of fit

varies erratically as the sample period prior to the crash is varied and shows

a marked improvement only when data subsequent to the crash are included. Thus,

the model “predicts” the crash only after it has occurred (pp. 330-34).

Sornette indicates that this is an “idiosyncrasy” of the model, which, of

course, calls into question its relevance for both theory and practice.

People will always be interested in stock market crashes. If they were

understood, it might be possible to forecast them which, of course, could lead

to vast riches. I wish Sornette good luck in his endeavor. Should he be

successful, I don’t expect he will tell us about it, however.

Endnotes: 1. George Stigler, The Theory of Price, Macmillan Company,

1966, p. 8. 2. Irving Fisher, The Rate of Interest, Macmillan Company,

1907, p. 213.

Gary Santoni’s recent publications include “Expected Dividend Growth,

Valuation Ratios and Rational Optimism,” in the Journal of Financial and

Economic Practice (Fall, 2002).