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Why Stock Markets Crash

D. Sornette

posted on 15 May 2003

reviewed by A. Johansen

The book "Why Stock Markets Crash" by Didier Sornette essentially consists of three parts. The first part presents a compelling collection of evidence suggesting that the paradigm underlying the efficient market hypothesis (EMH) is rather far from the truth at least on time scales of weeks, months and perhaps even several years. Beside a brief historical account of the most famous financial crashes and their preceding bubbles, such as the South Sea
Bubble, the Tulip Mania and the Great Crash of 1929 (chapter 1), the book
presents in chapter 2 the fundamental concepts underlying the EMH as well as
explaining some of the terminology of finance, such as "returns", "free lunch"
and the "trade-off" between risk and returns. From the basic physical concept
of random walks we are shown that no free lunches exist in a market populated by rational and informed traders. The book then in chapter 3 moves on trying to quantify why we have a special word for very large negative movements in a
given stock market index, namely the word "crash". Here, one should realize
that the "holistic" physics point of view ("power laws everywhere") is in fact
a minority view and that most part of society has no problems accepting that
crashes are special events and not just any price drop that did not stop. In
my (biased) opinion the book does a good job of quantifying that the largest
drops, i.e., the crashes, do not belong to the same distribution as the smaller drops representing close to 99\% of the distribution and that crashes hence are "outliers" and thus special. The book does this in large part by using the
concept of negative "runs" or "drawdowns" which by definition incorporate
correlations of higher order than two not captured by the distribution of
returns. We are shown several graphs of historical drawdown distributions
of major stock market index, currencies and gold which makes the outlier idea
quite palatable. Furthermore, we are shown non-parametric tests using surrogate data generated from real data, which further substantiates the outlier idea. In Chapter 4 we are introduced to the concept of positive feedbacks which further
justifies the outlier idea: At times traders on the stock market interacts in
such a way that positive feedback "loops" are created and a cooperative large
scale behaviour emerges destroying the randomness of properly anticipated
prices underlying the EMH. Examples from Physics, Biology and Sociology are
given which illustrate that positive feedback "loops" are not an uncommon
phenomenon in Nature and Society and thus also may be present in the financial
markets.

The second part of the book (Chapters 5-8) presents a working hypothesis for
the out-of-equilibrium behaviour often seen in the FM, in the folklore referred to as "a bubble", which more often than not ends in a crash. This part of the book is in some sense the Achilles heel of the book (and hence also in my own work with D. Sornette) as no microscopic model based on fundamental financial concepts is presented. Instead the book uses a compelling analogy (again in my biased opinion) between critical phenomena in Physics and the pre-crash bubble
behaviour of the financial markets and justifies this analogy by a large number
of case studies of real data. However, this analogy is not stated as explicit in the book as in some of the references carrying the author's name and the book goes a great length to reformulate on a financial basis, i.e., in terms of the "crash hazard rate". To make a long story short, the book makes an Ansatz for the crash hazard rate which means that average price trajectory in a financial bubble will obey a differential equation

dF(x)/dlog(x) = \alpha F(x) + higher order terms,

where \alpha is the critical (bubble) exponent which may take complex values, x = tc - t is the time to the (most likely) date for the crash tc and F is some proxy of the price, e.g., the price itself or logarithm of the price. Using the "no-arbitrage condition" it is possible to formulate a two rational expectation models, the risk-driven model and the price-driven model, which predicts the behaviour illustrated by the case studies presented. In
order to move beyond "case studies" we are shown that a kind of universality
exists with respect to the values of \alpha found in the different examples of financial bubbles presented in the book. Unfortunately, this is not done in
a single graph as in for example in paper cond-mat/0210509 by A. Johansen and
D. Sornette. In my opinion, the most intriguing prediction of the model
presented is that \alpha may be complex. As a consequence, the solution to
the above equations does not exhibit scale invariance in a conventional sense,
but instead a "Discrete Scale Invariance" (DSI) which restricts the models
predictions considerably and hence makes it easier to qualify/disqualify the
model by comparing it with real data. Specifically, we are shown that the real
part as well as the imaginary part of \alpha, which is responsible for the "log-periodic oscillations" born out of DSI are surprisingly robust with
respect to changes in historical time as well as market. Again we are presented
with tests both on surrogate and real data which further substantiates (in my
biased opinion, again) the claims that a "log-periodic power law behavior" is
present in speculative bubbles prior to crashes more often than not. Here I
must mention that further joint work by the author of the book and the author
of this review (cond-mat/0210509) not included in the book is a suggestion for
a classification of causes of market crashes in an exogenous and endogenous
source, where the latter can be understood in terms of the bubble-model
presented in the book and the former in terms of the EMH . This is done by
establishing an empirical link between the outlier idea and the different case
studies of speculative market bubbles ending with a crash.

The third part of the book deals with the difficult task of prediction. There
exists a Danish proverb which states that "It is very difficult to predict,
especially about the future". Instead of stating my own personal view on the
possibility of predicting, e.g., stock market crashes (which in part already
has been presented in reference [217] of the book) I will stop here and let the
reader of judge by himself. However, that it might not be an impossible task
is well-illustrated by chapter 9 of the book.

As a more personal comment, I must say that I find it incomprehensible that
D. Sornette in the preface has reduced my role in the work presented in the
book to that of a ``number cruncher''.

Overall, I find "Why Stock Markets Crash" by Didier Sornette an interesting book presenting some fascinating new ideas on the financial markets. I especially
like the smaller "inserts" with proofs, references to statements by
authorities such as G. Soros and A. Greenspan (where the former name can be
found in the index and the latter name not!) and specific illustration of the
idea presented. I believe the book constitutes interesting reading for both the
layman and the professionals although some may be put of by "Goldstone modes"
and "parity symmetry breaking". Whether it will have any impact on the
Econophysics community is left to be seen. But then, perhaps it was never
intended to have.