What would you do if you could use a time machine to travel back in time? If we leave aside schemes to rearrange the political landscape, a common answer is that the time traveler would return to a previous date with stock market information (perhaps a file of stock market close prices from the newspaper). With the perfect foreknowledge of the market, wealth would be assured.

The investor in search of a "sure thing" may be disappointed to learn that time travel is probably impossible (although opinions on this differ). Perhaps the disappointed prospective time traveler can be consoled with a method for predicting market crashes? As it happens, this is one of the central themes in Didier Sornette's book Why Stock Markets Crash: Critical Events in Complex Financial Systems.

Attempts to predict economic and markets trends have a long history. The Dow Jones Industrial Average, was originally developed to track the stock market to aid in the identification of market trends and cycles. Elliot Waves and many other theories have been used in an attempt to predict the future of stock prices. While they are dressed up in charts and obscured with mathematics, many of these techniques are little better than astrology for predicting the future. Markets rise and fall, with bubbles and crashes, but there is no reliable evidence for market cycles with repeatable periods (which would allow prediction).

On occasion authors of stock market newsletters have predicted coming market crashes. They loudly trumpet their oracular powers to increase their subscription base. Usually further predictions are wrong and they are, to a degree, discredited (but, as with the famous Weapons of Mass Destruction, there will always be those who believe in the face of contrary facts). The hype surrounding forecasting market crashes has given such an undertaking a reputation for poor science at best and fraud at worst.

At a quick glance it might be assumed that Didier Sornette's book Why Stock Markets Crash belongs with books on "technical analysis" which describe market trends using terms like "head", "shoulders", "barriers" and "candles". This characterization would be incorrect. Professor Sornette's book is the polar opposite of the weak science in technical analysis and the hype of stock market newsletters. Why Stock Markets Crash carefully builds up an argument for the thesis that the market bubbles that lead to crashes have a characteristic log periodic signature. These market bubbles may either deflate rapidly (a crash) or slowly, via a long decline. Professor Sornette also discusses "anti-bubbles" which are market declines with signatures that are similar to crashes in reverse.

Didier Sornette is a Professor of Geophysics in UC Los Angles' Earth and Space Sciences Department. Professor Sornette has an impressive body of publications in complex systems, discrete scale invariance, extreme events, like earthquakes and ruptures and finance. In addition to his many papers and Why Stock Markets Crash, Professor Sornette has also published a book titled Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder, (Second Edition, Springer 2004).

Markets are complex systems. In an orderly (non-bubble) market, pricing reflects the underlying value of the market instruments. As bubbles develop, the orderly behavior breaks down and markets display complex, non-linear behavior. Didier Sornette interest in the behavior of complex, dynamic systems is one of the factors that attracted him to the study of market behavior.

Why Stock Markets Crash does not require a background in finance or economics. Professor Sornette has read widely in finance and clearly explains basic financial and economic theory. In some cases I found his explanation helped me understand material I had already read (for example, Brian Arthur's paper on the "El Farol Bar" problem (Inductive Reasoning and Bounded Rationality (The El Farol Problem), American Economic Review (papers and Proceedings) 84).

Chapters 1 and 2 of Why Stock Markets Crash cover historical market crashes and the basics of markets, including stock return distribution and return autocorrelation. Chapter 3 discusses the statistical characteristics of market crashes and market losses (also known as "drawdowns"). The effect of positive feedback caused by the "herd" behavior of market traders and other sources for market bubbles and crashes is discussed in Chapter 4. Chapter 5 covers several market models that display bubble and crash behavior. From this base chapters 6 through 9 develop Professor Sornette's thesis that market bubbles (and anti-bubbles) have a log periodic signature.

One reader commented in an Amazon.com book review that this is a book that you need to read with your economics professor at your elbow, implying that the mathematics is daunting. Why Stock Markets Crash does not require more than than High School mathematics (plus an understanding of summation notation). There are no proofs and Professor Sornette clearly explains the material. However, the book is dense with ideas and covers a great deal of material. There are times when it becomes difficult to see the cloth created by all the threads that Professor Sornette weaves.

Popular science books like Albert-László Barabási book Linked: The New Science of Networks can be read in a day or two or a few more evenings. I read Why Stock Markets Crash over a period of two weeks or so, an hour or two each evening. Reading this book takes concentration and I put it aside when I got tired. As with many mathematics books, another reading would improve my understanding.

Markets are complex. Their behavior is effected by information the information flow represented in the evolving market prices. Markets are also effected by the social networks of traders (e.g., traders talk to each other). Why Stock Markets Crash would be more readable if a single thesis were chosen for market structure. For example, a market model based on "actors", perhaps noise traders and fundamental value traders. This would leave out sub-chapters like The Ising Model of Cooperative Behavior (in Chapter 4). While the end result of this kind of simplification might be more readable, it would miss the complexity that underlies real markets. Such a thesis would, in the end, be misleading.

Professor Sornette presents are carefully constructed argument for the idea that market crashes can be recognized. If we were to apply the methods described by Professor Sornette, will they make us rich? The answer is probably not, but this methodology might help us avoid losses.

In Why Stock Markets Crash Professor Sornette points out that bubbles do not always end in crashes. They have a finite chance of terminating in a long decline back to reasonable ("efficient") valuation. If this happens "shorting the market" (speculating via borrowed stocks) may be less profitable. Then there is the matter of timing. The log periodic signature of market bubbles takes place over a period of years. A non-linear data fitting algorithm is used. The resulting fit and have errors that are much worse than linear fitting algorithms. These factors conspire to limit the potential prediction to a rnage of months. This makes profiting from such a forecast more difficult.

Then there is the problem that a profitable predictive technique carries the seeds of its own destruction. As Professor Sornette points out, markets exhibit feedback. If enough people use a mathematical technique as a trigger for their actions, the application of this technique will change the behavior of the market. This in turn may reduce or destroy the usefulness of the technique.

There is also the problem that Didier Sornette's technique may simply tell us what we should be able to understand from observing the market without the help of mathematics. In the late 1990s it was obvious to anyone who did not buy into the Internet hype and the "new economics of the long economic boom" that a market crash was coming (obviously this was a minority view or the market bubble would have deflated). The key point here is that for a bubble to take place, there must be enough people who are willing to suspend disbelief. If someone is willing to believe the hype being promoted by stock market analysts like Henry Blodgett, they will probably ignore the result of a non-linear model. So if our eyes are open, we don't need the model and if our eyes are fixed on "pie-in-the-sky", we probably will not believe the model in any case.

I'm sure that the fact that this book deals with markets has lead to a larger readership. But in the end, much of this is beside the point of Why Stock Markets Crash. Fear and greed (profit and loss) are simply the driving forces for the market actors. The result of these forces is a complex system. The many facets of this complex system and its evolution into the extreme behavior of market bubbles and crashes is at the heart of Didier Sornette's interest in markets.

Ian Kaplan
May 2004
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