Buy low and sell high: In trading stocks this cliché is obvious, but its ramifications can be extremely painful for all those involved, as well as many who are not, especially when a large collection of traders act in concert and engage in massive sell-offs. Financial bubbles, stock market crashes, and out-of-control speculation have been the subject of countless books and research papers and dozens of Hollywood movies, and mathematicians, economists, systems analysts, and financial engineers have spent thousands of hours of time attempting to understand and predict financial meltdowns, all with varying degrees of success. Some of these researchers have argued that it is the large-scale, collective properties of the financial markets that must be understood if stock market crashes are to be predicted or at least anticipated quantitatively.
The author of this book, a geophysicist by training, is one of these and has taken the "buy low-sell high" strategy and some straightforward mathematical constructions to give an interesting and plausible explanation of why stock markets crash. Intuitively, traders synchronously try to buy low and sell high, and a "herding effect" results in a rapid sell-off that results in a market crash. This behavior is analogous to what one observes in physical systems that are close to a `critical point', where they can undergo `phase transitions' and their behavior as they near the critical point has been shown to be "universal" in the sense that quantities called `scaling exponents' can be calculated explicitly and measure the "universality" of the systems near the critical point.
Naturally the stock market crashes of 1929 and 1987 are ones that that will stand out in every reader's mind and ones that must be test examples for the author's assertions. He discusses these two examples and many others in enough detail that a convincing case is made. The techniques he uses however are out of the mainstream of econometrics, and no doubt some in this mainstream will there be highly skeptical of his conclusions. The physicist-turned-financial engineer however will be delighted, as there will be many familiar concepts and constructions throughout the book. There may be a few new ones to such a reader however, such as `algorithmic complexity' and `computationally irreducible'. The clarity of the author's writing and the many real-world examples that he employs makes the assimilation of these concepts and others much more palatable than would be the case in a standard mathematical monograph on the subject. In addition, the techniques he uses can be applied to areas of finance that are not discussed in the book, such as the mortgage "antibubble" in net credit losses for second-lien (HELOC) loans that began in the second quarter of 2006. And with respect to applications, the author is honest enough to note that he refrains from discussing many of them in detail since his involvement in them is strictly proprietary. Most refreshingly, charts, graphs, and tables appear throughout the book, as would be necessary in the validation of any algorithm or predictor in financial theory.
There are also many interesting "toy models" in the book that enhance the didactic quality. One of these concerns the dependences that can occur in successive price variations. The author constructs a model where there is zero correlation but where one can predict the current price variation with an accuracy of over 50% by only knowing the variations in the past two days. This example serves as a good counter to the idea that the frequency distribution and two-point correlation function must always be non-zero in order to obtain successful prediction. The author goes on to use this example to show how "drawdowns", rather than the correlation structure, play the predominant role in measuring price changes. This example, among others, also illustrates the author's belief that the "standard" models in the financial industry have great difficulty in dealing with large financial crashes.
Although the author uses somewhat elementary mathematics in the book, its implications are profound. One will find for example discussions of log-periodic oscillations in hierarchical systems, the renormalization group, and complex fractal dimension. Central to the author's case is the concept of discrete scale invariance, which is a specialization of the continuous case, and which is manifested in real data by log-periodic oscillations. These should be viewed as corrections to simple power law scaling. The author discusses a few natural systems that exhibit log-periodicity, such as bats and dolphins, and in evolutionary biology. He also discusses other examples in mathematics such as the Newcomb-Benford law. Pre-crash stock market data is fitted to expressions that have log-periodic corrections to a pure power law and the validity of the fits discussed in great detail. The author's arguments are powerful and convincing, and the formalism that he outlines needs to be part of every financial analyst's toolbox.
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Top reviews from other countries
riccardo
Very fascinating and mind opening book
Reviewed in Italy on November 18, 2019Vivek Gadodia
Still mid-way through the book. So far, I'd ...
Reviewed in India on November 6, 2017William J. Smith
but I would like to see a little more of the maths
Reviewed in the United Kingdom on July 18, 2014