Diversity of Ideas: Explaining the Mechanisms of Market Collapse with a Science of Complexity

Text / Yao Bin

Why did Michael Maubousson praise Didier Solnet’s “Why the Stock Market Crash” in “The Devil’s Investing” as “influential and endlessly read”? Because this book can be seen as a story, a scientific story about how to understand financial collapse by borrowing the most cutting-edge and complex concepts in modern science, namely the theory of complex systems and critical phenomena. This is also the first monograph I have read that explains market crashes with the science of complexity.

Solnet, though a geographer, was a pioneer in studying market bubbles. In Solnett’s research in finance, he introduced the concept of “log-periodic power-law singularity”. This is a difficult phrase to understand. Simply put, log cyclicality refers to the hierarchy of trading unit sizes and the result of nonlinear interactions between trend followers and value investors. Power laws often describe the fat-tailed distribution of financial returns. The power-law singularity describes the super-exponential growth of prices before a finite point in time, which is the singularity that distinguishes the bubble from the collapse. Solnet combined log periodicity with a power law and called it the “log periodic power law model” (LPPL).

The main basic generating processes of financial bubbles are related to imitation, follow-up, self-organized cooperative behavior, and positive feedback, which can all lead to the development of endogenous instability. According to this theory, most financial bubbles develop within their system, mature with increasing instability, and eventually mature into a bubble burst and subsequent crash. Solnett is convinced that the log-periodic power-law model does not inherently predict crises, but it can diagnose booms in stocks, commodities, derivatives, and real estate.

The stock market, with its potential for big returns and colorful and interesting personalities, tempts investors to try to “beat the market” by using or refining a few tricks. But the stock market is not a casino for naughty or stupid gamblers, it is fundamentally a vehicle for liquid exchange that allows the free and competitive market of capitalism to function effectively.

The total value of the world market in 1983 was 3.35 trillion US dollars, rose to 26.5 trillion US dollars in 1998, and soared to 38.7 trillion US dollars in 1999. However, two years after the dot-com bubble burst in 2001, the world’s total market capitalization has shrunk to $25.1 trillion. A 30% stock market crash equates to an absolute loss of $7.5 trillion. The stock market crash fascinated Solnet. This, he believes, reflects a class of phenomena known as “extreme events.” Extreme events characterize many natural and social systems, often referred to by scientists as “complex systems.”

For Solnett, the stock market crash provided an opportunity to explore the wonderful world of self-organizing systems. A crash is an example of the dramatic and natural occurrence of extreme events in self-organizing systems. Crash really is the perfect medium to carry the big ideas that need to deal with our risky world. The word “world” has several meanings here, as it can be the physical world, the natural world, the biological world, or even the inner intellectual and psychological world. Uncertainty and volatility are keywords that describe our ever-changing surroundings. Stagnation and equilibrium are hallucinations. Dynamics and non-equilibrium are the rules. The search for balance and permanence is ultimately a failure.

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In the world of finance, risks, rewards and disasters are repeated from generation to generation. Greed, pride, and systemic volatility brought us hundreds of extreme events like the Tulip Mania, the South Sea Bubble, the land-buying frenzy of the 1920s and 1980s, the Great Depression of 1929, and the October 1987 crash .

The vast majority of ways to explain crashes are simply searching for possible mechanisms or effects on extremely short time scales. But Solnet offers a completely different view than before: the root cause of the stock market crash is already apparent months or years before it happens – the gradual establishment of market coordination and effective interaction between investors, Often this translates into an accelerated rise in stock prices (bubble). According to this important point, the specific form of the stock market crash is not very important, the crash occurs because the market has entered a stage of instability, in which any small disturbance and process can trigger the market volatility. That is, the crash fundamentally has an internal source, and external stimuli are just the triggering factors. The root cause of a bridge collapse is the action of a particular mode of resonance, and many stock market crashes, like bridge collapses, stem from inherent instability. This instability is revealed by some small market disturbances that directly cause the market to crash. Therefore, the source of the crash is much more hidden than expected, and the crash is a self-organized and gradual formation of the market as a whole. In this sense, the instability of the system can be seen as the real cause of the crash.

Financial markets are not the only system with extreme events; they are one of many systems with complex organization and similar dynamics. A common feature of these systems is that they have many interacting parts that are often open to the outside world, organize internal structures, and have new and even unexpected macroscopic “emerging” properties. Now, the complex system approach that can “see” the whole picture and the interconnections and relationships between parts has been widely and deeply applied in modern engineering control and business management. This approach also plays an increasingly important role in most disciplines of the natural sciences, including biology, geology, and economics and social sciences. There is a growing realization that advances in these disciplines, as well as many of the pressing problems related to our future well-being and everyday life, must be addressed through complex systems and interdisciplinary approaches. This view overturns the previous approach to problem solving with an “analytical” approach. In analytical methods, people decompose the system into disjoint parts, arguing that to understand the overall function, it is only necessary to have a precise understanding of each part.

A central property of complex systems is that coherent large-scale, multi-institutional collective behavior can occur in the system due to repeated nonlinear interactions among its components: the whole is far greater than the sum of its parts. It is widely believed that most complex systems do not have an accurate mathematical description and can only be explored through “numerical experiments”. In the mathematical language of algorithmic complexity, many complex systems are computationally intractable, that is, the only way to discover how they evolve is to make them evolve in real time. Therefore, the dynamic evolution of complex systems is inherently unpredictable. However, this unpredictability does not affect the application of scientific methods to predict some new phenomena. For example, Leviner predicted the existence of Neptune by calculating perturbations in the orbit of Uranus; Einstein predicted that the sun’s gravitational field would cause light to shift; Watson and Crick, based on early Pauling and Bragg’s predictions, gave double Spiral structure. Instead, new phenomena are discovered thanks to an insatiable curiosity about the world to come. People are still willing to explore the unknown, even if there are “prophes” who have inspired or terrorized the masses throughout history.

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The idea that complex systems cannot be predicted has been proven. Supporting this view is the clear application of forecasting – the societal focus of earthquake forecasting. In addition to the continued failure of reliable earthquake prediction, the analogy between earthquakes and self-organized criticality illustrates this theoretically. This theory is based on a fractal framework, where there is no characteristic scale, and the power-law distribution of earthquake size reflects that large earthquakes are composed of many small earthquakes. Therefore, predicting large earthquakes, like predicting many small earthquakes, is obviously impossible.

The same holds true for all complex systems. Take our life as an example, we don’t really want to know in advance when we will go to a certain store and when we will drive on the highway. What we really care about is the major forks in life’s paths involving health, love, work, happiness, and more. Similarly, it is useless to predict every detail of the evolution of complex systems, all we care about is whether critical events like extreme events can be predicted.

In fact, most complex systems in the natural and social sciences do have very few very sudden phase transitions, and the timescales of phase transitions are smaller than the characteristic timescales of system evolution. More than anything else, these extremes illustrate that underlying forces often lurk in near-perfect equilibrium, thus offering the possibility of better understanding complex systems.

Decisive events have important social implications. It involves natural disasters, environmental degradation disasters, structural errors in engineering, large-scale armed conflicts and riots resulting from social unrest, stock market crashes, traffic jams, shrinking national and global economies, regional blackouts, diseases and epidemics. It is very important that the long-term behavior of complex systems is governed by these rare and catastrophic phenomena: the universe may have been created by the Big Bang; the nuclear fusion reactions in the big bang of supernovae produce important elements of daily life; the large area of ​​plate tectonics The deformation of California caused a very large earthquake every two centuries in California; the erosion of running water over millennia has changed the landscape more than any other erosion factor; large-scale volcanic eruptions brought extensive geological changes and severe climate damage ; According to contemporary views, evolution may consist of quasi-stagnation plus certain genes that come and go in fragments; a financial crash can instantly vaporize hundreds of billions of dollars, and can threaten and alter an investor’s mental state; Even our long-term lives are made up of several key decisions and events.

Because today’s markets are very strongly interconnected, systemic risk is likely to cause significant disruption, or even paralysis, of the entire market. The bankruptcy of a very small company can pose a serious threat to its own security systems, as LTCM is a typical case. Although the fund company has only $4.8 billion in assets, its bankruptcy has caused losses of up to $200 billion in the entire financial market.

These unanswered scientific questions are: How did such a large-scale catastrophic event gradually evolve from a series of small-scale events? In complex systems, the compositional structure of spatial and temporal correlations does not depend on the diffusion of system kernelization, but from the evolving global collaboration of the entire system caused by repeated interactions within the system. For example, scientific and technological discoveries occur almost simultaneously in several laboratories in different parts of the world. This is the signal of the maturation of the global natural sciences.

Most complex problems do not have theoretical analytical solutions. Solutions that use brute force computational solutions to equations (known equations) or evolutionary processes only work in the “center of the probability distribution” of the system, that is, when the system is far away from extreme events. Because only in this state can we collect good statistical parameters. Crises are rare, extreme phenomena with extraordinary effects, so their calculations would be highly unreliable if they relied solely on sampling. Even a supercomputer running teraflops per second is unlikely to change this fundamental limitation.

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The average investor pays more attention to future earnings expectations and others’ forecasts than to current economic conditions. When expectations for growth are inaccurate, inflated prices can turn into bubbles. History presents us with many examples of bubbles leading to crashes with unrealistic expectations for the future. The basics of these examples are repeated over and over again: initially sound economic fundamentals drive investors to self-generate unprecedented enthusiasm for investing through a process of imitation or herding, building what Burton Malkiel describes as “castles in the air.” The four major U.S. stock market crashes (October 1929, October 1987, August 1998, and April 2000) all fall into this category, except that the sectors that created the bubbles in each crash were different.

Solnett hypothesized that the reason for the stock market crash was the global cooperative behavior of the market caused by the gradual establishment of large-scale correlations. Crashes always break out and terminate in a critically short time after the collaborative behavior is large enough. Before the crash, mutual imitation and speculation spread in the market, leading to the gradual aggregation of investor groups to form an effective “super subject”; after the crash, it behaved like a super subject in the financial market returning to equilibrium The equilibrium price is quickly found in . After a long time, this “super subject” is disintegrated and dispersed, and the difference of behavior is restored.

Crashes share similarities, and the only thing that may not change is the way investors think and behave. One of the ideas that arises from this is that the organizational behavior of traders in financial markets can inherently cause “system instability”, which may come from the fundamental nature of human beings themselves, including herd behavior, greedy nature, instinctive psychology in pain , herd behavior, and risk aversion. The global behavior of the log-periodic power-law structure market emerging from the cooperative behavior of traders is reminiscent of the intellectual behavior process that individuals cannot perceive at the micro level, but emerges at the macro level. Biology is already studying this process, such as the problem of consciousness in ant colonies.

Solnet’s core hypothesis is that stock market crashes are caused by self-reinforcing imitation among intraregional investors. This process of self-reinforcing imitation led to the prevalence of bubbles. If the trend of investors imitating their friend’s behavior grows, there is a certain threshold (tipping point) where many investors will make the same (sell) decision at the same time, and a crash will occur. We need a probability to describe the interaction between progressively increasing imitation and ubiquitous noise: a crash is not the only possible outcome of a bubble, which can be described in terms of the risk rate, i.e., before a crash occurs, the next unit Probability of a possible crash over time. Since a crash is not the only result of a bubble, some rational investors will still hold stocks when the bubble occurs. They take the risk of a crash to get the stock’s high returns in a bubble. This is because the bubble has the potential to “soft-land”, i.e. the bubble does not end in a collapse.

On any time scale, price volatility is prevalent. These fluctuations are like the “pulsation” of the stock market. The “pulsation” is caused by the investor’s activity, which is so fascinating because it is spontaneous, yet reveals a form of existence that is as complex as the world around us. Not only that, but it limits our return on investment.

Investing in the stock market follows a very simple and straightforward rule: if you think the market is going to go up, you buy and hold until you think the market is going to reverse; if you think the market is going to go down, stay on the sidelines, or if you think the market is going to go down You sell short when the market allows it. But guessing where stocks will go in the future is hard, even if the noise can be completely ignored on the scale of decades. In fact, the smarter and harder an investor is, the more random price movements in the stock market tend to be. This represents the most fundamental difference between the stock market and natural events. The latter can be under the watchful eye of an observer, and scientists can come up with explanations and theories without interfering with the entire system themselves. In contrast, in social and financial systems, anyone is both the observer and the observed, which constitutes a feedback loop.

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A crash in financial markets is an outlier in itself. “Exception” is only a relative concept, it is relative to “normal”. In the financial world of Louis Bachelier and Paul Samuelson, returns follow a Gaussian distribution, and all returns can be measured with a basic “ruler” known as the standard deviation.

Consider a daily time series of the Dow Jones that has a standard deviation of about 1% and a daily return of more than 3% if calculated from a Gaussian distribution. In theory, it only occurs once every 1.5 years. The daily rate of return is higher than 4%, only once every 63 years, and the return rate of more than 5% has never happened in such a short time in human history. However, the daily drop of 22.6% on October 19, 1987 and the daily rebound of 9.7% on October 21, 1987 were both anomalous: under the standard Gaussian distribution, this is completely impossible. Their existence makes us realize that the market can deviate very significantly from the norm. The “yokai” created by these markets are called “outliers,” in other words, they arise when they are unlikely to happen.

In fact, returns do not follow a Gaussian distribution. The probability of being outside 10 standard deviations (equivalent to a return greater than 10%) is 0.000 045, which means it will happen once every 22,026 days or 88 years. In this case, the rebound of October 21, 1987 was not so normal. However, the daily decline on October 19, 1987 reached 22.6%, which happened only once in 520 million years under the exponential distribution, and this value is still an outlier. Clearly, a 10% daily return is not an “outlier” under an exponential model. Solnet found that whether returns at a particular value are normal or abnormal depends on our choice of model for the distribution of returns.

Solnet points out that when observations are too far from expected, we should keep a cool head and scrutinize every possible explanation. As Freeman Dyson put it wonderfully: “A scientist’s job in the face of a new theory is to prove it wrong. That’s what science is about, and it’s the way to be honest with it. Any new theory in order to survive. , you must accept a lot of criticism, sometimes even bitter criticism. Many new theories have been proven wrong, and what criticism has to do is to eliminate them and leave room for better theories in the future. Very few survive. Theories are strengthened and refined in the critique, and thus eventually join the growing ranks of scientific knowledge.”

The powerful investigative method implied in this passage is the so-called scientific method. In short, the scientific method consists of the following steps: 1. Observe the data. ② Make tentative explanations, that is, make assumptions that are consistent with the observed data. ③ Use the assumptions made to make predictions. ④ Test predictions through experimentation and further observations, and adjust hypotheses based on new results. ⑤ Repeat steps ③ and ④ theory until there is no or almost no contradiction between theory and practice or observation. But when the contradictions are reconciled, the hypothesis becomes the theory. A series of phenomena can be explained with this theory and some inferences derived from it. Therefore, a theory is a framework that can be used to explain observed phenomena and make predictions. If two theories can make the same predictions, the simpler one should be chosen. This is the “Occam’s Razor” principle.

In this way, Solnet’s research opens up the field of theory of complex systems and critical phenomena, from describing the wonderful organization happening around us, to realizing the critical importance of the self-organized/disorganized role of extreme events like major financial crashes , acknowledging the abrupt transition from a quiescent state to crisis and catastrophic events provides us with the most striking imprint of the dynamics of the system.

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