Wealth

Explaining the Market Crash Mechanism with Complexity Science

  Why did Michael Mobson praise Didier Solnet’s “Why the Stock Market Crashed” in “Devil’s Investing” as “far-reaching and never tire of reading”? Because this book can be seen as a story, a scientific story about how to borrow the most cutting-edge and complex concepts in modern science to understand financial crashes, namely the theory of complex systems and critical phenomena.
  Solnet was a pioneer in studying market bubbles. In financial research, he introduced the concept of “log-periodic power-law singularity”, which is a not easy to understand phrase. In short, log periodicity refers to the hierarchy of trading unit sizes and the result of non-linear interactions between trend followers and value investors. Power laws often describe fat-tailed distributions of financial returns. The power-law singularity describes the super-exponential growth process of the price before a finite time point, and this time point is the singularity point that distinguishes the bubble formation period from the collapse period. Solnet combined log-periodicity with a power law, calling it the “log-periodic power-law model” (LPPL).
  The basic generation process of financial bubbles is related to imitation, following trends, self-organizing cooperative behavior and positive feedback, which may lead to the development of endogenous instability. According to this theory, most financial bubbles develop within their systems, mature with increasing instability, and eventually mature into bursts and subsequent crashes. Solnet is convinced that the log-periodic power-law model does not inherently predict crises, but it can diagnose bubbles and booms in stocks, commodities, derivatives, and real estate.
  In Solnet’s view, the stock market crash provided an opportunity to explore the wonderful world of self-organizing systems. Crashes are examples of the dramatic natural emergence of extreme events in self-organizing systems. Crashes are indeed the perfect medium to carry the important ideas that need to be dealt with in our risky world. The word “world” here has several meanings, as it can be the physical world, the natural world, the biological world, or even the inner intellectual and psychological world. Uncertainty and variability are keywords that describe our ever-changing surroundings. Stasis and equilibrium are illusions. Dynamics and disequilibrium are the rules. The search for balance and permanence is doomed to failure.
The crash comes from within

  In the financial world, risk, reward and disaster repeat itself generation after generation. Greed, pride, and systemic volatility produced the Tulip Mania, the South Sea Bubble, the land-buying frenzy of the 1920s and 1980s, the Great Depression of 1929, and the Great Crash of October 1987, among a hundred other extreme events.
  Most approaches to explaining the crash have only searched for possible mechanisms or effects on extremely short time scales. But Solnet offers a completely different view: the root cause of the stock market crash was revealed months or years before it happened-the gradual establishment of market coordination and effective interaction between investors, Often this translates into an accelerated rise in stock prices (a bubble). According to this important point, the exact form of the stock market crash is not very important, the crash occurs because the market has entered an unstable phase, in which any small disturbance and process can cause violent market fluctuations. That is to say, the crash fundamentally has an internal source, and external stimuli are only inducing factors. Therefore, the source of the crash is much more hidden than expected, and the instability of the system can be regarded as the real cause of the crash.
  Financial markets are one of many systems with complex organizations and similar dynamics. The common feature of these systems is that they all have many interacting parts, which are often open to the outside world, organize the internal structure and have new and even unexpected macroscopic “emergent” properties. Now, the complex system approach of “seeing” the whole picture and the interconnection and relationship between various parts has been widely and deeply applied in modern engineering control and business management. This approach is simultaneously playing an increasingly important role in most disciplines of the natural sciences. It is increasingly recognized that advances in these disciplines, as well as many pressing problems related to our future well-being and daily life, must be addressed through complex systems and interdisciplinary approaches. This point of view overturns the previous method of solving problems with the “analytic” approach. In the analytical approach, people decompose the system into several discrete parts, thinking 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-agency collective behavior can occur in systems due to the recurrent nonlinear interactions among their components: the whole is much greater than the sum of its parts. It is generally accepted that most complex systems do not have exact mathematical analytical descriptions and can only be explored through “numerical experiments”. In the mathematical language of algorithmic complexity, many complex systems are computationally incomparable, that is, the only way to discover their evolution is to let them evolve in real time. Therefore, the dynamical 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, Levina predicted the existence of Neptune by calculating the perturbation of the orbit of Uranus; Einstein predicted that the gravitational field of the sun would cause the light to shift; spiral structure. Instead, new phenomena are discovered thanks to an insatiable curiosity about the world to come.
complex systems are unpredictable

  It has been proven that complex systems are unpredictable. Supporting this view is the explicit application of prediction—the societal focus of earthquake prediction. In addition to the continued failure of reliable earthquake prediction, the analogy between earthquakes and self-organized criticality makes the point theoretically.
  This point of view is equally applicable to all complex systems. Take life as an example. We don’t really want to know in advance when we will go to a certain store or drive on the highway. What we really care about are the major forks in life’s paths involving health, love, work, happiness, and so on. Similarly, it is useless to predict every detail of the evolution of a complex system. All we care about is whether key events such as extreme events can be predicted.
  In fact, most complex systems in the natural and social sciences do have very few very abrupt phase transitions, and the time scales of phase transitions are smaller than the characteristic time scales of phylogenetic evolution. These extremes, more than any other, illustrate the underlying forces that often lurk beneath an almost perfect balance, thus offering the possibility of a better understanding of complex systems.
  Decisive events have significant social impact. Importantly, the long-term behavior of complex systems is governed by these rare catastrophic phenomena: the possible creation of the universe by the Big Bang; nuclear fusion reactions in supernova Big Bangs that produced the essential elements of everyday life; The deformation of California has caused very large earthquakes every two centuries; the erosion of running water for thousands of years has changed the landscape more than any other erosion factor; large-scale volcanic eruptions have brought large-scale geological changes and severe climate damage. ;According to contemporary views, evolution may consist of a quasi-stasis state plus the occasional emergence and disappearance of certain genes; a financial crash, which can wipe hundreds of billions of dollars in an instant, can threaten and change the mental state of an investor; Even our long-term lives are made up of a few key decisions and events.

  Since today’s markets are very strongly interconnected, systemic risk is likely to cause severe disruption, or even paralysis, of the entire market. The bankruptcy of a very small company may pose a serious threat to its own security system. Long-term capital management company is a typical case. Although this fund company has only assets of 4.8 billion US dollars, its bankruptcy has caused losses of up to 200 billion US dollars in the entire financial market.
  Most complex problems do not have theoretical analytical solutions. A brute-force computational solution to the equations (known equations) or evolutionary processes is only applicable to the “center of the probability distribution” of the system, that is, the state of the system far away from extreme events. Because only in such a state can we collect good statistical parameters. Crises are rare extreme phenomena with extraordinary effects, so calculations of them would be highly unreliable if they relied entirely on sampling. Even supercomputers that operate at trillions of operations per second are unlikely to change this fundamental limitation.
foam again and again

  The average investor pays more attention to future profit expectations and other people’s forecasts than to the actual economic situation now. Inflated prices can turn into bubbles when growth expectations are inaccurate. The examples presented in history keep repeating: from the initial good economic fundamentals, investors promote the unprecedented enthusiasm for investment through imitation process or herd effect, and build the “air castle” described by Burton Malkiel. The four major crashes of the U.S. stock market all belong to this category, but the sectors that cause bubbles in each crash are different.
  Solnet hypothesizes that stock market crashes are caused by a global market-wide cooperative behavior caused by gradually established large-scale correlations, and that the crash always breaks out and terminates in a critical short period of time after the scale of this coordinated behavior is large enough. Before the crash, mutual imitation and speculative psychology 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’s return to equilibrium The equilibrium price is quickly found in . After a long time, this “super subject” was disintegrated and dispersed, and the differences in behavior were restored.
  Crashes are similar, and the only thing that may not change is the way investors think and behave. The resulting idea is that the organizational behavior of traders in the financial market will essentially cause “system instability”, which may come from the fundamental nature of human beings, including flocking behavior, greedy nature, and instinctive psychology in pain , herd behavior and risk aversion. The logarithmic periodic power-law structure market overall behavior emerging from the cooperative behavior of traders is reminiscent of the intellectual behavior process that cannot be perceived by individuals at the micro level, but emerges at the macro level.
  Solnet’s central hypothesis is that stock market crashes are caused by self-reinforcing imitation among intraregional investors. This process of self-reinforcing imitation leads to the prevalence of bubbles. If the trend of investors imitating their friends’ behavior grows, to a certain threshold (tipping point), 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 step-increasing imitation and ubiquitous noise: a crash is not the only possible outcome after a bubble is created, which can be described by the hazard rate, that is, before the crash occurs, the next unit The probability that it may crash within a certain period of time. Since a crash is not the only outcome of a bubble, some rational investors will still hold stocks when a bubble occurs. They take on the risk of a crash to get the high returns on stocks in a bubble because the bubble has the potential to have a “soft landing” that doesn’t end in a crash.
  Price volatility is ubiquitous on any time scale. These fluctuations are like the “pulse” of the stock market. The “Pulse” is caused by the investor’s activity, which is so fascinating because it arises spontaneously, yet reveals a life-form, as complex as the world around us. Not only that, but it constrains our return on investment.
  Investing in the stock market follows a very simple and straightforward rule: if you think the market is going up, you buy and hold until you think the market is going to reverse; If the market allows, you sell short. But predicting the future direction of stocks is difficult, even if the influence of noise can be completely discarded on a scale of several decades. In fact, the smarter and harder an investor is, the more random price movements in the stock market tend to be. In social and financial systems, anyone is both an observer and an observed, which constitutes a feedback loop.
The rate of return does not follow a Gaussian distribution

  The collapse of financial markets is an outlier in itself. “Abnormal” 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 by a basic “ruler”, which is the standard deviation.
  Consider a daily Dow Jones time series with a standard deviation of about 1% and a daily return of greater than 3% if calculated as a Gaussian distribution. The occurrence frequency of a daily rate of return higher than 4% is only once in 63 years, and the situation of a rate of return greater than 5% has never appeared in such a short period of human history. However, both the 22.6% daily decline on October 19, 1987 and the 9.7% daily rebound on October 21, 1987 were anomalous: completely impossible under the standard Gaussian distribution. These market-created “monsters” are called “outliers,” or in other words, they appear when they are unlikely to arise.
  In fact, returns do not follow a Gaussian distribution. The probability of being outside 10 standard deviations (equivalent to a rate of return greater than 10%) is 0.000045, that is to say, it will happen once in about 22026 days or 88 years. As such, the October 21, 1987 rally 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. It is quite clear that a 10% daily return is not an “outlier” under the exponential model. Solnet found that whether returns at certain values ​​are normal or abnormal depends on our choice of model for the distribution of returns.
  Solnet pointed out that when the observations are far from the expected results, we should keep a cool head and carefully check every possible explanation. As Freeman Dyson brilliantly described: “The duty of a scientist confronted with a new theory is to prove it wrong. That is what science is, and that is the way to be honest about it. Any new theory in order to survive , you must accept a lot of criticism, sometimes even bitter criticism. Many new theories have been proved to be wrong, and what the criticism has to do is to clear them away and leave room for better theories in the future. Very few surviving The theory is strengthened and perfected in being criticized, and thus finally joins the growing ranks of scientific knowledge.”
  The powerful method of investigation implied in this passage is the so-called scientific method. In short, the scientific method consists of the following steps: ① observation of data; ② tentative explanations, that is, hypotheses that are consistent with observed data; ③ predictions based on the assumptions made; ④ experimentation and further observation to test predictions and adjust assumptions based on new results; ⑤repeat step ③ and step ④ theory until there are no or almost no contradictions between theory and practice or observation. But when contradictions are reconciled, assumptions become theories. A series of phenomena can be explained by using this theory and some inferences derived from it. A theory is thus a framework that can be used to explain observed phenomena and make predictions.
  Thus, Solnet’s research sheds light on the field of theory of complex systems and critical phenomena, from describing the wonderful organizational happenings around us to realizing the crucial importance of the self-organizing/disorganizing roles of extreme events such as major financial crashes , the recognition of sudden transitions from a quiescent state to crises and catastrophic events provides us with the most striking imprint of the mechanisms of system dynamics.

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