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Revisit Newton - Towards Capital Market Behavior Theory

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THE MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY
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Isaac Newton

Sir Isaac Newton (Jan. 4, 1643 - March 31, 1727) is generally regarded as the most original and influential theorist in the history of science. His passion was to unite knowledge and belief, to reconcile the Book of Nature with the Book of Scripture. He transformed the structure of physical science with his three laws of motion and the law of universal gravitation, which he used to precisely predict the motions of stars, and the planets around the sun. Without Newton and his discoveries, our modern world would be far different than it is today.

In his late life, Newton lost most of his lifetime wealth as an investment victim of "the South Sea Bubble". When asked about the direction of the market, he was reported to have replied “I can calculate the motions of the heavenly bodies, but not the madness of the people.”

The South Sea Company was formed in 1711 to help deleverage the British government by assuming some of the government's debt and paying it off with the proceeds of a stock offering. In exchange for performing this service for the Crown, the company received a monopoly for trading with the Spanish colonies in South America and the exclusive right to sell slaves there. Demand for the company's stock was strong due to the expectation of great profits from these endeavors, although none ever materialized. In 1720, a speculative mania took flight and the stock soared. Newton, who was the Master of the Mint at the time, joined many other wealthy Englishmen in investing in the stock. It rose from £128 in January of l720 to £1,050 in June. Early in this rise, however, Newton realized the speculative nature of the boom and sold his £7,000 worth of stock.

By September 1720, the bubble was punctured and the stock price fell below £200, off 80% from its high three months earlier. It turned out, however, that despite having seen through the bubble earlier, Sir Isaac, like so many investors over the years, couldn't stand the pressure of seeing those around him make vast profits. He bought back the stock at its high and ended up losing £20,000.

The research goes beyond the Dow theory and the other existing theories are motivated by the fact that even the world's smartest men was not immune to the market emotions. We hope Newton could read the following information on Capital Market Behavior Theory (CMBT) so not to feel regret since his wish to "calculate the madness of people" has been coming true.

Dr. Charlie Q. Yang's 20-year research finds that the Newton's Three Laws of Motion are still valid when observing the market actions driving the prices up or down. With Newton's laws and the enhanced Dow Theory's principles (i.e. the new Capital Market Behavior Theory, see below), the market behaviors can be properly measured directly and the movements of such price behaviors should still closely follow the Newton's laws. The validation of such a new hypo thesis has been completed with the development of the new "Yin-Yang Index" real-time computing system.

Newton’s Three Laws for Stock Market

For a couple centuries before Einstein, Newton’s Laws were the basic principles of Physics. These laws are still valid and they are the basis for much engineering analysis today. The formal statements of Newton’s Three Laws are given below. Our explanations of Newton’s Three Laws as applied to stock market price movements are given below each formal statement.

Newton’s First Law:
An object at rest tends to stay at rest and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced external force.


Stock Market First Law Explanation (by Charlie Yang): Inertia is a property of stock market movement trend that resists changes in direction. If there is no fundamental events that cause material change of a company,  its stock's price trend will stay that way (up, down, or sideways) until a new material changing event that creates an external force to make the trend change or reversal. The price changes in an up or down trend will slow down due to friction caused by valuation concerns, and a new material event could accelerate the price changes and thus the slope of trend lines.

Newton’s Second Law:
The acceleration (a) of an object as produced by a net force F is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass m of the object: F = ma.


Stock Market Second Law Explanation (by Charlie Yang): A material event impact force F acting on a stock will accelerate its price movement in the direction of F (positive or negative), with acceleration a = F/m. Acceleration is the change of trend line slope. The mass m here is the present intrinsic value  of the company. If the intrinsic value has no quantifiable change by the force immediately, the price movement will change with a new accelerated up or down trend.

Newton’s Third Law:
For every action, there is an equal and opposite reaction.


Stock Market Third Law Explanation (by Charlie Yang): This law is familiar to many experienced investors or traders. A buy or sell trade order cannot be filled for any given stock unless there is a same quantity sell or buy order reacting to the initiating trade action.   For example, a stock sold by a seller with an opinion to be bearish, there is always a buyer with the opposite opinion to be bullish.
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The Crowd: A Study of the Popular Mind
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Gustave Le Bon

Gustave Le Bon (May 7, 1841 – Dec. 13, 1931) was a French social psychologist and physicist. He was the author of several works in which he developed theories of herd behavior and crowd psychology. His views on cultural evolution were based on his belief that it is the character or "soul" of the people that determines their progress, and that this character took the form of an unconscious "collective mind." This collective mind would also emerge in a crowd of people, influencing their behavior in ways not predicted by simply studying an individual.

Le Bon was born on May 7, 1841, in Nogent-le-Rotrou, France as the son of a civil servant. He obtained his medical degree in Paris, in 1866. He first practiced medicine in Paris, but decided to tour Europe, Asia, and North Africa in the 1870s and 1880s. During this time he wrote on archaeology and anthropology, making some money from the design of scientific apparatus. His first great success was the publication of Les Lois psychologiques de l'évolution des peuples (1894, The Psychological Laws of the Evolution of Peoples),  in which he hit upon a popularizing style that was to make his reputation secure. His best selling work, La psychologie des foules (1895;  English translation, The Crowd: A Study of the Popular Mind, 1896), followed soon after.

Le Bon was a man with an extended field of interests. His writings range from studies of crowd psychology, atomic energy, to physical anthropology and sociology. In his 1894 publication, The Psychology of Peoples, he developed the thesis that the development of people depends on their national character, and is driven by emotion rather than intellect. He made significant contributions to the field of social psychology, particularly in the study of crowd behavior. The main discoveries of Le Bon's theories are
  • Crowds exhibit a collective mind, different from the one that would be the sum of the individual persons.
  • The group mind is more primitive and instinctual, causing crowds to regress in behavior. Whereas individuals tend to act in a rational way, crowds exhibit more irrational traits. He suggested that this is because in the crowd one experiences a heightened state of suggestibility, falling under the influence of feelings of omnipotence.
  • In a crowd one also experiences a higher emotional level and may become subjugated to the will of the crowd. He wrote (1895): "In a crowd every sentiment and act is contagious, and contagious to such a degree that an individual readily sacrifices his personal interest to the collective interest. This is an aptitude very contrary to his nature, and or which a man is scarcely capable, except when he is part of a crowd".

If the ultimate goal of any scientific theory on stock market behaviors is to quantify the collective emotion of investors and traders, Le Bon's theories of herd behavior and crowd psychology are psychological foundations for our modern research on capital market behavior studies which led to the later findings by many others, including Daniel Kahneman's "Prospect Theory" and Charlie Yang's "Capital Market Behavior Theory".
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Prospect Theory: An Analysis of Decisions under Risk
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Daniel Kahneman

Daniel Kahneman (March 5, 1934 - ) is an Israeli-American psychologist notable for his work on the psychology of judgment and decision-making, as well as behavioral economics. With Amos Tversky and others, Kahneman established a cognitive basis for biased human behaviors and developed the Prospect theory (1979). Kahneman and Tversky’s papers on the Prospect theory were decisive in awarding Kahneman the Nobel Prize in Economics in 2002 (note: Tversky would surely have shared the prize had he not passed away in 1996 at the age of 59). Their empirical findings challenge the assumption of human rationality prevailing in modern capital market theory.

Prospect theory, a theory about how people make choices between different options or prospects, is designed to better describe, explain, and predict the choices that the typical person makes, especially in a world of uncertainty. The key points of the Prospect theory are:
  • Certainty (diminishing sensitivity) - People have a strong preference for certainty and are willing to sacrifice return to achieve more certainty.
  • Loss aversion (loss sensitivity) - People tend to give losses more weight than gains.
  • Relative positioning (reference dependence) - People tend to be most interested in their relative gains and losses compared to others as opposed to their own net returns and wealth.
  • Small probabilities (probability weighting): People prefer a slight chance of win big to a certain small gain, but also prefer a certain small loss to a slight chance of losing big. In other words, people overweight unlikely extreme outcomes.

Prospect theory is a model of decision making under risk. In 1984, when Daniel Kahneman,  with Amos Tversky and Richard Thaler, visited a Wall Street firm, he was so puzzled by what made one person buy and the other sell? Most of the buyers and sellers know that they have the same information; they exchange the stocks primarily because they have different opinions. The buyers think the price is too low and likely to rise, while the sellers think the price is high and likely to drop. The puzzle is why buyers and sellers alike think the current price is wrong. What makes them believe they know more about what the price should be than the market does? For most of them, Kahneman thinks that belief is an illusion.

Conventional thinking based on random walk theory believes that if all assets in a market are correctly priced, no one can expect either to gain or to lose by trading. Perfect prices leave no scope for cleverness, but they also protect fools from their own folly. We now know, however, that the theory is not quite right.  In his book, Thinking, Fast and Slow (2011), Kahneman stated: Few stock pickers, if any, have the skill needed to beat the market consistently, year after year. Professional investors, including fund managers, fail a basic test of skill: persistent achievement. The diagnostic for the existence of any skill is the consistency of individual differences in achievement. The logic is simple: if individual differences in any one year are due entirely to luck, the ranking of investors and funds will vary erratically and the year-to-year correlation will be zero. Where there is skill, however, the rankings will be more stable. The persistence of individual differences is the measure by which we confirm the existence of skill among car salespeople, orthodontists or golfers.

The fundamental difficulty in applying the Prospect theory in stock market investing is that it is often unclear what a gain or loss represents in any given situation. This difficulty remains a key challenging and unsolved problem. For example, we want to predict what kind of portfolio an investor with prospect theory preferences will hold. We need to define the investor's “gains” and “losses” first. This can be difficult because it refers to different definitions varying from an individual stock to a portfolio, from a market index to the relative return over the risk-free rate, from expected annual returns to shorter term price fluctuations.

The Prospect theory research has been applied to stock market investing in three main contexts:
  1. Why do some securities have higher average returns than others? The famous Capital Asset Pricing Model (CAPM) has not received much empirical support to solve this puzzle. This raises the question: Can we do a better job using the Prospect theory? Sometimes yes. Investors tend to overweight the unlikely state of the world in which they make a lot of money by investing in the positively skewed stock. As a result, they are willing to pay a high price for the stock, even when it means earning a low average return on it.
  2. Why the aggregate stock market return is much higher than safe investments? The Prospect theory, and loss aversion in particular, can explain the famous equity premium puzzle: the fact that the average return of the US stock market has historically exceeded the average return of Treasury bills by a much greater margin. This is because an individual investor is loss averse, the high dispersion of stock market distribution is very unappealing. To compensate for this, and thus to ensure that the investor is willing to hold his share of equity, the stock market needs to have a high average return, one that is significantly higher than a safe asset like Treasury bills.
  3. How people are trading financial assets over time? Investors have a greater propensity to sell stocks that have risen in value since purchase, rather than stocks that have fallen in value. This behavior is puzzling because based on momentum of price movements, investors should concentrate their selling among stocks with poor past performance—but they do the opposite. This apparent unwillingness to sell stocks at a loss relative to purchase price is more evident in the real estate market. This reluctance to sell assets at a loss follows naturally from the Prospect theory. The intuition is that the losing investor holds on to the stock (or the real estate) in the hope of breaking even later on. It is ultimately rooted in the Prospect theory in that it relies on the investor deriving emotional feeling from gains and losses rather than from absolute wealth levels.

Why do investors, both amateur and professional, stubbornly believe that they can do better than the market, contrary to an economic theory that most of them accept, and contrary to what they could learn from a dispassionate evaluation of their personal experience? The most potent psychological cause of the illusion is certainly that the people who pick stocks are exercising high-level skills. They consult economic data and forecasts, they examine income statements and balance sheets, they evaluate the quality of top management, and they assess the competition. All this is serious work that requires extensive training. Unfortunately, skill in evaluating the business prospects of a firm is not sufficient for successful stock trading, where the key question is whether the information about the firm is already incorporated in the price of its stock. Traders apparently lack the skill to answer this crucial question, but they appear to be ignorant of their own ignorance. As Kahneman had discovered from watching cadets on the obstacle field during his early army research experiences, subjective confidence of traders is a feeling, not a judgment.
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The Stock Market Emotion Index
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Charlie Yang

Charlie Q. Yang was born in Shanghai China. His childhood dream was to become a scientist like Einstein and a great thinker (philosopher). He has been conducting research on investors' behaviors since 1996 and summarized his findings in his "365 Principles of Investing - Why Smart Investors Make Foolish Mistakes", "Market Measurement", "Capital Market Behavior Theory", and "The Yin-Yang Index - Scientific Measuring Investor Behaviors for Stock Market Trend Detection".

In particular, the Yin-Yang Index has been developed by Yang as the real-time data system for scientifically back-testing and validating the Capital Market Behavior Theory (CBMT). The system is mainly based on Yang's CMBT principles as well as Newton's Three Laws of Motions and Dow Theory's Six Principles. Please note that the CBMT theory makes no over-simplified mathematical assumptions and derives all calculations based on real-time market trading data directly. An illustration of the new findings was documented in a working paper submitted to Market Technicians Association (MTA) in 2007 (see attached) and was understandably rejected because the reviewers commented on its significant divergence from the core philosophy of the existing technical analysis.

The new Yin-Yang Index system can be used to detect the market trend and measure the stock market psychological power for any securities traded on any US stock exchanges. It has been proven that the more timely of such measurement, the better the trend identification accuracy and predictability. The accuracy for the primary, secondary, or even minor trend reversal detection has been been very high (>90%). It has also been verified that the trend can make a sudden change anytime if the opposite power is strong enough as driven by future unexpected events.

When pursuing a Master of Applied Science and Ph.D. in Wireless Communication Theory in Canada from 1988 - 1993, Charlie Yang was so fascinated by the capital market's "random" behavior and its similarity with the wireless "signal and noise". He wanted to separate "signal" from "noise" for investors and therefore he studied the courses from the Canadian Securities Institute in 1993. He soon became passionate about investment research and moved to the U.S. in 1995.

While Yang was trying to improve statistical modeling for financial simulation from 1994 to 1996, he discovered a new probability distribution which he named as "Q-Distribution". It is a family of statistical distributions unifying the popular normal and log-normal distributions and many others. Yang was fascinated by the discovery and realized its application potential in almost any field as a significant accuracy improvement over the normal distribution (bell-curve). He documented the findings as a research paper titled "Q-Distributions - A Family of Generalized Normal Distributions" and moved on. This unpublished piece has continuously motivated him to further discover the deeper scientific principles governing the capital market behaviors. Increasingly he realizes that the market is so unpredictable and so difficult to model, but its movement is directly driven by human behaviors, less so and indirectly by various fundamental and technical factors. This research led to the discovery and formation of the Capital Market Behavior Theory (CMBT).

Summary of Capital Market Behavior Theory
  • The key to the development of modern portfolio theory (MPT) is the placing of severely simplifying assumptions on risks. The behavioral content is ignored and only price volatility characterized by the standard deviation or beta is considered. The MPT failed to interpret and prevent the global financial crisis and capital market panic in 2008.
  • Yang discovered a family of non-normal distributions and dual-mode market statistics in 1994. His research was later extended to become a new theory - the Capital Market Behavior Theory (CMBT). For the first time in history, the statistical assumptions of MPT are completely removed and so do the limitations. The findings have been extensively validated by real=time market data since 2000 and evolved to the systematic implementation of the Yin-Yang Index as a new scientific indicator of primary market trends.
  • The fundamental difference of CMBT vs. MPT is that the new CMBT quantifies the market behavior by sampling and processing order ticks and volume actions directly with a dual-mode non-symmetric statistical model instead of the oversimplified bell-curve normal distribution assumed by MPT.

Ten Fundamental Principles of CMBT Theory

CMBT theory is formed by the following 10 principles which provide a new behavioral interpretation of capital market pricing beyond Dow Theory.

1. A trend is driven only by those taking trading actions - The primary price movement trend is mainly driven by the behavior of those investors who take trading actions; not by anyone else who takes no trading actions.

2. Market trend reversal can be detected from early bullish or bearish trading actions - "Smart money" trades from institutions and related parties offer early signals of a trend reversal. Those trading actions with up or downticks supported by volumes contribute to trends and trend reversals.

3. A trend can be timely identified if net sentiment can be measured - Long-term or short-term trend reversals can be identified most of the times in advance or with a little delay if we can measure the net effect of bull or bear market sentiment.

4. A trend is determined by volumes and changes in prices,  not by absolute prices- Past prices have no direct impact on the future prices which are only affected by changes in prices and volumes by trading actions.

5. Trend reversal happens when the net effect of bulls and bears crosses zero - If any system can measure the total force of bullish buyers and the total force of bearish sellers, the trend reversal will then happen when the net effect of the combined force measure crosses zero. The trend reversal is subject to happen anytime.

6. The effect of all events will affect the market trend - Any events, including but not limited to earnings, investor expectations, research reports, and political policies will all create a certain impact to affect the market trend. If the effect is strong enough, the primary trend reversal can be triggered.

7. Fundamental value can be created or destroyed by trading actions - Through trading actions, the market prices can be inflated and deflated and thus the perceived value can change over time. It, in turn, can create or destroy the fundamental value of the underlying business due to the availability of capital market funding. The stock market is not a zero-sum game as some may falsely believe.


8. The market price is just the value perceived by all interested buyers and sellers - Market price is determined by the collective effect of all bullish and bearish investors’ perception of the value at any given time. Fundamental value is a factor but it does not directly determine the market prices.

9. Risk control can only be done by design, not by short-term timing - Investment portfolio risk management can be optimized by asset allocation design, not by short-term timing of secondary or minor trends. If a primary long-term bull or bear trend can be detected, the weighting towards more aggressive or more conservative can enable a portfolio to out-perform the market. If the primary trend cannot be detected (side-way market), portfolio re-balancing will add value.

10. The stock market is a leading economic cycle indicator - The stock market overall driven by trading actions is a good long-term economic indicator.


CMBT Interpretation of Stock Market Predictability

When the 2013 Nobel Prizes in Economics were announced, both financial academics and practitioners became somehow confused. The  awards were given to Eugene Fama, who is best known for originating the Efficient Market hypothesis, and Robert Shiller, who once claimed the efficient market hypothesis as “one of the most remarkable errors in the history of economic thought,” and professor Lars Peter Hansen, whose work seemed not really connected to Fama and Shiller at all. The prizes were awarded “for their empirical analysis of asset prices,” but what the three had done are quite different, if not having opposite arguments.

The scientific answer about the stock market behaviors turns out to be more complicated than markets are efficient — or markets are inefficient. Charlie Yang's CMBT helps improve our understanding of human behaviors by answering the question of how and when we can predict and/or detect the stock market movement.
  • Why - why is the stock market trend sometimes predictable, sometimes detectable only, and sometimes random? It is because future forces (various events) are unpredictable in terms of timing and exact scale, such as political policy changes.
  • When - the stock market trend may be predicted when the economical cycles are gradually improving or deteriorating without significant new forces or material events.
  • Who - the stock market movements are driven only by those people who place trade orders to support (buy) or vote against (sell) the underlying prices.
  • Where - the stock market trend reversal happens where the overall bullish forces are overtaking the overall bear forces in controlling the market direction or vice versa.
  • What - except encountering sudden significant forces, the movements of the stock market are gradually pushed by what is known as "smartness" of the money flows, i.e., the smart money acts early and the general public money always trades the last.
  • How - a new computing process can be implemented to explain how to predict and/or detect the market trend. It is done by sampling trading ticks weighted by volumes from everyday trades and then processing the samples to derive the ultimate market trend signals. This process makes no simplified assumptions, in contrast to the theories proposed by Harry Markowitz and Eugene Fama.

Good thoughts and research efforts have always been motivated by passion instead of daily jobs and careers.  Luckily, Yang's recent employers have also offered him not only the opportunity to best serve investors with his passion but also the possibility to meet and interview thousands of investors, observe and understand their real-life investment behaviors. The experiences allow his thinking to continue and spare time research being refined and validated with good statistical samples. The journey to the destination could still be far. Most of Yang's research was proprietary in the past, including fat-tailed and skewed probability distributions for modeling stock prices and asset return statistics (Black Swan Model), and theory of capturing and measuring crowd emotion (Human Emotion Index), among many others. It is his plan to gradually publish these scientific findings on this site to share with all investors for research and education purposes.

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