What is it about?
Coherence or consistency is necessary for market equilibrium. Neoclassical economic and financial theories assume that economic agents are independent, homogeneous, and ever-rational. They maximize a utility in terms of wealth or welfare only in judgment and decision-making. For the models available, rational coherence and preference completeness and transitivity in utility maximization have become fundamental assumptions in Expected Utility Theory, General Equilibrium Theory, Capital Asset Pricing Model, Arbitrage Pricing Theory, Etc. However, it tests false for the price of random walks, homogeneous individuals, and rationally coherent decision makings. What is the underlying coherent behavior in the dynamic market equilibrium if the rational coherence and the preference completeness and transitivity do not hold over price in the stock market? It is challenging and fundamental and has yet to have a widely accepted solution for a long time. Now a research team led by Leilei Shi of the University of Science and Technology of China (USTC) and Haitong Securities Co. Ltd, P. R. China, replied to it in a paper published at China Finance Review International. It is entitled “The Underlying Coherent Behavior in Intraday Dynamic Market Equilibrium”. The authors apply a trading volume-price probability wave differential equation (Shi, 2006) to propose a conceptual theory. It has innovative behavioral interpretations of intraday dynamic market equilibrium price, in which traders' momentum, reversal, and interactive behaviors play roles. Market traders are intelligent. They are sensitive to price fluctuation and prefer to buy or sell stock over a price range rather than obey the law of one price to maximize the utility (Lamont and Thaler, 2003). They buy more at low prices and sell more at high prices. Thus, there is a shortage at low prices and a surplus at high prices. A shortage or a surplus occurs when the price diverges from an equilibrium price, at which the shortage and surplus are zero in the dynamic market equilibrium. A V-shaped curve roughly illustrates the shortage and surplus and represents a reversal trading utility function in the price and volume coordinates. An equilibrium price is a price at which the corresponding cumulative trading volume achieves the maximum value. The most trading volume price is an optimal price the buyers and sellers confirm through many transactions. It is a singular point in the trading probability wave differential equation and a reference point in behavioral economics (Kahneman and Tversky, 1984). It is an arbitrary (Ariely, Loewenstein, and Prelec, 2003), high-dimensional rather than reasonable price in intraday dynamic market equilibrium. The authors illustrate how intelligent traders adapt, cooperate, and generate dynamic market equilibrium by simple V-shaped shortage and surplus curves. A probability wave denotes that probabilities, instead of amplitudes, measure a wave's intensity (it is widely used in quantum mechanics). The authors select intraday cumulative trading volume distribution over price as revealed preferences and measure price fluctuation intensity and uncertainty by the trading volume probabilities instead of traditional time interval price amplitudes or returns in time series statistics. Based on the existence of the equilibrium in social finance where traders’ interaction must consider (Shi, Wang, Guo, and Li, 2021), the authors propose a testable interacting traders' preference hypothesis without imposing the invariance criterion of rational choices. Interactively coherent preferences signify the choices subject to interactive invariance over price. The new mathematical method or research route characterizes the nature of innovation. It will help understand investors' behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance. The authors find that interactive trading choices generate a constant frequency over prices and intraday dynamic market equilibrium in a tug-of-war between momentum and reversal traders. The equilibrium price jumps from time to time. The authors explain the market equilibrium through interactive, momentum, and reversal traders. The intelligent interactive trading preferences are coherent and account for local dynamic market equilibrium, holistic dynamic market disequilibrium, and the nonlinear and non-monotone V-shaped probability of selling over profit (BH curves) (Ben-Divid and Hirshleifer, 2012).
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Why is it important?
Modern behavioral economics and finance have developed tremendously over the past 50 years (Tversky and Kahneman, 1974; Shiller, 1981). Momentum (Jegadeesh & Titman, 1993), reversal (De Bondt & Thaler, 1985; Bloomfield et al., 2009), social interaction (Jackson, 2014; Hirshleifer, 2020), and intraday dynamic market equilibrium (Shi, Wang, Guo, and Li, 2021) have become vital empirical evidence against underlying assumptions in neoclassical economics and finance. However, academics need a unified theory justifying market dynamics subject to different trading behaviors. The subjects’ intelligent trading volume-price probability wave differential equation is the best candidate to develop a unified theory in the financial markets, in which momentum, reversal, and interactive trading actions play essential roles in the market dynamics. It reveals the mechanism of the market dynamics subject to different reversal trading utilities. It captures investors’ trading behaviors in local dynamic market equilibrium and adaptive learning in the jump process of an equilibrium price in market evolution. By the level of a high-dimensional equilibrium price, the theory incorporates many behaviors, such as overreaction, underreaction, overconfidence, disappointment, greed, panic, attention, sentiment, entertainment, gambling, and various economic variables, such as macroeconomic indexes, news announcements, economic events, mergers and acquisitions, IPO, SEO, Etc. It will explain many market anomalies in evolution, such as excessive returns, price jumps, closed fund puzzles, financial bubbles, financial crises, Etc. It will help policy decision-makers in the market administration and practitioners in the financial industry.
Perspectives
There are many intelligent behaviors, such as communication, verbal language, perception, memory and storage, work for a goal, computation, generation, adaptive learning Etc. Here, the authors define intelligence as capable of complex adaptive learning or interactively adaptive learning. It can generate interactively trading coherent patterns in response to discriminative stimuli and expected outcomes in complex adaptive learning systems. It is interactive, cooperative, generative, adaptive, and learning in evolutionary feedback loops in reinforcement coordinates, based on behavior analysis in psychology (Skinner, 1938; Staddon, 2016) and the subjects’ intelligent trading volume-price probability wave differential equation in social finance (Shi, Guo, Fenu, Wang, 2023). The subjects’ intelligent trading volume-price probability wave differential equation can consolidate the theory of the Adaptive Market Hypothesis in finance (Farmer and Lo, 1999; Lo, 2004; Lo and Zhang, 2022), develop a behavioral game theory in economics (Camerer, 1997), and derive a complex adaptive learning theory in intelligent science. The paper adopts a new analytical framework to uncover subjects' intelligent, interactively trading behaviors and market dynamics. It can develop a unified theory understanding the market dynamics subject to different reversal trading utilities from the critical mathematical derivation based on a trading utility function in behavioral and social finance. The authors can apply the subjects’ intelligent behaviors to artificial intelligence (AI), deep learning, and financial technology. Understanding the behavior of interacting individuals or units will help risk management beyond the frontiers of the financial market, such as governance in an organization, social violence in a country, and Coivd-19 pandemics worldwide. The new methodology brings a paradigm shift in economics and finance. It is disrupting existing rational assumptions, the price of random walks, and many equilibrium theories. It will propel economics in a new direction through profound insights into the market dynamics subject to different reversal trading utilities in future economic and financial studies. It uncovers the mechanism of the complexity of the financial markets.
Leilei Shi
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This page is a summary of: The underlying coherent behavior in intraday dynamic market equilibrium, China Finance Review International, January 2023, Emerald,
DOI: 10.1108/cfri-08-2022-0149.
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Resources
The Volume and Behaviour of Crowds
Volume is a comparatively neglected variable in academic finance – price and return usually attract far more research interest. An interesting recent exception to this rule, which examines the interaction of volume with behavioural finance, is “Market crowd trading conditioning, agreement price, and volume implications” by a group of Chinese researchers. Automated Trader discusses the paper with its lead author, Leilei Shi of the University of Science and Technology of China.
Does security transaction volume–price behavior resemble a probability wave?
Motivated by how transaction amount constrain trading volume and price volatility in stock market, we, in this paper, study the relation between volume and price if amount of transaction is given. We find that accumulative trading volume gradually emerges a kurtosis near the price mean value over a trading price range when it takes a longer trading time, regardless of actual price fluctuation path, time series, or total transaction volume in the time interval. To explain the volume–price behavior, we, in terms of physics, propose a transaction energy hypothesis, derive a time-independent transaction volume–price probability wave equation, and get two sets of analytical volume distribution eigenfunctions over a trading price range. By empiric test, we show the existence of coherence in stock market and demonstrate the model validation at this early stage. The volume–price behaves like a probability wave. Keywords: Price volatility; Volume kurtosis; Volume–price behavior; Coherence; Probability wave
A Price Dynamic Equilibrium Model with Trading Volume Weights Based on a Price-Volume Probability Wave Differential Equation
Guided by a price-volume probability wave differential equation in a new mathematical method, we study intraday market dynamic equilibrium in stock market. We select intraday cumulative trading volume distribution over a price range as individual mental representation and determine a price equilibrium point by the maximum volume utility price. We propose the hypothesis that a stock price can deviate away from the equilibrium point in momentum and restore to it in reversal, and the volume distribution embodies market dynamic equilibrium. Then, we examine it by a set of explicit price dynamic equilibrium models with trading volume weights from the differential equation against a large number of the price-volume distribution using tick-by-tick high frequency data in Chinese stock market in 2019. It holds true. We can infer that the theory is applied for a broader scope because it embraces core mathematical components in expected utility theory, prospect theory, and reflexivity theory. JEL classifications: G40; C61; D53; B41 Keywords: Behavioral finance theory, Mathematical method, Market dynamic equilibrium, Volume distribution over price, Momentum and reversal
The Underlying Coherent Behavior in Intraday Dynamic Market Equilibrium
Abstract Purpose: This paper applies a volume-price probability wave differential equation to propose a conceptual theory and has innovative behavioral interpretations of intraday dynamic market equilibrium price, in which traders' momentum, reversal and interactive behaviors play roles. Design/methodology/approach: The authors select intraday cumulative trading volume distribution over price as revealed preferences. An equilibrium price is a price at which the corresponding cumulative trading volume achieves the maximum value. Based on the existence of the equilibrium in social finance, the authors propose a testable interacting traders’ preference hypothesis without imposing the invariance criterion of rational choices. Interactively coherent preferences signify the choices subject to interactive invariance over price. Findings: The authors find that interactive trading choices generate a constant frequency over price and intraday dynamic market equilibrium in a tug-of-war between momentum and reversal traders. The authors explain the market equilibrium through interactive, momentum and reversal traders. The intelligent interactive trading preferences are coherent and account for local dynamic market equilibrium, holistic dynamic market disequilibrium and the nonlinear and non-monotone V-shaped probability of selling over profit (BH curves). Research limitations/implications: The authors will understand investors’ behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance. Practical Implications: The authors can apply the subjects’ intelligent behaviors to artificial intelligence (AI), deep learning and financial technology. Social Implications: Understanding the behavior of interacting individuals or units will help social risk management beyond the frontiers of the financial market, such as governance in an organization, social violence in a country and COVID-19 pandemics worldwide. Originality/Value: It uncovers subjects’ intelligent interactively trading behaviors. JEL Classification: C60; G40; D01; G10; D90 Keywords: Complexity Economics; Interactively Coherent Preference; Interactive Trader; Momentum and Reversal Trader; Local Equilibrium; BH Curve Manuscript Classification: Research Paper
When Do Investors Freak Out? Machine Learning Predictions of Panic Selling
From MIT Laboratory for Financial Engineering, MIT Sloan School of Management, MIT Computer Science & Artificial Intelligence Laboratory, and MIT Department of Electrical Engineering and Computer Science, a research group cited our working paper (2011) in their their 2022 publication.
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