Distribution Of Trading Volume Research Articles

Asymmetric information and the distribution of trading volume

We propose the Volume Coefficient of Variation (VCV), the ratio of the standard deviation to the mean of trading volume, as a new and simple measure of information asymmetry in security markets. We use a microstructure model to demonstrate that VCV is strictly increasing in the proportion of informed trade. Empirically, we obtain VCV from daily observations of trading volume and provide extensive evidence supporting the hypothesis that VCV indicates information asymmetry, by studying return reversals, institutional ownership, and extant firm-level measures of asymmetric information in the cross-section of US stocks. Moreover, VCV increases following exogenous reductions in analyst coverage induced by brokerage closures, and steeply decreases around earnings announcements and other information disclosures.

The underlying coherent behavior in intraday dynamic market equilibrium

PurposeThis 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/approachThe 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.FindingsThe 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/implicationsThe authors will understand investors' behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance.Practical implicationsThe authors can apply the subjects' intelligent behaviors to artificial intelligence (AI), deep learning and financial technology.Social implicationsUnderstanding 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/valueIt uncovers subjects' intelligent interactively trading behaviors.

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.

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 for 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.

Carbon trading volume and price forecasting in China using multiple machine learning models

Motivated by reducing carbon emissions, carbon trading market have been opened to promote environmental protection. Accurate carbon trading volume and price forecasts have far-reaching implications for environmental and energy policy formulation. As the country with the most massive carbon emissions in the world, China’s carbon price trends, carbon trading volume trends, and policy orientation are of great significance. As matters stand, there are few studies on carbon price and trading volume forecasts, and no research paper has covered carbon price and trading volume forecasts for all carbon trading markets in China. In order to provide a relatively complete reference for the carbon price and trading volume in China, this paper uses six machine learning models to predict the daily carbon price and trading volume of eight carbon markets in China, including Beijing, Shenzhen, Guangdong, Hubei, Shanghai, Fujian, Tianjin, Chongqing. The prediction models include extreme gradient boosting, random forest, kernel-based nonlinear extension of the Arps decline model optimized by grey wolf optimizer (GWO-KNEA), support vector machine optimized by particle swarm optimizer, support vector machine optimized by fruit fly optimizer and simulated annealing algorithm, and radial basis function neural network (RBFNN). Moreover, an advanced data denoising method, i.e., complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), is used in the models to smooth the raw data. Because the eight carbon trading markets have different carbon price and trading volume distribution characteristics in time series, by comparing the prediction results, more suitable models for the specific carbon market can be obtained. The prediction results show that CEEMDAN-GWO-KNEA and CEEMDAN-RBFNN are more competitive in predicting carbon prices and trading volume in China because of their best performance in many datasets. The average accuracy of CEEMDAN-RBFNN and CEMDAN-GWO-KNEA in carbon price prediction is 98.40% and 97.89%, respectively. The predictive stability of each model in different application scenarios is also discussed. The results show that high prediction accuracy does not mean better prediction stability, but CEEMDAN-RBFNN and CEMDAN-GWO-KNEA can still guarantee high stability in most datasets.

Coherent Preferences in Stock Market

In this paper, we study individual trading behaviors by cumulative trading volume distribution over a price range. We select intraday volume distribution as individual revealed preferences over a price range and determine beliefs by the maximum volume price in stock market. We propose a coherent preferences hypothesis in stock market where momentum, reversal, and interactive trading behaviors coexist in the framework of a price-volume probability wave differential equation. Then, we examine it by a set of explicit models of coherent preferences in interaction using tick by tick high frequency trading data of an ETF in Chinese stock market against a large number of the price-volume distributions. We evidence that subject individuals behave coherent preferences significantly. Finally, we find that individuals behave disposition effect or inverse disposition effect, and explain them by asymmetry and nonlinear coherent preferences. The bounded rational hypothesis combines individual preferences, beliefs, and cognitive limits, and has a set of unified and better models available in behavioral finance. It can help us to understand excessive price change or bubble and study nonlinear equilibrium and risk in financial market.

Coherent Preferences and Price Reference Point Jumps in Stock Market

In this paper, we study individual trading behaviors by cumulative trading volume distribution over a price range. We select intraday volume distribution as individual revealed preferences over a price range and determine beliefs by the maximum volume price in stock market. We propose a coherent preferences hypothesis in stock market where momentum, reversal, and interactive trading behaviors coexist in the framework of a price-volume probability wave differential equation. Then, we examine it by a set of explicit models of coherent preferences in interaction using tick by tick high frequency trading data of an ETF in Chinese stock market against a large number of the price-volume distributions. We evidence that subject individuals behave coherent preferences significantly. Finally, we find that individuals behave disposition effect or inverse disposition effect, and explain them by asymmetry and nonlinear coherent preferences. The bounded rational hypothesis combines individual preferences, beliefs, and cognitive limits, and has a set of unified and better models available in behavioral finance. It can help us to understand excessive price change or bubble and study nonlinear equilibrium and risk in financial market.

Asymmetric Information and the Distribution of Trading Volume

We use the Kyle (1985) model to characterize the distribution of trading volume as a function of the proportion of informed trade. If most orders are submitted by uninformed traders and are hence uncorrelated, order imbalance is small compared to observed trading volume, and the distribution of trading volume resembles a Normal distribution. On the other hand, if most orders are correlated because they are submitted by informed traders, the order imbalance is large and needs to be absorbed by market makers. The trading volume distribution is in this case more skewed and has a higher coefficient of variation (ratio of standard deviation to mean). We find that the volume coefficient of variation (VCV) is highly correlated to alternative measures indicative of informed trading in the cross section of stocks. Moreover, the VCV sharply decreases after earnings announcements, which resolve information asymmetries. Finally, the post earnings announcement drift is stronger for stocks with a low VCV prior to the announcement.

Reference Price Updating, Adaptation, and Trading Volume

Trading an individual stock in mental accounting, crowd’s traders usually buy and sell in terms of narrowly defined gain and loss relative to a reference price about a behavioral value rather than a fundamental value on a trading day. A reference price is the price where trading volume or trading weight is the maximal across different prices on a trading day. The trading action generates a limited number of patterns about cumulative trading volume distribution over a price range because of mental accounting, loss aversion, trading weight, and coherence or agreement in trading. However, a reference price is updated to realize a significant gain and loss from time to time after a large imbalance on a trading day. We study how a past gain or loss elicits people to trade more or less frequently in a time series. We examine their adaptive behaviors to gain or loss in trading by analyzing correlation between realized gain or loss and change in total trading volume in any two consecutive trading days. Crowd’s traders update a reference price about the value of an individual stock via learning and generate a significant realized gain or loss. They adapt to the gain and loss realized by the updating via trading volume increase or decrease significantly in any two consecutive trading days. Our study makes distinction on two types of a reference price in multiple reference prices in trading: a reference price about a value in a time interval and a reference price about realized gain or loss in a time series. It also captures the coexistence of apparently contrary attitudes to risk from crowd’s traders in stock market: risk aversion from sellers and risk seeking from buyers in the gains of high probability; and risk seeking from sellers and risk aversion from buyers for the losses of high probability.

A Unified Theory: Prospect Theory and Market Dynamics

We measure crowd’s decision weights in trading by cumulative trading volume distribution and determine a reference price about crowd’s assessment value of an individual stock by the maximal volume price in stock market. We assume that prospect theory traders derive behavioral utility in trading not only from the liquidity utility expressed in terms of final trading wealth but also from a trading weight utility and a gain-loss utility relative to the reference price. We find a mathematical relation between them, derive a price-volume differential equation, and obtain two sets of explicit trading volume distribution models. One is the models in crowd’s independent trading, and the other is the behavioral models of reference-dependent preferences in crowd’s interactive trading. Finally, we propose an explicit S-shaped value function in prospect theory from the models in crowd’s interactive trading. The unified theory is successful, consistent with empirical tests in high frequency data.

Prospect Theory and Measurement on Crowdds Subjective Behaviors in Trading

We measure crowd’s decision weights in trading by trading volume distribution and determine a reference price about crowd’s assessment value of an individual stock by the maximum volume price in stock market. We examine a reference-dependent preferences hypothesis in trading by two sets of explicit trading volume distribution models, which are connected to an explicit S-shaped value function in prospect theory. It is true with 82.42% in our tests, using high frequency data in China stock market. We explain the patterns of volume distribution by four behavioral features: mental accounting, disposition, decision weight, and coherence or agreement. Moreover, crowd’s traders update a reference price about the assessment value of an individual stock in jump from time to time. It takes place about 11.92% on a trading day. The measure of subjective behaviors by a volume dimension suggests the new openings of asset pricing models and test methodologies in financial economics.

The determinants of trading volume distribution: Evidence from globally cross-listed stocks

This paper documents the global trading volume distribution of cross-listed stocks and examines factors that make a host market competitive in attracting order flows between host and home markets. We hand-collect a sample of 642 cross-listed firms in 10 host countries with 771 cross-listings from 39 home countries between 1981 and 2010. We document that, for the first time, whether a host market shares the language or legal origin with the home markets has significant impact on attracting order flows. We also find that host markets are more successful in attracting trading volume when they have a higher information factor, have lower bid-ask spreads, provide better investor protection and information disclosure, and are closer to the home market. Additionally, small but mature high-tech firms with high growth rate, volatile stock returns and high foreign sales are prone to execute more trading in host markets.

How efficiency shapes market impact

We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e. the impact per share of large metaorders is smaller than that of small metaorders. We formulate a stylized model of an algorithmic execution service and derive a fair pricing condition, which says that the average transaction price of the metaorder is equal to the price after trading is completed. We show that at equilibrium the distribution of trading volume adjusts to reflect information, and dictates the shape of the impact function. The resulting theory makes empirically testable predictions for the functional form of both the temporary and permanent components of market impact. Based on the commonly observed asymptotic distribution for the volume of large trades, it says that market impact should increase asymptotically roughly as the square root of metaorder size, with average permanent impact relaxing to about two-thirds of peak impact.

How Efficiency Shapes Market Impact

We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e. the impact per share of large metaorders is smaller than that of small metaorders. We formulate a stylized model of an algorithmic execution service and derive a fair pricing condition, which says that the average transaction price of the metaorder is equal to the price after trading is completed. We show that at equilibrium the distribution of trading volume adjusts to reflect information, and dictates the shape of the impact function. The resulting theory makes empirically testable predictions for the functional form of both the temporary and permanent components of market impact. Based on the commonly observed asymptotic distribution for the volume of large trades, it says that market impact should increase asymptotically roughly as the square root of metaorder size, with average permanent impact relaxing to about two thirds of peak impact.

Long-term correlations and multifractality in trading volumes for Chinese stocks

We investigate the temporal correlations and multifractal nature of trading volume of 22 liquid stocks traded on the Shenzhen Stock Exchange in 2003. We find that non-universal long memory exhibits size-dependence on the trading volume, while the multifractal nature is independent of the trading volume. No crossover in the power-law dependence of the detrended fluctuation functions is observed. Our results show that the intraday pattern in the trading volume has negligible impact on the long memory and multifractality. We also find that both the long memory and probability distribution of trading volume have important influence on the multifractal nature.

Determinants of Investor Demand for Cross‐Listed Firms

By focusing on the decisions of investors to invest in cross‐listed stocks, this paper presents new evidence on why we observe striking differences in the percentage of trade in foreign markets for cross‐listed stocks. With a large sample of Toronto Stock Exchange (TSX) stocks cross‐listed in the U.S. and Canada, we document the effect of investor recognition and risk characteristics on the distribution of trading volume. Firms that are more visible to American investors are traded more heavily in the U.S. At the same time, firms that offer diverse risk characteristics are attractive to Americans. While investors understand the benefits of international diversification, as they are attracted to stocks that are different (e.g., the stock of small firms with few assets in the U.S.), they also seek stocks that provide them with high returns.

An Empirical Study of the Tails of Mutual Fund Size

The mutual fund industry manages about a quarter of the assets in the U.S. stock market and thus plays an important role in the U.S. economy. The question of how much control is concentrated in the hands of the largest players is best quantitatively discussed in terms of the tail behavior of the mutual fund size distribution. We study the distribution empirically and show that the tail is much better described by a log-normal than a power law, indicating less concentration than, for example, personal income. The results are highly statistically significant and are consistent across fifteen years. This contradicts a recent theory concerning the origin of the power law tails of the trading volume distribution. Based on the analysis in a companion paper, the log-normality is to be expected, and indicates that the distribution of mutual funds remains perpetually out of equilibrium.

Statistical properties of trading volume of Chinese stocks

The cumulative distribution of trading volume is investigated for Chinese stocks. Different from the power-law scaling of mature markets, the distribution is well fitted by a stretched exponential function f ( x ) ∼ e − α x γ . With the autocorrelation function and the detrended fluctuation analysis, the long-range autocorrelation of trading volume is revealed. The conditional dependence of volume on volatility and the volume–volatility cross-correlation are studied, and a positive long-range correlation between volume and volatility is observed.

Multi-Market Trading and Liquidity: Theory and Evidence

In this paper, we develop and test a theoretical model of multi-market trading to explain the differences in the foreign share of trading volume of internationally cross-listed stocks. The model derives an equilibrium which predicts that, under fairly general conditions, the distribution of trading volume across exchanges competing for order flow is related to the correlation of the cross-listed asset returns that arise in the respective markets. That is, volume migrates to the exchange in which the cross-listed asset returns have greater correlation with returns of other assets traded on that market. We test this prediction with monthly stock returns and volume data on 275 non-U.S. stocks cross-listed on major U.S. exchanges. We find strong empirical support for the prediction, even after controlling for other firm-specific, issue-specific and country-level factors.

Where is the Market? Evidence from Cross-Listings in the U.S.

We explore two main questions. First, can two markets for a company's shares coexist and, if so, what determines the distribution of trading volume across them? For firms cross-listed in the U.S. we find that in most cases the U.S. market attracts a significant fraction of total trading volume, and tends to be more active when the company is based in a country that is geographically close, has low financial development and relatively poor anti-insider trading protection. Moreover, the relative size of the U.S. market is larger if the company is small, volatile and high-tech. Second, we ask whether developing an active foreign market entails lower domestic trading activity. We find that for firms based in developed markets, the domestic turnover rate increases in the wake of cross-listing and remains permanently higher. In contrast, emerging market firms tend to experience a decrease in domestic trading activity.