# Trading Imbalance in Chinese Stock Market—A High-Frequency View

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## Abstract

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## 1. Introduction

## 2. Methods and Materials

#### 2.1. Trading Polarity

#### 2.2. Data

#### 2.2.1. Sample Period: 2015 Stock Market Crash of China

#### 2.2.2. Transaction Records

#### 2.2.3. Stock Prices

## 3. Results

#### 3.1. Summary Statistics of the Trading Polarity

#### 3.1.1. Market-Level Polarity

#### 3.1.2. Stock-Level Polarity

#### 3.2. Polarity and Return

#### 3.2.1. Market Polarity and Return

#### 3.2.2. Stock Polarity and Return

#### 3.3. The Flipping of Polarity and Stock Returns

#### 3.4. Using Polarity to Signal the Market Changes

#### 3.4.1. The Changing of the Polarity-Return Correlation

#### 3.4.2. How Does the Flipping Polarity Relates to Market Changes?

- Flipping Depth

- Length before Flipping

- Using entropy to characterizing the state of market

#### 3.4.3. Market Polarity and Emotions

## 4. Conclusions and Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Illustrations of how polarity is calculated. For simplicity purpose, suppose that the presented limit orders are all submitted from 9:30 am to 9:31 am (within one min interval) for stock i on day d. All the limit orders are at the same price and are ordered according to the quote sequence. We view one order as one man-time, which is the most micro decision unit in stock market. There are two buy limit orders and three sell limit orders involved in the three transactions happened, indicating $NO{B}_{i,[t-1,t],d}=2$ and $NO{S}_{i,[t-1,t],d}=3$. Note that the third sell limit order is not fully fulfilled and might be involved in the next minute.

**Figure 2.**The relationship between ${\mathrm{entropy}}_{i,t,d}$ and ${\mathrm{polarity}}_{i,t,d}$. For the convenience of visualization, here we take the stock “000001.SZ” on 8 May 2015 for example. The two indicators are on a one-minute basis.

**Figure 3.**The Shenzhen Stock Exchange Component (SZSC) index from 4 May 2015 to 31 July 2015. The SZSC index is an index of 500 stocks that are traded at the Shenzhen Stock Exchange. The index shows that the market experienced a large rise and fall in this segment. On 12 June, there was a peak at 18098.27 points. From 15 June to 6 July, this figure experienced a sharp decline. Thereafter, the index reached its lowest value in July and rose slightly from 8 July to 31 July. We accordingly cut the sample period into three parts in this order, and they are indicated by different backgrounds.

**Figure 4.**The correlation distribution over a couple of days. Using the one-minute frequency data, we obtain the whole set of polarity-return correlation coefficients for all the stocks on day d. These trading days are representatives for different market conditions. May 29 belongs to the bull market period (before crash). On 26, 30 June, and 2 July, over one thousand stocks hit the price limit of −10%, and these trading days belong to the crash period (during crash). The rest belong to the after crash period.

**Figure 5.**The Kullback–Leibler(KL) divergence from ${Q}_{d-1}\left(x\right)$ to ${Q}_{d}\left(x\right)$. The higher the KL divergence is, the more diverse the correlation distribution will be compared to the prior day. It is clear that the KL divergence increases in crash and post-crash periods.

**Figure 6.**Polarity flipping depth. The box plot graphically depicts groups of the numerical depths of 1646 stocks on the corresponding day through their five-number summaries: the smallest observation, lower quartile ($Q1$, 25th percentile), median ($Q2$, 50th percentile), upper quartile ($Q3$, 75th percentile), and largest observation. If we denote the spread between $Q3$ and $Q1$ as h, then the outliers are defined as those less than $Q1-1.5h$ or greater than $Q3+1.5h$. In each box with this representation, outliers are ignored to make the graph clear.

**Figure 7.**Probability density function ($p\left(X\right)$, blue) of the length before flipping and the fitted power-law distribution on 8 May 2015. Subfigure (

**a**) shows the positive flipping length distribution of all the stocks, where the positive flipping length is defined as the time span between two positive polarities. Subfigure (

**b**) shows the negative flipping length distribution of all the stocks, where the negative flipping length is defined as the time span between two negative polarities. The dashed lines are power-law fittings.

**Figure 8.**The fitted power-law exponent $\alpha $ of the positive and negative flipping length distribution for each day. The daily distribution is a mixture of all the stocks’ daily flipping lengths. The error bars are the estimated standard errors for $\alpha $ on the corresponding day.

**Figure 9.**The burstiness parameter B for the daily distributions of positive and negative flipping lengths. The daily distribution is a mixture of all the stocks’ daily flipping lengths.

**Figure 12.**The trading polarity value correlated with the market emotion indicator. Based on the online emotions of investors, $RJ{F}_{d}$ on the x-axis is defined as the ratio of joy (greed) to fear ($RJF$) on day d, $RJ{F}_{d}=\frac{{X}_{joy,d}}{{X}_{fear,d}}$. The market polarity on the y-axis is the average polarity of the stocks when the SZSC index reaches its daily minimum.

Panel A: Descriptive Statistics | ||||||||

Mean | Std.dev. | Skewness | ||||||

4 May 2015–31 Jul 2015 | 0.07 | 0.11 | − 0.17 | |||||

pre-crash | 0.07 | 0.06 | 0.61 | |||||

crash | 0.14 | 0.10 | − 0.11 | |||||

post-crash | 0.02 | 0.13 | − 0.14 | |||||

Panel B: 1 min Autocorrelations | ||||||||

lag 1 | lag 2 | lag 3 | lag 4 | lag 5 | lag 10 | lag 15 | lag 30 | |

4 May 2015–31 Jul 2015 | 0.92 | 0.87 | 0.82 | 0.77 | 0.72 | 0.55 | 0.45 | 0.21 |

pre-crash | 0.92 | 0.86 | 0.80 | 0.74 | 0.69 | 0.49 | 0.39 | 0.12 |

crash | 0.93 | 0.89 | 0.84 | 0.80 | 0.77 | 0.64 | 0.56 | 0.34 |

post-crash | 0.93 | 0.88 | 0.82 | 0.78 | 0.75 | 0.60 | 0.48 | 0.26 |

Panel A: Descriptive Statistics | ||||||||

Mean | Std.dev | Skewness | Cap | Mean | Std.dev | Skewness | ||

4 May–31 Jul | 0.08 | 0.34 | −0.17 | small | 0.07 | 0.33 | −0.13 | |

mid | 0.08 | 0.34 | −0.18 | |||||

large | 0.08 | 0.34 | −0.25 | |||||

pre-crash | 0.07 | 0.33 | −0.22 | small | 0.06 | 0.33 | −0.16 | |

mid | 0.07 | 0.33 | −0.23 | |||||

large | 0.08 | 0.32 | −0.31 | |||||

crash | 0.14 | 0.34 | −0.11 | small | 0.12 | 0.34 | −0.11 | |

mid | 0.14 | 0.34 | −0.11 | |||||

large | 0.14 | 0.34 | −0.11 | |||||

post-crash | 0.04 | 0.35 | −0.18 | small | 0.05 | 0.34 | −0.14 | |

mid | 0.04 | 0.35 | −0.18 | |||||

large | 0.02 | 0.36 | −0.25 | |||||

Panel B: 1 min autocorrelations | ||||||||

lag 1 | lag 2 | lag 3 | lag 4 | lag 5 | lag 10 | lag 15 | lag 30 | |

May–Jul | 0.46 | 0.31 | 0.25 | 0.21 | 0.20 | 0.15 | 0.10 | 0.03 |

pre-crash | 0.46 | 0.31 | 0.25 | 0.21 | 0.19 | 0.15 | 0.09 | 0.03 |

crash | 0.47 | 0.29 | 0.22 | 0.20 | 0.20 | 0.12 | 0.10 | 0.01 |

post-crash | 0.45 | 0.32 | 0.27 | 0.22 | 0.21 | 0.15 | 0.11 | 0.04 |

**Table 3.**Regressions of intraday one minute market returns $M{R}_{t,d}$ on ${\mathrm{market}\mathrm{polarity}}_{t-k,d}$.

Panel A: 4 May to 31 Jul. | ||||

lag k | average coefficient | percent positive | percent positive and significant | percent negative and significant |

0 | −0.0061 | 14.06% | 0.00% | 43.75% |

1 | 0.0025 | 73.44% | 23.44% | 1.56% |

2 | 0.0017 | 67.19% | 21.88% | 6.25% |

3 | 0.0018 | 67.19% | 12.50% | 1.56% |

4 | 0.0009 | 65.63% | 7.81% | 4.69% |

5 | −0.0007 | 45.31% | 3.13% | 12.50% |

Panel B: 4 May to 14 Jun (pre-crash). | ||||

lag k | average coefficient | percent positive | percent positive and significant | percent negative and significant |

0 | −0.0068 | 13.33% | 0.00% | 53.33% |

1 | 0.0034 | 86.67% | 40.00% | 0.00% |

2 | 0.0031 | 73.33% | 30.00% | 0.00% |

3 | 0.0019 | 73.33% | 10.00% | 0.00% |

4 | 0.0005 | 53.33% | 3.33% | 3.33% |

5 | −0.0012 | 46.67% | 3.33% | 16.67% |

Panel C: 15 Jun to 7 Jul (crash). | ||||

lag k | average coefficient | percent positive | percent positive and significant | percent negative and significant |

0 | −0.0084 | 13.33% | 0.00% | 33.33% |

1 | 0.0039 | 80.00% | 13.33% | 6.67% |

2 | 0.0013 | 73.33% | 13.33% | 6.67% |

3 | 0.0018 | 53.33% | 13.33% | 0.00% |

4 | 0.0019 | 73.33% | 6.67% | 6.67% |

5 | −0.0014 | 33.33% | 0.00% | 20.00% |

Panel D: 8 Jul to 31 Jul (post-crash). | ||||

lag k | average coefficient | percent positive | percent positive and significant | percent negative and significant |

0 | −0.0029 | 16.67% | 0.00% | 38.89% |

1 | −0.0002 | 44.44% | 5.56% | 0.00% |

2 | −0.0006 | 50.00% | 11.11% | 16.67% |

3 | 0.0017 | 72.22% | 16.67% | 5.56% |

4 | 0.0011 | 83.33% | 16.67% | 5.56% |

5 | 0.0008 | 55.56% | 5.56% | 0.00% |

Panel A: 4 May to 31 Jul | ||||

lag k | average coefficient | percent positive | percent positive and significant | percent negative and significant |

0 | −0.0009 | 23.13% | 1.55% | 31.45% |

1 | 0.0008 | 77.22% | 16.27% | 0.54% |

2 | 0.0006 | 75.40% | 13.70% | 0.54% |

3 | 0.0003 | 64.62% | 7.70% | 1.33% |

4 | 0.0000 | 54.08% | 3.69% | 2.31% |

5 | 0.0000 | 50.36% | 2.69% | 2.76% |

Panel B: 4 May to 14 Jun (pre-crash). | ||||

lag k | average coefficient | percent positive | percent positive and significant | percent negative and significant |

0 | −0.0013 | 10.92% | 0.32% | 46.13% |

1 | 0.0004 | 70.16% | 11.19% | 0.87% |

2 | 0.0006 | 80.01% | 16.83% | 0.34% |

3 | 0.0004 | 74.34% | 11.43% | 0.49% |

4 | 0.0002 | 62.16% | 5.34% | 1.17% |

5 | 0.0001 | 54.57% | 3.33% | 2.01% |

Panel C: 15 Jun to 7 Jul (crash). | ||||

lag k | average coefficient | percent positive | percent positive and significant | percent negative and significant |

0 | −0.0007 | 34.23% | 2.43% | 18.71% |

1 | 0.0012 | 82.60% | 18.34% | 0.23% |

2 | 0.0007 | 72.24% | 11.44% | 0.58% |

3 | 0.0002 | 57.89% | 4.59% | 1.66% |

4 | −0.0001 | 48.54% | 2.19% | 2.88% |

5 | −0.0001 | 45.72% | 1.98% | 3.57% |

Panel D: 8 Jul to 31 Jul (post-crash). | ||||

lag k | average coefficient | percent positive | percent positive and significant | percent negative and significant |

0 | −0.0005 | 38.02% | 3.31% | 13.46% |

1 | 0.0013 | 87.20% | 25.33% | 0.13% |

2 | 0.0005 | 68.92% | 9.50% | 0.94% |

3 | 0.0000 | 50.53% | 2.91% | 2.80% |

4 | −0.0002 | 42.34% | 1.65% | 4.19% |

5 | −0.0001 | 45.71% | 2.02% | 3.63% |

Variable | Average Coefficient | Percent Positive | Percent Positive and Significant | Percent Negative and Significant | |
---|---|---|---|---|---|

May–Jul | positive length | 0.0010 | 81.0% | 49.2% | 12.7% |

negative length | −0.0021 | 17.5% | 11.1% | 49.2% | |

depth | −0.0003 | 19.0% | 3.2% | 65.1% | |

polarity | −0.202 | 0% | 0% | 100% | |

pre-crash | positive length | 0.0008 | 73.3% | 43.3% | 13.3% |

negative length | −0.0029 | 6.7% | 0.0% | 53.3% | |

depth | −0.0004 | 10% | 3.3% | 70% | |

polarity | −0.2221 | 0% | 0% | 100% | |

crash | positive length | 0.0010 | 93.3% | 66.7% | 6.7% |

negative length | −0.0031 | 26.7% | 20% | 60% | |

depth | −0.0006 | 13.3% | 0% | 80% | |

polarity | −0.2118 | 0% | 0% | 100% | |

post-crash | positive length | 0.0015 | 83.3% | 44.4% | 16.7% |

negative length | 0.0001 | 27.8% | 22.2% | 33.3% | |

depth | 0.0000 | 38.9% | 5.6% | 44.4% | |

polarity | −0.1602 | 0% | 0% | 100% |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Lu, S.; Zhao, J.; Wang, H.
Trading Imbalance in Chinese Stock Market—A High-Frequency View. *Entropy* **2020**, *22*, 897.
https://doi.org/10.3390/e22080897

**AMA Style**

Lu S, Zhao J, Wang H.
Trading Imbalance in Chinese Stock Market—A High-Frequency View. *Entropy*. 2020; 22(8):897.
https://doi.org/10.3390/e22080897

**Chicago/Turabian Style**

Lu, Shan, Jichang Zhao, and Huiwen Wang.
2020. "Trading Imbalance in Chinese Stock Market—A High-Frequency View" *Entropy* 22, no. 8: 897.
https://doi.org/10.3390/e22080897