Black swan events in China's stock markets: Intraday price behaviors on days of volatility

International Review of Economics and Finance xxx (2018) 1–17

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Black swan events in China's stock markets: Intraday price behaviors on days of volatility Wen-Yuan Lin a, I-Chun Tsai b, * a b

Department of Finance, Beijing Normal University, Zhuhai, China Department of Finance, National University of Kaohsiung, Taiwan

A R T I C L E I N F O

A B S T R A C T

Keywords: Black swan event China stock market Intraday data Price convergence Unit root quantile test

China's stock market crash on August 24, 2015 affected global stock markets, indicating a possible black swan event. This study looked at trading days when sudden rises and drops occurred in 2015 in its stock markets to examine the intraday fluctuation behaviors of stock prices in order to answer several questions: (a) How did the market resume stability after volatility in stock prices occurred? (b) Did the corrections after days of sudden rises differ from those after days when sudden drops occurred? (c) Which of the investigated trading days could be classified as black swan events? Five trading days with the highest and lowest daily returns in 2015 in the Shanghai and Shenzhen stock markets were selected as the days of volatility. The quantile autoregression unit-root test was used to test whether stock price indices converged or dispersed on days of high volatility as time passed. The results reveal that a black swan event was identifiable only for the sudden drop on May 28. On other trading days, China's stock markets exhibited notable corrections of mean reversion, and the speed of market recovery increased with the extent of price volatility. In addition, wave patterns of slow rises and rapid falls in intraday stock price fluctuations and corrections were observable after occurrences of stock price volatility, showing that overreactions and underreactions happened consecutively.

1. Introduction The Shanghai Stock Exchange (SSE) opened for transactions on December 19, 1990, making it a relatively young stock market compared with others around the world, but this emerging market quickly attracted substantial capital investment. According to the World Federation of Exchanges in 2015, the total market value of SSE ranked third globally, preceded by only the New York Stock Exchange and the Nasdaq market in the U.S. SSE has exerted an increasingly larger influence on the world economy, because of its considerable market value and trading volume. Nevertheless, the extent of short-term fluctuations in this market has been relatively large, which not only has increased investors’ capital risk, but also compounded the turmoil in global stock markets and economies. Fig. 1 showed the performance of SSE in 2015, whereby on the opening day (January 9) it was at 3285 points, and on the closing day (December 31) it was at 3539. The index change throughout 2015 appeared to be moderate. However, the SSE index peaked at 5166 on June 12. In other words, it rose by 57% from the beginning of 2015 to June 12 and then fell by 31% by December. Volatility caused panic among traders, prompting the China government to control market fluctuations with stringent measures. On January 1, 2016, the “index fuse” mechanism was first launched with the aim at suspending trading. However, in contrast to expectations, this mechanism

* Corresponding author. Department of Finance, National University of Kaohsiung, No. 700, Kaohsiung University Rd., Nanzih District, 811, Kaohsiung, Taiwan. E-mail address: [email protected] (I.-C. Tsai). https://doi.org/10.1016/j.iref.2018.10.005 Received 11 January 2017; Received in revised form 31 July 2018; Accepted 9 October 2018 Available online xxxx 1059-0560/© 2018 Elsevier Inc. All rights reserved.

Please cite this article in press as: Lin, W.-Y., & Tsai, I.-C., Black swan events in China's stock markets: Intraday price behaviors on days of volatility, International Review of Economics and Finance (2018), https://doi.org/10.1016/j.iref.2018.10.005

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International Review of Economics and Finance xxx (2018) 1–17

Fig. 1. Shanghai Stock Exchange performance in 2015.

compounded the liquidity risk. Within 4 days, the stock market was “fused” four times. This system proved to be incapable of stabilizing the market and was suspended as of January 8. The “fuse” mechanism implemented by SSE was based on the stabilizing mechanism that the United States proposed in 1988 in response to the 1987 stock market crash. However, when SSE implemented the mechanism, the authorities did not consider several market characteristics. For instance, the market had daily uplimit and downlimit restrictions on share prices, small investors comprised a relatively high proportion of the daily volume, and the national economy and stock market policies were highly connected. For the aforementioned characteristics, studying the high volatility of SSE stock prices can be very critical, as previous studies observed stock market volatility according to days, months, and seasons. However, the data did not display the volatility characteristics of China's stock markets. For example, merely considering stock returns in 2015 could lead to a spurious conclusion that its markets were stable. One characteristic of its stock markets has been their change in high-frequency data. Therefore, this study investigated the intrinsic fluctuating characteristic of China's stock markets, as they could influence the global economy. This study aimed at determining whether previous trading days that exhibited volatility could be categorized as “black swan events” in China's stock markets. By focusing on trading days when sudden rises and drops occurred in 2015 in these stock markets, the intraday fluctuation behaviors of stock prices could be examined. According to ref., two requirements must be satisfied for a trading day to be considered a black swan event: a small probability of occurrence and a substantial influence on subsequent trading days (in the form of intraday volatility pattern changes). Regarding the research scope, the authors investigated trading in the year 2015, when SSE had the greatest change and exerted the maximal influence. Five trading days with the highest and lowest daily returns were selected as the days of volatility. Intraday 1-min index data and the quantile autoregression unit-root test were adopted to analyze the intraday index changes on the days of volatility and those in the subsequent five trading days. Because China has two stock exchanges, in addition to data from SSE, the Shenzhen stock market was also employed to comprehensively illustrate the characteristic of China's stock markets. This study investigated whether stock price indices converged or dispersed on days of high volatility as time passed. Before the fuse mechanism was implemented, if stock indices resumed stability under increased trading volumes, regardless of stock market shocks, then such stable stock indices might confirm that stringent policies such as the fuse mechanism would have been unnecessary, and that the government should have been confident in the self-stabilizing capacity of the market. Unlike previous studies (Desai, Modi, Dave, & Desai, 2012), the present study examined days of volatility from an objective perspective. Without presuming these days as black swan events, the present study determined whether they could be categorized as black swan events according to the extent to which they satisfied the characteristics of black swan events. The results of Aleskerov and Egorova (2012) implied that when a day of high volatility appears, an appropriate tool that accurately predicts black swan events can facilitate selecting profitable investment portfolios. By proposing an objective evaluation method, the present study enabled investors to effectively consider tail risks. Using intraday data the goal of this paper was to examine whether the stock price behaviors observed on the selected trading days were consistent with the requirements of a black swan event and to answer the following questions: (a) How did the market resume stability after the volatility in stock prices occurred? (b) Did the corrections after days of sudden rises differ from those after days when sudden drops occurred? This study then went on to verify that two common stock price behaviors in daily and monthly data also exist in intraday data: (a) slow rises and rapid falls and (b) stock price corrections exhibit wave patterns. Explanations regarding the types of trader behavior implied by these fluctuation characteristics are subsequently offered. The rest of this paper is as follows. Section 2 presents the literature review. Section 3 discusses our empirical models. Section 4 provides data and empirical results. Section 5 concludes the paper. 2. Literature review The black swan theory was proposed by Taleb (2007), who mentioned that “this combination of low predictability and large impact makes the Black Swan a great puzzle.” Taleb (2007) claimed that in comparison with general situations (white swan events), a black swan event exhibits the following three characteristics: (a) an outlier event, which is an unprecedented and/or unexpected event; (b) an event with a substantial influence on related events and things; and (c) people rationalizing the black swan event with oversimplified 2

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International Review of Economics and Finance xxx (2018) 1–17

explanations. Black swan events could be anything from a natural disaster or terrorist attack to a financial crisis. In summary, they are unlikely events that actually occur, and considerable impacts arise due to a lack of preparation. Although black swan events have constituted only a few outliers in stock markets, these events could determine the probability of an investment's profit or loss. Estrada (2008) analyzed daily return data of the Dow Jones Industrial Average, S&P500 Index, and indices in 15 other markets, identifying outliers such as the maximal and minimal rates of daily return. Subsequently, at the end of the sampling period, Estrada calculated the final return of the total amount invested in the market since the beginning of the period. The rates of return of the outliers were shown to have a marked influence on the final returns, meaning that when markets were impacted by specific black swan events, extreme rates of return were generated, which affected long-term investment performance. Estrada (2009) analyzed the rates of return of the Dow Jones Industrial Average from 1990 to 2006, finding that because the number of outliers was far greater than the expected amount, the rate of return series did not follow a normal distribution. Furthermore, these data of return rates were used to calculate investment performance. The results showed that when 10 days with optimal daily rates of return were deleted from the total of 29,190 days, the final return that investors gained would be 65% lower than that obtained using the buy and hold strategy. By contrast, when the 10 days with the lowest daily rates of return were deleted, the final return investors’ gained was 206% higher than that obtained using the buy and hold strategy. These results indicate that black swan events do have a substantial influence on long-term investment performance. Adams and Thornton (2013) examined the daily, weekly, and monthly sequential data of the return rates of the S&P500 Index from 1979 to 2009, again disapproving the perspective that the rates of return followed a normal distribution. In addition, figures were employed to demonstrate the existence of black swan events. Because the rates of return did not follow a normal distribution, Adams and Thornton (2013) suggested that value at risk (VaR) is not a valid index for assessing risks. In calculating VaR, the skewness and kurtosis of the distribution were not considered. Therefore, using VaR could underestimate the effect of black swan events. The aforementioned studies showed that a single black swan event can reverse the return rate of an investment from positive to negative. Although black swan events are unpredictable, Aleskerov and Egorova (2012) proved that if traders can identify current events as white or black swan events at a probability slightly higher than 50%, then their average investment return can remain positive. While other studies indicated that investors do not need to know how to predict black swan events if they can identify whether stock market volatility has signified the occurrence of a black swan event, traditional financial theories can still aid investors in targeting profits. For example, Estrada and Vargas (2012) analyzed 47 national markets and 57 industries for a period of approximately 40 years. They found that when negative black swan events occurred in markets, high-beta investment portfolios depreciated more significantly than low-beta ones did, indicating that the beta coefficient is an effective tool for risk assessment. Estrada and Vargas suggested that investors utilize high-beta portfolios when negative black swan events occur and low-beta portfolios when positive black swan events occur. This indicated that the aforementioned investment strategies achieve more satisfactory performance than the passive buy and hold strategy. In summary, Estrada and Vargas explained that as long as “investors can identify the appearance of a Black Swan, beta remains a useful tool to select investment portfolios.” However, how to identify a black swan event remains an enigma. Desai et al. (2012) adopted the daily return of the Sensex Index in India's stock market from July 1997 to November 2001 as the research scope, setting investment strategies and comparing the performance of those strategies with that obtained by using the buy and hold strategy. By preventing the negative effects of negative outliers (i.e., black swan events) on investment portfolios, Desai et al. obtained improved investment strategies. Empirical studies such as the one by Desai et al. lack a theoretical basis, as the authors merely concluded their findings from a simple strategy. Although such strategies achieved satisfactory performance when applied to historical data, they exhibited little explanatory power for general and extreme future events. Therefore, investors could obtain little investment information from the estimated results of these strategies. In addition to serving as a basis of comparison with the stock price behaviors of other frequency data (i.e., daily, weekly, and monthly), intraday stock price behaviors could provide analysts with information that facilitates determining whether extreme behaviors had been generated on days of stock price volatility. Moreover, they could indicate whether such extreme behaviors significantly influence subsequent trading days, even changing the price movement. Previous studies on persistence with high frequency data mentioned that a few days of subsequent market reaction are noteworthy after an event/market's conditional impact (Ho, Shi, & Zhang, 2013; Kalev, Liu, Pham, & Jarnecic, 2004; Patell & Wolfson, 1984). Junior, Lima, and Gaio (2014) indicated the presence of persistent effects of shocks on volatility, volatility asymmetry, and delayed volatility reaction due to market changes. Andersen, Bollerslev, and Cai (2000) found out that high-frequency (5-min) returns revealed the existence of important long-memory interdaily volatility dependencies. Han (2005) also characterized the volatility process of real-time high frequency (5-min) returns in the Korean won (KRW)– US dollar ($) exchange rates. The estimation results presented that the exogenous shocks and the multiple breaks associated with a crisis in the market seemed to induce greater long memory dependency during the crisis. Han (2005) further provided estimations that were performed for each individual month of the 5-min KRW–$ data during the period of the crisis. The present study hence investigated a period of drastic volatility during 2015 in China, which was the year that SSE underwent the most substantial changes and had the largest influence. The five trading days that generated the highest and lowest daily returns in 2015 were selected. Intraday 1-min index data were adopted to analyze the intraday index changes on these days of volatility and in the subsequent five trading days. Our data frequency (1-min) referred to the setting of the empirical window by Drienko and Sault (2013) and was adjusted by the same proportion for the duration of the study.1 Compared to the aforementioned studies, the present study

1 Drienko and Sault (2013) examined abnormal returns and trading volumes that accrue to shareholders immediately after an announcement responding to a trading induced query, analyzing longer event windows' [0, þ5 days] impacts on the query announcements as employed throughout their work.

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investigated whether fixed patterns are observable in trading days exhibiting volatility. 3. Empirical models An autoregression model estimates the level to which current asset prices are influenced by previous prices. In other words, it assesses the influence persistence of information on the price. Asset prices fully reflect all available information in the market based on the efficient markets hypothesis, and therefore there is no autocorrelation. A unit root test examines the unit root in data to determine whether the influence of certain events on asset prices tends to disperse or converge. The test is often adopted for assessing market efficiency. Quantile regression is a key derivative of a conventional regression model that can estimate in detail the influence of independent variables under dependent distribution conditions. Using the previously widely used augmented Dickey-Fuller (ADF) test, Koenker and Xiao (2004) proposed the quantile autoregression (QAR) unit-root test, which highlights the influence of a fat-tailed data distribution by incorporating the concept of quantiles. Because financial and economic data often possess asymmetric characteristics, quantile models have continually been developed and applied (Baur, Dimpfl, & Jung, 2012; Clements, Galv~ao, & Kim, 2008; Koenker & Zhao, 1996; Zietz, Zietz, & Sirmans, 2008). Nikolaou (2008) modified the QAR unit-root test, which was proposed by Koenker and Xiao (2004), and used the sign of the intercept to capture the influence of the appreciation or depreciation of exchange rates. In addition, Nikolaou (2008) applied the concept of quantile to discuss the effects that positive and negative exchange rate volatilities have on mean reversion. Subsequent studies discussed numerous instances of asset price convergence and its persistence by using this method (e.g., Koenker & Xiao, 2006; Lima, Gaglianone, & Sampaio, 2008; Lin & Lin, 2013; Lin & Tsai, 2016). These studies attempted to use a quantile model to examine the persistence and correction speed of asset prices. This concept was applied in our study to discuss the correction behavior of China's stock market indices. The following model explained the test model. First, a conventional ADF model was adopted: yt ¼ α1 yt1 þ

q X

αjþ1 Δytj þ ut ; t ¼ 1; 2; …; n

(1)

j¼1

where yt was the outlier series, in which the mean was removed; and ut was a random variable with a zero mean and constant variance. Under the aforementioned setting, if α1 ¼ 1, then a unit root exists in yt . Conversely, if α1 6¼ 1(jα1 j < 1), then yt converges. On the basis of this model, Koenker and Xiao (2004) introduced quantile regression. According to the information set Ft1 of the previous term (i.e., t  1), quantile τ in yt can be expressed as a function of yt1 and the lagged value of Δyt : 0

Qyt ðτjFt1 Þ ¼ xt αðτÞ 0

(2) 0

0

where xt ¼ ð1; yt1 ; Δyt1 ; …; Δytq Þ , αðτÞ ¼ ðαu ðτÞ; α1 ðτÞ; …; αqþ1 ðτÞÞ , αu ðτÞ was quantile τ in ut , and α1 ðτÞ captured the persistence of all quantiles in yt . The QAR model developed in the present study was as follows: Qrt ðτjFt1 Þ ¼ α0 ðτÞ þ α1 ðτÞrt1

(3)

where Qrt ðτjFt1 Þ was the stock index return of quantile τ at time t, rt1 was the stock index return at time t-1, and α1 ðτÞ was employed to assess the autocorrelation between the current and previous returns of all quantiles. A negative (positive) intercept item (α0 ðτÞ) indicated that the fluctuation rate of stock prices negatively (positively) deviated from that of the previous term (Nikolaou, 2008). Test statistic (t value) showed the significance of the stock price rise or drop. By contrast, a low (high) quantile of α1 ðτÞ signified the stock price index behavior for a price drop (rise). A unit root test was subsequently administered to the autocorrelation coefficient α1 . If α1 achieves significance, then the result indicates that the stock price index is stationary, and that mean reversion exists. In other words, stock prices bounce and are revised. If α1 does not achieve significance, then a unit root exists, meaning that a random walk can be observed in stock prices, and that stock price dispersion persists. The t values for each quantile showed the level of significance of the unit root test in various volatilities. This implied that the influence of the information or policy on the market continues to progress, leading to persistent price rises or drops. Using QAR enabled this study to examine the convergence of stock prices in various volatilities. Following the aforementioned model, if α1 achieves significance, then no unit root exists and the time series data conform to a stationary distribution, indicating that asset prices converge after the shock and can generate a half-life value (Lin & Lin, 2013; Nikolaou, 2008). Half-life has been frequently adopted to assess the convergence speed of the price index (Lin & Lin, 2013; Nikolaou, 2008).2 The concept refers to the time for a series to return to half of its previous state after being subjected to a designated information shock. If α1 is within 1, then the half-life value can be calculated by the following equation: log(0.5)/log(jα1 j). By contrast, if jα1 j  1, then price fluctuations disperse instead of converge, and the half-life value is considered as infinite (Nikolaou, 2008). This paper employed the half-life calculation to note the convergence speed of China's stock market indices within/after the shock, further reflecting the price behaviors exhibited within the markets.

2 Lin and Lin (2013) mentioned that the speed of convergence of RER towards the long-run equilibrium level is often measured using half-life, which means that given a shock, how much time will pass before the effect of the shock is reduced by half.

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Table 1 The QAR test and half-life estimates of the SSE Composite Index on days of sudden drops. Date (Return)

8/24 (8.87%)

7/27 (8.87%)

1/19 (8.02%)

6/26 (7.69%)

5/28 (6.73%)

Quantile

t

Half-life

t

Half-life

t

Half-life

t

Half-life

t

Half-life

10% 20% 30% 40% 50% 60% 70% 80% 90%

2.29* 2.14* 3.17** 3.54** 4.10** 3.83** 3.82** 3.87** 3.31**

1.95 1.82 1.66 1.50 1.36 1.41 1.48 0.80 0.42

5.51** 3.22** 3.78** 3.42** 3.48** 3.49** 3.03** 4.14** 4.43**

1.62 1.95 1.85 2.28 2.23 2.07 1.50 1.01 0.62

1.52 1.67 1.71 1.70 1.74 1.88 1.55 234.94** 295.47**

∞ ∞ ∞ ∞ ∞ ∞ ∞ 0.21 0.20

4.40** 4.38** 4.83** 4.51** 4.49** 4.58** 3.95** 3.63** 5.18**

0.58 0.83 0.79 0.92 1.12 1.08 0.85 0.55 0.32

2.58** 2.80** 3.08** 3.10** 3.65** 4.21** 4.84** 7.18** 6.43**

4.31 4.79 4.39 4.08 3.64 3.27 2.68 2.02 2.10

Notes: This table reported the QAR test and half-life estimates of the SSE Composite Index on days of sudden drops according to Eq. (3). A significant negative value of t indicated that asset prices converged after the shock and could generate a half-life value. * and ** denoted significance at 5% and 1%, respectively. ∞ denoted the price fluctuations dispersed instead of converged.

4. Data and empirical results 4.1. Sample data selection This study analyzed the Shanghai and Shenzhen stock markets by using their composite stock price indices - namely, the SSE Composite Index (SH00001) and Shenzhen Component Index (SZ399001) - as the research sample. Regarding the research scope, the year 2015 was investigated as the empirical range, during which these two stock markets showed the highest volatility and exerted the greatest influence. The 1-min intraday research data were obtained from the Tinysoft Co. database (http://www.tinysoft.com.cn). Under the black swan theory, Taleb (2007) specified that a black swan event is an outlier event. Therefore, this paper analyzed the daily fluctuations in SSE by selecting the five trading days with the highest and lowest levels of daily fluctuations as the target days of investigation. This study referred to these days as days of volatility, which can be categorized as days of sudden rises or days of sudden drops. The average return and critical value of the 99% confident interval of negative fluctuations were respectively 2.1% and 2.6%. By contrast, the average return and critical value of the 99% confident interval of positive fluctuations were respectively 1.7% and 2%. In descending order of returns, the days with sudden rises were as follows: October 12 (7.41%), July 9 (5.60%), July 30 (5.38%), August 27 (5.20%), and August 10 (4.80%). By contrast, in ascending order of returns (from the day with the highest level of price drop), the days of sudden drops were as follows: August 24 (8.87%), July 27 (8.87%), January 19 (8.02%), June 26 (7.69), and May 28 (6.73%). The performances of these selected dates were far from the average performances of the markets. It was thus safe to consider these selected dates as event dates that may have significant impacts on the markets. Instead of applying the conventional time series approach, this study sequenced these sample dates according to the extent of the price rise or price drop rather than according to time. The purpose of this was to objectively investigate the appropriateness of labeling these trading days as black swan events. Samples were first collected according to one of the definitions of black swan events - namely, an outlier value - and further sequenced according to the degree of outlier. Subsequently, the persistence of intraday market influence resulting from drastic fluctuations was examined to illustrate the market stability and correction mechanisms. For each day of volatility, the authors collected research data on the day of volatility to the five subsequent trading days. The data referred to the 1-min price rate of change. The QAR model (Equation (3)) was adopted to test the price convergence on the day of volatility (Day 0) and the following five trading days (Days 1–5). This study used the t value to examine the level of price convergence. When the results satisfied the requirements for convergence, the half cycle was calculated. A trend chart of the half cycle subsequently illustrated the convergence.

4.2. Empirical results In this section, the empirical investigations were divided into four parts to provide explanations about the information from stock price behaviors on days of sudden drops/rises and such behaviors on 5 days following the days of sudden drops/rises. The process of analysis was first employed based on an objective evaluation method to focus on the five trading days that generated the highest and lowest daily returns in 2015. Close attention was paid on the phenomenon of divergence/convergence of stock index return behaviors on the day of the event and in the subsequent five trading days. Extended discussion of market effects was based on the black swan theory. The analysis results can provide important implications for market supervision. 4.2.1. Intraday stock price behaviors on days of sudden drops Table 1 showed the QAR test and half-life estimates of the SSE Composite Index on days of sudden drops. Table 2 presented the QAR test and half-life estimates of the Shenzhen Component Index on days of sudden drops. According to Table 1, among the 5 days of sudden drops in 2015, the SSE Composite Index did not converge only on January 19, on which day the half-life values in most quantiles were ∞, except for those in the two quantiles with less extreme price drops (i.e., 80% and 90%). No stock price convergence was observed for this day, indicating that the price drop did not stop. Table 2 showed that the Shenzhen Component Index did not converge at several 5

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Table 2 The QAR test and half-life estimates of the Shenzhen Component Index on days of sudden drops. Date (Return)

8/24 (8.87%)

7/27 (8.87%)

1/19 (8.02%)

6/26 (7.69%)

5/28 (6.73%)

Quantile

t

Half-life

t

Half-life

t

Half-life

t

Half-life

t

Half-life

10% 20% 30% 40% 50% 60% 70% 80% 90%

4.14** 4.75** 0.26 4.52** 0.84 3.19** 3.79** 0.55 193.22**

2.47 3.00 ∞ 1.60 ∞ 0.75 0.67 ∞ 0.17

3.74** 3.58** 3.35** 4.00** 4.43** 4.90** 4.99** 4.83** 3.76**

1.77 1.84 2.35 2.37 2.26 2.06 1.97 1.45 0.68

1.04 2.05* 2.02* 1.92 2.01* 1.88 1.66 196.32** 240.51**

∞ 0.87 0.85 ∞ 0.63 ∞ ∞ 0.17 0.15

3.31** 3.37** 4.09** 3.85** 3.96** 4.25** 4.57** 6.40** 3.32**

0.88 1.57 1.47 1.29 1.21 1.13 0.92 0.76 0.43

2.85** 4.00** 4.60** 4.65** 5.43** 5.11** 5.43** 4.70** 2.28*

3.15 3.88 3.74 3.80 3.22 3.29 3.05 2.81 3.15

Notes: This table reported the QAR test and half-life estimates of the Shenzhen Composite Index on days of sudden drops according to Eq. (3). A significant negative value of t indicated that asset prices converged after the shock and could generate a half-life value. * and ** denoted significance at 5%, and 1% respectively. ∞ denoted the price fluctuations dispersed instead of converged.

Table 3 The QAR test and half-life estimates of the SSE Composite Index on days of sudden rises. Date (Return)

10/12 (7.41%)

7/09 (5.60%)

Quantile

t

Half-life

t

Half-life

t

6/30 (5.38%) Half-life

t

8/27 (5.20%) Half-life

t

8/10 (4.80%) Half-life

10% 20% 30% 40% 50% 60% 70% 80% 90%

4.97** 4.86** 4.27** 4.36** 4.76** 4.38** 3.91** 2.46** 2.19*

2.20 1.81 1.94 2.07 2.01 2.15 2.23 2.76 3.24

7.54** 6.59** 4.82** 3.55** 3.30** 3.77** 3.64** 4.34** 5.92**

1.65 1.68 1.98 1.90 1.68 1.38 1.62 1.26 0.97

5.06** 6.37** 5.56** 7.70** 6.87** 9.02** 9.56** 10.99** 7.93**

1.22 1.07 1.02 1.21 1.25 1.04 1.04 0.96 0.70

5.63** 6.39** 6.79** 6.37** 5.78** 4.12** 3.83** 3.21** 3.76**

0.42 0.81 0.91 0.99 1.01 1.29 1.19 1.20 1.58

1.89 3.87** 4.56** 4.22** 4.09** 3.80** 3.20** 2.76** 1.58

∞ 0.89 1.20 1.29 1.29 1.42 1.59 1.52 ∞

Notes: This table reported the QAR test and half-life estimates of the SSE Composite Index on days of sudden rises according to Eq. (3). A significant negative value of t indicated that asset prices converged after the shock and could generate a half-life value. * and ** denoted significance at 5% and 1%, respectively. ∞ denoted the price fluctuations dispersed instead of converged.

Table 4 The QAR test and half-life estimates of the Shenzhen Component Index on days of sudden rises. Date (Return)

10/12 (7.41%)

7/09 (5.60%)

Quantile

t

Half-life

t

Half-life

t

6/30 (5.38%) Half-life

t

8/27 (5.20%) Half-life

t

8/10 (4.80%) Half-life

10% 20% 30% 40% 50% 60% 70% 80% 90%

4.45** 6.19** 6.46** 5.37** 4.61** 4.11** 3.22** 3.01** 1.68

1.43 1.82 1.80 1.94 2.05 1.90 2.46 3.11 ∞

1.04 5.44** 6.18** 5.59** 5.21** 4.74** 4.10** 3.09** 3.24**

∞ 2.23 2.29 2.18 2.42 2.38 2.41 2.68 2.13

14.24** 4.36** 4.61** 5.04** 5.04** 5.21** 5.14** 5.65** 13.68**

1.37 1.50 1.74 1.75 1.83 1.61 1.39 1.13 0.76

6.17** 5.74** 7.14** 6.49** 5.41** 4.84** 4.13** 3.64** 3.76**

0.49 0.68 0.93 1.07 1.21 1.39 1.36 1.31 1.39

6.18** 3.76** 3.39** 3.65** 3.84** 3.53** 3.51** 3.05** 1.92

0.83 1.05 1.68 1.77 1.63 1.74 1.48 1.40 ∞

Notes: This table reported the QAR test and half-life estimates of the Shenzhen Composite Index on days of sudden rises according to Eq. (3). A significant negative value of t indicated that asset prices converged after the shock and could generate a half-life value. ** denoted significance at 1%. ∞ denoted the price fluctuations dispersed instead of converged.

quantiles on August 24 and January 19. On these two days the results of the unit root quantile test showed non-significant refusal, and the after-shock half-life of the stock price was ∞. A comparison between the results in Tables 1 and 2 revealed that on the day of the largest price drop in 2015 (i.e., August 24), the SSE Composite Index exhibited obvious convergence behavior. When prices dropped drastically after the shock occurred, the index stabilized at the same level. The index then quickly bounced back, exhibiting a half-life of 1.95, even when the price drop was at its largest (at the lowest quantile). However, the Shenzhen Component Index on August 24 continued to drop. August 24 was the day that China's stock market crashed. From the results for this particular day, the performance of the Shenzhen stock market was more worrying than that of the Shanghai stock market. A lack of market efficiency or the irrational herding of investors provided the momentum for stock index non-convergence. From this perspective, the efficiency of the stock market and rationality of investors in Shenzhen required more attention from China's government.

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Table 5 The QAR test and half-life estimates of the SSE Composite Index within 5 days following the days of sudden drops. Date (Return)

8/24 (8.87%)

7/27 (8.87%)

1/19 (8.02%)

6/26 (7.69%)

5/28 (6.73%)

Quantile

t

Half-life

t

Half-life

t

Half-life

t

Half-life

t

Half-life

10% 20% 30% 40% 50% 60% 70% 80% 90%

7.98** 11.98** 11.75** 10.88** 10.17** 9.31** 8.21** 11.38** 7.91**

0.92 1.01 1.15 1.26 1.34 1.40 1.49 1.35 0.97

6.37** 8.44** 10.46** 10.38** 10.50** 11.77** 12.76** 11.00** 10.86**

1.14 1.31 1.34 1.52 1.49 1.52 1.42 1.16 0.77

13.02** 11.49** 12.18** 14.90** 15.77** 15.22** 9.56** 11.25** 13.07**

0.83 1.10 1.20 1.25 1.21 1.15 1.41 1.48 1.34

13.04** 17.50** 14.97** 13.69** 15.45** 14.39** 14.28** 10.86** 16.76**

0.96 0.94 1.00 1.13 1.18 1.22 1.03 1.00 0.73

8.16** 6.26** 7.62** 10.72** 11.88** 10.35** 10.12** 12.45** 9.01**

3.20 3.24 2.99 2.85 2.61 2.32 2.15 1.71 1.44

Notes: This table reported the QAR test and half-life estimates of the SSE Composite Index within 5 days following the days of sudden drops according to Eq. (3). A significant negative value of t indicates that asset prices converged after the shock and could generate a half-life value. ** denoted significance at 1%. ∞ denoted the price fluctuations dispersed instead of converged.

Table 6 The QAR test and half-life estimates of Shenzhen Component Index within 5 days following the days of sudden drops. Date (Return)

8/24 (8.87%)

Quantile

t

Half-life

7/27 (8.87%) t

Half-life

1/19 (8.02%) t

Half-life

6/26 (7.69%) t

Half-life

5/28 (6.73%) t

Half-life

10% 20% 30% 40% 50% 60% 70% 80% 90%

4.83** 8.98** 10.47** 10.30** 11.07** 11.31** 10.18** 9.68** 7.48**

1.03 1.15 1.18 1.26 1.32 1.34 1.34 1.20 0.93

11.17** 9.75** 9.47** 9.34** 9.63** 9.39** 9.76** 8.87** 10.99**

1.04 1.52 1.49 1.65 1.72 1.69 1.63 1.38 0.89

14.18** 21.23** 16.87** 17.03** 16.59** 14.36** 13.99** 11.77** 8.99**

0.55 0.61 0.69 0.76 0.78 0.85 0.87 0.90 0.93

10.17** 10.32** 13.19** 13.34** 10.68** 10.48** 11.70** 11.49** 8.79**

1.23 1.41 1.41 1.45 1.56 1.58 1.40 1.22 0.88

10.89** 6.97** 6.85** 8.45** 10.25** 9.99** 11.75** 12.26** 8.40**

2.78 2.72 2.49 2.35 2.22 2.10 2.04 1.79 1.44

Notes: This table reported the QAR test and half-life estimates of the Shenzhen Composite Index within 5 days following the days of sudden drops according to Eq. (3). A significant negative value of t indicated that asset prices converged after the shock and could generate a half-life value. ** denoted significance at 1%. ∞ denoted the price fluctuations dispersed instead of converged.

4.2.2. Intraday stock price behaviors on days of sudden rises Tables 3 and 4 respectively showed the QAR test and half-life estimates of the SSE Composite Index and Shenzhen Component Index on days of sudden rises. According to Table 3, among the 5 days of sudden rises in 2015, the SSE Composite Index exhibited considerable price rise persistence only on August 10, and only in two quantiles (10th percentile and 90th percentile), at which time the half-lives were ∞. The performance of the Shenzhen Component Index on days of price rises was also relatively irrational. In total, price rises did not converge in three trading days (i.e., October 12, July 9, and August 10). Therefore, the Shenzhen Component Index showed more significant volatility than did the SSE Component Index on both days of sudden rises and sudden drops. These results implied that investors who benefit from bull markets should invest in the Shenzhen Component Index on the day when information of a possible sudden rise in China's stock markets is exposed. However, when China's stock markets start to crash, investors should avoid investing in the Shenzhen stock market. A comparison of the stock price behaviors on days of sudden drops and sudden rises revealed obvious patterns of stock price fluctuations for sudden drops, but not for sudden rises. Tables 1 and 2 showed that on the 5 dates of sudden drops, most of the half-lives observed at the low quantiles, namely the day of the largest price drop (10th percentile), were greater than those observed at the high quantiles (90th percentile). These results showed that at the time of the largest price drop among the dates that sudden drops occurred, because market investors became relatively panicked, they engaged in substantially more stock selling, further compounding the stock price drop and postponing price convergence. By contrast, a similar trend was not obvious on days when sudden rises occurred. For example, regarding the SSE Composite Index on August 10 and the Shenzhen Component Index on July 9, the half-lives were ∞ at the time when the price rises were at their smallest. Such a difference in patterns indicated that on days of volatility, investors were more prone to panicking about price drops than chasing price rises. On days of both sudden drops and sudden rises, the half-lives of the Shenzhen Component Index were higher than those of the SSE Composite Index. The authors further compared the convergence statistics of these two markets in general situations (i.e., in the 50th percentile), finding that in all the days that convergence was reached, the Shenzhen Component Index exhibited slower convergence than the SSE Component Index did. This phenomenon occurred for both sudden rises and sudden drops, with price volatility persisting longer in the Shenzhen stock market than in the Shanghai stock market. 4.2.3. Intraday stock price behaviors within 5 days following the days of sudden drops The QAR test was used to observe asset price convergence and its persistence, and the half-life estimations were employed to explain the convergence speed of China's stock price indices. Tables 5 and 6 respectively showed the QAR test and half-life estimates of the SSE 7

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Table 7 The QAR test and half-life estimates of the SSE Composite Index within 5 days following the days of sudden rises. Date (Return)

10/12 (7.41%)

7/09 (5.60%)

6/30 (5.38%)

8/27 (5.20%)

8/10 (4.80%)

Quantile

t

Half-life

t

Half-life

t

Half-life

t

Half-life

t

Half-life

10% 20% 30% 40% 50% 60% 70% 80% 90%

10.80** 10.66** 11.06** 11.64** 11.28** 10.38** 8.89** 8.38** 7.74**

1.42 1.57 1.60 1.58 1.56 1.59 1.53 1.62 1.34

10.29** 10.18** 9.93** 10.67** 10.00** 9.97** 9.35** 11.13** 11.21**

1.16 1.42 1.71 1.83 1.94 2.09 1.85 1.61 1.32

13.87** 14.61** 11.38** 10.17** 10.20** 10.83** 9.20** 9.71** 14.44**

0.77 0.87 1.03 1.07 1.20 1.21 1.09 0.92 0.72

10.16** 8.97** 8.85** 9.13** 9.48** 10.45** 10.30** 8.68** 8.45**

1.01 1.27 1.37 1.40 1.39 1.31 1.26 1.11 0.66

9.75** 8.04** 9.68** 10.21** 10.52** 11.34** 11.77** 11.68** 10.50**

1.49 1.88 2.00 1.84 1.79 1.62 1.55 1.35 1.07

Notes: This table reported the QAR test and half-life estimates of the SSE Composite Index within 5 days following the days of sudden rises according to Eq. (3). A significant negative value of t indicated that asset prices converged after the shock and could generate a half-life value. ** denoted significance at 1%. ∞ denoted the price fluctuations dispersed instead of converged.

Table 8 The QAR test and half-life estimates of Shenzhen Component Index within 5 days following the days of sudden rises. Date (Return)

10/12 (7.41%)

Quantile

t

Half-life

t

7/09 (5.60%) Half-life

t

6/30 (5.38%) Half-life

t

8/27 (5.20%) Half-life

t

8/10 (4.80%) Half-life

10% 20% 30% 40% 50% 60% 70% 80% 90%

10.88** 9.59** 10.81** 9.61** 9.48** 9.20** 8.26** 8.29** 7.75**

1.95 1.95 1.95 2.11 2.24 2.18 2.40 2.13 1.82

9.01** 9.84** 8.23** 9.10** 8.59** 7.98** 7.73** 8.64** 6.70**

1.18 1.72 2.01 1.99 2.03 2.01 1.79 1.79 1.29

11.38** 11.73** 9.33** 11.65** 10.51** 10.76** 10.76** 9.70** 9.90**

1.07 1.15 1.23 1.36 1.41 1.32 1.27 1.08 0.77

8.10** 9.28** 8.65** 9.07** 10.36** 10.68** 10.38** 9.97** 7.04**

1.05 1.22 1.40 1.37 1.37 1.37 1.22 1.03 0.77

9.57** 7.49** 10.18** 10.93** 10.31** 10.53** 10.62** 10.77** 9.84**

1.72 1.96 1.96 1.94 1.95 1.83 1.66 1.51 1.27

Notes: This table reported the QAR test and half-life estimates of the Shenzhen Composite Index within 5 days following the days of sudden rises according to Eq. (3). A significant negative value of t indicates that asset prices converged after the shock and could generate a half-life value. ** denoted significance at 1%. ∞ denoted the price fluctuations dispersed instead of converged.

Composite Index and Shenzhen Component Index within 5 days following the days of sudden drops. Tables 5 and 6 illustrated that both stock indices reach convergence in all quantiles, indicating that even on days of sudden drops, stock market performance was highly irrational, persistently failing to reach a stop in the drop; the stock indices would stabilize within 5 days afterwards and then resume rational fluctuations. The stabilizing speed was relatively slow only on one particular day when a sudden drop occurred - namely, May 28. In terms of the SSE Composite Index, at the time of the largest price drop (10th percentile), half of the influence of the shock required 4.31 min to be handled. Five days after May 28, half of the influence of the shock still required 3.20 min to be handled. The persistence of stock price drop of this day was several times that of other days of sudden drops, showing that the recovery capability of the stock market was several times lower on May 28 than on other days of sudden drops. Only on May 28 did the SSE Composite Index exhibit greater half-lives in quantiles indicating larger price drops (10th to 50th percentiles) than did the Shenzhen Component Index. Although Tables 1–4 presented this trend in general, the convergence speed of the Shenzhen Component Index was relatively slow, with May 28 being an exception. Only on May 28 and the following 5 days did the price drop in the Shanghai stock market persist longer than that in the Shenzhen stock market, indicating that the sudden drop on May 28 caused a larger effect on the Shanghai stock market than those on other days when sudden drops occurred. 4.2.4. Intraday stock price behaviors observed within 5 days following the days of sudden rises Tables 7 and 8 respectively showed the QAR test and half-life estimates of the SSE Composite Index and Shenzhen Component Index within 5 days after sudden rises occurred. Comparing with the estimates for days when sudden drops occurred, the corrections on days when sudden rises occurred were slower than those on days when sudden drops occurred. An observation of the half-lives within 5 days of the event's volatility revealed that the half-lives generated after days when sudden rises occurred were relatively high. For example, for the half-life estimates in the 50th percentile, the half-lives of the 5 days after a sudden drop were 1.32, 1.72, 0.78, 1.56, and 2.22, respectively, whereas the half-lives of the 5 days after a sudden rise were 2.24, 2.03, 1.41, 1.37, and 1.95, respectively. Except for May 28, the correction in the following days when sudden drops occurred was very rapid. These results implied that the correction for price drops was relatively rapid, resulting in relatively low persistence in a downward trend. However, the correction for price rises was relatively slow, resulting in relatively high persistence for an upward trend. Several studies (e.g., Bekaert & Wu, 2000; Tsai, 2017) showed, through numerous low-frequency data, that slow rises and rapid falls could be observed in stock fluctuation trends. By contrast, the convergent time of May 28 was about twice that of other impact dates. The correction for price drops was relatively slow, resulting in relatively high persistence in downward trends (low quantile). There was an asymmetric pattern, which reflected the recovery of falling prices was relatively slow. The present study identified a similar phenomenon in the intraday patterns for days of volatility. 8

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Fig. 2. The half-lives of the SSE Composite Index in different quantiles on the days of volatility.

The following paragraphs present the intraday patterns of days of volatility in figures. Figs. 2 and 3 respectively showed the half-lives of the SSE Composite Index and Shenzhen Composite Index in different quantiles on the days of volatility. Fig. 2 presented that the halflife increases as the quantile decreases (10th and 20th quantiles) when sudden drops occurred on most impact dates, except for January 19, when the half-life increases as the quantile decreases (10th and 20th quantiles). In other words, the larger the price drops were, the slower the downward movement was stopped. By contrast, on days when sudden rises occurred, except for July 9 and June 30, the halflife increased with the price rise (90th percentile), showing that the upward movement tended to persist. Fig. 2 showed a different trend compared with that of the SSE Composite Index. However, most of the half-lives in Fig. 3 were higher than those in Fig. 2, indicating that on days of volatility the Shanghai stock market resumed stability very quickly, except for the few times when substantial price rises and drops occurred, when the convergence speed was relatively slow. In contrast, the Shenzhen stock market did not exhibit a considerably slower convergence speed on days when substantial price rises or drops occurred. The results presented that the market did not resume 9

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Fig. 3. The half-lives of Shenzhen Composite Index in different quantiles on the days of volatility.

stability quickly in the other quantiles. Figs. 4 and 5 respectively showed the half-lives of SSE Composite Index and Shenzhen Composite Index in different quantiles within 5 days of the volatility event. Except for May 28, Fig. 4 indicated that 5 days within the sudden rise or drop of the SSE Composite Index, the market resumed stability. The half-life pattern showed that it was difficult for volatility to persist. Fig. 4 showed that the half-lives decreased as the fluctuations become more extreme (in high or low quantiles), resulting in an inverted U-shaped pattern, which differed completely from the pattern observed on days of volatility (Fig. 3). Fig. 4 indicated that within 5 days of a sudden rise or drop, the market resumed its general status, in which it was difficult for relatively extreme fluctuations to persist. Nevertheless, July 27 presented that after the sudden drop occurred, the half-life increased as the quantile decreased (10th and 20th quantiles), but it still has an asymmetry inverted U-shaped pattern. Five days within the sudden rise or drop, the market resumed stability faster. By contrast, it is important to note that the half-life pattern within 5 days of May 28 remained identical to that of the day under shock (i.e., May 28), 10

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International Review of Economics and Finance xxx (2018) 1–17

Fig. 4. The half-lives of SSE Composite Index in different quantiles within 5 days of volatility event.

indicating that the shock on May 28 not only caused a sudden drop on that day, but it also changed the market fluctuation pattern in the subsequent 5 days, when stability was not restored. The authors considered that this situation was relatively consistent with the definition of a black swan event. Prior to May 28 China's stock markets steadily rose every day. The drop on May 28 had a marked effect on market transactions thereafter. Specifically, the market exhibited relative difficulty reaching convergence 5 days after the sudden drop, which was not observed on other days of volatility. From late June, China's stock markets showed more frequent price drops than price rises. China's market crash in the second half of 2015 was likely initiated by the black swan event on May 28. In this study, the black swan event was identified according to the data on the impact date and the five subsequent trading days. According to a comparison of the intraday stock price patterns of these days, May 28 showed a greater likelihood of being classified as a black swan event. Although days of volatility could not be predicted, if investors had reduced their investment amounts in China's stock markets within the five trading days following May 28, they could have avoided losses from the stock market crash that began on June 12. 11

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Fig. 5. The half-lives of Shenzhen Index in different quantiles within 5 days of volatility event.

Fig. 5 presented the half-life of the Shenzhen Component Index in various quantiles within 5 days of stock market volatility occurring. Similar to the SSE Composite Index, traces of the black swan event were present in the Shenzhen Component Index on May 28. In addition, on January 19 the half-life pattern differed from that of other days of volatility, in which the market gradually stabilized. On this day, the more the price dropped, the quicker the index returned to its original level, showing a sign of market reversal. The marked rise in China's stock markets in the first half of 2015 could be detected on January 19, when a pattern of reversal emerged. Figs. 6 – 9 depicted how the market stabilized after days of volatility, respectively presenting the half-life patterns of the SSE and Shenzhen Component Indices from Days 1–5 after days of volatility. Based on a low (high) quantile of signifies the stock price index behavior for a price drop (price rise) as aforementioned (Lin & Lin, 2013; Lin & Tsai, 2016; Nikolaou, 2008). More extreme

12

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International Review of Economics and Finance xxx (2018) 1–17

Fig. 6. The half-life pattern of the SSE Composite Index from Days 1–5 after days of sudden drops.

quantiles (in low/high quantiles) reflected the extreme level of price drop/rise. The figures presented the half-life trend chart of the five subsequent trading days (Days 1–5) of the six quantiles (10th, 20th, 30th, 70th, 80th, and 90th quantiles) that exhibited the price corrections on days when sudden drops/rises occurred, showing the price correction patterns after the impact date. The half-life trend chart of the five subsequent trading days (Days 1–5) showed that the corrections in China's stock markets exhibited wave patterns, regardless of whether price rises or drops occurred. Another notable phenomenon was that most of the correction time on Day 1 after price volatility occurred was not the shortest half-life in the 5 days. After a day of volatility, China's stock markets swung between slowness, quickness, and slowness in correction time. The result was likely due to intermittent overreactions and underreactions to market prices. When overreactions occurred in the market, the likelihood of a market reversal increased, resulting in a rapid correction. Conversely, when underreactions were observed in the market, price rises or drops were relatively

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Fig. 7. The half-life pattern of the SSE Composite Index from Days 1–5 after days of sudden rises.

highly persistent, hence leading to a slow correction. 5. Conclusion This study investigated the correction patterns of intraday stock prices on days of extreme volatility. As no trading day can be presumed to be a black swan event when subjectively evaluated, in this study the authors proposed a research scope on rises and drops in China's stock markets in 2015, including the 5 days following the highest daily returns and the 5 days after the lowest daily returns to examine the effect of extreme market events. The intraday index changed on these days and the subsequent five trading days were investigated using 1-min index data. The two requirements for a black swan trading day are a low probability (extreme market performance) and a substantial effect on subsequent trading days. This study investigated whether the impacts of volatility on stock market 14

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International Review of Economics and Finance xxx (2018) 1–17

Fig. 8. The half-life pattern of Shenzhen Component Indices from Days 1–5 after days of sudden drops.

indices disappeared over time, and whether market stability could be restored. The results showed that volatility was normal in China's stock markets. Moreover, stock transaction disorder was rare on days of shock events. In other words, the prices rarely dispersed, regardless of unstoppable downward or persistently upward movements. Therefore, stringent policies, such as a fuse mechanism, are unnecessary. China's government should trust in the self-stabilizing capacity of the market. The authors determined that only the sudden drop on May 28, 2015 can be classified as a black swan event. Prior to this event, China's stock markets were in a bull phase, but they did not return to their original state 5 days after this event, and the likelihood of considerable price drops to further occur remained high. Nevertheless, on other trading days, within 5 days of a sudden rise or drop, it was difficult for market volatility to persist. The reaction of the Shenzhen Component Index to events of sudden rises and drops was larger than that of the SSE Composite 15

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Fig. 9. The half-life pattern of Shenzhen Component Indices from Days 15 after days of sudden rises.

Index, indicating that investors who benefit from bull markets should invest in the Shenzhen Component Index on the day when information of a possible sudden rise in China's stock market is revealed. However, when China's stock markets start to crash, investors should avoid investing in the Shenzhen stock market. The results also showed that on days of volatility, investors exhibited more obvious behaviors of panic than of chasing price rises. Price patterns of slow rise and quick fall were identified in intraday stock market fluctuations. Finally, the authors explained that intermittent occurrences of overreaction and underreaction to stock market price fluctuations caused the corrections in China's stock markets to exhibit wave patterns, irregularly constituting rapid and slow corrections. Black swan events have been an unsolved phenomenon in financial markets. As the first study to employ intraday behavioral data to analyze stock price behaviors on days of volatility and subsequent market stability, the present study offers a direction for future studies, the aim of which is to develop an early warning index for black swan events on the basis of high-frequency data. 16

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Acknowledgements The authors would like to thank Prof. Carl Chen, the Editor, and the three anonymous referees for the constructive comments of this paper. This research was supported by the Guangdong Province Innovative Talents Project, China (Grant Number: 201712012QX) and BNUZ 'Ability to promote' research program. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.iref.2018.10.005.

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