Exploring the predictability of intraday returns in China's stock market

. With the rapid development of high-frequency trading, intraday trading has become more and more popular due to its important role in understanding the efficiency of the intraday market and capturing more trading opportunities. This article explores whether there is momentum effect and reversal effect in China’s stock market by studying the correlation and predictability between half-hour returns. The results show that there is an intraday momentum effect between the first half-hour and full-day returns. After the investment strategy, it is found that this effect has economic significance, but after considering the transaction costs, the momentum effect cannot make investors obtain excess returns. These costs are the reason for the long-term predictability of intraday returns.


Introduction
With the rapid development of high-frequency trading, intraday trading is gaining popularity due to its important role in understanding intraday market efficiency and capturing more trading opportunities.However, intraday predictability received little attention prior to the seminal work of Gao [1], who extended Moskowitz [2] 's standard time-series momentum to intraday levels in US equities and found that the first half-hour returns are more than the second half-hour Returns have significant predictive power.Since then, this form of intraday return forecasting has been extended to several other markets, including Chu [3] who introduced this forecasting method to the Chinese stock market.Since the data sample date selected by Chu is from April 4, 2015 to December 31, 2015, the sample time is earlier, so this paper will continue this method and lock the sample time and object to the Chinese stock market after 2019.
Compared with the US stock market, the Chinese stock market has a special trading mechanism.Specifically, the U.S. stock market trades from 9:30 to 16:00 Eastern Time, while the Chinese stock market trades from 9:30 am to 11:30 am and 13:00 pm to 15:00 pm Beijing time.Different trading hours can lead to very different intraday momentum patterns between the U.S. and Chinese stock markets.The U.S. stock market has a 13.5-hourrate of return, however, the Chinese stock market has only an 8.5-hour rate of return per trading day, and more importantly, the Chinese stock market has a 90-minute lunch break where investors can learn New information or processing earlier information, thereby affecting intraday trends.The trading volume is closely related to the attention of investors and the processing of information.Figure 1 shows the average half-hour trading volume of the Shanghai Composite Index.It can be seen from the figure that the average trading volume from the first hour to the last half hour presents a "W" shape, and the trading volume in the first hour is much higher than other times of the day After three hours, the transaction volume gradually decreased.After the lunch break, the transaction volume rebounded, and the last hour ushered in a small peak.This trading volume pattern reflects that the most active periods of the market are the beginning of the day, after the lunch break, and before the end, and these half-hours are also the time periods that this paper focuses on in the empirical process.
This paper studies the predictability of intraday returns in Chinese stock markets and makes some contributions to the existing literature.First, this paper explores whether there is a momentum effect and a reversal effect in the Chinese stock market by studying the correlation and predictability between half-hour returns, focusing on the first half hour, the fourth half hour, and the fifth Half-hour and eighth-half-hour predictability, combined with variables such as overnight returns, refine the model to further explore the predictability of each half-hour and full-day returns.
This paper selects the intraday data of the Shanghai Composite Index, the Shenzhen Stock Exchange Component Index, and the CSI 300 Index from January 2, 2019 to September 1, 2021 to study the predictability of intraday returns.First, we used univariate linear regression to explore the correlation between full-day and half-day returns, and then divided the opening time of the Chinese stock market into eight and a half hours to explore the correlation and predictability of half-hour returns.Finally, the univariate linear regression model was refined and new explanatory variables were added to explore the predictability of returns for each half-hour of the day.
After obtaining the results at the statistical level, this paper further studies whether this effect has an economic impact on investment: According to the empirical results, two active investment strategies and a set of control strategies are constructed, the annual rate of return of each strategy is calculated separately, and the economic significance is calculated.from the perspective of evaluating the obtained results.

Literature review
Momentum and reversal are two well-known return patterns.For example, the seminal work of Jegadeesh and Titman [4] found a well-known momentum strategy whereby buying past winners and selling past losers produces significantly positive returns over holding periods of 3 to 12 months; Daniel [5] proposed a theory based on investor overconfidence and the change in confidence due to biased self-attribution of investment outcomes, which implies that investors overreact to private information signals and underreact to public information signals, indicating that positive Return autocorrelation may be the result of persistent overreaction; Du [6] believed that momentum and reversal coexist in international stock indexes; Andrei and Cujean [7] proposed a joint theory of timeseries momentum and reversal based on rational expectations model, in The necessary condition for generating momentum in this framework is that information flows at an increasingly faster rate; Gang [8] research investigates the profitability of momentum and reversal strategies for different investment horizons in Chinese stock markets, and the results show that momentum strategies are more effective for less than one-week investment.The investment period is profitable.For longer investment horizons, reversal strategies can be profitable; Zaremba [9] conducts a comprehensive test of long-term reversals of national stock indices, examining data from 1830-2019 for 71 countries, finds that past long-term returns are negative predictors of future performance, but very volatile over time.However, these studies have mainly focused on investigating cross-sectional momentum and reversal effects.In contrast to this cross-sectional momentum, Moskowitz [2] demonstrated the monthly time-series momentum of stock returns.Most studies have explored this effect based on lowfrequency data (such as weekly or monthly), ignoring high-frequency data.
Gao [1] studied the intraday momentum effect of the US market for the first time, that is, the first half-hour return of the US stock market positively predicted the second half-hour return.Due to the digestion and reflection of new information, the trading volume in the first half-hour was very high. .Since then, a growing body of research has focused on exploring intraday momentum across a broad range of asset classes.Sun [10] and Renault [ 11 ] demonstrated that high-frequency investor sentiment can predict intraday stock returns, and Zhang [12] , Chu [3] , and Li [13] provided strong evidence for intraday time-series momentum in Chinese stock markets.Similarly, Jin [14] observed intraday momentum for four Chinese futures contracts, soybean, copper, steel, and soybean meal; however, Yang [15] showed that intraday strategies in the Chinese commodity futures market could not generate high excess returns due to transaction costs.

Empirical analysis 3.1 Data
This paper studies the predictability of intraday returns using the intraday data of the Shanghai Composite Index, the Shenzhen Stock Exchange Component Index, and the CSI 300 Index.The total sample is from January 2, 2019 to September 1, 2021, a total of 650 working days, of which the data in the sample is from January 2, 2019 to December 31, 2020, a total of 487 working days.All data come from Wind economic database and Reis database.The business hours of the China Stock Exchange are 9:30 am to 11:30 am and 1:00 pm to 3:00 pm Yield every half hour( -)， Among them, this article focuses on the first half-hour yield and the last half-hour yield of each trading time period, namely , , , .In addition to this, this paper also considers the full-day yield ( ), half-day yield ( , ) and overnight yield ( ).

Model Construction
According to Wen et al.'s method to explore the predictability of China's crude oil futures market through intraday trading data, this paper first constructs the following two models: Where is the rate of return for the i-th half-hour on day t, is the rate of return for the j-th half-hour on day t.Referring to the methods of existing literature and the definitions of momentum effect and reversal effect, in this part of this paper, the first half-hour return and the last half-hour return of each day are mainly used as variables.
In order to test whether the predictors in predictive regression are still significant when recursive estimation is performed, the article uses out-of-sample regression and calculates out-of-sample , the formula is as follows: (3 Where m is the number of days in the sample, that is, the working days between January 2, 2019 and December 31, 2020, a total of 487 days, and T is the total sample days, that is, January 2, 2019 to September 1, 2021.The working days between days, i.e. 650 days.is the actual rate of return, is the forecast rate of return, and is the historical average rate of return.

Descriptive Statistics
In order to ensure the integrity of market data, this paper uses the intraday data of the Shanghai Composite Index, the Shenzhen Stock Exchange Component Index, and the CSI 300 Index, where represents the daily return (take the logarithmic return, the same below), and represent the first and second half-day returns, respectively, and -represent the first half-hour to Eighth and a half hour earnings.Table 1 shows the descriptive statistics of the sequences.Descriptive statistics show that the average value of the entire day's returns is positive, and the first half of the day's returns and the second half of the day's returns are also positive.From the perspective of specific half-hour earnings, the fifth and sixth half-hour earnings are negative, the remaining six and a half hours are positive, and the first half-hour has the highest rate of return.In terms of standard deviation, high returns in the first half hour correspond to higher standard deviations, but higher returns in the last half hour correspond to lower standard deviations.A positive excess kurtosis value proves that the distributions of all given return series have thick tails.

Full-day and half-day yield correlation
In order to explore the correlation of intraday data of Chinese stock market, this paper first performs regression on r whole , r half 1 and r half 2 , and the results are shown in Table 2. Judging from the regression results of the first, second and fourth rows of Table 2, the daily rate of return of the previous day and the full-day rate of return of the next day, the rate of return of the second half of the previous day and the rate of return of the first half of the next day And there is no significant relationship between the full-day return on the previous day and the first half-day return on the following day.
Judging from the regression results in the third row, there is a correlation between the first halfday rate of return and the second half-day rate of return, and the regression coefficient is 0.1294, which means that the first-half-day rate of return has a positive impact on the second-half-day rate of return.There is an intraday momentum effect between the two indices, which is confirmed in the regressions with the three indices as samples, and all of them are significant at the 1% level.
From the regression results of the fifth row, there is a correlation between the daily rate of return of the previous day and the rate of return of the second half of the next day.The regression coefficient is -0.0534, which means that the daily rate of return of the previous day has a similar effect on the rate of return of the second half of the next day.Negative effects, this result is also confirmed in the regression with the three indices as samples, which are significant at the 1% and 5% levels.

Half-hourly return correlation
Next, this paper further explores the correlation between intraday half-hour returns.Since the opening time of the Chinese stock market is in the morning and afternoon, considering the concentration of investors and the digestion of information when the market is closed.In this part of the regression test, this paper mainly focuses on four special half-hours, namely the first half-hour of the morning period and the last half-hour of the morning period, the first half hour of the afternoon period and the last half hour of the afternoon period.Table 3 presents the regression results for these four special half-hourly returns.From the regression results in Table 3, at the 1% confidence level, there is a positive correlation between the first half-hour rate of return and the fifth-hour rate of return, which is also consistent with the first half-hour rate of return and the fifth half-hour return are the highest of the day and the results are consistent with the positive correlation between the first and second half-day returns.Except for the results in the second row, the regression results of the rest of the series are not significant, which indicates that there is no significant correlation between the half-hour returns, whether it is the intraday data of the current day or the intraday data of the previous day and the next day.Although the correlation regression results between the first half-hour return and the fifth halfhour return are significant in-sample, but out-of-sample is not significant, so future returns cannot be predicted recursively.

Refine the model
Next, this paper improves the above univariate model and adds new explanatory variables.First, considering the impact of the previous day's yield and overnight yield, investors further digest the previous day's information or overnight information, and their emotions are reflected in the stock price of the next day; secondly, considering whether the trading day is Monday or Friday, and The corresponding dummy variables are added to the model.The expanded model is as follows: (4) Where ( ) represents the return rate of the ith half-hour on day t (t-1), represents the overnight return rate, defined as the percentage change of the opening price on day t relative to the closing price of the previous day, and is a dummy variable, if the day is Monday, then , otherwise take 0, similarly if the day is Friday, then , otherwise take 0. Table 5 shows that the new model outperforms the univariate model.Horizontally, and are highly significant, that is, the first half-hour rate of return and overnight rate of return has a high explanatory power for other half-hour rates of return.From the regression coefficient, the of the first half-hour returns are mostly negative, and the absolute value gradually decreases over time, which indicates that there is a reversal effect in the day, that is, the first hour returns are high It is very likely that the yield on the trading day will be negative in the next half hour.
The first half-hour has a positive coefficient on the full-day rate of return, that is, the first halfhour has a positive impact on the full-day rate of return, and there is an intraday momentum effect between the first half-hour and the full-day rate of return.The last row is the out-of-sample for these regressions, and it can be found that compared to the univariate model, the refined model is still applicable out-of-sample for most regressions, especially when the dependent variable is an integer The p-value for out-of-sample is only 0.0000000214 for daily returns.Therefore, using this model to make predictions is statistically valid.

Economic significance
In order to test whether the measurement results can achieve excess returns in the market, that is, whether there is economic significance.This paper constructs two investment strategies based on the regression results.
The first is the MR Strategy.The specific operation of this strategy is that if the rate of return in the first half hour is positive, we will go long at the end of the second half hour.If the first half hour return of the next day is still positive, we will continue to hold.If the first half hour of the next day is negative, we will close the position at the end of the second half hour.

Figure 1 .
Figure 1.Half-hour average trading volume of Shanghai Composite Index

Table 1 .
Descriptive Statistics for Correlated Sequences

Table 2 .
Regression results of full-day and half-day returns

Table 3 .
Regression results of half-hour returns

Table 4 .
Out-of-sample regression results

Table 5 .
Regression results after perfecting the model