The Dynamic and Causal Relationship between Stock Return and Volume

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Student Name: Decheng Ou Student Number: 2067196 Email: 2067196@student .rug.nl

The Dynamic and Causal

Relationship between Stock

Return and Volume

Evidence from the Chinese Market

Master Thesis

University of Groningen

Faculty of Economics and Business

DECHENG OU

July, 2011

Supervisor:

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Table of Content

Abstract ... 1

1. Introduction ... 2

1.1 Research Area and Research Topic ... 2

1.2 Background and Context of This Research ... 3

1.3 Purpose of This Research ... 5

1.4 Contribution of This Research ... 5

1.5 Structure of This Paper ... 6

2. Literature Review... 6

2.1 Theoretical Framework ... 6

2.1.1 The Sequential Information Arrival Model (SIA) ... 6

2.1.2 The Mixture of Distributions (MD) Model ... 7

2.1.3 The Noise Trader Model ... 8

2.1.4 The Market Microstructure Theory ... 8

2.1.5 Other Theories ... 9

2.2 Empirical Literature ... 9

2.2.1 Empirical Studies Worldwide ... 9

2.2.2 Empirical Studies in the Chinese Market ... 12

2.3 Hypotheses Development ... 13

3. Data ... 13

4. Methodology ... 15

4.1 Stationary Tests ... 15

4.2 Contemporaneous Return–Volume Relationship ... 17

4.3 Causal Relationship between Return and Trading Volume ... 17

4.4 Trading Volume and Return Volatility ... 18

5. Empirical Finding ... 20

5.1 Contemporaneous Return-Volume Relationship ... 20

5.2 Causal Relationship between Stock Return and Trading Volume... 23

5.3 The Relationship between Trading Volume and Return Volatility ... 24

6. Conclusion ... 26

6.1 Summary ... 26

6.2 Limitations and Further Development ... 27

Reference ... 28

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1 Abstract

This paper examines the contemporaneous as well as the causal and dynamic relationship between stock return and trading volume in Chinese market using daily data from 1996 to 2010. We divide the whole sample into bullish and bearish market periods and employ single variable regression model as well Granger causality test in a VAR context. In addition, we use an EGARCH model to examine whether trading volume can affect stock return by influencing return volatility. We find that (1) A

Positive contemporaneous relationship exists between stock price and trading volume. (2) A Significant causal relationship running from stock return to trading volume exists in most of our sub-sample periods. (3) As trading volume may have important role in estimating the conditional variance of stock return, inclusion of trading volume as a proxy of information arrival into the conditional variance estimation of the EGARCH model cannot reduce the persistence of return volatility.

Keywords: Stock return, Volume, VAR, Granger Causality, EGARCH, Chinese stock market

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2 1. Introduction

1.1 Research Area and Research Topic

There is an old Wall Street saying, ‘it takes volume to make the price move’. The relationship between stock return and volume has been the topic of an important and ongoing debate in finance. This debate has a long history which traces back to Osborne (1959), whose paper proposed a relationship between stock price and trading volume. Ying (1966) investigated the interaction between the S&P 500 index return and trading volume and arrived at the view that the correlation between price and volume exists to some extent. Since then, sizable researchers publish their paper concerning this issue.

Early studies examined the contemporaneous relationship between trading volume and price change as well as trading volume and absolute value of price change. More recent studies investigated the dynamic linear and non-linear causal relationship between these two variables. Most of the papers report a significant contemporary relationship between price and volume, but the findings on the causal relationship are mixed. In the last 10 years, this research extended to a new direction examining the ability of trading volume to explain the volatility of stock return in both a contemporaneous and a dynamic framework. For example, some studies include trading volume in the estimation of the conditional variance in the GARCH model. However, there is quite limited literature on this topic for the emerging markets and most of the papers focus on Asian and Latin countries.

On the other hand, financial researchers set up different approaches attempting to explain why stock return and trading volume are correlated. These theories include Intertemporal Capital Asset Pricing Model (ICAPM), Sequential Information Arrival Moedel (SIA), Mixture of Distribution (MD) Model, Noise Trader Model, and Market Microstructure Theory,

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information spread through the market and to the extent which market prices convey the information. Secondly, this relationship is essential to identify the empirical distribution of price changes. Many previous studies point out that daily return are leptokurtic because they come from a mixture of intraday distributions with different conditional variances. Through empirical study, we can find evidence to support or against this hypothesis.

Thirdly, the price-volume relationship can help to improve the degree of accuracy in event studies that use a combination of price and volume data. For example, Richardson et al. (1986) examined the existence of dividend clienteles using price changes and trading volume. If trading volume and price change are jointly determined, employing the price-volume relationship can increase the accuracy of the test. Fourthly, the price-volume relationship can applied to asset pricing and risk management in practice.

1.2 Background and Context of This Research

The Chinese stock market has grown rapidly since it was established in the early 1990s. The Shanghai Stock Exchange (SHSE) started on December 19, 1990 and the Shenzhen Stock Exchange (SZSE) started on July 3, 1991. The two exchanges are self-regulated and companies cannot cross list in these two exchanges. At the end of 1991, there were fewer than 20 stocks listed on the Shanghai and the Shenzhen Stock Exchanges. The annual trading volume of 1991 was less than 1 billion shares. By the end of 2010, the average daily trading volume hit 21 billion shares.

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Chinese gross domestic product (GDP). Many Chinese firms have successfully made IPOs on some major international stock exchanges, including the NYSE and the NASDAQ. In the first half year of 2010, the Chinese stock market was the most active market all over the world in IPOs, with 161 IPOs in that period involving 22.6 billion US dollar.

Table 1 Comparison of key indicators in three stock markets Source: The World Bank 2009

Country US Japan China

Market capitalization (billion US Dollar) 15,077 3,377 5,007 Market capitalization (% of GDP) 106.8 66.6 100.4

Number of total domestic

listed companies

4,401 4,161 1,700

Annual trading volume

(% of GDP)

331.0 _82.7 _179.6

Annual turnover ratio (%) 348.6 127.1 229.6

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5 1.3 Purpose of This Research

Motivated by the evidence above, it is of great meaning to investigate the volume-return relationship, but very few previous studies base on the fast-growing Chinese market context. This paper focuses on the Chinese Mainland stock market and aims to study the causal and dynamic relationship between stock return and trading volume by investigating 4 Chinese Mainland common use indices.

In addition, we separate the full sample into six sub-sample periods and intend to investigate the possible differences between bullish and bearish market periods by comparing the findings from different sub-periods. In order to meet these purposes, we define our research questions as follow. 1) What is the impact of the current and lag trading volume on the current stock return? 2) Is there causal relationship running from stock return to trading volume, or the other way around? 3) Is there a different relationship between bullish and bearish market periods? 4) Can trading volume affect stock return indirectly by influencing return volatility?

1.4 Contribution of This Research

This paper contributes to the existing literature in the following aspects:

Firstly, we use longer horizon and more recent data than previous studies to obtain a better understanding of the relationship between stock return and trading volume in the Chinese market. Secondly, we extend the literature on the information transmission mechanism in emerging stock markets by investigating the contemporaneous as well as the causal relationship between stock return and trading volume for 4 indices in 2 Mainland China exchanges.

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and enables us to detect the asymmetry effect on volatility.

1.5 Structure of This Paper

The structure of the remainder of this paper is follows. In Section 2, a comprehensive literature review regarding the return-volume relationship is given. Section 3 provides a description of the data. Section 4 encompasses the research design and the methodology implemented. In Section 5 reports and discusses the main findings of the models. Section 6 contains a summary and conclusion.

2. Literature Review

2.1 Theoretical Framework

The relationship between stock price and trading volume has been the interest of financial researchers from a few decades ago to now. An original motivator for the empirical study on these relationships is two old Wall Street adages: (1) it takes volume to make the stock prices move, and (2) volume is relatively heavy in the bull markets and light in the bear markets.

Theoretically, stock price changes when new information arrives in the market. Therefore, if trading volume is considered as the information flow entering into the market, then it also implies the existence of a relationship between trading volume and stock price changes. Since the 1970s’, several theoretical models have been established trying to explain the contemporary and the causal relationship between trading volume and stock return

2.1.1 The Sequential Information Arrival Model (SIA)

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there is no short selling and technical trading in the model. As a result, there are a number of temporary equilibriums before reaching the final equilibrium because the uninformed traders cannot perfectly shift their demand curve according to the new information. Within this context, volume is used as a proxy for the information arrival speed in the market. Thus, trading volume has an explanatory power on the price movement and also the other way around. In other words, there is not only a causal relationship transmitting from trading volume to stock return but also from stock return to trading volume. Furthermore, some economists (e.g., Hiemstra & Jones, 1994) argued that the SIA model allude a positive causal relation in either of the two direction, because this information arrival pattern generates a sequence of momentary equilibriums. Thus, the lagged stock return may be able to estimate the current trading volume, and vice versa.

2.1.2 The Mixture of Distributions (MD) Model

A second explanation is the Mixture of Distributions model developed by Clark (1973) and Epps and Epps (1976). This model indicates an alternative return–volume relationship, which is critically dependent on the rate of information flow into the market. Contradicting to the Sequential Information Arrival Model, the MD model assumes that all traders simultaneously receive the new information and the daily return is the sum of intraday return, which has independent normal distribution. In addition, the number of intraday equilibrium is depended on the number of new information flow into the market.

Because the number of new information come into the market cannot observe from the model, Clark (1973) uses trading volume as a proxy measurement for the new information arrival. Also, in the MD model of Epps and Epps (1976), trading volume is considered as a measurement of disagreement among traders as they adjust their reservation prices according to the arrival of new information. As a result, the MD model suggests a positive causal relation running from stock return to trading volume, but not the other way around.

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detecting the speed of information flow, which services as a potential common factor that explains the relationship between variance of price change and trading volume. As a result, trading volume may be able to influent stock return indirectly by affecting the stock return volatility.

2.1.3 The Noise Trader Model

In addition, the Noise trader model developed by Beja and Goldman (1980) provides another explanation for a causal relation between stock return and trading volume. The model assume that there are noise traders in the market in the short run and their trading activities are not based on economic fundamentals, but in the long run the noise traders will be vanish. Therefore, a transitory mispricing component of stock price is possible to exist in the short run. Consequently, in the short run the aggregate stock return is assumed to have a positive autocorrelation. However, in the long run miss pricing is tend to vanish, which produce mean reversion, hence stock return are negatively auto-correlated. As in the short run, high return attracts more noise trader and consequently increases trading volume, this model suggests that there is a positive causal relationship running from stock return to trading volume.

2.1.4 The Market Microstructure Theory

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maximization by optimal timing of the capital gains and loss realization during the calendar year

2.1.5 Other Theories

There are other theories attempting to clarify the relationship between stock return and volume. Lo and Wang (2006) studied the implication of trading volume in an Intertemporal Capital Asset Pricing Model (ICAPM) framework. They found that a hedging portfolio constructed on the base of individual stock trading volume consistently perform better than the portfolio base on the other future performance estimators. Their result infers that there is valuable information, which can be used to predict future market return contain in the trading volume.

He and Wang (1995) built a rational expectation model and analyzed the dynamic relationship between trading volume and stock return. Their model assumes that investors have different information concerning the underlying value of certain stock. Trading volume is also used as a proxy measurement of information flow in the market. Based on this setting, they try to examine how trading activities among different trader reveal their private information. Their model indicates that volume may have the ability to provide information to predict the expected future stock return.

Blume, Easley, and O'Hara (1994) pointed out that valuable information can be observed from the past price and volume. Their model infers that the quality or the accurateness of information about the past price movements can be obtained by looking at the volume data, and thus traders will perform better than the average if volume is included in their technical analysis.

2.2 Empirical Literature 2.2.1 Empirical Studies Worldwide

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stated that numerous results supported a positive volume and absolute price change correlation (18 of 19 studies) and a positive correlation between volume and price change per se (12 of 16 studies).

Rogalski (1978), Smirlock and Starks (1988), and Jain and Joh (1988) used data from U.S. market to test linear and/or non-linear causal relationship between stock return and trading volume. Their results show evidence of unidirectional Granger causality from stock return to trading volume. Hiemstra and Jones (1994) also reported evidence of unidirectional Granger causality from the Dow Jones stock return to changes of the trading volume in New York Stock Exchange. Nevertheless, their result is different from the previous papers because they found a significant bidirectional nonlinear causality between stock return and trading volume.

Chordia and Swaminathan (2000) used individual stock data in American to test whether trading volume contains information that helps to predict the short-term stock return. They found trading volume is a significant determinant of the lag patterns observed in the stock return and the daily and weekly return on the high volume portfolios lead return on low volume portfolios. The authors attempted to explain the findings by arguing the differences of price adjustment speed to new information between two kinds of stocks; stocks in the high volume portfolio respond faster to the new market-wide information than their low volume counterparts.

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In the case of emerging markets, there is little research concerning this topic with most studies based on the Asian and Latin American trading system. Moosa and Al-Loughani (1995) used monthly stock return and trading volume data to examine the price-volume relation in Malaysia, Singapore, Thailand and Philippines. They found strong evidence of a causal relationship running from stock return to trading volume in Malaysia, Singapore, and Thailand. However, the causal relationship from trading volume to stock return is significant only in Singapore and Thailand. Moreover, they reported no causal relationship between these two variables for Philippines. Silvapulle and Choi (1999) studied the dynamic relationship between stock return and trading volume in South Korea using both linear and nonlinear Granger Causality test. Their result shows a bi-directional linear and nonlinear causality between stock return and trading volume change in South Korean stock market. For Latin American markets, Saatcioglu and Starks (1998) studied 6 Latin American markets, Argentina, Brazil, Chile, Columbia, Mexico, and Venezuela using monthly data for each index. They found a causal relationship from trading volume to stock return in most of these markets, which contradict to the evidence documented by the earlier studies on developed markets.

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when analyzing the intraday data for the individual Dow Jones stocks. They also conducted a Granger Causality test and found a significant causal relationship running from trading volume to return volatility for 12 of 30 stocks. Kim (2005) documented that US trading volume Granger cause the return volatilities in the main Asia-Pacific markets such as Australia, Japan, Hong Kong and Singapore.

Overall, previous empirical researches tend to be data based, rather than by rigorous, equilibrium model guidance. Most of the models are more statistics than economic in character optimize or completely clarify the information structure. We think the informal modeling methods were commonly applied because the intrinsic difficulties of constructing a rigorous, plausible and implementable model for price, volume, and volatility.

2.2.2 Empirical Studies in the Chinese Market

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13 2.3 Hypotheses Development

According to the theories and the results of previous empirical studies mentioned, we have the following threehypotheses we want to test in this paper.

H0: There is no relationship between stock return and trading volume.

H11 There is contemporaneous relationship between stock return and trading volume.

H11a: Trading volume and stock return have a positive contemporaneous

relationship in the bull market periods.

H11b: Trading volume and stock return have a negative contemporaneous

relationship in the bear market periods.

H12: There is a dynamic and causal relationship between stock return and trading

volume.

H12a: There is a causal relationship running from stock return to trading volume.

H12b: There is a causal relationship running from trading volume to stock return.

H13: Stock return and trading volume have an indirect relationship. Trading volume

can influence stock return by affect stock return volatility.

3. Data

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sufficient for data statistical analysis. The data is supplied by Datastream.

Table 2 Time range for each sub-sample period

Period Time range Period Time range

Bull markets Bear markets

Period 1 1996/12/16- 1997/05/12 Period 2 1997/05/13- 1998/05/18 Period 3 1998/05/19- 2001/06/14 Period 4 2001/06/15- 2005/06/06 Period 5 2005/06/07- 2007/10/16 Period 6 2007/10/17- 2010/12/31

The dataset used in this study comprises of daily equity indices close price and the corresponding trading volume series. Since 1996, when the China Securities Regulatory Commission (CSRC) published new regulations to limit the daily price change for each stock within ±10%, the Chinese stock market has become more regulated and stabilized. Because many previous studies (see Liu (2008)) indicate a significant diverse price-volume relationship in the bull market and in the bear market, the whole sample is segmented into 6 non-overlapping sub-periods, 3 sub-periods for bull market and 3 sub-periods for bear market. We classify the bullish and the bearish market period according to the Turning Point Theory as developed by Bry and Boschan (1971). Specially, we define each of our bull market periods as which prices have increased for a substantial period since their previous (local) bottom. For each of the bear market periods, we define that as prices have decreased for a substantial period since their previous (local) peak

Based on the daily the closing price daily return are calculated as:

𝑅𝑡 = 100 × [ln(𝑝𝑡) − ln⁡(𝑝𝑡−1)] (1)

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15 Table 3 descriptive statistics

Below the sample period, number of observations, mean, standard deviation, skewness, excess kurtosis and Jarque-Bera test value for daily stock index return and trading volume for the four indices-Shanghai A Share index(SH_A), Shanghai B Share index(SH_B), Shenzhen A Share index(SZ_A) and Shenzhen B Share index(SZ_B) are reported.*,** denote statistical

significance at the 5%, 1% level.

Index SH_A SH_B SZ_A SZ_B

Sample period 1996/12/16 -2010/12/31 1996/12/16 -2010/12/31 1996/12/16 - 2010/12/31 1996/12/16 -2010/12/31 Observations 3391 3360 3351 3326

Panel A descriptive statistics for stock return

Mean (%) 0.026 0.036 0.015 0.021

SD (%) 0.017 0.023 0.019 0.022

Skewness -0.378 0.097 -0.379 0.039

Kurtosis 7.514 6.493 6.716 6.272

Jarque-Bera 1879** 1713** 2008** 1485**

Panel B descriptive statistics for trading volume Mean (million share) 4572 60.83 2515 57.88 SD 5558 69.37 2777 54.58 Skewness 1.588 3.123 1.562 1.866 Kurtosis 4.793 16.138 4.616 7.941 Jarque-Bera 2960** 2930** 1728** 5314**

Because the sample of trading volume is substantially skewed, which is reported in Table 2, the approximation provided by the central limit theorem can be poor, and the resulting confidence interval will likely to have a wrong coverage probability. In order to have better statistical properties for confidence intervals and hypothesis tests, we use natural logarithmic to transform the volume data in our regression analysis.

LV𝑡= ln(𝑣𝑡) (2)

4. Methodology

4.1 Stationary Tests

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Unit Root test for stationary to detect whether there is an unit root in the stock return and trading volume series for each sub-period presented as follow:

∆𝑅𝑡 = 𝑎0+ 𝛾𝑅𝑡−1+ ∑𝑛𝑖=1𝛽𝑖∆𝑅𝑡−𝑖+ 𝛿𝑋𝑡+ 𝜀𝑡₍₃₎

∆𝐿𝑉𝑡= 𝑎0+ 𝛾𝐿𝑉𝑡−1+ ∑𝑛𝑖=1𝛽𝑖∆𝐿𝑉𝑡−𝑖+ 𝛿𝑋𝑡+ 𝜀𝑡 (4)

The Rt and LVt denote stock return and natural logarithmic trading volume respectively. The ADF statistics are computed with a linear time trend and a constant term and the number of lag(s) is automatically selected based on Schwarz Info Criterion. Results of ADF test is presented in Table 4.

Table 4 Results of ADF test

This table reports the results of the augmented Dickey-Fuller (ADF) Test for unit roots. The ADF statistics are computed with a linear time trend and a constant term. The lag length (n) for the ADF test is selected based on Schwarz Info Criterion. Null hypothesis of AFD test is ‘the series is not stationary’. The critical value for both statistics at the 5% (1%) level is −2.86 (−3.43). *,** denotes statistical significance at the 5%, 1% level.

Time Variable SH_A SH_B SZ_A SZ_B

Period 1 Rt -10.72** -10.48** -9.42** -8.45** LVt -3.03* -3.89** -4.93** -3.46** Period 2 Rt -16.28** -13.52** -15.59** -14.60** LVt -4.11** -7.68** -5.26** -3.67** Period 3 Rt -25.95** -23.61** -25.24** -23.42** LVt -4.56** -3.25** -4.08** -3.08** Period 4 Rt -30.69** 30.20** -30.88** -31.11** LVt -6.26** -6.27** -6.64** -7.10** Period 5 Rt -24.28** -21.63** -23.64** -22.14** LVt -3.15* -3.51** -3.33* -3.20* Period 6 Rt 27.98** -26.34** -26.35** -26.97** LVt -4.40** -5.37** -3.82** -4.34**

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4.2 Contemporaneous Return–Volume Relationship

As Karpoff (1987) summarized most of the empirical studies in that period and stated

that numerous empirical results support a positive contemporaneous relationship between trading volume and price change (12 of 16 studies), we first investigate whether a contemporaneous return-volume relationship can also be found in Chinese market by estimating regression model shown below:

𝑅𝑡= 𝑎 + 𝛽𝐿𝑉𝑡+ 𝜀𝑡 (5)

Where LVt, Rt are defined as the natural logarithmic volume at time t and stock return at time t respectively. The term εt is the residual of the regression.

4.3 Causal Relationship between Return and Trading Volume

In the Sequential Information Arrival Model (SIA), Copeland (1976) concluded that there is a causal relationship transmitting from trading volume to stock return but that relation can be either positive or negative depending on whether the hypothesis of sequential information arrival is hold. Moreover, in the Mixture of Distributions (MD) Model, Epps and Epps (1976) suggested a positive causal relationship running from stock return to trading volume, but not the other way around.

We conduct the causality test developed by Granger. According to Granger (1969), if an event Y happens before an event X, then X is Granger caused by Y. Formally, Y Granger-causes X if using past Y to estimate X is more precise than that without using past Y in the mean square error sense. In order to conduct linear Granger Causality Test, a bivariate Vector Autoregressive (VAR) Model is applied as follow:

𝐿𝑉𝑡= 𝛼0+ ∑𝑛𝑖=1𝛼𝑖𝐿𝑉𝑡−𝑖+ ∑𝑛𝑖=1𝛽𝑖𝑅𝑡−𝑖+ 𝜀𝑡 (6)

𝑅𝑡= 𝜆0+ ∑𝑛𝑖=1𝜆𝑖𝐿𝑉𝑡−𝑖+ ∑𝑛𝑖=1𝛾𝑖𝑅𝑡−𝑖+ 𝜀𝑡 (7)

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In Equation 5, if βi is statistically significant, we can conclude that including the past return yields a better forecast of the future volume. Therefore, stock return Granger causes trading volume. If the standard F-test does not reject the null hypothesis that βi = 0 for all the i lags, then stock return do not Granger cause trading volume.

For the same mechanism, in Equation 6, causality runs from trading volume to stock return if λi is jointly different from 0. If βi and λi are both significantly different from zero, then a feedback relation exists between stock return and trading volume. Since the result is sensitive to the selection of lag lengths, we use Schwarz Information Criterion to choose the optimal lag(s) used in the model.

4.4 Trading Volume and Return Volatility

In this part, we investigate whether trading volume can influent stock return indirectly by affecting stock return volatility. In the Mixture of Distributions (MD) Model of Clark (1973) and Sequential Information Arrival Model (SIA) of Copeland (1976), they pointed out that trading volume can be used as a proxy for detecting the speed of information flow, which services as a potential common factor that explains the relationship between variance of stock return and trading volume. Therefore, to investigate whether trading volume has an impact on return volatility, we employ an exponential version of GARCH model.

As stated in Lamoureax and Lastrapes (1990), the Mixture of Distribution Model (MD) employed by Clark (1973) provides theoretical support for the application of GARCH family models to investigate the volume-volatility relationship. The fundamental idea is as follows. Assume that the total return in the trading day is the sum of intraday equilibrium return λi, shown as

⁡𝑅_𝑡= ∑𝑛_𝑖=1𝑡 𝜆_𝑖⁡⁡⁡𝜆_𝑖∼ 𝑁(0, 𝜎2)⁡⁡⁡⁡ (8)

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Now, suppose that the number of information arrivals for each day follows an autoregressive process as follow:

⁡𝑛𝑡 = 𝑎 + 𝑓(𝐿)𝑛𝑡−1+ 𝜀𝑡 (9)

Where 𝑓(𝐿) is a function of the lag operator L, α is a constant term and εt is the error term. The conditional variance of the daily return Rt can be defined as

𝜎𝑅𝑡|𝑛𝑡

2 _{= E(𝑅}

𝑡2|𝑛𝑡) = 𝜎2𝑛𝑡 (10)

Substituting the autoregressive process from equation (9), we can translate the mixture distribution of Rt into conditional variance:

𝜎_𝑅2_𝑡_|𝑛_𝑡 _{= ⁡α𝜎}2_{+ 𝑓(𝐿)𝜎} 𝑅𝑡−1|𝑛𝑡−1

2 _{+ 𝜎}2_𝜀

𝑡 (11)

Because we cannot observe nt in practice, we need to find a proxy. As stated in Coreland (1976) and Clark (1973), trading volume can be treated as a measure of information flow that comes into the market, and also since trading volume is a mixing variable, it can be combined into the Generalized Autoregressive Conditional Heteroscedastic (GARCH) Model as shown below:

𝑅𝑡= 𝑎0+ 𝑎1𝑅𝑡−1+ 𝜀𝑡 (12)

ℎ𝑡 = 𝛽0+ 𝛽1𝜀𝑡−12 + 𝛽2ℎ𝑡−1+ 𝛽3𝑉𝑡−1 (13) 𝜀𝑡∼ (0, ℎ𝑡) denotes the stock return that cannot be estimated in the model. If

trading volume can be service as a proxy measurement of new information flow, it is expected that β3will be significantly larger than 0 and the persistence in volatility β1

+β2 will close to zero.

Since trading volume can be incorporated into the GARCH process based on the proof above, a modified version of the GARCH model can also be applied. The EGARCH approach we employ is an exponential version of the GARCH Model:

𝑅𝑡 = 𝛼0+ ∑𝑛𝑖=1𝛼𝑖𝑅𝑡−𝑖+ 𝜀𝑡⁡ (14) ⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡ln(ℎ𝑡) = 𝛽0+ 𝛽1𝐿𝑉𝑡−1+ 𝜆1(|𝜀𝑡−1 | √ℎ𝑡−1) + 𝜆2𝑙𝑛(ℎ𝑡−1) + 𝜆3( 𝜀_𝑡−1 √ℎ𝑡−1) (15)

Where Rt, LVt, and ht are stock return, natural logarithmic volume and conditional

variance respectively. The coefficient λ1 captures the asymmetric effect on

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The coefficient λ2 measures the persistence of volatility while λ3 measures the

GARCH effect on the conditional variance. The coefficient β1 measures the impact of

natural logarithmic volume on the conditional variance. For the sake of consistency, the lag length (p) chosen for the AR process in the mean equation is the same lag length as previously used in the VAR model.

The EGARCH model is superior to the common GARCH model for the following reasons. Firstly, the EGARCH model demonstrably indicates the asymmetry effect in return volatility and has no positive constraints on estimated parameters, which produce the possibility of misspecification in the volatility process. Secondly, the EGARCH model expresses the conditional variance of a given time series as a non-linear function of its own past values and the past values of standardized innovations (Darrat et. al. (2002).

5. Empirical Finding

5.1 Contemporaneous Return-Volume Relationship

Table 4 and Table 5 reports the result of contemporaneous relationship between stock return and trading volume. Expect for period 2, all the coefficients are positive and significant at 5% level for both A Share and B Share indices. These results indicate a significant contemporaneous positive relationship between volume and return in both bullish and bearish market although the scale is small. This evidence shows that high stock return is accompanied with high trading volume, as stated in the Wall Street adages that trading volume is relatively heavy in the bull market and light in the bear market.

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Table 5 Contemporaneous return-volume relationships for A Share indices

This table reports the result of the Contemporaneous return-volume relationships for Shanghai A Share index and Shenzhen A Share index. Panels A and B display the

coefficients and t-statistics estimated in bull market and bear market respectively from the following respective regressions:

⁡𝑅𝑡 = 𝑎 + 𝛽𝐿𝑉𝑡+ 𝜀𝑡 (5) Where LVt and Rt denote natural logarithmic volume at time t and continues compounding return at time t, where α is a constant and b measure the impact of natural

logarithmic volume on continues compounding return. AR(4) is the test statistics for 4 lags ARCH LM test. *, ** denote statistical significance at the 5%, 1% level Index Shanghai A share index Shenzhen A share index

Panel A for bull market

Time Period 1 Period 3 Period 5 Period 1 Period 3 Period 5

α -0.1724 -0.0631 -0.0367 -0.5195 -0.0544 -0.0462

t-statistic (-2.02)* (-4.62)** (-2.33)* (-4.70)** (-3.65)** (-2.35)*

b 0.0111 0.0040 0.0023 0.0331 0.0034 0.0029

t-statistic (2.04)* (4.66)** (2.53)* (4.73)** (3.62)** (2.52)**

AR(4) 2.87* 12.79** 4.20** 1.21 13.89** 4.70**

Panel B for bear market

α -0.0135 -0.0874 -0.1505 -0.0292 -0.0757 -0.1345

t-statistic (-0.35) (-6.86)** (-5.07)** (-0.60) (-5.55)** (4.75)**

b 0.0009 0.0054 0.0082 0.0018 0.0048 0.0076

t-statistic (0.34) (6.80)** (5.04)** (0.57) (5.50)** (-4.76)**

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22

Table 6Contemporaneous return-volume relationships for B Share indices

This table reports the result of the Contemporaneous return-volume relationships for Shanghai B Share index and Shenzhen B Share index. Panels A and B display the

coefficients and t-statistics estimated in bull market and bear market respectively from the following respective regressions:

𝑅𝑡= 𝑎 + 𝛽𝐿𝑉𝑡+ 𝜀𝑡 (5) LVt and Rt denote natural logarithmic volume at time t and continues compounding return at time t, where α is a constant and b measure the impact of natural logarithmic

volume on continues compounding return. AR(4) is the test statistics for the 4 lags ARCH LM test. *, ** denote statistical significance at the 5%, 1% level

Index Shanghai B share index Shenzhen B share index Panel A for bull market

α -0.1247 -0.0387 -0.0456 -0.0079 -0.0438 -0.0312

t-statistic (-2.11)* (-3.47)** (-3.27)** (4.51)** (4.06)** (-2.04)*

b 0.0106 0.0032 0.0036 0.0011 0.0037 0.0025

t-statistic (2.20)* (3.65)** (3.48)** (-4.06)** (-3.99)** (2.18)*

AR(4) 0.17 26.30** 18.73** 0.28 19.04** 15.49**

a -0.0741 -0.0250 -0.0775 0.0020 -0.0328 -0.0675

t-statistic (-1.91) (-2.93)** (-3.59)** (0.72) (-3.03)** (3.40)**

b -0.0060 0.0019 0.0058 -0.0260 0.0026 0.0050

t-statistic (1.84) (2.79)** (3.58)** (0.83) (3.02)** (3.40)**

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23

5.2 Causal Relationship between Stock Return and Trading Volume

Table A1 presents the result of the VAR model in bullish and bearish market periods for the Shanghai A Share and Shenzhen A Share index respectively. Panel A1 and B1 report when LVt is dependent variable while panel A2 and B2 report results when Rt is dependent variable. As shown in the panel A1 and B1, the coefficient estimate of α1 and β1 is positive and significant at 5% level for both indices in all periods, which indicate the first lag of trading volume and stock return have significant positive impact on current trading volume. In addition, the second lag of trading volume also has influence to the current volume in the bear market for these 2 indices. Furthermore, the F-statistics are large which significantly reject the null hypothesis that all the coefficients in the regression are equal to 0. For panel A2 and B2, we notice that except for the first period, most of the coefficients are not significant and the F-statistics are low, which indicate that the lagged trading volume and return cannot explain the current return.

In Table A2 we present the results of the VAR model for Shanghai B Share and Shenzhen B Share Index. We find similar result that lagged trading volume and stock return have strong explanatory power on the current trading volume, while most of the current stock return cannot explained by past stock return and trading volume. In addition, there isn’t notable different price-volume relationship between bullish and bearish market periods.

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24

period. Besides that, we find no notable difference between A Share indices and B Share indices and no remarkable discrepancy in bullish and bearish market periods.

Overall, our finding strongly support that stock return cause trading volume in the Chinese stock market, while there is very weak evidence that trading volume can cause stock return.

5.3 The Relationship between Trading Volume and Return Volatility

Table A3 and A4 reports the estimated parameters of the AR (p)-EGARCH (1, 1) model with asymmetric effect for each index, given by Equation 14 and 15. The number of lags selected for the AR process in the mean equation is the same as that used in the VAR estimation in order to be consistent.

The Maximum Likelihood statistics (not shown in the table) are high for all the indices in each period, which illustrate that the EGARCH model is a suitable method to describe the time dependence variance in the daily return.

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25 Table 7 Results of the Granger Causality Test for sub-sample periods

This table provides the F-statistic for linear Granger Causality conducted in a bivariate Vector Autoregressive (VAR) Model. Null Hypothesis of the term Return → Volume: Rt does not Granger cause LVt

Null Hypothesis of the term Volume→ Return: LVt does not Granger cause Rt An *,** denotes statistical significance at the 5%, 1% level

Time Type Shanghai A share index Shanghai B share Shenzhen A share Shenzhen B share

Period 1 Return → Volume 2.73* 3.14* 1.94 2.06

Volume→ Return 8.39** 0.34 6.96** 3.86*

Period 2 Return → Volume 11.41** 1.31 1.25 2.17

Volume→ Return 1.12 2.52 11.16** 2.06

Period 3 Return → Volume 27.62** 6.23** 21.46** 3.74**

Volume→ Return 1.34 2.03 1.56 2.29*

Volume→ Return 3.06** 3.61* 2.29* 2.29*

Volume→ Return 0.76 1.42 0.83 0.19

Period 6 Return → Volume 29.59** 4.31** 27.64** 2.65*

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26 6. Conclusion

6.1 Summary

In this paper, we investigate the contemporaneous as well as the causal and dynamic relationship between stock return and trading volume for 4 stock indices in China Mainland. Our data comprises daily index return and trading volume in these 4 indices. The data sample is divided into 3 bullish market sub-sample periods and 3 bearish market sub-sample periods. Our study uses a single-variable regression and a linear Granger causality test in a VAR model context to examine whether stock return can explain trading volume or vice versa volume can explain stock return. In addition, we employ an EGARCH model to investigate whether trading volume can affect stock return indirectly by influencing stock return volatility. The main findings in this paper are as follows:

Firstly, a positive contemporaneous relationship between stock price and trading volume exists in most of our sub-sample periods (5 of 6) in all the 4 indices. This evidence suggests that current trading volume has a positive impact on the current stock return in both bullish and bearish market period.

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In a nutshell, our findings suggest that the lagged trading volume cannot impact the current stock return for either direct or indirect way, but the lagged stock return have strong power on estimating the current trading volume.

6.2 Limitations and Further Development

In this paper, we conduct a linear Granger causality test to investigate the causal relationship between stock return and trading volume. However, some researchers have found a significant non-linear causal relationship between these two variables. For this reason, the traditional linear Granger causality test might overlook a significant nonlinear relation between stock return and trading volume. For the further development of our research, we suggest to undertake a causality test in both linear and non-linear context.

In addition, we only investigate the price-volume relationship on the index level, which may overlook the price-volume relationship within individual companies. It leaves the possibility to conduct a further research on individual stocks and compare the difference between the finding on individual companies and the finding on indices.

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28 Reference

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32 Appendix

Table A1 Results of the VAR estimation for Shanghai A Share Index and Shenzhen A Share Index in all sub-periods

This table reports the result of the Vector Autoregressions (VAR) estimated for Shanghai A Share and Shenzhen A Share Index by the following models:

𝐿𝑉𝑡 = 𝛼0+ ∑𝑛𝑖=1𝛼𝑖𝐿𝑉𝑡−𝑖+ ∑𝑛𝑖=1𝛽𝑖𝑅𝑡−𝑖+ 𝜀𝑡 (6)

LVt and Rt denote natural logarithmic volume at time t and continues compounding return at time t. α0 and λ0 are constant, αi and βi measure the impact of

volume and return at time t-i on the current volume, while λi and γi indicate the influence of volume and return at time t-i on the current return. The optimal

lag length (k) in the model is selected by Akaike Information Criterion (AIC). However, for the sake of brevity, the table only reports the results up to 5 lags, which is statistically significant. Panel A1 and B1 report the results when the natural logarithmic volume (LVt ) is the dependent variable in the regression

model. Panel A2 and B2 reports the results when the continues compounding return (Rt) is the dependent variable. The relevant F-statistics test the hypothesis

that all the parameters in the regression are equal to zero. The t-statistics are given in the parenthesis. *, ** denotes statistical significance at the 5%, 1% level.

Index Shanghai A share Shenzhen A share

Panel A1 coefficient estimates of EQ2 in bull market period

Period 1 Period 3 Period 5 Period 1 Period 3 Period 5

Lag(k) 3 3 4 3 3 4

α0 1.6314(1.48) 1.4160(5.06)** 0.5528(3.36)** 7.0869(2.92)** 1.1974(4.88)** 0.6778(4.11)

α1 0.5577(4.77)** 0.6813(17.62)** 0.6883(16.26)** 0.5059(4.17)** 0.6560(16.57)** 0.7131(16.92)**

α2 0.0322(0.24) 0.0235(0.5 1) 0.0347(0.67) -0.2004(1.52) 0.0835(1.79) -0.0101(-0.19)

α3 0.1914(1.27) 0.1243(2.70)** 0.0380(0.73) 0.2286(1.54) 0.1437(3.09)** 0.0823(1.60)

α4 N/A N/A 0.0631(1.76) N/A N/A 0.1776(4.31)**

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β2 0.2096(0.15) 2.3821(3.51)** 0.7019(1.52) 0.1611(1.61) 1.6817(2.75)** 0.4096 (1.11)

β3 -1.9754(-1.56) 1.6489(2.43)* 1.4541(3.20)** 0.3375(0.22) 1.0463(1.72) 1.5490(4.25)**

β 4 N/A N/A -0.0501(-0.15) N/A N/A 0.3326(0.92)

F-statistics 20.8484 44.7786 132.1611 5.7018 48.2041 125.0845

R2 0.6933 0.8472 0.9547 0.3821 0.8612 0.9524

Panel A2 coefficient estimates of EQ 3 in bull market period

λ0 0.0162(0.18) -0.0214(1.36) -0.0156(-0.96) -0.0994(0.50)** 0.5528(3.36)** -0.0227(-1.11)

λ1 0.0295(3.09)** 0.0044(1.93) 0.0055(1.31) 0.0200(2.02)* 0.0062(2.35)** 0.0038(0.73)

λ2 -0.0502(-4.72)** 0.0003(0.11) -0.0050(-0.98) -0.0476(-4.43)** -0.0016(-0.51) -0.0057(-0.89)

λ3 0.0226(1.84) -0.0006(-0.23) 0.0021(0.41) 0.0309(2.56)* -0.0001(-0.03) 0.0074(1.15)

λ 4 N/A N/A -0.0039(-0.79) N/A N/A -0.0045(-0.87)

γ1 -0.0815(-0.70) 0.0280(0.72) -0.0210(-0.49) 0.0247(0.20) 0.0303(0.76) 0.0104(0.24)

γ2 0.1858(1.67) -0.0784(-1.94) -0.0565(-1.23) 0.2682(2.32)* -0.0944(-2.31)** -0.0434(-0.94)

γ3 0.2096(2.04)* 0.0627(1.55) 0.0338(0.75) 0.1840(1.53) -0.0653(-1.61) 0.0396(0.87)

γ 4 N/A N/A 0.0411(1.07) N/A N/A 0.0538(1.19)

F-statistics 3.6026 2.0453 60.7498 3.2942 1.9033 2.4606

R2 0.2809 0.0247 0.9364 0.2632 0.0239 0.0378

Panel B1 coefficient estimates of EQ2 in bear market periods

Lag(k) 2 7 4 2 7 5

α0 1.7231(3.67)** 1.3581(4.24)** 1.5610(5.40)** 1.8966(3.99)** 1.1313(4.09)** 1.1054(4.69)**

α1 0.7809(12.12)** 0.5804(16.80)** 0.5931(15.73)** 0.7860(12.10)** 0.6115(17.86)** 0.6746(17.87)**

α2 0.1057(1.66) 0.1764(4.48)** 0.1636(3.80)** 0.0907(1.42) 0.1800(4.05)** 0.1039(2.31)*

α3 N/A 0.0396(0.99) 0.0952(2.23)* N/A 0.0375(0.92) 0.0681(1.51)

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Table A2 Results of the VAR estimation for Shanghai B Share Index and Shenzhen B Share Index in all sub-periods.

α 4 N/A -0.0266(-0.66) 0.0631(1.76) N/A -0.0607(-1.48) 0.0135(0.30)

α 5 N/A 0.0927(2.30) N/A N/A 0.0748(1.83) 0.0369(0.82)

β1 3.2030(4.17)** 4.3550(6.16)** 3.3866(10.76)** 2.6905(4.30)** 4.0592(6.83)** 3.0953(11.62)**

β2 -1.2946(-1.69) -1.0397(-1.43) 0.2763(0.81) -0.8887(-1.43) -0.9315(-1.52) -0.0305(-0.10)

β3 N/A -0.5454(-0.75) 0.0576(0.71) N/A -0.5047(-0.82) 0.1580(0.54)

β 4 N/A 0.5652(0.76) -0.0501(-0.15) N/A 0.0482(0.07) 0.3177(1.10)

β 5 N/A -0.0334(-0.04) N/A N/A 0.6724(1.09) -0.0058(-0.02)

F-statistics 17.7540 16.7747 49.7971 17.5031 20.4039 53.0587

R2 0.7860 0.7512 0.8524 0.7834 0.7879 0.8999

Panel B2 coefficient estimates of EQ 3 in bear market periods

Shanghai A share Shenzhen A share

λ0 0.0355( 0.90) -0.0091(-0.57) -0.0615(1.78) 0.0428(0.87) 0.0024(0.14) -0.0780(-2.34)*

λ1 0.0050(0.92) 0.0038(2.21)* 0.0117(2.61)* 0.0067(1.00) 0.0020(0.97) 0.0135(2.52)*

λ2 -0.0073(1.37) 0.0024(1.20) -0.0031(-0.60) -0.0096(1.45) 0.0046(1.97)* -0.0055(-0.86)

λ3 N/A -0.0024(-1.24) -0.0020(-0.39) -0.0018（-1.99）* -0.0023(-0.98) -0.0015(-0.24)

λ 4 N/A -0.0031(-1.55) -0.0033(-0.79) N/A -0.0029(-1.23) 0.0044(0.69)

λ 5 N/A 0.0017(0.88) N/A N/A 0.0001(0.08) -0.0072(-1.14)

γ1 -0.0424(-0.65) -0.0257(-0.73) -0.0354(-0.95) 0.0074(0.11) -0.0244(-0.70) 0.0278(0.73)

γ2 -0.0993(-1.54) -0.0896(-2.50)* -0.0648(1.61) -0.1013(-1.57) -0.0615(-1.72) -0.0947(2.32)*

γ3 N/A -0.0003(-0.01) 0.0056(0.13) 0.0191（0.56） -0.0179(-0.49) -0.0049(-0.12)

γ 4 N/A 0.0330(0.92) 0.0411(1.07) N/A 0.0106(0.29) 0.0416(1.02)

γ 5 N/A -0.0144(-0.40) N/A N/A 0.0240(0.67) -0.0687(-1.71)

F-statistics 0.8788 2.2519 1.4976 1.0665 1.6725 1.7391

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This table reports the result of the Vector Autoregressions (VAR) estimated for Shanghai B Share and Shenzhen B Share Index by the following models:

𝐿𝑉_𝑡 = 𝛼₀+ ∑𝑛_𝑖=1𝛼_𝑖𝐿𝑉_𝑡−𝑖+ ∑𝑛_𝑖=1𝛽_𝑖𝑅_𝑡−𝑖+ 𝜀_𝑡 (6)

LVt and Rt denote natural logarithmic volume at time t and continues compounding return at time t. α0 and λ0 are constant, αi and βi measure the impact of

volume and return at time t-i on the current volume, while λi and γi indicate the influence of volume and return at time t-i on the current return. The optimal

lag length (k) in the model is selected by Akaike Information Criterion (AIC). However, for the sake of brevity, the table only reports the results up to 5 lags, which is statistically significant. Panel A1 and B1 report the results when the natural logarithmic volume (LVt ) is the dependent variable in the regression

model. Panel A2 and B2 reports the results when the continues compounding return (Rt) is the dependent variable. The relevant F-statistics test the hypothesis

that all the parameters in the regression are equal to zero. The t-statistics are given in the parenthesis. *, ** denotes statistical significance at the 5%, 1% level.

Index Shanghai B share Shenzhen B share

Panel A1 coefficient estimates of EQ2 in bull market periods

Lag(k) 2 5 4 2 5 3

α0 2.9732(3.23)** 1.0214(4.50)** 0.6658(3.28)** 3.2624(1.77) 0.7451(2.97)** 0.7676(3.40)**

α1 0.7663(6.67)** 0.7009(18.60)** 0.6543(15.22)** 0.5722(2.97)** 0.5658(12.92)** 0.6546(15.33)**

α2 -0.0099(-0.09) 0.0465(1.01) 0.0135(0.26) 0.1533(0.85) 0.1395(2.79)** 0.0026(0.05)

α3 N/A -0.0384(-0.83) 0.0850(1.66) N/A 0.1561(3.11)** 0.1791(3.57)**

α4 N/A -0.0056(-0.12) 0.2104(5.04)* N/A -0.0229(-0.49) N/A

α5 N/A 0.0865(1.88) N/A N/A 0.0310(0.66) N/A

β1 2.9665(1.96) 2.1261(3.15)** 2.4373(4.11)** 4.7296(1.50) 3.4223(4.29)** 2.9257(4.92)**

β2 -1.6153(-1.07) 1.4308(2.09)* 0.5679(0.94) -4.2901(-1.41) 0.1536(0.19) 0.9861(1.63)

β3 N/A 1.8624(2.71)* 2.2797(3.83)** N/A 0.1278(0.15) 1.4312(2.38)*

β 4 N/A 0.4080(0.59) -0.0490(-0.11) N/A 0.0039(0.01) N/A

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β 5 N/A 1.0361(1.52) N/A N/A 0.4440(0.73) N/A

F-statistics 29.5481 26.0571 48.3788 6.1011 19.2103 38.2184

R2 0.6431 0.8269 0.8880 0.2976 0.8192 0.8602

Panel A2 coefficient estimates of EQ 3 in bull market periods

λ0 -0.0446(-0.63) -0.0167(-1.30) -0.0210(-1.40) -0.0994(0.50)** -0.0199(-1.44) -0.0081(-0.50)

λ1 0.0067(0.77) -0.0031(-1.44) 0.0037(1.15) 0.0200(2.02)* -0.0004(-0.15) -0.0016(-0.53)

λ2 -0.0028(-0.39) 0.0030(1.18) -0.0066(-1.75) -0.0476(-4.43)** 0.0004(0.14) 0.0014(0.37)

λ3 N/A -0.0030(-1.14) 0.0053(1.41) 0.0309(2.56)** -0.0001(-0.03) -0.0009(-0.25)

λ 4 N/A -0.0036(-1.31) -0.0019(-0.47) N/A -0.0040(-1.30) N/A

λ 5 N/A 0.0020(0.75) N/A N/A 0.0007(0.23) N/A

γ1 -0.1091(-0.95) 0.1305(3.44)** 0.0846(1.93) 0.0247(0.20) 0.1412(3.23)** 0.0996(2.34)*

γ2 0.1168(1.02) -0.0074(-0.19) -0.0480-1.08) 0.2682(2.32)* -0.0488(-1.11) -0.0888(-2.05)*

γ3 N/A 0.1040(2.71)* 0.0396(0.90) 0.1840(1.53) 0.0300(0.66) 0.0676(1.56)

γ 4 N/A -0.0488(-1.18) 0.0465(1.05) N/A -0.0058(-0.14) N/A

γ 5 N/A 0.0047(0.11) N/A N/A 0.0073(0.17) N/A

F-statistics 1.4415 2.8778 1.6676 3.2942 2.3887 2.0211

R2 0.0808 0.0501 0.0266 0.2632 0.0534 0.0315

Lag(k) 3 3 6 2 7 4

α0 3.7942(5.14)** 1.3652(5.97)** 1.5610(5.40)** 1.9938(3.77) 1.4157(5.12)** 1.2883(4.73)***

α1 0.5521(8.85)** 0.5870(17.80)** 0.5776(16.11)** 0.6657(9.58)** 0.5546(16.73)** 0.5203(14.50)***

α2 0.0278(0.38) 0.1844(4.87)** 0.0623(1.50) 0.1612(2.36)* 0.1532(4.08)** 0.1876(4.65)***

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37

Table A3 Results for AR (p)-EGARCH (1, 1) model for Shanghai A share Index and Shenzhen A Share Index

α3 0.0497(0.58) 0.0959(2.52)* 0.0586(1.41) N/A 0.0469(1.23) 0.0866(2.15)**

α 4 N/A N/A 0.0601(1.45) N/A 0.0679(1.65) N/A

α 5 N/A N/A 0.0054(0.13) N/A 0.0050(0.12) N/A

β1 2.2996(2.30)* 2.0960(2.57)* 1.9029(4.31)** 1.4672(1.41) 4.0550(5.62)** 1.2702(2.86)***

β2 -0.5418(-0.53) -1.7944(-2.21)* 0.3090(0.69) -1.7417(-1.69) 0.1910(0.26) 0.1204(0.27)

β3 0.0660(0.06) -0.9811(-1.21) 0.3445(0.77) N/A -0.0566(-0.07) -0.0246(-0.05)

β 4 N/A N/A 0.5669(1.27) N/A 0.8165(1.83) N/A

β 5 N/A N/A 0.5133(1.15) N/A 0.3997(0.89) N/A

F-statistics 21.5700 28.1082 13.3455 67.7632 119.7785 24.7155

R2 0.4492 0.7276 0.6920 0.6129 0.6844 0.7419

λ0 -0.0387(-0.80) 0.0097(1.05) -0.0570(-2.17)** -0.0209(-0.58) 0.0177(1.38) -0.0463(-2.08)**

λ1 0.0072(1.78)* 0.0009(0.68) 0.0049(1.65) 0.0093(1.98)* 0.0018(1.20) 0.0045(1.52)

λ2 -0.0125(-2.64)* 0.0033(2.19)* 0.0014(0.42) -0.0076(1.65) 0.0017(0.98) -0.0015(-0.44)

λ3 0.0052(1.10) -0.0038(-2.51)* 0.0006(0.18) N/A -0.0041(-2.31)** -0.0011(-0.32)

λ 4 N/A N/A -0.0044(0.75) N/A 0.0027(0.82) N/A

λ 5 N/A N/A -0.0044(-1.31) N/A -0.0010(-0.31) N/A

γ1 0.1979(3.04)** 0.0199(0.60) 0.0485(1.34) 0.0648(0.92) -0.0209(-0.62) 0.0264(0.73)

γ2 -0.1472(-2.21)* -0.0398(-1.22) -0.0414(-1.13) -0.0038(-0.05) -0.0478(-1.41) 0.0083(0.22)

γ3 0.1556(2.37)* -0.0047(-0.14) 0.0158(0.43) N/A 0.0354(-1.05) -0.0438(-1.21)

γ 4 N/A N/A 0.0395(1.08) N/A 0.0488(1.33) N/A

γ 5 N/A N/A -0.0566(-1.55) N/A 0.0265(-0.72) N/A

F-statistics 2.7163 2.6248 1.4551 1.0788 2.0442 1.2008

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38 This table reports the estimation for the following AR (p)-EGARCH (1, 1) model:

𝑅_𝑡= 𝛼₀+ ∑𝑛_𝑖=1𝛼_𝑖𝑅_𝑡−𝑖+ 𝜀_𝑡⁡ (14)

⁡⁡⁡⁡⁡ln(ℎ𝑡) = 𝛽0+ 𝛽1𝐿𝑉𝑡−1+ 𝜆1(_√ℎ|𝜀𝑡−1|

𝑡−1) + 𝜆2𝑙𝑛(ℎ𝑡−1) + 𝜆3( 𝜀𝑡−1

√ℎ𝑡−1) (15)

Where Rt-i, LVt-i, and ht-i are the return, natural logarithmic volume and conditional variance at time t-i respectively. The coefficient λ1 captures the asymmetric

effect on standardized residuals on conditional variances. A negative value of λ1 illustrate that negative residuals produce higher conditional variances than

positive ones in the immediate future. The coefficient λ2 measure the persistence of volatility while λ3 measure the GARCH effect on the conditional variance.

The coefficient β1 measures the impact of natural logarithmic volume on conditional variance. For the sake of consistency, the lag length (p) chosen for the

AR process in the mean equation is the same lag length previously used in the VAR estimation. However, for the sake of brevity, the table only reports the results up to 5 lags. The t-statistics are reported in parenthesis. An *, ** denotes statistical significance at the 5%, 1% level.

α0 0.0044(3.46)** 0.0002(0.32) 0.0019(2.71)** 0.0045(2.03)* -0.0004(-0.64) 0.0014(1.79)

α1 -0.3641(-3.16)** 0.0599(1.41) -0.0150(-0.34) -0.0331(-0.30) 0.0495(1.19) 0.0657(1.52)

α2 0.0158(0.17) -0.0343(-0.89) -0.0245(-0.56) -0.0490(-0.58) -0.0498(-1.24) 0.0035(0.08)

α3 0.0823(0.89) 0.0658(1.76) 0.0277(0.59) -0.0575(-0.69) -0.0235(-0.59) 0.028(0.65)

α 4 N/A N/A 0.0673(1.87) N/A N/A 0.0654(1.66)

β0 -3.3318(-0.90) -0.8744(-2.82) -1.0532(-4.00)** -0.6269(-0.09) -0.2542(1.14) -8.0942(-3.95)**

β1 0.0952(0.42) 0.0103(0.58) 0.0365(3.70)** -0.1503(-0.34) -0.0136(1.07) 0.3085(3.93)**

λ1 1.4197(5.53)** 0.3153(6.90)** 0.0684(2.32)* 1.2271(4.72)** 0.2534(7.76)** 0.0807(1.15)

λ2 0.5984(3.51)** -0.0661(-2.40)* 0.0265(1.27) -0.0704(-0.33) -0.0365(-1.91) -0.1884(-3.27)**

λ3 0.9176(14.34)** 0.9448(70.85)** 0.9607(87.35)** 0.7446(8.80)** 0.9697(10.72)** 0.6676(7.28)**

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39

Table A4 Results for AR (p)-EGARCH (1, 1) model for Shanghai B share Index and Shenzhen B Share Index

This table reports the estimation for the following AR (p)-EGARCH (1, 1) model:

𝑅𝑡= 𝛼0+ ∑𝑛𝑖=1𝛼𝑖𝑅𝑡−𝑖+ 𝜀𝑡⁡ (14) ⁡⁡⁡⁡⁡ln(ℎ𝑡) = 𝛽0+ 𝛽1𝐿𝑉𝑡−1+ 𝜆1(|𝜀𝑡−1 | √ℎ𝑡−1) + 𝜆2𝑙𝑛(ℎ𝑡−1) + 𝜆3( 𝜀_𝑡−1 √ℎ𝑡−1) (15)

Where Rt-i, LVt-i, and ht-i are the return, natural logarithmic volume and conditional variance at time t-i respectively. The coefficient λ1 captures the asymmetric

effect on standardized residuals on conditional variances. A negative value of λ1 illustrate that negative residuals produce higher conditional variances than

positive ones in the immediate future. The coefficient λ2 measure the persistence of volatility while λ3 measure the GARCH effect on the conditional variance.

The coefficient β1 measures the impact of natural logarithmic volume on conditional variance. For the sake of consistency, the lag length (p) chosen for the

α0 0.0017(1.49) -0.0011(-2.52)* -0.0013(-1.60) 0.0008(0.87) -0.0006(-1.40) -0.0010(-1.11)

α1 -0.0643(-1.32) 0.0023(0.06) 0.0159(0.39) -0.0234(-0.46) -0.0152(-0.39) 0.0691(1.76)

α2 -0.1145(-1.98)* -0.0325(1.00) -0.0097(-0.25) -0.0578(-1.11) -0.0182(1.05) -0.0392(-1.05)

α3 N/A 0.0250(0.76) 0.0550(1.53) N/A 0.0352(0.01) 0.0367(0.95)

α 4 N/A -0.0014(-1.39) 0.0539(1.44) N/A -0.0084(-0.26))* 0.0645(1.72)

α 5 N/A -0.3181(-0.96) N/A N/A -0.0205(-0.57) -0.0245(-0.63)

β0 -0.2145(-22.02)** -0.2590(-1.59) -0.2139(-0.75) -0.2259(-0.88) -0.4472(-2.16)* 0.0302(0.10)

β1 0.0108(12.84)** -0.0185(-1.86) -0.0169(-0.82) 0.0046(0.28) -0.0034(-0.29) -0.0386(-1.47)

λ1 -0.0771(-7.48)** 0.2113(6.00)** 0.1436(4.09)** -0.0798(-9.53)** 0.1923(5.71)** 0.1092(3.15)**

λ2 0.0148(1.74) -0.0944(-4.95)** -0.0767(-3.63)** -0.0312(-1.70) -0.0910(-4.67)** -0.0843(-4.19)**

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40

AR process in the mean equation is the same lag length previously used in the VAR estimation. However, for the sake of brevity, the table only reports the results up to 5 lags. The t-statistics are reported in parenthesis. An *, ** denotes statistical significance at the 5%, 1% level.

α0 0.0079(2.93)** 0.0013(1.30) 0.0008(0.85) 0.0007(0.31) 0.0002(0.21) 0.0008(0.89)

α1 -0.3580(6.25)** 0.1466(3.33)** 0.1255(2.38)* 0.0286(0.41) 0.1050(2.47)* 0.1546(2.95)**

α2 -0.1176(-1.28) -0.0178(-0.44) 0.0063(0.11) 0.1004(2.38)* -0.0619(-1.50) -0.0258(-0.53)

α3 N/A 0.0568(1.56) 0.0155(0.33) N/A 0.0319(0.78) 0.0245(0.49)

α 4 N/A -0.0646(-1.51) 0.0663(1.58) N/A -0.0229(-0.53) N/A

β0 0.2575(0.21) -1.9551(-3.99)** -2.9336(-5.01)** -0.1123(-5.63)** -0.9901(-3.66)** -2.1248(-5.93)**

β1 -0.0513(-0.95) 0.0255(1.25) 0.0941(3.46)** -0.0001(-2.01)** 0.0001(1.60) 0.0001(3.94)**

λ1 -0.3477(-4.27)** 0.3826(6.36)** 0.3220(-6.07)** 0.8981(2.41)* 0.1915(5.59)** 0.3312(6.12)**

λ2 0.1182(0.89) 0.0413(1.28) -0.0356(-0.98) -0.0648(-0.33) 0.0032(0.15) -0.0417(-1.06)

λ3 0.9215(17.76)** 0.8260(20.09)** 0.8221(25.30) -0.4667(-1.91) 0.8915(26.91)** 0.7901(19.90)**

α0 -0.0021(-1.27) -0.0009(-1.56) 0.0002(0.20) -0.0039(-1.98)* 0.0001(-0.05) -0.0004(-0.50)

α1 0.2228(2.82)** 0.0233(0.65) 0.0729(1.62) 0.1080(1.21) 0.0192(0.54) 0.0552(1.40)

α2 -0.1422(-1.90) -0.0337(-0.93) -0.0402(-0.99) -0.0002(0.01) -0.0211(-0.63) 0.0363(1.03)

α3 0.0142(0.20) 0.0307(0.93) 0.0232(0.55) N/A 0.0230(0.73) 0.0010(0.20)

α 4 N/A -0.0072(-0.20) -0.0157(-0.38) N/A -0.0136(-0.37) 0.0404(1.02)

α 5 N/A -0.0778(-2.07) N/A N/A -0.0481(-1.34) 0.0177(0.45)

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41

β1 0.2547(1.88) -0.0029(-0.46) -0.0257(-1.06) 0.0001(1.56) 0.0001(-1.58) 0.0002(0.68)

λ1 0.3920(3.58)** 0.1890(6.39)** 0.3593(8.87)** 0.5002(3.88)** 0.2647(8.02)** 0.0735(3.03)**

λ2 -0.2365(-3.18)** -0.0953(-5.66)** -0.1014(-4.35)** 0.0704(1.00) -0.0286(-1.49) -0.1164(-6.89)**