Print Reference This Reddit This

Relationship Between Trading Volume And Stock Index Return Finance Essay

The purpose of this paper is to investigate the relationship between the trading volume and stock index return in China and UnitedStates, one of them is the largest and fastest developing socialist country around the world, the other one is the most developed capitalist country in the world. The differences and similarities between these stock markets can be used as a consideration in China financial system reform. The data is chosen from Shanghai Stock Exchange Composite Index and SP500 index,which are the typical stockindices ofChina and United States. The period of the daily data is from 1, March 2009 to 1, March 2011 on the Yahoo finance. This period starts before the financial crisis in 2009 and ends in the age of early economic recovery. By observing the sample distributed data, the relationship between the trading volume and stock index price can be found intuitively and obviously in China and United States. The summaries of statistics analyses show the structure and characters of the data from China and United States. Time series trend regress of trading volume in China and United States is both significant. The regression results of trading volume and the value of price changes in China and United States shows their significant relationship. The non-stationary of the series of trading volume and stock index return in China and United states is emerged in unit roots test. The regression of trading volume and stock return confirms their significant relationship. The problem of whether the change of trading volume causes the changes of stock return or the change of stock return causes the change of trading volume is solved by the application of Granger Causality test. At the end the effect of the information of financial crisis is added in the analysis. The results suggest that the information of financial crisis affected the trading volume and the trading volume affected the return and volatility of the stock market. Overall, the relationship between the trading volume and stock return in China and United States is both significant. But in several analyses their results are slightly different.

Introduction

During the last decades, there is a rapid development of economy in China. The financial system in China got developing quickly likewise. With the capital continuous expanding capital and rapid improving of all kinds of business, many financial instruments are applied in China, including stocks and several derivatives. The United States is the most developed country around the world, has the most perfect and advanced financial system. However, in China, the system of the stock market still in an imperfect condition after several reformations.

Numerous researchers and people whose interest is closely related to stock market, has been attracted by the relationship of stock price and trading volume. Various kinds of analysis techniques are applied to investigate whether there is an unsymmetrical relation between them and make vast studies. Those studies gathered many evidence to proof the correlation between stock return and trading volume.These analytical techniques employed in exploring the relationship of stock return and trading volume in different countries, are also introduced into the research area of financial derivatives. And they are found to be valid across different countries and different financial derivatives.

This paperwill focus on impact of trading volume to the stock market index return and its volatility in China and United States, as well as their interaction. It tries to find the differences and similarities of these two markets. Whether those analytical techniques are suitable in China is the main objective in this article. And whether The rate of information arrival affect the relationship of volume and share price is a basic argument.In general, in order to explain the correlation between stock price and trading volume, a hypothesis of competingwas introduced. Even so, in the real world, various information impacts from daily eventsis unpredictable and its influence is significant. It similarly affects the trading volume so information should be considered as another famous competing hypothesis. Many studies reported the contemporaneous correlation and correlation between stock return and trading volume. These research results now are used to analyze the contemporaneous correlation and casual relationship in China and United States, in order to find the differences and similarities in these two markets. Then they would make a contribution of finding an appropriate way to develop the financial system in China.

The remains of my paperis organized as follows: a brief description is exhibited on in section 2. And section 3 enumerates the empirical methods used in this article and the details of the data, which is used in this investigation. Section 4 summarizes the research resultsfor the interaction of trading volume and return and its volatility in China and United States, produced by the analytical methods shown in section 3. Section 5 presents the result, summary and conclusion of this article.

Literature Review

Logical order

In consideration of the trading volume’s important status around those effect factors which have influence on the stock price and return, trading volume has attracted numerous researchers and turn out lots of research results, which can demostrate the relationship of trading volume and stock return. McKenzie and Faff (2003) have discovered that trading volume represents one of the main factors in predicting stock return and return volatility. Suggested by Morgan (1999),the major factor which has a strong influence on the volatility of return is trading volume especially in less liquid and small markets including emerging markets. Ying (1966) found that trading volume had led stock price changes by about four business days.

Several literatures provide the basic ideas and perspective of the relationship of stock market returns and trading volume. The basic influence factors such as structured change of trading volume have greater influence during early nineties based on market capitalization.The basic relationship is studied by Rogalski (1978),Figlewskiand Cornell (1981). For a student of P-V relations, Karpoff (1986, 1987)’s contributions are of significance.The review of the previousresearches on the subject of several findings has provided considerable ammunition for those who wishes to carryout empirical study in this fied. Granger and Morganstern (1963), Crouch (1970), Galant, et.al (1992),and Epps and Epps (1976) etc. establish the fundamental structure and conception in the area of P-V relations. Hiemstra and Jones(1994),andCampbell et.al (1993)examined the linear and non-linear causality relationship of stock prices and trading volume and confirmed their relationship.The relationship between trading volume and its variance is examined by Omran and Mckenzie(2000) and they found there is a significant interactionin both returns and volumewith their outliers.Gallant et al. (1992), who carry on examining the co-movement of price and volume relation by a method called semi-nonparametric method with the data from New York Stock Exchange Data. To conclude, there four findings: (i) the correlation between trading volumereturn volatility is positive, (ii) that large price movements are always followed by high volume, trading volume has an intuitive influence on the price, (iii) the leverage effect is attenuated by conditional lagged volume, and (iv) the risk-return relationis positivebased on the conditional lagged volume,. Morse (1980) obtains a result which shows the correlation of stock return and trading volume, high returns always comes in the high volume period.The relationship between aggregate trading volume and the continuing correlation of daily stock return is explored byGrossman and Wang (1993). Chance forstock price to decrease is lower on a high trading volume day than on a low trading volume day

Trading volume of the stock market is extensive and important, but the mostly concerned point is the relationship of volume and the volatility of stock returns. LeBaron, Sentana and Wadhwani (1992) show the autocorrelations of daily stock returns volatility with the variance of returns. A number of papers have proofedthat the return volatility are related with volume, such as Mulherin and Gerety (1999), Jain and Joh (1998) and Crouch (1970) all found a positive interaction between absolute value of price returns and stocktrading volumein the finance marketfor both individual stocks and stock indices.By studyingthe transaction data form NYSE stocks in America, results of Wood, et.al (1985) alsoshows a positive relationship between trading volume and stock return, and they found the effect of trading volume is significant on price return. A positive correlation between price returns and trading volume was confrimed by Rogalski (1978) and Touchen, Westerfield (1977)and Pitts (1983), among others. Stickel and Verrecchia n a 1994 study shows that the P-V relation on the U. S. exchange at the information of earning announcements is significant. Their findings indicated that large price returns based on weak volume tendency but large price increases based onhigh trading volume tendencywhich lead to a further price increasing. There are four models established from thepevious P-V relation studiesto examinethe significance of the relationship with price returns and trading volumesof shock market, which have been established by Chen, et.al (2001) in his studies. The four models are: the DO model (differences of opinion), the REAP model (rational expectation asset pricing),and the SAI model (sequential arrival of information),the MD model (mixture of distributions)and the REAP model (rational expectation asset pricing) model

The trading volume can be affected by the influence of information, so the information becomes to be the research factor in many papers. By combining the asymmetric information of the market, Epps and Epps (1976),Clark (1973), Tauchen and Pitts (1983) and Harris (1986) made several models to research on the relationship of stock return and trading volume. A no-arbitrage model is used by Ross (1989) to explain why information transmissionis the main determinant of volatility of price returns,and the effect of information is represented by the effect of trading volume . Furthermore, how the trading volume is affected by the information of market price fluctuation and investor confidence and expectations Harris and Raviv (1993). The rise and fall in trading activity is almost symmetric. I t can be explained by publicly available information as well as by non-infromation trader, such as insiders and short selling traders.These factors are external factors which are effective to the generalize the price behavior in the stock market, confirmed byCampbell, Grossman and Wang (1993).Political events are found to be a factor which isinfluencing the stock price due to the fluctuating of trading volume (Nishat, M. and Mustafa, K. 2002). In the case of pre-nuclear test, the result is likely to be dominatedbased on the data from Dec 14, 1991 to Dec 31, 2001 in Pakistan (Pakistan had a nuclear test on May 28, 1998 which lead toan enormous impact on KSE100,and the index of KSE100 declines from 1040.19 to 789.15, at the same time, trading volume declines from Rs (Rupee) 16 million to Rs9 million.

In order to examine the relationship between stock market returns and trading volume, several analytical techniques are developed.Abhyankar (1998),Fujihara and Mougoue (1997), and Hiemstra and Jones (1994) carried out nonlinear causality tests. These studies declared that the interaction between economic variables and financial time series is mainly nonlinear. Engle et al. (1990) add an interpretation representing the information with time series to examine their linear relation.In order toconfirm the P-V relation, the Granger causality method (Granger, 1969) has been a useful analytical technique. Studies by Rogalski (1978), Jain and Joh (1988), Hiemstra and Jones (1995),Campbell, et.al (1993), Saatcioglu and Starks (1998),Martikainen, et.al (1994), Kamath and Wang (2006) and Chen, et.al(2001) , are examples which applied the Granger causality methodology. VAR (vector auto regression model) is used to explore the causality between trading volume and stock returns. Campbell, Grossman and Wang (1993) found that in the low volume days the prices changes low and in high volume condition the level of price changes is quite high. Stochastic time series model also can focus on the relationship of trading volume and stock returns. The phenomenon of price change is significant by using three different values of daily trading volume for the stock market index.

Those analytical methods are valid in different price &volume research, such as the gold market and financial derivative market.Literatures based on various data from different countries have finished by several researchers, and the focus extended to derivative market.Bertus and Stanhouse (2001) suggest that the characteristics of gold market prove a better pricing relationship forgold when it compared to other derivatives.. In fact, the supply of it is not subject to wide swings and the stock of gold is larger than the others’ annual production. The ability to forecast price movement accurately based on the research of the relationship between returns and trading volume of the futures in the market may improve arbitragestrategies. Several recent studies concentrating on these issues are Kocagil and Shachmurove (1998), ,Moosa and Silvapulle (2000),andFujihara and Mougoue (1997). McCarthy and Najand (1993) make a sequential information hypothesis in the currency futures market. The evidence of bi-directional interaction of the price return and trading volume in the agricultural futures market is foundby Malliaris and Urrutia (1998). After concerning the nonlinear causality, Hiemstra and Jones (1994) find evidence of bi-directional interaction based on the data form the U.S market. In the crude oil future market, Moosa and Silvapulle (2000) confirmed bi-directional causality, although Fujihara and Mougoue (1997) find only there only exists a unidirectional causality from volume to price.

Those analytical methods are valid in the different areas around the world. Gordon (1968) discovered that in the U.S. market trading volume lead the market index price in a high position for months. Thestudy of Martikainen, et.al (1994) focused on the Finnish stock market and found a bi-directional interaction between stock returns and volume. Chen, et.al (2001) focused on nine developed national equity marketsto find the P-V relation. By using the model created by Bessembinder and Seguin (1993),they documentedan unsymmetrical volatility response to unforeseeableimpacts in trading volume,Ragunathan and Pecker (1997) shows in the Australian future market that there is a positive relationship between trading volume and volatility.Data across Asia-Pacific stock markets is tested by Deo, Srinivasan and Devanadhen (2008), result in the conclusion that the relevance is significant across all national market.Karpoff (1987) wrote an article shows that, in the spot and future market, return and volume relationship is positive related.Karachi Stock Exchange (KSE) 100-index is examed byMalik, Hussain& Ahmed (2009) , the relationship of trading volume and stock returns is significant, by using testing the unit roots and volatility of trading volume & stock return. Graph of log price, log volume and log return was plotted in their article, intuitionally shows that the relevance of trading volume and stock return. Deo, Srinivasan and Devanadhen (2008) used six different tables to describe results of their research on the relationship of trading volume and stock return. Data is selected from stock markets in,TaiwanTokyo, Indonesia,Korea , Malaysia, Hong Kongand India in the period of January 1, 2004 to March 31, 2008. Each index value is the average value of daily opening, high, low and closing prices.By means of examining the data from Asia-Pacific stock market, Deo, Srinivasan and Devanadhen (2008) found that the relationship among stock market returns, trading volume and volatility is significant. Trading volume and the absolute value of stock return have a contemporaneous relationship. Their articles indicate that the phenomenon of returns causing volume is more obvious than volume causing returns. The positive association between return and lagged trading volume also be found by Deo, Srinivasan and Devanadhen (2008). Their research of data from different countries shows that the relation is robust across all national markets.

Due to the literatures before, the relationship of trading volume and stock return is significant. The analytical technique in this area is full-fledged which can be applied in the examining of relationship of trading volume and stock return in China. The literate review shows that in the result of relationship test in China should be similar, most of the financial experience from developed country can be applied in China.

Methodology, Research Design and Data

3.1 Data

The datasets selected from the representative index in China and United States: Shanghai Stock Exchange Composite Index and SP500. The index is available on a daily basis from 1st March, 2009 to 1st March, 2011. This period covers the beginning of the subprime crisis in the year of 2009 and the economic recovery in recent months.The trading volume availability for the statistical analysis is well regulated and corresponding. The data set of trading volume and stock price are collected from “Yahoo Finance”. The daily opening, high, low and closing price of index is the sample data. The index price I used in this article is the average of these four data. The return in this paper is where Ptand Pt-1 arethe index price on the day t and t-1 respectively.The software STATA is used for data analysis and interpretation.

3.2 Methodology

By using different analytical techniques, we can get the resultsfrom China stock market and US stock market. Through those results, the differences and similarities of China and United States can be found.

Statistics Summary and Curve Graph

The fundamental statistics such as sample size, standard deviation, mean,kurtosis, skewness and Jarque-Bera(a goodness-of-fit measure of departure from normality, based on the sample kurtosis and skewness, named after Carlos Jarque and Anil K. Bera. ) will be explored. These basic statistics of data describe the character of stock price returns and trading volume in the sample period from 1st March, 2009 to 1st March, 2011.

Put the daily data of stock market index price and trading volume into a Curve Graph can make it intuitionally being observed. How the data distribute across those days can be clear at a glance with the application of Curve Graph in this article.

Linear & Non-Linear Trend in Trading Volume

In considering previous studies, the trading volume can be regard as a time related variable Chen et.al (2001). The trading volume is detrendedby regressing the time series on a deterministic function of time, with the estimators of, and as the following regression equation:

Wheret and t2 are linear and quadratic trading volume, andis the trading volume in each market, is the residuals. The significance of each coefficient states the structure of the regression.

Testing for Unit Roots

In statistics, the unit roots test tests the time series, whether is a non-stationary when using an autoregressive model. In this article, the contemporaneous and interaction between trading volumes, stock return and its volatility is tested by Vector Autoregression (VAR) model. Hence, whether the time series data for trading volumes and stock index returns will be checked by using Augmented Dickey Fuller (ADF) test, this test is developed by John Denis Sargan and AlokBhargava (1989). As in the following equation:

Where x is the variable uses for unit root test. In order to test the contemporaneous and casual relationship with VAR model, the stationary is important.

Trading Volume and Stock Price Returns

We examine whether the stylized facts relating to stock returns and trading volumes relation fit the data for selected China and United States stock market by testing with the help of contemporaneous correlation.The used widely method is the unary linear regression model. To test the two competing alternative forms of stock price by deriving the following regressions:

Where,the independent variable is the natural logarithm of the stock market index price and its absolute value.is the detrended trading volume of dependent variable and The null hypothesis of this regression is that and is zero. If the t-test rejects the null hypothesis of these coefficients, the relation between stock market index return and trading volume is significant.

Causality between Trading Volumes andStock Price Changes

The analysis in this paper is based on the method developed by Chen et.al (2001). Specifically, the bivariateautoregressionis used to test the interaction between the two variables, trading values and stock returns. And the question that whether the high trading volumeslead tohigh price changes or high price changes lead tohigh trading volumes can be figured out by applying this bivariate autoregression. A bivariate autoregression model in this paper is as following:

Where, is the trading volume at the time t and is the index return at time t. If coefficients of are significant, then the past trading volume gives a good forecast for today’s trading volume. Similarly, If the coefficients of are significant, the past index price changes gives a good forecast for today’s trading volume. This can be denoted as return causes volume.The time lag, i and j, is decided by using AIC (Akaike information criterion) in the VAR (Vector autoregressive) model. If both coefficients of and are different from zero, there is a relationship between the stock marketindex price returns and trading volumes.

Trading Volume and Conditional Volatility

In the end, the finding of contemporaneous relationship between trading volume and conditional variance in the aggregated market are modified by conditional variance equation of EGARCH model. The EGARCH model lessens this problem by modeling the standardized residual as moving average repressors in the variance equation while the preserving estimation of the magnitude effect.

In econometrics, ARCH (autoregressive conditional heteroskedasticity) models are used to characterize and model observed time series (Engle, 1982). When a AMRA (autoregressive moving average) model is assumed for error variance, the model then becomes GRACH (generalized auto regressive conditional heteroskedasticity) model (Bollerslev, 1986). However,the tendency of negative shocks to be associated with increased volatility can be captured by EGARCH (exponential generalized auto regressive conditional heteroskedasticity) models (Nelson, 1991). To estimate stock return volatility EGARCH(1,1) model as following will be used:

In consideration of the effect of information, we have used trading volume as a proxy for information innovations. Systematic variations in trading volume are assumed to be caused only by the arrival of new information into the market, and it is evaluated by daily trading volume. Therefore, a new variable V is added into the EGARCH model:

This mixture model combines the EGARCH model and the effect of information. The persistence of variance as measured by should become negligible if accounting for the uneven flow of information (V) explains the presence of EGARCH in the data.

Empirical Results of the Analyses and Discussion of Findings

The analysis begins with the curve graph on the stock index price and trading volume in China and United States. Graph 1&2 plot the data from Shanghai Stock Exchange Composite Index and S&P500 during the sample period from 1st March, 2009 to 1st March, 2011. By the observation of these two graphs, high stock index price always comes with a high trading volume. In the graph of Shanghai Stock Exchange Composite Index, the trading volume is at a peak of wave in 29 July, 2009, 24 November, 2009 and 18 October 2010. At the similar time, the stock index prices are also at the peak of wave. Likewise, in the SP500 graph high index price comes with a high trading volume around May in the year of 2010. The prediction can be forecasted that the relationship between stock index price and trading volume are both significant in China and United States. The influences of trading volume are similar in both countries, so that we can get experience from the stock market of United States. It is meaningful to learn the knowledge summarized from those developed capitalist countries.

Table 1 is about a range of summary statistics on returns and trading volume with mean, standard deviation, skewness, kurtosis,Jarque-Bera and probability.In Table 1 the daily return of stock index return for United States is higher than that for China. The China stock index has a volatile market with standard deviation measured at 0.0161516, which is higher than the figure of United States. The standard deviation of trading volume for China is higher than United States, this suggests that the market in United States in more stable and well-developed when compared with China. The values of the skewness are high in both China and United States, which meant that the tail is particularly extreme. The figures of kurtosis in Table 1 are all exceed the normal value of 3 from returns and trading volumes in China and United States.According to the Jarque-Bera test, the given series is non-normal distributed for both Shanghai Stock Exchange Composite Index and SP500, which reject the null hypothesis that the series from Shanghai Stock Exchange Composite Index and SP500 are normally distributed. Through the analyses and summary of the data from Shanghai Stock Exchange Composite Index and SP500, the market in China is quite similar to United States. On the other hand, the market in United States is far more stable and well-developed. The financial structure and policy used in United States can be referenced by China.

Linear and non-linear relationship of trading volume and returns is tested and the output of quadratic time series trend is reported in Table 2. It predicts the coefficient results by regressing trading volume for both linear and non-linear time trend variables are statistically significant for both China and United States market and fit to be high at 1 percent level of significance. The imperfection of this regression emergesby both results in China and United States have a low R2. By this analytical technique, in China and Unite States the trading volume can be regressed by its time series. However, the linear and non-linear time series are not enough to make the regression of trading volume perfect. From this aspect, the properties of trading volumes in China and United States are analogous. The strategies which have an effect to stabilize trading volume in U.S. should be learned.

The applying of test of unit root is shown on Table 3. Unit root test is to be achieved by using Augmented Dickey Fuller test. The test result suggest that the null hypothesis for stock returns and trading volume follow a stationary process at 1 percent level of significance in both China and United States except the trading volume of United States market at 5 percent level of significance. Hence, the hypothesis that these two variables are not stationary is strongly rejected. This proved that the two series of stock return and trading volume are stationary. The stationary of trading volume in United States is a kind of weak, this show that the subprime crisis made a considerable influence to U.S. market. China should learn U.S.s’ lesson from the cause of the subprime crisis in 2009.

The results of regression for daily detrended trading volume on stock returns and absolute return was reported in Table 4, broken into Panel A and B for the stock market in China and United States. In Panel A the coefficient for China is statistically significant at 1 percent level. The United States market envisage with 10 percent level of significance. The intercept estimators are significant at 1 percent level in both China and United States market.Panel B shows the regression results for daily trading volume on absolute stock returns for China and United States market. The estimators of intercept and coefficient are significant at 1 percent level in both China and United States. Nevertheless, four regression analyses all have a quite low R2. This suggests that, although the variables of stock return and absolute stock return are meaningful the regression is too simple and incomplete. These regression analyses are suitable for stock market in China and further development is needed to regressthe moving of index.

By using the bivariate autoregressive model, the causality between the two variables trading volumes and stock returns can be tested. Table 5 present the contemporaneous relationship between and trading volume based on the Vector Autoregressive (VAR)model by using Panel A and B. F-statistics and their corresponding level of significance are also explored. Panel A shows the results for the test of the null hypothesis that returns donot Granger-cause volume and their F-statistics significant at 1 percent level for both China and United States market. It suggests that the trading returns and past trading volumescause current trading volumes. In Panel B, we test the null hypothesis the volume does not Granger-cause returns. The hypothesis is rejected for China at 1 percent level. But for United States the hypothesis, the volume does not Granger-cause returns has been accepted. It suggests that the past returns lead to current returns but the influence of trading volume is weak. This finding implies the presence of current and past returns, trading volume adds some significant predictive power for future returns in both China and United States.The result from Panel A and B implies that there is a feedback relation between stock index return and trading volume in China. Hence, this suggests the returns are influenced by volume and volumes are influenced by return in stock market of China. The details in Panel A and B suggest strongly that returns causing volume than volume causing returns. Noticing the different contemporaneous relationship is important when preparing a market analysis in China, as there is a feedback relationship in China based on this causality relation analysis.

In Table 6 the flow of returns and the volatility of return are examined by using EGARCH model. Penal A&B present the results of selected parameters for estimated EGARCH model. In Penal A the conditional mean predicted with significant at 1 percent level for China’s market and the conditional variance signifies with 1 percent level in both China and United States market. In both China and United States,the log-likelihood envisages with large statistics, and these suggest that the EGARCH model is more fabulous for capturing the temporal dependence on index return volatility and index return behavior. Otherwise, the coefficient of β is found to be quite higher than λ in conditional variance, implying that large market shock induces relatively small revisions in future volatility. Panel B shows the results the result for trading volume is included in the conditional variance specifications. The conditional coefficient β is significant in 1 percent and λ signifies at 10 percent significant level.The values of log-likelihood statistics are also very high. Trading volume regard as a representation of the information variable and it does not reduce the importance of λand β in explaining the existence in volatility of returns in China and United States. However, the coefficient of trading volume is not stable and significant in both China and United States market. In the case of U.S., this coefficient accepts the null hypothesis that the lagged trading volume has no influence on the index returns. The EGARCH model with the flow of trading volume indicates a new way to analyze data from China’s market, which can be used to develop the existing analytical techniques to fit for China expressly.

Summary & Conclusion

This study investigates the interaction between stock market trading volume, daily index stock returns and volatility within the period of 1st March, 2009 to 1st March, 2011. The study also identifies the differences and similarities between China market and U.S. market.Through the unit roots test, regressions and Granger causality test and GRARCH model, this paper aim to confirm the utility of the common statistic analysis techniques in the market of China, find the differences and similaritiesbetween market in China and United States, and make a contribution to the development of China’s market.

The result suggests that there is a significant contemporaneous relationship between trading volumes and absolute stock returns in both China and United States. The casual relationship between stock index returns and trading volume is estimated by using the VAR model in both China and United States.

The evidence in the casual relation tests shows that stronger return causing volume than volume causing returns.Even so, a feedback system exists in the case of China. Finally, by applying the EGARCH model, it shows that there is a positive association between return variance and lagged trading volume in China.

After noticing these differences and similarities, the applicable methods will be found for China. Existing analytical technique can be reformed to predict China’s market after considering the current conditions of stock market in China. As the vast market potential in China, it is meaningful to introduce advanced financial structure and analytical science to the market of China.

Tables and Graphs

Graph 1: Curve graph of the Shanghai Stock Exchange Composite Index and its trading volume

Graph 2: Curve graph of SP500 index and its trading volume

Table 1: Descriptive Statistics for Returns and Tading Volume

Country

China

USA

Index

Shanghai Stock Exchange Composite Index

SP500

Observations

485

504

Return

Mean

0.0006755

0.0012356

Std.Dev.

0.0161516

0.0128946

Skewness

-0.5857881

0.2152979

Kurtosis

4.854365

6.128561

Jarque-Bera

97.22755282

209.4394401

Probability

0.0000000

0.0000000

Trading Volume

Mean

1202.446

490.2286

Std.Dev.

401.2783

134.403

Skewness

0.7103601

0.4852333

Kurtosis

3.409102

4.327513

Jarque-Bera

44.17158381

56.78601992

Probablity

0.0000000

0.0000000

Table 2: Linear and Non-linear Trend in Trading Volume

Country

China

USA

α

1598.644***

(51.1271)

657.3331***

(14.879)

Β1

-3.11492***

(0.4858347)

-.9638252***

(0.1360687)

Β2

0.0045864***

(0.000968)

0.000898***

(0.0002609)

R2

0.1360

0.3218

Note: ***, **&* Indicate Statistical Significance at 0.01, 0.05 & 0.1

Table 3: Unit Root Test for Return and Trading Volume

Using ADF (Augmented Dickey-Fuller)

Country

China

USA

Return

Lags(k)

3

1

τ(t)

-10.024***

-16.776***

Volume

Lags(k)

3

11

τ(p)

-4.537***

-3.639**

Note: ***, **&* Indicate Statistical Significance at 0.01, 0.05 & 0.1

Table 4: Regression Analysis

Panel A: Regression for daily Detrended Trading Volume on Stock Return

Country

China

USA

α

1201.445***

(6.68027)

489.6679***

(3.405207)

β

1471.736***

(519.8863)

454.1982*

(263.1353)

R2

0.0163

0.0059

Note: ***, **&* Indicate Statistical Significance at 0.01, 0.05 & 0.1

Panel B: Regression for daily Detrended Trading Volume on Absolute Stock Return

Country

China

USA

α

1170.022***

(10.3302)

467.6434***

(4.54751)

β

3284.28***

(803.9391)

2488.551***

(351.4061)

R2

0.0041

0.0908

Note: ***, **&* Indicate Statistical Significance at 0.01, 0.05 & 0.1

Table 5: Granger Causality test

Panel A: Vector Autoregressive (VAR) analysis for the relation between Return and Volume

Country

China

USA

α0

136.7609***

(30.75377)

61.68187***

(16.33855)

α1

.5077501***

(0.0454184)

0.5344102***

(0.0447285)

α2

.1796517***

(0.0507036)

0.1842843***

(0.0512966)

α3

.055667

(0.0511701)

0.021435

(0.0518262)

α4

.0694036

(0.0508227)

0.0181454

(0.0510635)

α5

.0672194

(0.043999)

0.1120133**

(0.0449887)

β1

6259.347***

(721.1235)

-510.2905***

(291.1278)

β2

3581.692***

(820.8147)

-314.5835

(292.3199)

β3

256.1893

(838.0796)

624.895**

(289.1426)

β4

1943.687**

(828.9514)

-195.8376

(290.3897)

β5

-261.7398

(788.6564)

259.2343

(288.4963)

F-statistic

172.7753***

80.29566***

R-Squared

0.7826

0.6167

Note: ***, **&* Indicate Statistical Significance at 0.01, 0.05 & 0.1

Panel B: Vector Autoregressive (VAR) analysis for the relation between Volume and Return

Country

China

USA

α0

0.0016017

(0.0019415)

-0.0020958

(0.0025124)

γ1

0.3580767***

(0.0455246)

-0.086496*

(0.0447669)

γ2

-0.1447791***

(0.0518181)

-0.0237893

(0.0449502)

γ3

0.1062214**

(0.0529081)

-0.0538778

(0.0444617)

γ4

-0.0125372

(0.0523318)

0.0462799

(0.0446534)

γ5

-0.0903232*

(0.049788)

-0.0146283

(0.0443623)

δ1

3.82e-06

(2.87e-06)

3.27e-06

(6.88e-06)

δ2

-5.75e-06*

(3.20e-06)

3.51e-06

(7.89e-06)

δ3

4.26e-06

(3.23e-06)

-4.57e-06

(7.97e-06)

δ4

-1.18e-06

(3.21e-06)

.0000123

(7.85e-06)

δ5

-2.08e-06

(2.78e-06)

-7.20e-06

(6.92e-06)

F-statistic

7.237849***

1.221082

R-Squared

0.1310

0.0239

Note: ***, **&* Indicate Statistical Significance at 0.01, 0.05 & 0.1

Table 6: EGARCH

Penal A: Log Likelihood Model for examining the flow of Returns

Country

China

A

a

0.3020427***

(0.0421242)

-0.0534589

(0.0517453)

b

-0.97337***

(0.0098268)

-0.9810845***

(0.0078033)

ω

-16.87483***

(0.2213514)

-0.2454907***

(0.0838834)

λ

-0.0287747

(0.0244246)

-0.0949074***

(0.0265003)

ζ

0.1091441***

(0.0326517)

0.2159128***

(0.0337635)

β

-0.9243425***

(0.0232108)

0.9706771***

(0.0093792)

Log Likelihood

1442.047

1530.4

Note: ***, **&* Indicate Statistical Significance at 0.01, 0.05 & 0.1

Penal B: Log Likelihood Model for examining the Flow of Information to explain the Volatility of Returns

Country

China

USA

a

0.2762467***

(0.0474453)

-0.053403

(0.0518765)

b

-0.951115***

(0.017186)

-0.9811416***

(0.0078237)

ω

-17.32391***

(0.1006725)

-0.2454756***

(0.0839928)

λ

-0.0371052*

(0.0190413)

-0.0947716***

(0.0264937)

ζ

0.1089469***

(0.0238444)

0.2159574***

(0.03378)

β

-0.9845236***

(0.008301)

0.9706796***

(0.0093894)

x

-5.99e-06**

(2.78e-06)

-7.95e-08

(3.15e-06)

Log Likelihood

1452.588

1530.4

Note: ***, **&* Indicate Statistical Significance at 0.01, 0.05 & 0.1

Need help with your literature review?

Our qualified researchers are here to help. Click on the button below to find out more:

Literature Review Service

Related Content

In addition to the example literature review above we also have a range of free study materials to help you with your own dissertation: