The purpose of this study is to investigate the relationship between stock price and volume in India. To capture this, time series stock market data were culled from April 2000 to March 2015, covering 16 financial years. The study has to underscore the importance of the stock price in influencing stock volume and vice-versa in India. The model was implemented in EViews ver 7. Inputs to the software are the variable data, like: closing price and volume of Bombay Stock Exchange.
Table 1: Descriptive Statistics of Daily Returns
Basis Closing Price Volume
Observation Period July 2003-April 2015 July 2003-April 2015
Number of Observation 142 142
Mean 15110.25 20354.23
Median 16386.77 17300
Maximum 29220.12 61400
Minimum 3792.61 8400
Std. Dev. 6248.481 10570.97
Skewness 0.038689 1.573785
Kurtosis 2.464727 5.605065
Jarque-Bera 1.730648 98.77024
Source: Calculated from the data taken from BSE official Website for the selected period.
Note:
a. Skewness is a measure of asymmetry of the distribution of the time series around its mean.
b. Kurtosis measures the peakedness or flatness of the distribution of the series.
c. Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution.
d. ARCH-LM test statistics is the Lagrange Multiplier test statistic for the presence of ARCH. Under the null hypothesis of no heteroskedasticity, it is distributed as a chi- square.
Descriptive statistics on Bambay Stock Exchange’s Price and Volume are summarised in the Table 1above. The skewness statistics for price and Volume are found to be different from zero indicating that the return distribution is not symmetric, but for the later it is more asymmetry in comparison to former. Furthermore, the relatively large excess kurtosis suggests that the underlying data are leptokurtic or heavily tailed, and sharply peaked
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about the mean when compared with the normal distribution, which is more in case of Volume as compared to Price. The Jarque-Bera statistics calculated to test the null hypothesis of normality rejects the normality assumption. The results confirm the well-known fact that, Closing Prices are not normally distributed but are leptokurtic and skewed. The results of the current study are similar to that of Ou and Wang (2011), where they remarked that, their facts suggest a highly competitive and volatile market. To sum up, the analysis indicates that, the Closing Price and Volume of the Indian Stock Market are non-normal, and exhibits volatility.
Figure 1: The trend of Stock Price and Volume for BSE in India
Source: Based on the data taken from BSE India website for the selected period.
Descriptive investigation of the plot of Closing Price and Volume of Bombay Stock Exchange (figure 1) reveals that, the Closing Price continuously fluctuated around the mean value that was close to zero. In comparison to Closing Price, Volume volatility is more; but initially the former volatility was less as depicted from figures. From the time series graph of the returns for both Closing Price and Volume, it is analysed that high volatility are followed by high volatility and like low volatility are followed by low volatility. That means time series have important time varying variances. Additionally, it is appropriate to put conditional variance into the function to clarify the impact of risk on the returns.
The presence of unit root in a time series is tested with the help of Augmented Dickey-Fuller Test. It tests for a unit root in the univariate representation of time series. For a return series yt, the ADF test consists of a regression of the first difference of the series against the series lagged t times as follows:
Where, α is a constant, β the coefficient on a time trend and the lag order of the autoregressive process. Imposing the constraints α = 0 and β = 0 corresponds to modelling a random walk and using the constraint β = 0 corresponds to modelling a random walk with a
0 10000 20000 30000 40000 50000 60000 70000
01/07/2003 01/07/2004 01/07/2005 01/07/2006 01/07/2007 01/07/2008 01/07/2009 01/07/2010 01/07/2011 01/07/2012 01/07/2013 01/07/2014
Closing Price Volume
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drift. The null hypothesis is H0: δ = 0 and H1: δ < 1. The acceptance of null hypothesis implies non-stationarity.
Table 2: Unit Root Testing of Daily Returns
Closing Price Volume
t-Statistic Prob. t-Statistic Prob.
Augmented Dickey-Fuller
(ADF) test statistic -11.6054 0.0001 -10.8376 0.0001 Test critical values: 1% level -3.47748 -3.47783
5% level -2.88212 -2.88227
10% level -2.57782 -2.57791
Source: Calculated from the data taken from BSE website for the selected period.
Augmented Dickey-Fuller (ADF) test to check the unit root problem of data, where the result tends to reject the null hypothesis as the test result gives less than 5% probability and it is also tested in the other way that test statistics are more than the Critical value at their first difference. So finally all data are stationary for all the variables of Bombay Stock exchange.
The preceding analysis helps to make the point that the series, Closing Price and Volume are non-stationary which means that each series individually contains unit root. But, the questions is, either these series share a common trend, so that the gap will not grow without bound. Therefore, I have further conducted an alternative analysis by using the co- integration techniques. The notion of co-integration among variables has introduced a new flexibility into the modelling of economic time series. As defined by Engle and Granger (1987), two variables are cointegrated of order (1, 1), if each variable individually is stationary in first differences (integrated of order 1), but linear combination of the variables is stationary in level (integrated of order 0). More generally, a set of variables is co-integrated of order (d, b) if each variable individually is integrated of order d, but at least one linear combination exists which is of order (d-b). Most of the researchers focuses on the case d =1 and b = 1 and I have done the same here.
Table 3: Result of Co-integration Test
No. of Cointegrating
equation (s)
Trace Statistics Max-Eigen Value Statistics Trace
Statistic
0.05 Critical
Value Prob.
Max- Eigen Statistic
0.05 Critical
Value Prob.
None 6.934991 15.49471 0.5852 6.142552 14.2646 0.595
At most 1 0.792439 3.841466 0.3734 0.792439 3.841466 0.3734 Sources: Calculated from the data taken from BSE website for the selected period.
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Like Trace Statistic and Max-Eigen Statistic of co integration test to check the long run relationship for both stock price and Volume give the result at 4 lags for both the statistics respectively, which conclude the existence of no long run relationship.
In order to investigate the causal directions associated with the change of Closing Price and Volume, the Granger causality test is applied. The Granger Causality test is used here.
Table 4: Granger Causality Test
Null Hypothesis: F-Statistic Prob.
Volume does not Granger Cause Closing Price 1.3064 0.2711 Closing Price does not Granger Cause Volume 3.6588 0.0074 Sources: Calculated from the data taken from BSE website for the selected period.
The findings lend a support of unidirectional relationship from Closing price to volume. The casual direction for higher lag values has been investigated but, there is no causal relationship from Volume to Closing Price for higher lag values that is why the test results are not reported for higher lag values. Akaike Information Criteria (AIC) has been used to detect the number of lags, which is resulted to 4 lags for the minimum AIC value of 36.465, because the time series (April 2000 to March 2015) follows a repeating pattern 4 years period.