The purpose of this chapter is to discuss on the empirical results obtained from the tests that have been conducted in order to study the implication of futures trading introduction on FBM KLCI volatility. Section 4.0 is basically about the brief introduction on this chapter. As for section 4.1 is discuss on the analysis of descriptive statistics for the FBM KLCI returns. Section 4.2 provides the information and discussion on the result obtained from the unit root tests such as Augmented Dickey-Fuller test. In section 4.3, the result on whether there is existence of ARCH or GARCH effects in the model. Section 4.4 provides the analysis of GARCH model for three types of periods; whole-, pre- and post-period. Last but not least, section 4.5 which is the chapter remark for this chapter.
4.1 Analysis of descriptive statistics
Statistics Period
Whole Pre Post
Mean -0.020586 -0.005466 -0.024636
Maximum 20.81737 9.712200 20.81737
Minimum -24.15339 -6.651376 -24.15339
Standard Deviation 1.901861 1.505852 2.002639
Skewness 0.519950 0.281344 0.542328
Kurtosis 33.29854 8.441159 34.16520
Jacque-Bera (JB) 85589.59 624.6391 70218.71
Probability 0.0000 0.0000 0.0000
No of observations 2235 501 1733
Table 2: Summary of descriptive statistics
Table 2 shows the descriptive statistics of the daily returns for the FBM KLCI Index. There are 2235 daily time series observations. The results from this table show that during the whole period of FBM KLCI which includes pre- and post-introduction of futures trading, FBM KLCI Index has a mean return of -0.020586 percent with a standard deviation of 1.901861 percent. During the pre-futures period, which is from 3 December 1993 till 14 December 1995, the daily mean return is -0.005466 percent and standard deviation of 1.505852 percent. As for post-futures period which is from 15 December 1995 till 31 December 2002, the daily mean return is -0.024636 percent and standard deviation of 2.002639 percent.
From these results show that, post-futures period has the lowest daily mean return but has the highest standard deviation followed by whole period. Such results could be due to the economic crisis happened in year 1997(which is a part of whole period and post introduction period). Pre-futures period has the highest daily mean return and lowest standard deviation among the three periods. This implied that the introduction of futures into the FBM KLCI has made the underlying market to be more volatile as well as in whole period. While, during pre-introduction of futures period, the market is less volatile. Hence, this can be concluded that higher volatility not necessary offers the possibility of higher rate of returns as higher volatility poses higher risk to the investors.
The daily return series for all periods show positive skewness indicating that the distribution has long right tail. The excess values for kurtosis that is greater than 3 indicate fat tails characteristics of the asset returns distribution. The probability of Jarque-Bera (JB) test of normality for all the periods are greater than 0.05 at 5% significance level. Therefore, there is presence of volatility clustering in all return series. These results are similar to those of Pok and Poshakwale (2004) and Ryoo and Smith (2004).
4.2 Unit root test
Return series at level based on SIC, (max lag = 26)
FBM KLCI
ADF-test statistic -20.91163 [0]*
Critical values
1% level -3.433086
5% level -2.862635
10% level -2.567399
Table 3: ADF unit root test for FBM KLCI index return series based on SIC at level
Notes: [.] refers to the probability of ADF test statistic
Augmented Dickey-Fuller (ADF) test is conducted for this study in order to check whether the FBM KLCI time series returns are stationary or not stationary. This test is important to enable this study to examine the dynamic of volatility of return over time (Islam, 2013). Based on the result from Table 3 shows that ADF test statistic is -20.91163 in which is smaller than the critical value of -2.862635 at 5% significant level for all the FBM KLCI returns. Therefore, ADF test statistic rejected the null hypothesis of the existence of unit root in the return series. Thus, this can be concluded that there is stationarity in the return series of FBM KLCI index.
4.3 Testing on ARCH effects
No of lag R2 LM Test statistics (n*R2) ?? 2(.) Pro. ?? 2(.) F-Statistic Akaike
1 0.004124 9.1965 3.841 0.0024 4.616843 8.659842
2 0.005649 12.5916 5.991 0.0018 4.220929 8.659205
3 0.023025 51.2997 7.815 0.0000 13.12739 8.642471
4 0.023678 52.7309 9.488 0.0000 10.89538 8.642494
5 0.026118 58.1387 11.070 0.0000 11.93962 8.641092
Table 4: Test for ARCH effects
Notes: The LM version of the test statistic is defined as n*R2 (where n is the number of observations and R2 is the coefficient of correlation, (.) refer to order of lag, critical value of ?? 2 at 5% significant level
No of lag AC PAC Q-Stat Probability
1 -0.031 -0.031 2.2086 0.137
2 0.031 0.030 4.3233 0.115
3 -0.013 -0.011 4.6814 0.197
4 0.114 0.113 33.916 0.000
5 0.099 0.107 55.650 0.000
6 0.012 0.013 55.970 0.000
7 -0.007 -0.010 56.081 0.000
8 -0.016 -0.029 56.677 0.000
9 0.052 0.028 62.742 0.000
10 0.007 -0.002 62.846 0.000
Table 5: Ljung-Box Q-statistics test results
Before applying the GARCH model, it is important to determine the existence of ARCH effects in the time series data. This is important to prevent any unnecessary mistakes happened during the application of GARCH model as this model needs iterative processes in order to get desire results. Besides, according to Islam (2013), although linear structural model assumes that variance of the errors is constant over time but this notion is not valid for stock prices that exhibit time-varying heteroskedasticity.
To test the ARCH effects in this study time series data, Breusch-Gofrey Serial Correlation LM test is used to check whether the there is any ARCH effect in the series. Before that, first, AR (1) model for the returns series of each individual index need to be considered as:
r_t= ??_0+ ??_1 r_(t-1)+ u_t (5)
And then, run the linear regression on it to obtain the residuals, u_t. After that, a regression of squared OLS residuals (u_t^2) obtained from equation (5) is run on n lags of squared residuals to test for ARCH of order n (n is represents as the number of autoregressive terms in the model).
In testing the existence of ARCH, from the Table 4, the LM statistics for all the lags are greater than the critical value from the ?? 2 (q) distributions at 5% significant level (where q indicates number of lag). Therefore, the null hypothesis of no ARCH effects in equation (5) is rejected up to lag 5 in this index as LM test statistics seemed to be highly significant for all circumstances. This finding is supported by Islam (2013) who also found alike outcomes. This then further implies that the variances of the return series are non-constant over time and thus GARCH model is suitable to be used in this study.
The same conclusion also can be achieved for the Ljung-Box Q-statistics which is used to test autocorrelation in the residuals. The results show in Table 5 indicate that P-values after the 4th lag are all zero to four places and therefore led to reject the null hypothesis of no ARCH effects at 5% significant level. Autocorrelation coefficients (AC) and partial autocorrelation coefficients (PAC) are all non-zero. Hence, there is enough evidence to believe that there is presence of serial correlation in the residuals. These results obtained are similar to those of Xie and Huang (2014).
4.4 GARCH analysis
Variable Whole Period
Coefficient Std. Error Z-Stat P-Value
?? 0.049069 0.010948 4.482040 0.0000
?? 0.149267 0.011009 13.55921 0.0000
?? 0.843678 0.009542 88.41351 0.0000
?? -0.006659 0.009634 -0.691266 0.4894
?? + ?? 0.992945
Table 6: GARCH (1,1) with dummy estimates of whole period
Notes: ?? represents intercept, ?? represents ARCH coefficient, ?? represents GARCH coefficient, ?? represents dummy coefficient
After have seen the existence of ARCH effects in return series data, GARCH (1,1) model is used in this study to examine the volatility effects in whole period, pre-introduction futures period and post introduction futures period. Since this study does not put emphasize on asymmetric effects, therefore GARCH (1,1) model alone is enough and appropriate for this study and GARCH (1,1) conditional variance model in Chapter 3, equation (4) is employed.
In order to measure the effect of the introduction of futures on FBM KLCI index in term of whole period, dummy variable is introduced into the conditional variance equation. This dummy variable takes the values zero and one to represent pre- and post-futures periods respectively. The results as shown in Table 6 imply that the dummy variable estimated coefficient is negative and statistically insignificant at 5% significance level. These indicate that futures trading do not have any stabilisation or destabilisation implication on the underlying market volatility. This finding is also supported by Pok and Poshakwale (2004) who also found that futures trading have insignificant effects on Kuala Lumpur Stock Exchange.
?? and ?? estimated coefficients in Table 6 show that both of these coefficients are positive and statistically significant at 5% significance level and are within the parametric restrictions. The coefficient of ??, 014926 is much smaller as compared to coefficient of ??, 0.843678. This indicates that old news has more persistent impact on the underlying stock market volatility due to the onset of the futures trading. Besides, sum of ?? and ?? equals to 0.992945 is approaching to unity which implies that volatility shocks in the underlying market are persistent and volatility clustering will have longer periods.
Variable Pre-Introduction Period
Coefficient Std. Error Z-Stat P-Value
?? 0.035029 0.019597 1.787416 0.0739
?? 0.094239 0.017534 5.374659 0.0000
?? 0.890448 0.020456 43.53090 0.0000
?? + ?? 0.984687
Table 7: GARCH (1,1) estimates of pre-introduction period
Notes: ?? represents intercept, ?? represents ARCH coefficient, ?? represents GARCH coefficient
Variable Post Introduction Period
Coefficient Std. Error Z-Stat P-Value
?? 0.044175 0.006206 7.118064 0.0000
?? 0.165212 0.013146 12.56777 0.0000
?? 0.832300 0.010602 78.50147 0.0000
?? + ?? 0.997512
Table 8: GARCH (1,1) estimates of post introduction period
Notes: ?? represents intercept, ?? represents ARCH coefficient, ?? represents GARCH coefficient
Table 7 and Table 8 show the results for the GARCH (1,1) models for the pre-introduction period and post introduction period of futures trading on FBM KLCI index. ?? and ?? coefficients in both of the periods are in positive numbers and are statistically significant at 5% significance level.
Based on the tables, ?? coefficient in pre-introduction period has increased from 0.094239 to 0.165212 in post introduction period. This suggests that news is impounded into prices more quickly after the introduction of the futures trading on the stock index. While, volatility persistent which is refers to ?? coefficient, shows that the value of this coefficient has decreased from 0.890448 to 0.832300 in post introduction period. This is implies that old news has less persistent impact in prices changes upon the introduction of futures trading as current news is disseminate more quickly than old news.
In measuring the persistence of volatility shocks, ?? + ?? in both periods showed sum of unity close to zero. However, in comparing the both periods, ?? + ?? in pre-introduction period has increased from 0.984687 to 0.997512 in post introduction period (as shown in Table 7 and Table 8). This increment suggests that there is high degree of volatility persistence upon the onset of futures on stock index. Since the ?? coefficient has increased in post introduction period while ?? coefficient shows reduction of value, the information is disseminate into stock prices more quickly and therefore, volatility of underlying market is increased. Furthermore, in the presence of futures trading, old news have less impact in determining the volatility of the stock market as current news is circulating into prices more quickly than old news. These results also supported by Ryoo and Smith (2004) which have almost similar findings as this study.
4.6 Chapter remark
In conclusion, in testing the existence of the stationarity in the time series data, Augmented Dickey-Fuller is employed. Besides, Breusch-Gofrey Serial Correlation LM test and Ljung-Box Q-statistics also employed in this study to test the presence of ARCH effects in the residuals before doing the GARCH model. The basic descriptive statistics on three periods in this study are analyse based mean, standard deviation, kurtosis, skewness and Jacque-Bera in respective period. Lastly, is the analysis of GARCH (1,1) model. The inclusion of dummy variable does not has any significant effect on the underlying market volatility. Besides, the current news is disseminating into the stock prices faster than old news. In other words, old news only acts a small role in impacting the underlying market volatility. Since the news information circulating more quickly, this has therefore increase the volatility. However, at the same time, this has decreased the persistence of the volatility.