INVESTMENT OPPORTUNITIES IN BSE-IT sector: A study based on asymmetric GARCH modeling

Jatin Trivedi

Associate Professor at Amity University



This paper empirically tests volatility clustering, leverage effects and the impact of news on financial market of BSE-IT sector. Bombay stock exchange, well known as BSE is one of the most attractive emerging stock market in Asia. The exchange represents over 15 individual sector categories including BSE-IT. This paper represents volatility shocks and volatility clustering from 1999:02-2015:02. The study covers the journey from the base index to sectorial growth and also forecast the opportunity for the investment besides the sector. This study covers 4010 daily observations from year Feb 99’ to Feb 15’. The paper follows application of Generalized Autoregressive Conditional Heteroscadasticity class models to capture stylized facts and asymmetric effect. The main findings are forefold. First, BSE-IT index have strong empirical evidence of volatility clustering and abnormal shocks. Second, GARCH class models fitted well on the financial series and the impact of good and bad news on the market computed in degree of magnitudes. Third, abnormal volatility contains high and low shocks with different magnitudes. The stylized fact indicates that BSE-IT sector impacts more factorable during the negative side moments than the positive side. The complete GJR test results available including the summary of statistics. The series volatility sketches and empirical results described in details. GJR-GARCH class model fitted well to estimate impact of news on BSE-IT sector index.

Keywords: Financial econometrics, GARCH, Financial markets, Stock market, Volatility

JEL Code: G110, G170, C580

*Asia Index Private Limited (AIPL) has cancelled S&P BSE MID CAP, S&P BSE SMALL CAP, S&P BSE HEALTHCARE, S&P BSE IT and S&P BSE FMCG indices and replaced them with S&P BSE MidCap, S&P BSE SmallCap, S&P BSE Healthcare, S&P BSE Information Technology and S&P BSE Fast Moving Consumer Goods, respectively from April 16, 2015. We failed to get data for the month Feb, 2015. Hence the paper includes data from Feb 99’ to Jan 15’ that covers 3989 observations.


Stock exchange provides platform to buy and sell shares of the listed companies. Bombay stock exchange, well known as BSE is one of the largest stock exchange in Asia. Over 15 individual specified sector indexes listed under this exchange. BSE-IT represents one of them and represents India’s listed information technology companies. Any attempt to buy or sell the stock is called trade. An over million trades executes at immediate start of exchange. This creates volatility in stock price and that excites investors to invest. When the index price moves ups and down swiftly is called volatility. Emerging financial markets represent wobbly stock price moments compared to developed stock markets. Hence it creates elevated risk and return opportunity term. Indisputably, it excites investors, researchers and academicians to explore the possible predictions to estimate the stock index moments. Equity market investments can never possible without highest degree of risks and, this is not question investors worry about. It is the returns for what the investors look for research. The shortest investment time and maximum return, this term identified as ideal for equity market investors. If some research can be in position to suggest the estimate about stock index moments, which can help investors to decide about profit booking or further investment or even can give idea about hold. This is recognized by academicians, statisticians and econometric experts. More explored concepts came into light i.e leverage effect, stylized facts. Black (1976) introduce concept of leverage effect in financial markets. It suggests that loose have higher influence on future volatility than do the gains. Engle (1982) introduced ARCH model to estimate the volatility of stock market. ARCH has been an innovative model in the history of financial market exploration but limited to its long lag lengths term. Bollerslev (1986) introduced GARCH model and that overcome the limitation of ARCH model that further improvised by Nelson (1991).

GARCH stands for Generalized Autoregressive Conditional Heteroskedesticity, this is most used econometric model to estimate stock market volatility all over the world. But the area, financial markets are so huge, requires upgrading in model methodology, new innovative models to explore more. A research perused accurately with data management and empirical analysis, always valued high. Such research work has changed the face of research work in financial markets and given a new extent to investor class. Exponential GARCH or EGARCH by Nelson (1991) an extended version of GARCH (1, 1) model, GJR GARCH by Glosten, Jagannathan and Renkle (1993) alternate of EGARCH and extended version of GARCH (1, 1) has changed the entire concept of financial market explorations. The model used widely to explore asymmetry and leverage effect in financial markets. Emenike and Friday (2012) have analyzed the Nigerian stock market and found the volatility asymmetry, there was no evidence of leverage effect. Asymmetry volatility suggests that volatility in market is higher at downswings than the upswings. Leverage effect suggests that losses have greater influence than do gains.

Empirical outcomes

This paper fundamentally objects empirical outcomes of BSE – IT sector index. These covers empirical analysis of stylize facts, asymmetric effect and impact of good and bad news on BSE-IT sector. We failed to get data for the final and last month i.e. Feb, 2015 and thus the total number of observations is not 4010. We now deal with 3989 daily observations which represent time line from first day transactions (base price) Feb 1999 to last day transactions of Jan 2015. The statistical evaluation is based on GARCH family models. GARCH, Generalized Autoregressive Conditional Heteroscadasticity is most used and famous econometric model for the financial market evaluation. To obtain this paper objective, we employ EGARCH (Exponential GARCH) (Nelson 1991) and GJR- GARCH (Glosten, Jagannathan and Renkle (1993). Both of these econometric GARCH type models are capable to test asymmetric effect, EGARCH model is limited to provide test statistics for good and bad impact of news on the series. Hence we use GJR-GARCH to obtain test statistics of impact of news on volatility of BSE – IT financial series. GARCH family model run process is followed by conversion of original data into log difference and tested by ADF Test (Augmented Dickey Fuller test).

Augmented Dickey Fuller test (ADF test) is augmented version of Dickey Fuller test and used to determine if variable is stationary. The financial time series may face autocorrelation problem and thus it can be augmented by adding various lagged dependable variables. We mention here the ADF version formula.

In the above formulation the correct value of m represents number of lags. The aim of augmented dickey fuller test is to maximize the amount of information. During the test of BSE – IT financial series we confirmed ARCH effect and no unit root problem at level of 10%, 5% and 1%. We consider the series at degree level of 5%. The complete result of ADF test series provided along with original series (see figure1).

Generalized Autoregressive Conditional Heteroskedesticity model, well known as GARCH, first introduced by Engle (1982) and further extended by Bollerslev (1986) and Nelson (1991). The GARCH (1, 1) model is not capable to explore the stylized facts in financial series. The equity market investment recognized as one of the top priority investment option in the coming days by mastermind statisticians. Hence, the concept of econometric and advance econometric methods came into existence to estimate, forecast and predict the volatility level of financial market. The GARCH model progressed and improvised. Nelson (1991) introduced Exponential GARCH or known as EGARCH model which captures stylized facts in financial series. The stylized fact provides idea about leverage effect or called more detailed analysis of financial series. Glosten L R, Jagannathan R. and Runkle D.E (1993) introduced GJR GARCH model, that explores stylized facts and in addition also provide impact of good and bad news on financial market of BSE – IT.

Asymmetric GARCH models provide statistics about leverage effects with asset prices. It means that positive shocks have lesser effect on the conditional variance than the negative shocks. The same is incorporated by Gloston, Jagannathan and Runkle by using dummy variable. Hereunder we provide the GJR GARCH specimen model.

ht =  + 1ut-12 + 1 ht-1 +  It-1 ut-12

In the above model I represent dummy variables. This takes value of 1 when shock is less than 0 or called negative and 0 otherwise. The alternative of GJR GARCH model is Exponential GARCH or EGARCH by Nelson (1991). This model has number of more advantages than the GARCH model. It provides non-negative constraints do not need to be imposed and the asymmetric are also allowed for using this model.

Log ht =  + 1 log ht-1 + 1[Vt-1 + {|Vt-1| - E|Vt-1|} ]

The above model takes a long form and adds an additional term for leverage effect. We have provided the complete statistic results for EGARCH and GJR GARCH. Both the model includes 1 AR effect. We also explored GJR GARCH model for detailed study and analysis. The table 1 shows summary of test statistics for BSE-IT by using 3989 daily observations. The stationary data presentation also shows leverage effect. The basic statistics of BSE-IT suggests that the value for mean and median are about to

Fig1. BSE-IT financial series (original and stationary series) from year 02:1999:01-2015

Source: Using BSE-IT historical prices from Feb 99 to Jan 15 (OBS) 3989

Zero, the minimum value (0.222984) and maximum value 0.1749 represents large difference. The degree of risk 0.0247 and we can see negative skewness (0.3510) and higher degree of kurtosis 6.95627. This represents impact of leverage effect and creates long tail. This statistics suggests that the certain degree of rise in BSE-IT index does not impact similar degree of rise in the stock value.

The Fig1 consist of two graphical presentations which represents the moment of original financial series of BSE-IT and the stationary data. We can clearly identify the volatile moment of index from base index of 1000 to the approaching level of 13000. The same identified by long sketches in following graph. We find long positive shock in BSE-IT in year 2000-2001 where index level approached to over 8500 i.e 8.5 times rise in journey of two years (1999 to 2001). The further index followed matured moments, the global financial crisis also visible during year 2008-2009. We note here that after 2009, the index of BSE-IT is seems to move further positively and measurable negative minor shocks.

Table1. Summary Statistics, using the observations 1999-02-01 - 201-01-31

for the variable d_l_BSEIT (3989 valid observations)

Mean / Median / Minimum / Maximum
0.000605167 / 0.000705827 / -0.222984 / 0.174907
Std. Dev. / C.V. / Skewness / Ex. kurtosis
0.0247047 / 40.8229 / -0.351073 / 6.95627
5% Perc. / 95% Perc. / IQ range / Missing obs.
-0.0367550 / 0.0388779 / 0.0213703 / 1

Source: Using BSE-IT historical prices from Feb 99 to Jan 15 (OBS) 3989

This index sector BSE-IT provides large platform to invest for the long term perspective as the statistics suggest the green prospectus for long term investment. We confirmed significance of BSE-IT financial series at level of 5% and now we proceed to formulate the EGARCH and GJR GARCH models (see table2). The conditional mean are significant in both estimated models, both the models captures the asymmetric effect. The volatility of BSE-IT is very explosive redolent of an integrated process. EGARCH (1, 1) and GJR GARCH (1, 1) confirm the presence of leverage effect.

Table2 suggests mean and equation variance statistics for EGARCH and GJR GARCH. We found that the financial data series of BSE-IT fitted well in EGARCH and GJR GARCH model. Both the model commonly follows ARCH term(1), GARCH term (1), Mean regressors (null), AR lag value (1) and follows normal distribution with constant. EGARCH (1, 1) test statistics confirms existence of leverage effects in BSE-IT financial series. That also ensures that volatility of BSE-IT series is asymmetric. In other words bad news impacts greater than the good news on volatility.

Tabel-2 Model: EGARCH (1, 1) [Nelson] and GJR GARCH (1, 1) using Normal distributions_ BSEIT financial series.

EGARCH(1,1)*3989 / GJR (1,1)*3988
Stats / Coefficients / p-Value / Coefficients / p-Value
const / 0.00114444 / 0.0001*** / 0.00121382 / 8.92e-05 ***
AR1 / 0.0548225 / 0.0092 *** / 0.0620803 / 0.0019***
omega / -0.448158 / 0.0031 *** / 0.0000159366 / 0.0020 ***
alpha / 0.245589 / 4.43e-05 *** / 0.156331 / 1.16e-05 ***
gamma / -0.0535668 / 0.0011 *** / 0.151775 / 0.0010 ***
beta / 0.965966 / 0.0000 *** / 0.821036 / 1.58e-121 ***
Llik: 9906.66928 AIC: -19801.33856 / Llik: 9887.39068 AIC: -19762.78137
BIC: -19763.59229 HQC: -19787.95645 / BIC: -19725.03510 HQC: -19749.39925

Source: Using BSE-IT historical prices from Feb 99 to Jan 15 (OBS) 3989

Finally we conclude that BSE-IT financial series confirms strong and abnormal volatility shocks and presence of leverage effect in the specimen time-series. EGARCH (1, 1) model exploration would be available on request; we provide you alternate model exploration. GJR GARCH model can be explored as follows;

Rt= 0 . 0 0 1 2 1 3 8 2 + 0 . 0 6 2 0 8 0 3 + et

ht = 1 . 59e-05 + 0.1 5 6 3 3 1ut-12 + 0 . 1 5 1 7 7 5ht-1 + 0.8 2 1 0 3 6It-1 ut-12

From the above estimated GJR GARCH model, it is clear that good news has impact of 0.156331 magnitude and the bad news has impact of 0.156331-0.821036= -0.66471 magnitude. GJR GARCH investigates that negative news curve is more than four time stronger than positive news curve on BSE-IT index. The abnormal volatility shocks are comparatively more in number of total shocks compared with global financial crisis. The BSE IT index has suffered much more and most major shocks at time of 2000 to 2004. The index recovery found stronger and stable at long prospect.


The volatility of BSE-IT stock returns have been investigated and modeled using two non-linear asymmetric models i.e EGARCH and GJR GARCH and news impact curve. We found that BSE-IT series returns have leverage effects exhibits other stylized facts such as volatility clustering and leptokurtosis effect. Further the investment criterion in BSE-IT provides risk at degree of 0.02470 and the approximate possibility of good news curve 0.0156331 where as negative news curve -0.66471. Nevertheless the emerging financial markets always consists higher degree of risks and returns for long term investment planning. There are many positive shocks found which promoted the index level more than 8 times in less than 3 years. It represents the potential and generates interests for the green prospect.


[1] Bollerslev, T., (1986), “Generalized autoregressive conditional heteroskedasticity”, Journal Economic., 31: pp. 307-327.

[2] Engle, R. (1982), “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of UK Inflation”, Econometrica, Vol. 50, 987-1008.

[3] Elsheikh M.A., S. Zakaria., (2011) “Modeling stock market volatility using GARCH models evidence from Sudan”, International journal of business and social science, vol.2 no.23.

[4] Dickey, D.A., W.A. Fuller, (1979), “Distribution of the estimators for autoregressive time series with a unit root”, J. Am. Stat. Assoc., 74: 427-431

[5] Engle, R. F. and Rangel, J. G. (2004), “The Spline GARCH Model for Unconditional Volatility and Its Global Macro-Economic Causes”, Review of Financial Studies, Vol. 21, No. 3, 1187-1222

[6] J.Trivedi, (2014), “Modeling volatility and financial market behavior using symmetric and asymmetric models : The case study of Athex stock exchange”,Journal of Business Quantitative Economics and Applied Management Research, ISSN : 2349-5677

[7] J.Trivedi, R.Birau (2013), “Modeling and estimating long term volatility in RPGU stock markets”, Recent advances in energy, environment and financial planning, ISBN: 978-960-474-400-8, PP 272-280, 2014

[8] D. deAlmeida, L. K.Hotta, (2014), “The leverage effect and the asymmetric of the error distributions in GARCH based models: The case of Brazilian market series” Pesquisa Operactional.vol.34no.2Rio de Janeiromay-aug2014.

[9] H.Goudarzi, C.S.Ramanarayanan, (2011), “Modeling asymmetric volatility in Indian stock market”, International Journal of Business and Management, Vol-6, No-3, pp.221-231

[10] Nelson D.B (1991), “Conditional Heteroskedasticity in Asset returns: A new approach. Econometrica, 59(2), pp 347-370.