Case Study For Stock Market
Case Study For Stock Market
Case Study For Stock Market
Bedanta Bora
Anindita Adhikary
Sikkim Manipal University
(bedanta.b@smit.smu.edu.in)
DOI: 10.26573/2021.15.1.4 (anindita.a@smit.smu.edu.in)
Volume 15, Number 1
January 2021, pp. 47-58
This paper examines volatility of Indian Stock Market returns using GARCH
models that capture the volatility clustering and leverage effect. The analysed
data used in the study are daily closing prices of Nifty index during 2005 to
2019. GARCH (1,1), EGARCH (1,1) and TGARCH (1,1) models are employed
after confirming unit root test, volatility clustering and ARCH effect.
Asymmetric GARCH models reveal a presence of leverage effect and also
confirm the effect of conditional volatility. Findings exhibit that the coefficient
has a likely indication both in EGARCH (negative, significant) and TGARCH
(positive, significant) models. EGARCH (1,1) model fits better to capture the
asymmetric volatility.
Keywords: Nifty, Asymmetric Volatility, GARCH Models, Volatility
Clustering and Leverage Effect
1. Introduction
Stock markets experience volatility that estimates the uncertainty of a security. It
replicates the array to which the price of a security rises or declines. If the prices of a
security change hastily and unpredictably in a given time span, it is referred to elevated
volatility. If the prices of a security vary gradually, it is referred to low volatility.
Financial markets are habitually anxious to the extent of asset returns which is
estimated as standard deviation (Poon, 2005).
Volatility is of quite significance to investors involved in the stock markets and it
portrays dispersion from a likely value. Considerable fluctuations in the share market
returns result in major unfavourable effects on investors. Fluctuations may also impact
consumption pattern, business investment, business cycle and macro-economic
variables (Daly, 2011). The rising stock market can be interpreted as a rise in consumer
spending which is directly associated with wealth effect. Rising wealth has a positive
impact on consumer spending as it strengthens consumers’ confidence and willingness
to spend more. Conversely, declining stock market weakens the consumers’
confidence leading to a fall in the consumer spending (Ludvigson and Steindel, 1999;
Poterba, 2000). An increase in stock market volatility contributes to an increase in
threats of equity investments, which leads to shift in business investments to less risky
assets. In other words, volatility leads to a rise in the cost of funds to businesses (Zuliu,
1995). The stock market plays a vital role in macroeconomic growth and in business
48 AIMS International Journal of Management 15(1)
phases. The key theme is that higher volatility results in higher unpredictability about
future economic situation. Higher uncertainty, in turn, leads to lesser expenditure and
investment spending and this downfall in aggregate demand cause an economic
deceleration. (Raunig and Scharler, 2010).
Arise in stock market volatility leads to a considerable fluctuation in share prices,
which was evident from 1929 to 1939, in the period of America's Great Depression
(Schwert, 1990). In October 1929, the price of shares declined wiping out billions of
dollars of wealth indicating a Great Depression. Over the subsequent years,
consumer spending and investment dropped, industrial output declined, workers
lost their jobs, and thousands of banks failed.
The volatility of a market tends to be greater when a market is in a downward trend
and volatility tends to be lower in an upward trend. This pragmatic experience is
termed as asymmetric volatility. The explanation of asymmetric volatility may be
attributed to factors such as leverage effect, distress selling, serial correlation etc
(Wu.G, 2001). A decline in the share price (negative return) boosts financial leverage
making the share riskier and increases its volatility (Pindyck, 1984). The occurrence
of such instability is visible during the collapse of stock market when a greater
downturn in share price is accompanied by a rise in volatility. The fluctuation in share
prices can be observed in investors’ anticipation of volatility and their hesitation to
purchase a share or eagerness to sell in expectation of an unstable market.
2. Literature Review
The association of share price and its fluctuation have concerned stock market
researchers. Abundant investigations have been embarked on in modelling the
movements within the share market. Mandelbrot (1963) and Fama (1965) initiated the
assessment on returns from stock market. Stock market returns with time series
regularly show signs of volatility clustering. It refers to the observation that “large
changes tend to be followed by large changes, of either sign, and small changes tend
to be followed by small changes”. Engle (1982) termed such movement in the
sequence as Autoregressive Conditional Heteroskedasticity (ARCH). Stock market
researchers further investigated the fluctuation of rising share markets by applying
ARCH models. GARCH model was a generalized and extended version of ARCH
technique advocated by Bollerslev (1986). Both the models were a better framework
to describe the behaviour of return volatilities. GARCH (1,1) is regarded as excellent
technique to capture conditional volatility from a wide range of financial data (Matei
2009). GARCH (1,1) technique has also been successful in predicting the instability
in US share market as compared to other techniques (Akgiray, 1989).
Although, the ARCH and the GARCH techniques have been considered as better in
capturing the fluctuation of the fiscal time sequence information, they have been
unsuccessful in assessing the leverage effect where the conditional variance is likely
to react asymmetrically to affirmative and pessimistic market information. Stocks
react harshly during the market downturn, showing volatility asymmetry (Bekaert and
Wu, 2000). The emerging nations exhibit greater asymmetric volatility at the time of
financial instability (Jayasuriya and Rossiter, 2008). Several expansions of GARCH
techniques have been put forward to apprehend the leverage effect. An exponential
GARCH (EGARCH) technique based on logarithm of the conditional volatility in the
Bora, Adhikary 49
financial time series information was applied for further assessing the stock market
volatility (Nelson 1991). Thereafter, a number of amendments were put forward.
Amongst them, is the establishment of Threshold ARCH (TGARCH) model for
studying the effect of affirmative and pessimistic information (Zakoian 1994). Further
research works reflect that the EGARCH and TGARCH techniques attained better
results in anticipating the stock market information (Chen and Lian, 2005).
A few research initiatives have been carried out on fluctuations in share market
returns in emerging nations. The volatility was examined in the stock market in India
and investigated the existence of fluctuation during 1990s (Roy and Karmakar, 1995).
A study of Indian market has also revealed the presence of asymmetric volatility
(Goudarzi and Ramanarayanan, 2011). Unexpected shocks cause asymmetric
volatility and positive news lead to favourable results than adverse news (Entorf and
Darmstadt, 2007). The existence of asymmetry was revealed in the returns of Indian
market through the application of TGARCH(1,1) model as well. The research work to
predict the fluctuations in Indian stock market was undertaken by comparing the
results of unconditional and conditional volatility techniques (Ajay, 2005). GARCH
technique was applied in assessing the co-movement and volatility transmission in
Indian and US share market (Kumar and Mukhopadhyay, 2002). The effect of
introducing index options and futures on fluctuations in stock index was examined by
the application of GARCH technique (Shenbagaraman, 2003). The volatility in the
daily return of NSE was assessed using GARCH model where this model proved to
predict the fluctuations better compared to other techniques (Banerjee and Sarkar,
2006). The volatility was examined by considering the daily information from stock
indices of Middle East namely the Egyptian CMA index and the Israeli TASE-100
index. The study applied the GARCH class of model and revealed that the coefficient
of EGARCH model depicted a negative and significant value for both indices. The
study further indicated the presence of the leverage effect (Floros, 2008). Time-
varying volatility forecasting exercise was carried out for the National Stock
Exchange. Both symmetric and asymmetric GARCH models advocated that the
volatility of the National Stock Exchange returns was persistent and asymmetric in
nature, which was the outcome of the crisis (Tripathy and Gil-Alana, 2015). The
volatility of the Indian stock market was examined considering the time series data of
daily closing prices of S&P CNX Nifty Index from 2003 to 2012. The investigation
was carried out applying both symmetric and asymmetric GARCH models. The study
confirmed the presence of asymmetric effect as depicted by EGARCH (1,1) and
TGARCH (1,1) models and further proved that unfavourable news has considerable
effect on volatility (Banumathy and Azhagaiah, 2015). The study intended to assess
the volatility of Indian equity market from 2003 to 2015 by the application of the
GARCH family models. The study confirmed the presence of volatility that revealed
the clustering and persistence of stocks. The study further proved that the good and
bad information responded asymmetrically. The unfavourable news reported more
volatility than the unfavourable news of the same magnitude for the selected stocks
(Amudha and Muthukamu, 2018). The volatility and leverage effect of four emerging
share markets namely Brazil, India, Indonesia and Pakistan were examined. The
research work considered the returns of 5 years from 2014 to 2018. The investigation
was carried out by the use of GARCH family model and the leverage effect was
examined by EGARCH model. The result provided the evidence of presence of
50 AIMS International Journal of Management 15(1)
volatility clustering and leverage effect where the favourable news affected the stock
market than unfavourable news (Kumar and Biswal, 2019).
Most of the studies attempted on modelling volatility have been applied on stock
market data from developed countries. Even though, a few research studies have been
focused on Indian market, the study for long period of 15 years using ARCH and
GARCH methods is scanty. As such, the authors are motivated to make an effort to
estimate volatility clustering and leverage effect in India stock market.
4. Research Methodology
4.1 Data Source
The current research work is based on S&P CNX Nifty index value acquired from the
website of National Stock Exchange (NSE). The data embodied in the study are Nifty
index’s daily closing prices. The data spans from April 2005 to March 2019. The year
from 2005 to 2019 presents an economy where there has been a blended experience of
global financial crisis and boom in Indian economy that affected the stock market. The
study considers closing values on everyday basis. S&P CNX Nifty index is considered
as a representative sample of share value in India as it is believed to reflect the
performance of the entire stock market.
test of stationarity is performed by ADF test (Dickey and Fuller, 1979) and PP test
(Phillips and Perron, 1988).
The outcome of a time series that is not static can be calculated for the precise
occasion only and assessment cannot be universal. So, a series must be stationary.
Moreover, a non-static time sequence cannot give pragmatic results for prediction
purpose. As Nifty index return happens to be a time series variable, it must be static in
character otherwise movements cannot be predicted. Hence, the index returns
information used in this paper requires examination to confirm the existence of unit
root by using the Augmented Dickey Fuller test.
where rt is the return of the asset at time t, μ is the average return and ε t is the residual
return and where ω>0, α ≥ 0, β ≥ 0. The degree of factor α and β denote the variability
in time series. If (α + β) is close to unity, it states that a distress at time t will carry on
for future period.
52 AIMS International Journal of Management 15(1)
5. Empirical Results
Table 1 shows descriptive analysis of Nifty index returns during the study period. As
reflected in the Table, mean returns of Nifty are 0.000216 and a standard deviation of
0.000347. The returns mean is positive which portrays that there is a rise in the share
price during that period. Skewness of the distributions of Nifty returns is negative.
Negative skewness connotes a higher chance of generating returns that is greater than
mean. Kurtosis of the distributions of Nifty index returns is leptokurtic (>3) depicting
fat tail in the return sequence with a normal distribution. It is further confirmed by
Jarque-Bera test that is significant at 1% level. Thus, the null hypothesis of normality
is rejected.
Figure 1 portrays volatility clustering of S&P CNX Nifty return from April 2005 to
March 2019. It can be noted that the stage of low volatility has a tendency to be
followed by the stage of low volatility for a longer period and the stage of elevated
volatility is followed by the stage of elevated volatility for a longer period. This
specifies that the volatility is clustering and the Nifty index return series change about
the constant mean but the variance is changing with time.
0.1
0.05
-0.05
-0.1
Close Price
The test for stationarity is carried out by ADF test and PP test. Table 2 presents the
result of unit root test of index return series using ADF and PP tests. The p values of
ADF and PP are less than 0.05 which specify that the index return series during the
research period are stationary. ADF test and PP test reject the null hypothesis that there
is a presence of a unit root in the index return series in all three levels of significance.
Hence, the result of ADF test and PP tests statistics validate that the series is stationary.
The estimated result of ARCH-LM test is shown in Table 3. The ARCH-LM test is
used to assess the existence of arch effect in the residuals of the return series. Since p
>0.05, the null hypothesis of ‘no arch effect’ is accepted. This concludes that the test
statistics do not support for any further arch effect remaining in the residuals of the
models.
Table 4 represents the estimated outcome of GARCH (1,1) model. It reflects that
the factor of GARCH is noteworthy. In the mean equation, constant value is positive
and significant as p<0.05. The coefficients on both the lagged squared residual
(ARCH) and lagged conditional variance (GARCH) in variance equation are highly
significant. In the conditional variance equation, the β coefficient is noticeably high as
compared to α coefficient. This infers that the share market has a memory extended to
more than one era. At the same time, the volatility is more responsive to its lagged
values compared to the recent shocks in the market reflecting that the volatility is
persistent. The sum of the coefficients (α and β) is 0.9942, which is close to unity
signifying that volatility is quite recurring in nature. Thus, the GARCH model proved
that conditional variance is repeated in the Indian stock market. The AIC and SC
criteria of the model are -7.650418 and -7.642357 respectively.
LOG(GARCH)=C(2) + C(3)*ABS(RESID(-1)/@SQRT(GARCH(-1)))+
C(4)*RESID(-1)/@SQRT(GARCH(-1))+C(5)*LOG(GARCH(-1))
Variance Coefficient Std. Error z-Statistic Prob.
Mean Equation
C(µ) 0.000219 7.8e-5 2.760954 0.0062
Variance Equation
C(2)(ω) -0.335728 0.030573 -10.98363 0.0000
C(3)(α) 0.186781 0.011218 16.66170 0.0000
C(4)(β) -0.079592 0.007012 -11.36654 0.0000
C(5) (γ) 0.981511 0.002398 410.6656 0.0000
Akaike info. Criterion -7.667898 Schwarz Criterion -7.657812
Bora, Adhikary 55
The leverage effect is measured through TGARCH (1, 1) model and the outcome of
the model is shown in Table 6. The C(4)*(RESID(-1)^2*(RESID(-1)<0) is positive
and statistically significant. This supports the statement that leverage effect exists in
the model and unfavourable information has greater effect on conditional variance than
the favourable information. The AIC and SC criteria of the model are -7.665572 and -
7.655483 respectively.
The best fitted model in the GARCH family of models is chosen based on the lowest
AIC and SIC value. The AIC and SIC values (-7.667898 and -7.657812) of EGARCH
model is the lowest. Therefore EGARCH (1,1) model appears to be a satisfactory
explanation of volatility.
6. Conclusion
This research work examines the volatility of S&P CNX Nifty index returns. The daily
closing prices of the index are gathered for fifteen years from 2005 to 2019 and
examined applying GARCH methods. The methods captured the volatility clustering
and leverage effect during the study period. The test of unit root, volatility clustering
and ARCH effect are confirmed and established. The Nifty index returns are further
analysed by GARCH (1,1), EGARCH (1,1) and TGARCH (1,1) models. In GARCH
(1,1) model, α coefficient and β coefficient are highly significant and the β coefficient
is noticeably high compared to α coefficient which concludes that the share market has
a memory extended to more than one period. Further, the sum of the coefficient of α
and β is 0.9942, which reflects that the volatility is quite recurring in nature. EGARCH
(1,1) model reveals the existence of leverage effect which specifies any change in price
responds asymmetrically to the favourable and adverse information in the market. The
leverage effect measured through TGARCH (1,1) model is positive and statistically
significant concluding the existence of leverage effect throughout the study period.
Finally, to select the best fitted model amongst the GARCH models, AIC and SIC are
applied and EGARCH (1,1) model is proved to be the finest model to apprehend the
share market volatility. The overall conclusion of this research work supports the
results of earlier studies conducted by Floros (2008), Banumathy & Azhagaiah (2015)
and Kumar and Biswal (2019).
56 AIMS International Journal of Management 15(1)
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