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8/7/2019 Stock market volatility in india - case of select scripts
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STOCK MARKET VOLATILITY IN INDIA:
A CASE OF SELECT SCRIPTS
Section I: Introduction
In general terms, volatility may be described as a phenomenon, which characterizes
changeableness of a variable under consideration. Volatility is associated with
unpredictability and uncertainty. In literature on stock market, the term is synonymous
with risk, and hence high volatility is thought of as a symptom of market disruption
whereby securities are not being priced fairly and the capital market not functioning as
well as it should be. As a concept volatility is simple and intuitive. It measures the
variability or dispersion about a central tendency. However, there are some subtleties that
make volatility challenging to analyse and implement. Since volatility is a standard
measure of financial vulnerability, it plays a key role in assessing the risk/return trade-
offs. Policy makers rely on market estimates of volatility as a barometer of the
vulnerability of the financial markets. The existence of excessive volatility or noise
also undermines the usefulness of stock prices as a signal about the true intrinsic value
of a firm, a concept that is core to the paradigm of international efficiency of the markets.
Considerable research effort has already gone into modeling timevarying conditional
heteroskedastic asset returns. It is important because if both returns and volatility can be
forecasted, then it is possible to construct dynamic asset allocation models that use time
dependent meanvariance optimization over each period. Financial econometrics
suggests the use of non- linear time series structures to model the attitude of investors
toward risk and expected return. In this context, Bera and Higgins (1993) remarked, a
major contribution of the ARCH literature is the finding that apparent changes in the
volatility of the economic time series may be predictable, and result from a specific type
of non-linear dependence rather than exogenous structural changes in variables. When
the variance is not constant, it is more likely that there are more outliers than expected
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from the normal distribution, i.e., when a process is heteroskedastic it will follow heavy
tailed or outlierprone probability distribution. According to Mc Nees (1979), the
inherent uncertainty or randomness associated with different forecast periods seem to
vary over time, and large and small errors tend to cluster together.
Although there is a plethora of research concerning stock market volatility, most of the
studies have been done for stock market of the developed country as a whole, making use
of aggregate information data. There are varying few studies, which have gone into the
volatility issues at the level of specific industries or the companies in an industry. More
specifically, this paper is an attempt towards explaining the stock market volatility at the
individual script level and at the aggregate indices level. In the light of the above, the
objective of this paper is to explain how volatility changes means whether it shows the
same trend or it varies across the selected sectors.
The rest of the paper is as follows: Review of literature is explained in section II, Section
III, explains the data and methodology of the study. Section IV, presents the empirical
results.Finially, conclusions are presented in section V.
Section II: Review of Literature
Many traditional asset-pricing models (e.g Sharpe 1964; Merton, 1973) postulate a
positive relationship between a stock portfolio s expected return and the condition
variance as a proxy for risk. More recent theoretical works (Whitelaw 2000, Bekaert and
Wu 2000; Wu 2001) consistently assert that stock market volatility should be negatively
correlated with stock returns.
Earlier studies for instance French et.al. (1987) found a positive and significant
relationship and studies such as Baillie and DeGennaro (1990) Theodossiou and Lee
(1995) reported a positive but insignificant relationship between stock market volatility
and stock returns. Consistent with the asymmetric volatility argument, many researchers
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(Nelson 1991, Glosten et.al 1993, Bekaert and Wu 2000, Wu 2001; Brandt and Kang
2003) recently report negative and often significant relationship between the two.
Researchers have empirically demonstrated (e.g. Harvay 2001, Li et.al 2003) that the
relationship between return and volatility depends on the specification of the conditional
volatility. In particular, using a parametric GARCH-M model, Li, et.al (2003) finds that a
positive but statistically insignificant relationship exists for all the 12 major developed
market. By contrast, using a flexible semi parametric GARCH-M model, they document
that a negative relationship prevails in most cases and is significant in 6 out of 12
markets.
Malkiel and Xu (1999) used a disaggregate approach to study the behaviour of stock
market volatility. While the volatility for the stock market as a whole has been
remarkably stable over time, the volatility of individual stocks appears to have increased.
There are some possible reasons to believe that volatility in the stock market as a whole
should have increased over recent decades. Improvments in the speed and availability of
information, the growth in the proportion of trading done by institutional investors and
new trading techniques all may have increased the responsiveness of markets to changes
in the sentiment and to the arrival of new information. The facts, however, at least with
respect to the market as a whole, do not suggest that the volatility has increased. They
have not looked at the market portfolio but rather at individual stocks and industry
average. By looking at the disaggregated volatility of stock prices, they reached a
different conclusion that volatility in the stock market has infact increased considerably
during the past quarter century. Most of the time series data used in the study are
constructed from the 1997 version of CRSP (Center for Research in Security Prices) tape.
Data measuring in the daily return are available from January 1,1963 to December 31,
1997 and monthly returns are available from January 1926 to December 1997. In the
analysis, both exchange traded stocks (New York Stock Exchange (NYSE) and American
Stock Exchange (AMSE) and NASDAQ files are used.
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In order to study the robustness of their findings of increasing idiosyncratic volatility.
They approached the issue from both a correlation structure and diversification
perspective. Idiosyncratic volatility is precisely the kind of volatility that is uncorrelated
across stocks and thus is completely washed out in a well-diversified index portfolio,
According to Capital Asset Pricing Model; such an increasing in the idiosyncratic
volatility should not command an added risk premium on the market. Thus, while it is
possible to argue that the volatility of individual stock has increased, as long as their
systematic risk remain unchanged, there should be no consequence for asset pricing, at
least according to Capital Asset Pricing Model holds, an increase in the idiosyncratic
volatility will have an important effect on the number of the securities one must hold in a
portfolio to achieve full diversification. The general conclusion is that while market as a
whole has been no more volatile in the recent decades, the idiosyncratic volatility of the
individual stocks has exhibited an upward trend.
Yu (2002) evaluates the performance of nine alternative models for predicting stock price
volatility. The data set he used is the New Zealand Stock Market Exchange (NZSE40)
capital index, which covers 40 largest and most liquid stocks listed and quoted on the
New Zealand Stock Market Exchange, weighted by the market capitalization without
dividends reinvested. The sample consists of 4741 daily returns over the period from 1
January 1980 to 31 December 1998.The competing models contain both simple models
such as the random walk and smoothing models and complex model such as ARCH type
models and a stochastic volatility model. Four different measures are used to evaluate the
forecasting accuracy. The main results are (i) the stochastic model provides the best
performance among the candidates;(ii) ARCH type models can perform well or badly
depending on form chosen the performance of the GARCH (3,2) model, the best model
within ARCH family, is sensitive to the choice of assessment measures; and(iii) the
regression and exponentially weighted moving average models do not perform well
according to any assessment measure, in contrast to the results found in various markets.
Li,et.al (2003) examined the relationship between expected stock returns and volatility in
the twelve largest international stock markets during January 1980 December 2001.
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Consistent with the most previous studies they found the estimated relationship between
return and volatility sensitive to the way volatilities are examined. When parametric
EGARCH-M models are estimated ten out of twelve markets have positive but
statistically insignificant relationship. On the other hand, using a flexible semi parametric
specification of conditional variance, they found that negative relationship between return
and volatility prevails in most of the markets. Moreover, the negative relationships are
significant in six markets based on the whole sample period and seven markets after the
1987 international stock market crash. They have used weekly data from November
1987 to December 2001 for the 12 largest stock market in the world in terms of market
capitalization.
Batra (2004) examined the time variation in volatility in the Indian stock market during
1979-2003.He has used the asymmetric GARCH methodology augmented by structural
changes. The paper identifies sudden shifts in the stock price volatility and nature of
events that cause these shifts in volatility. He undertook an analysis of the stock market
cycles in India to see if bull and bear phases of the market have exhibited greater
volatility in recent times. The empirical analysis in the paper reveals that the period
around the BOP crisis and subsequent initiation of the economic reforms in India is the
most volatile period in the stock market. The time period he has taken for Sensex is
1979:04-2003:03 and for IFGC is 1988:01-2001:12.The data have been taken from SEBI,
RBI and BSE has been used. As a conclusion one may therefore say that liberalization of
the stock market or the FII entry in particular does not have any direct implication in the
stock return volatility. Level of volatility does not show much change pre and post
liberalization. Significants developments in the market indicators-turn over or market
capitalization does not lead to volatility shifts in the stock return.
Volatility estimation is important for several reasons and for different people in the
market. Pricing of securities is supposed to be dependent on volatility of each market.
Raju and Ghosh (2004) used the International Organization of Securities Commission
(IOSCO) clarification to categories countries into emerging and developed market. There
are six countries from developed capital market and twelve from emerging markets
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including India. Bloomberg data base is used by them as the data source. For India two
indices BSE Sensex and S&P CNX Nifty.Amongest emerging markets except India and
China, all other countries exhibited low returns. India with long history and China with
short history, both provides as high a return as the US and the UK market could provide
but the volatilities in both countries is higher. The third and fourth order moments exhibit
large asymmetry in some of the developing markets. Comparatively, India market shows
less of skewness and kurtosis. Indian markets have started becoming information ally
more efficient. Contrary to the popular perception in the recent past, volatility has not
gone up. Intraday volatility is also very much under control and has come down
compared to past years.
Shin (2005) examined the relationship between return and risk in a number of emerging
stock markets. The main contribution of this study is to present more reliable evidence on
the relationship between stock market volatility and returns in emerging stock market by
exploiting a recent advance in non parametric modeling of conditional variance. This
study employed both a parametric and semi parametric GARCH model for the purpose of
estimation and inference. The data for this study covers 14 relatively well-established
emerging markets which have stock price index series available from the International
Finance Corporation (IFC) emerging market data base. Regionally speaking there are six
Latin American emerging markets (Argentina, Brazil, Chile, Colombia, Mexico and
Venezuela), six Asian emerging markets (India, Korea, Malaysia, Philippins, Taiwan and
Thailand) and two European emerging markets (Turkey and Greece). The sample period
is from January 1989 to May 2003, after and before the 1987 international stock market
crash. This study examines the impact of the 1987-1998 global emerging stock market
crisis on GARCH parameters in the line with Choudhary (1996), who studies the impact
of the 1987 stock market crash using monthly data between January 1976 and August
1994.
The findings of this study also suggest fundamental differences between emerging
markets and developed markets. Investors in emerging markets are often compensated for
bearing relevant local market risk, while investors in developed markets are often
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penalized by bearing irrelevant local market risk. Another factor could be related to the
most commonly known characteristics of emerging stock market-that their stock market
volatility is notoriously high compared to developed markets.
Section II: Methodology
The assumption of the Classical linear regression model that variance of the errors
is constant is known as homoscedasticity. If the variance of the errors is not constant, this
is known as heteroscedasticity. It is unlikely that in the context of stock return data that
the variance of the errors will be constant over time. Hence, it makes sense to consider a
model that does not assume that the variance is constant, and which describes how the
variance of errors evolves. The prime motivation behind the development of conditional
volatility models emanated from the fact that the then existing linear time series models
were inappropriate, in the sense that they provided very poor forecast intervals and it was
contended that like conditional mean, variance (volatility) could as well evolve over time.
One particular non-linear model in widespread usage in finance is the ARCH model.
Engle (1982) introduced the ARCH process, which allows the conditional
variance to change over time. In ARCH model, the variance is modelled as a linear
combination of squared past errors of specified lag. Under the ARCH model, the
autocorrelation in volatilities modelled by allowing conditional variance of the error
terms, to depend on the immediately previous value of the squared error.
t t ~ N ( 0 , ht ) (1)
ht = var ( t | t-1 ) = 0 + 1 t-12 , 0 > 0 , 1 0
The ARCH models provide a framework of analysis and development of time series
models of volatility. However, ARCH models themselves have a number of difficulties.
i) It is very difficult to decide the number of lags (q) of the squared residual in the model.
One approach to this problem would be the use of likelihood ratio tests. ii) The number of
lags of the squared error that are required to capture all of the dependence in the
conditional variance might be varying large. This would result in a large conditional
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variance model that was not parsimonious. Engle (1982) circumvented this problem by
specifying an arbitrary linearly declining lag length on an ARCH (4). iii) Other things
being equal, the more parameters there are in the conditional variance equation, the more
likely it is that one or more of them will have negative estimated values. Non-negativity
constraints might be violated.
To overcome these limitations, GARCH model was introduced. In this model
artificial constraints have been imposed to make the model satisfy the non-negativity
condition. The Generalised Autoregressive Conditional Heteroscedasticity model was
developed independently by Bollerslev (1986). GARCH models explain variance by two
distributed lags, one on past squared residuals to capture high frequency effects or news
about volatility from the previous period measured as lag of the squared residual from
mean equation, and second on lagged values of variance itself, to capture long term
influences.
t t ~ N ( 0 , t2 ) ( 2 )
2 2
0
1 1
var( )q p
t t t i t i i t i
i i
h = =
= = + + , 0 > 0 , i 0 , i 0
In the GARCH (1,1) model, the variance expected at any given data is a combination of a
long run variance and the variance expected for the last period, adjusted to take into
account the size of the last period s observed shock. In the GARCH model estimates for
financial asset returns data, the sum of coefficients on the lagged squared error and
lagged conditional variance is vary close to unity. This implies that shocks to the
conditional variance will be highly persistent and the presence of quite long memory but
being less than unity it is still mean reverting. In other words, although volatility takes a
long time, it ultimately returns to the mean level of volatility. It implies that current
We have consistently chosen the lag length 5 for all the indices on the assumption that the changes in
return variation will influence upto 5 days (i.e, one week). The choice of this lag length is somewhat
arbitrary.
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information has no effect on long run forecast. A large sum of these coefficients will
imply that a large positive or a large negative return will lead future forecasts of the
variance to be high for a protracted period. The variance intercept term 0 is very small,
while the coefficient on the lagged conditional variance GARCH is larger at 0.9. When
the sum of the coefficient is equal to one, the unconditional variance does not exist and
the asymptotic properties of the maximum likelihood estimates are not clear.
Ever since the GARCH model was developed, a large number of its extensions and
variants have been proposed. Many of the extensions to the GARCH model have been
suggested as a consequence of the perceived problems with standard GARCH (p,q)
models. First, the estimated model may violate the non-negativity conditions. The only
way to avoid this for sure would be to place artificial constraints on the model
coefficients, in order to force them to be non-negative. Second, GARCH models cannot
account for leverage effects, although they can account for volatility clustering and
leptokurtosis in a series. Finally, the model does not allow for any direct feedback
between the conditional variance and conditional mean.
It is possible that conditional variance, a proxy for risk, can affect stock market return.
Engle, Linien and Robins (1987) introduced the ARCH-in-Means (ARCH-M)methodology, which allows conditional standard errors (or variances) to affect return.
Bollerslev, Engle and Wooldridge (1988) used GARCH (1,1)M formulation to employ
the Capital Asset Pricing Model for a market portfolio, consisting of stocks, bonds and
Treasury-bills and reported a significant trade off among these asset categories. Assets
with high-expected risk must offer a high rate of return to induce investors to hold them.
In this case, increases in conditional variance should be associated with increases in the
conditional mean. Since GARCH models are now considerably more popular than
ARCH, it is more common to estimate a GARCH-M model. An example of GARCH-M
model is given by the specification
Yt = + ht-11/2 + t ( 3 )
ht = 0 + 1 t-12 + i h t-1
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If is positive and statistically significant, then increased risk, given by an increase in the
conditional variance, leads to a rise in the mean return. Thus can be interpreted, as a
risk premium in some empirical applications, the conditional variance term, h t-1, appears
directly in the conditional mean equation, rather than in the square root formh t-1,.
Merton (1973) derives an equation that relates the expected return on market linearly
related to the conditional variance of the market. Most studies used in finance support
that investors should be rewarded for taking additional risk by obtaining a higher return.
Section III: Empirical Analysis
This sub section reports the results of the empirical application. This study based on the
daily closing values of five broad based indices drawn from the Bombay Stock Exchange,
Mumbai. The indices chosen are: BSE Sensitive Index, BSE 200 Index, Nifty, CNX
Nifty Junior and S&P CNX Nifty. Since the primary objective of this paper is to
understand the volatility process at the aggregate and disaggregate scrips / company
level, the study has identified twenty individual companies belonging to various sectors
namely, Electrical, Machinery, Mining, Non-Metalic and Power Plants sector. These
companies have been chosen such that they fairly represent the different sectors of the
economy. Four companies from each sector have been choosen based on the performance
of the ARCH, ARCH-M and GARCH model. The list of twenty companies chosen for
the study is given in appendix towards the end of the paper. The data is drawn from the
Center for Monitoring Indian Economy (CMIE) PROWESS database. The data are daily
closing prices and adjusted for dividends. The study period spans over the period January
1, 1990 to November 30, 2004, thus involving around 3414 number of data points, which
provide rich data set for the analysis.
The objective of this paper is to examine the daily price volatility of the stock return. The context and
output differs if we use weekly and monthly data.
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For analysis purpose the data are converted into continuously compounded rate of
return ( Rt ) by taking the first difference of the log prices i.e. R t = ln ( Pt / Pt-1 ).The
summary statistics of the aggregate indices and individual companies are reported in table
1. It is strikingly clear from the table that the stock returns do not follow normal
distribution. Jaque-Bera and LM tests reject the normality in returns for all the companies
in the eight sectors. The results of the aggregate indices show that BSE Sensex follows
the risk-return parity perfectly, i.e, low return with low risk. Though CNX Nifty has
highest return, its standard deviation is not found to be the highest one. Hence, it asserts
that investors may earn highest return in CNX-Nifty without showing high risk. It
contradicts the general principle of risk-return frame-work. In the Power Plants sector,
Ahmdabad electricity has the lowest mean but highest standard deviation which
contradicts the theory. The entire individual sector shows the presence of ARCH effect.
The time varying volatility models call for a preliminary check to assess the
presence of ARCH effect in stock return series. To carry out this, we perform Lagrange
Multiplier (LM) test on the residuals to test for the presence of ARCH effect within a
maximum lag of 5. The results from ARCH test presented along with the summary
statistics in the table 1 show that the null of no ARCH effect is rejected in all cases at 1
per cent level of significance. This outcome confirms the presence of ARCH effects and
hence the stock returns exhibit time-varying heteroskedasticity. Hence this study
proceeds further to employ time-varying models of ARCH and GARCH, to explain the
return variability over time.
Coming to the ARCH models, four different specifications viz., ARCH (1),
ARCH (2), ARCH (3) and ARCH (4) are considered. We do not go beyond the order four
because a typical ARCH models provides a parsimonious representation of higher order
ARCH models. The order for the lag q determines the length of time for which a shock
persists in conditioning the variance of the subsequent errors. The selection of lag length
is based on investors perception about the volatility existence and hence, investors choose
different values of q, depending on how fast they think volatility is changing. The effect
of a return shock i periods ago ( i q ) on current volatility is measured by the parameters
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i in equation ( 1 ). To test the impact of past errors in conditioning current error, this
study employs ARCH (1), ARCH (2), ARCH (3) and ARCH (4).These tests are carried
on aggregate market indices as well as on individual companies. For the aggregate
indices, the relevant results are reported in tables 2, 3, 4, 5 and 6.
Excepting in CNX Nifty Junior the remaining aggregate indices namely, BSE
Sensex, BSE 200 Index, Nifty, S&P CNX Nifty, satisfy the shock persistence
characteristics in ARCH model. Normally, the distant past news has less effect on current
volatility. If the coefficient is statistically significant it ensures that the volatility is
changing. For all the aggregate indices, ARCH coefficients are statistically significant.
The highest ARCH coefficient (1=0.3956) is for BSE 200 and The lowest ARCH
coefficient (3=0.1718) is for CNX Nifty Junior. For the aggregate indices, as the results
show ARCH in Mean model, the risk factor is positive but not statistically significant.
The estimates of ARCH and ARCH in Mean model for all the individual sectors
such as: electrical, machinery, mining, non-metalic and power plants sector are reported
in table 7 to 26.Among the four companies in this sector, the Blue Star Ltd has the
highest ARCH coefficient (1=0.4112) and ARCHM coefficient. (1=0.4166). Exide
Industries has the lowest ARCH (4= -0.0215) and ARCH-M (
4= -0.0062) coefficient.
Among the four companies in this sector Thermax Ltd has the highest ARCH coefficient
1=0.3170) and Cummious India Ltd has the lowest ARCH coefficient (4=0.0323) and
ARCH-M coefficient. FAG Bearings India Ltd has the highest ARCH-M coefficient.
Among the four companies in this sector Avaya Global Connect Ltd has the highest
ARCH coefficient (1=0.3926) and lowest ARCH coefficient found in ONGC
4=0.0220). Among the four companies in this sector Gujarat Ambuja Cements Ltd has
the highest and lowest ARCH coefficient (1=0.3227) and (4=0.0084) respectively.
Avaya Global Connect Ltd has the highest ARCH-M coefficient and Insilco Ltd has the
lowest ARCH-M coefficient.The estimates of Power Plants sector are reported in table 44
to 47. Among the four companies in this sector Ahmadabad Electricity Co Ltd has the
highest and the lowest ARCH coefficient (1=0.4732) and (4=0.0491) respectively.
Ahmadabad Electricity Co Ltd has the highest and the lowest ARCH-M coefficient.
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Normally, the distant past news has less effect on current volatility. Investors
choose different values of lag length, depending on how fast they think volatility is
changing. That is why the highest ARCH coefficient is found for BSE 200 in the first lag
and the lowest ARCH coefficient is for CNX Nifty Junior in the third lag. As the lag
increases the news has less effect on current volatility. For all the individual sectors the
same trend in results is reflected. The highest ARCH coefficient is found in the first lag
and the lowest ARCH coefficient is for the third or fourth lag. If the ARCH coefficients
are significant, it ensures that volatility is changing. Most of the ARCH coefficients are
significant for twenty companies in the five sector.
Assets with high-expected risk must offer a high rate of return to induce investors
to hold them. Investors should be rewarded for taking additional risk by obtaining a
higher return. If the risk factor () is positive and statistically significant, then increased
risk, given by an increase in conditional variance, leads to a rise in mean return. For the
aggregate indices, as the results show, is positive but not statistically significant. The
highest ARCH in Mean coefficient is found in the first lag and the lowest ARCH in Mean
coefficient is for the third or fourth lag. is positive and statistically significant for all the
four companies in the Electrical sector, Machinery sector, Ahmadabad Electricity Ltd and
Reliance Energy Ltd in power plant sector.
Though ARCH / ARCH-M models provide better description of asset returns,
GARCH and its family may provide additional conformation on return variability. We
now turn to the GARCH models. More specifically the following four models are
considered in this study GARCH (1, 1), GARCH (1,2), GARCH (2,1) and GARCH (2,2).
The models as specified in equation ( 3 ) and estimated for both aggregate indices as
well as individual companies.
The parameter estimates (table 27 to 31) show that higher order GARCH model
(2,2) generates coefficient values that lead to non-stationary conditional variance for all
the aggregate indices, which is not justified empirically. For BSE 100, Sensex and BSE
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200, GARCH (1,2) and GARCH (2,1) are significant. In case of Nifty, S&P CNX 500,
CNX Nifty Junior, GARCH (1,2) and (2,1) are insignificant. GARCH (1,1) is significant
for all the aggregate indices.
The parameter estimates of the GARCH model of the individual sector are
reported in table (32 to 51). Among the four companies the coefficient + is exactly
equal to one for the Blue Star Ltd. GARCH (1,1), GARCH (2,1), GARCH (2,2) shows
persistence characteristics for Whirlpool India Ltd and Birla Corporation Ltd. For Exide
Industries GARCH (1,1) and GARCH (2,1) shows the persistence characteristics.
Two GARCH model, GARCH (1,1) and GARCH (2,1) is highly persistent for
three companies in machinery sector such as Kirloskar Oil Engines Ltd, Cummious India
Ltd and FAG Bearings India Ltd, three companies in the mining sector such as Aban
Loyd Chiles Offshore Ltd, Avaya Global Connect Ltd and Insilco Ltd.Three GARCH
model such as GARCH (1,1), GARCH(2,1) and GARCH (2,2) shows the persistence
characteristics for Thermax Ltd and ONGC.GARCH (1,2) and GARCH (2,2) models are
non convergent, the lagged values of variance and lagged values of error term does not
satisfying non-negativity condition.
Section IV: Conclusion
1. The Lagrange Multiplier test confirms the presence of ARCH effect in the aggregate
indices and hence the aggregate returns exhibit time-varying heteroscedasticity. All the
selected indices except CNX Nifty Junior satisfy the shock persistence characteristics.
2. Normally, the distant past news has less effect on current volatility. Investors choose
different values of lag length, depending on how fast they think volatility is changing.
That is why the highest ARCH coefficient is found for BSE 200 in the first lag and the
lowest ARCH coefficient is for CNX Nifty Junior in the third lag. As the lag increases
the news has less effect on current volatility. For all the individual sectors the same trend
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in results is reflected. If the ARCH coefficients are significant, it ensures that volatility is
changing. Most of the ARCH coefficients are significant for twenty companies in the five
sectors.
3. How ever with respect to aggregate indices the results show, is positive but not
statistically significant. The risk factor () is positive and statistically significant for all
the four companies in the Electrical sector, Machinery sector and Ahmadabad Electricity
Ltd and Reliance Energy Ltd in power plant sector. The risk factor is positive but not
statistically significant for Mining sector, Solar International Ltd, Moser Bear India Ltd,
Hitachi Home and Life Solution Ltd, Insilco Ltd, Aban Loyd Offshores Ltd and Avaya
Global Connect Ltd. Risk factor is negative and insignificant for ONGC and Non-metalic
sector. Investors should be rewarded for taking additional risk by obtaining a higher
return. If the risk factor () is positive and statistically significant, then increased risk,
given by an increase in conditional variance, leads to a rise in mean return.
4. All the five sector mostly showing the same trend for the persistence characterstics.
GARCH (1,1) model is persistent for all the companies in the different sector and it is
exactly equal to one in Blue Star Ltd. The GARCH (1,2) is not persistent for a single
company in the seven sector. Out of the twenty company in the different sector for only
five companies such as Whirl Pool of India Ltd, Birla Corporation, Thermax Ltd, ONGC,
Gujarat Sidhee Cement Ltd GARCH (1,1), GARCH (2,1) and GARCH (2,2) shows the
persistence characteristics.
* Stock market volatility is generally a cause of concern for both policy makers as well as
investors. To curb excessive volatility, SEBI was prescribed a system of price bands. The
price bands or circuit breakers bring about a coordinated trading halt in all equity and
equity derivatives markets nation-wide. An index-based market-wide circuit breaker
system at three stages of the index movement either way at 10%, 15% and 20% has been
prescribed. The breakers are triggered by movement of either S&P CNX Nifty or Sensex,
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whichever is breached earlier. As an additional measures of safety, individual scrip-wise
price bands have been fixed below:
Daily price bands of 5 % (either way) on a set of specified securities depending on
volatility. Daily price bands of 10 % (either way) on another set of specified securities
depending on volatility. Price bands of 20% (either way) on all the remaining securities
(including debentures, warrants, preference shares etc. which are traded on CM segment
of NSE). No price bands are applicable on securities on which derivative products are
available or securities included in indices on which derivative products are available. For
auction market the price bands of 20% are applicable.
If the study period is divided into two sub-sample periods, for instance, prior to NSE inception and after
inception, this would have thrown much light on stock volatility in Indian stock market. Because of time
constraint we can take this study for future research.
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Table 1: Summary Statistics and LM Statistics for Aggregate Indices
Index MeanStandardDeviation
Skewness KurtosisJaque-Bera LM
StatisticsSensex 0.0002 0.0002 -0.218 3.558 1659.928 231.496
(0.000)Nifty 0.0004 0.0002 0.3128 9.213 11036.623 259.184
(0.000)BSE -200 0.0003 0.0012 0.0910 871.669 9307.126 88.703
(0.000)S&P CNX-500 0.0003 0.0002 -0.488 4.523 1833.1992 294.495
(0.000)CNX-Nifty Junior 0.0006 0.0003 -0.478 4.142 1396.281 260.772
(0.000)Exide Industries
Ltd0.0001 0.0011 0.1391 3.917 1823.378
130.580(0.000)
Whirlpool of IndiaLtd
-0.0006 0.0013 0.3933 2.324 769.07439.270(0.000)
Blue Star Ltd 0.0004 0.0015 -0.0663 4.051 2072.266215.012(0.000)
Birla CorporationLtd.
0.0007 0.0014 0.1550 1.595 272.53682.351(0.000)
Thermax Ltd 0.0003 0.0009 0.2126 1.946 363.42083.813(0.000)
Timken India Ltd. -0.0005 0.0013 0.5601 7.695 6925.18896.356(0.000)
FAG BearingsIndia Ltd
0.0002 0.0012 0.0763 2.533 747.53342.712(0.000)
Kirloskar OilEngines Ltd.
0.0010 0.0013 0.0703 1.475 255.781 113.313(0.000)
Cummins IndiaLtd.
0.0007 0.0007 L 0.5198 5.445 3789.007 56.565(0.000)
Aban Loyd ChilesOffshores Ltd.
0.0011H
0.0013 0.3461 2.724 921.883 84.306(0.000)
AvayaGlobalconnectLtd.
0.0007 0.0017 0.2654 3.101 1227.687 146.120(0.000)
Insilco Ltd. -0.0001L
0.0018 0.5408 4.806 2723.607 78.821(0.000)
Oil & Natural GasCorpn-Ltd
0.0002 0.0008 L 0.644 9.209 7700.433 108.002(0.000)
Dalmia Cements(Bharat) Ltd.
0.0015H 0.0014 0.2507 2.692 689.068 20.363(0.000)
Gujarat AmbujaCements Ltd.
0.0005 0.0007 L 0.0455 3.030 1180.969 161.933(0.000)
Gujarat SidheeCements Ltd.
-0.0009L
0.0034 H 0.1844 13.313 20517.801 73.288(0.000)
India CementsLtd.
0.0004 0.0012 0.1189 2.789 953.849 112.527(0.000)
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AhamadabadElectricity Ltd
-0.0001L
0.0014 H 0.2330 6.424 4982.936 190.040(0.000)
Gujarat IndustriesPower Co.Ltd
-0.0003 0.0011 0.3553 3.3015 1237.470 208.9783(0.000)
Reliance EnergyLtd
0.0002 0.0010 0.0649 14.118 2557.346 289.572(0.000)
Tata Power
Co.Ltd
0.0008H
0.0009L
-0.1066 7.490 7194.422 194.021
(0.000)
Table 2
Estimates of ARCH and ARCH in Mean Models: Aggregate Indices BSESensex
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
0.0003(1.141)
0.0003
(1.3313)
0.0002
(0.8971)
0.0003
(1.262)
-4.0582e-
04
(-0.9154)
-2.2333
(-0.4753)
-1.5157
(-0.3301)
0.0001
(0.241)
AR (1) 0.1456
(7.44)
0.1593
(7.501)
0.1381
(6.079)
0.1406
(5.846)
0.1509
(6.750)
0.1520
(6.380)
0.1465
(5.9983)
0.1278
(4.898)
0 0.0002(37.814)
0.0001
(27.064)
0.0001
(26.197)
0.0001
(18.866)
1.9911e-04
(37.902)
1.6755e-04
(27.305)
1.4095e-04
(23.417)
0.0001
(19.244)
1 0.2690(9.813)
0.2453
(9.199)
0.2017
(7.956)
0.2165
(7.343)
0.2640
(9.452)
0.2284
(8.328)
0.2351
(7.982)
0.1987
(6.716)
2 - 0.1639(6.416)
0.1338
(5.629)
0.1204
(5.146)
- 0.1517
(5.930)
0.1192
(5.087)
0.1234
(5.062)
3 - - 0.1085(5.702)
0.1099
(5.393)
- - 0.1229
(5.915)
0.1194
(5.496)
4 - - - 0.1088(4.813)
- - - 0.0979(4.189)
- - - - 0.0633(1.866)
0.0395
(1.054)
0.0511
(1.325)
0.0506
(1.236)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 3: Estimates of ARCH and ARCH in Mean Models:
Aggregate Indices BSE 200 Index
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
0.0004 0.0004 0.0004 0.0005 0.0000 0.0001 -8.9251e- 0.0003
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(1.596) (1.691) (1.583) (1.787) (0.014) (0.453) 05
(-0.206)
(0.682)
AR (1) 0.2043
(11.719)
0.2286
(13.049)
0.1846
(7.650)
0.19952
(7.868)
0.2158
(11.167)
0.2286
(11.275)
0.1932
(7.524)
0.1902
(7.013)
0 0.0001
(43.218)
0.0001
(24.706)
0.0001
(22.721)
0.0001
(18.513)
0.0001
(41.907)
0.0001
(23.055)
1.1081e-04
(21.705)
0.0001
(17.421)1 0.3956
(20.750)
0.4094
(20.453)
0.3376
(15.181)
0.34008
(14.800)
0.4023
(18.774)
0.4002
(18.117)
0.3389
(14.195)
0.3442
(13.810)
2 - 0.1789(7.819)
0.1525
(6.746)
0.1426
(6.525)
- 0.1814
(7.352)
0.1485
(16.579)
0.1381
(6.313)
3 - - 0.13349(7.969)
0.1389
(7.770)
- - 0.1418
(8.000)
0.1491
(7.730)
4 - - - 0.0455*
(2.116)
- - - 0.0490*
(2.157)
- - - - 0.0289*
(1.911)
0.0171*
(0.772)
0.0516
(1.750)
0.0340*
(1.117)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 4: Estimates of ARCH and ARCH in Mean Models:
Aggregate Indices
NiftyCoefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCH(3) ARCHM(4)
0.0004(1.421)
0.0002
(1.022)
0.0002
(0.798)
0.0002
(0.898)
-2.8002e-
04
(-0.614
0.0000
(0.2079)
0.0000
(0.1666)
0.0002
(0.469)
AR (1) 0.1507
(7.373)
0.1761
(9.530)
0.1504
(6.701)
0.1535
(6.420)
0.1442
(6.421)
0.1790
(7.937)
0.1546
(6.350)
0.1460
(5.663)
0 0.0002(84.617)
0.0001
(29.749)
0.0001
(26.046)
0.0001
(21.527)
2.0734e-04
(51.548)
0.0001
(28.954)
0.0001
(24.204)
0.0001
(21.404)
1 0.1452
(7.832)
0.16669
(7.360)
0.1464
(7.058)
0.1468
(6.666)
0.0717
(7.777)
0.1609
(7.009)
0.1529
(6.898)
0.1369
(6.481)2 - 0.2141
(9.486)
0.1885
(8.864)
0.1830
(90.074)
- 0.2128
(8.896)
0.1809
(8.881)
0.1887
(8.998)
3 - - 0.1132(6.705)
0.1263
(6.526)
- - 0.1370
(7.094)
0.1334
(6.619)
4 - - - 0.0525(2.675)
- - - 0.0489*
(2.389)
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- - - - 0.0582(1.641)
0.0033
(0.098)
0.0186*
(0.496)
0.020*
(0.506)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 5: Estimates of ARCH and ARCH in Mean Models: Aggregate IndicesS&P CNX 500
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
0.0004
(1.395)
0.0006
(2.000)
0.0008
(2.351)
0.0007
(2.004)
-1.4063e-
04(-0.277)
9.0343e-04
(1.788)
0.0005
(1.123)
0.0003
(0.582)
AR (1) 0.1654
(6.905)
0.2187
(9.860)
0.1726
(6.404)
0.1792
(6.358)
0.1695
(6.422)
0.2207
(8.471)
0.1796
(6.278)
0.1754
(5.763)
0 0.0001(36.910)
0.0001
(21.014)
0.0001
(18.514)
0.0001
(15.220)
1.8428e-04
(35.490)
1.484e-04
(19.905)
0.0001
(18.000)
0.0001
(14.971)
1 0.3011(9.739)
0.2787
(8.160)
0.2317
(7.433)
0.2247
(7.034)
0.3027
(9.451)
0.2632
(7.707)
0.2312
(7.280)
0.2285
(6.862)
2 - 0.1710(6.298)
0.1504
(5.718)
0.1353
(5.305)
- 0.1911
(6.483)
0.1485
(5.557)
0.1336
(5.149)
3 - - 0.1451(7.501)
0.1466
(7.056)
- - 0.1559
(7.416)
0.1481
(6.993)
4 - - - 0.0764(2.853)
- - - 0.0800
(2.880)
- - - - 0.0698(1.865)
-0.0318*
(-0.816)
0.0177*
(0.426)
0.0431*
(0.972)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation
i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 6: Estimates of ARCH and ARCH in Mean Models: Aggregate IndicesCNX Nifty Junior
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4
0.0008 0.0006 0.0008 7.9813e- 0.0003 1.0462e-03 0.0005 4.8893e-04
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(2.097) (1.870) (2.243) 04
(2.026)
(0.5184) (1.932) (1.015) (0.826)
AR (1) 0.1346
(5.654)
0.1970
(11.551)
0.1505
(5.404)
0.1539
(5.449)
0.1376
(5.607)
0.1930
(8.493)
0.1574
(5.425)
0.1596
(5.419)
0 0.0002
(40.972)
0.0001
(22.145)
0.0001
(17.237)
1.5431e-
04(16.330)
0.0002
(39.025)
1.8406e-04
(20.978)
0.0001
(16.435)
0.0289
(0.643)
1 0.2718(6.891)
0.2190
(6.198)
0.2059
(5.751)
0.2125
(5.598)
0.2748
(6.657)
0.2151
(6.011)
0.2119
(5.603)
1.5526e-04
(15.997)
2 - 0.3367(9.521)
0.2893
(8.272)
0.3085
(8.342)
- 0.3614
(9.590)
0.3041
(8.294)
0.2035
(5.237)
3 - - 0.1597(8.010)
0.1731
(7.712)
- - 0.1718
(7.891)
0.3086
(8.117)
4 - - - -0.0126(-0.571)
- - - 0.1781
(8.117)
- - - - 0.0502(1.351)
-0.0525
(-1.5543)
0.0202*
(0.456)
-9.4962e-03
(-0.396)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 7: Estimates of ARCH and ARCH in Mean Models: Electrical Sector - Exide
Industries Ltd.
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
-0.00018(-0.295)
-0.00013
(-0.221)
-0.00029
(-0.478)
-0.00041
(-0.669)
-0.0016
(-1.898)
-0.0018
(-2.159)
-0.0015
(-1.750)
-0.0012
(-1.398)
AR (1) 0.0160
(0.696)
0.0163
(0.607)
0.0426
(1.619)
0.0841
(3.076)
-0.0011
(-0.044)
0.0300
(1.069)
0.0704
(2.571)
0.0865
(2.885)
0 0.00071(46.095)
0.00058
(40.610)
0.00047
(27.328)
0.00040
(22.468)
0.00070
(44.276)
0.00057
(39.317)
0.00047
(2.571)
0.00040
(21.318)
1 0.3176(11.064)
0.2924
(10.722)
0.2772
(9.594)
0.2233
(7.058)
0.3054
(10.103)
0.2651
(8.958)
0.2247
(6.678)
0.2377
(6.917)
2 - 0.1546
(7.608)
0.1493
(7.328)
0.1168
(6.115)
- 0.1607
(7.486)
0.1255
(6.006)
0.1250
(5.994)
3 - - 0.1231(7.640)
0.1087
(4.990)
- - 0.1363
(7.182)
0.1159
(4.889)
4 - - - 0.1266(6.123)
- - - 0.1040
(4.602)
- - - - 0.0925(2.441)
0.0925
(2.441)
0.0763
(2.073)
0.0425
(1.175)
Note:
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Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 8: Estimates of ARCH and ARCH in Mean Models: Electrical Sector -
Whirlpool of India Ltd.
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
-0.0017(-2.373)
-0.0014
(-1.843)
-0.0017
(-2.150)
-0.0014
(-1.779)
-0.0030
(-2.832)
-0.0032
(-2.778)
-0.0032
(-2.840)
-0.0026
(-2.253)
AR (1) 0.0533
(2.322)
0.0728
(2.778)
0.0676
(2.538)
0.0678
(2.459)
0.0731
(3.033)
0.0650
(2.391)
0.0688
(2.499)
0.07004
(2.410)
0
0.0010
(43.182)
0.00098
(33.392)
0.0008
(25.297)
0.0008
(23.284)
0.0011
(41.097)
0.0009
(32.046)
0.00087
(24.812)
0.00083
(22.336)
1 0.2250(8.615)
0.2005
(7.282)
0.2040
(7.208)
0.1955
(7.128)
0.1983
(7.107)
0.1961
(7.116)
0.1893
(6.901)
0.2025
(7.039)
2 - 0.1023(4.816)
0.0851
(4.317)
0.0572
(2.970)
- 0.1015
(4.634)
0.0622
(3.127)
0.0468*
(2.630)
3 - - 0.1187(5.737)
0.0907
(4.587)
- - 0.1083
(5.273)
0.0834
(4.271)
4 - - - 0.0557(2.533)
- - - 0.0467*
(2.047)
- - - - 0.0810
(2.453)
0.0835
(2.215)
0.0822
(2.151)
0.0657
(1.638)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 9: Estimates of ARCH and ARCH in Mean Models: Electrical Sector - Blue
Star Ltd.
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
-0.00085(-1.413)
0.0003
(0.515)
0.0007
(1.282)
0.00039
(0.672)
-0.0013
(-1.644)
-0.00089
(-1.048)
-0.00063
(-0.724)
-0.0005
(-0.590)
AR (1) -0.0353
(-1.998)
-0.0650
(-2.902)
-0.0564
(-2.349)
-0.0527
(-2.026)
-0.0364
(-1.959)
-0.0834
(-3.499)
-0.0649
(-2.422)
-0.0005
(-0.590)
0 0.00087 0.0006 0.00052 0.0004 0.0008 0.00064 0.00052 0.00045
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(52.382) (29.577) (24.792) (21.518) (39.547) (28.513) (24.584) (21.047)
1 0.4112(13.014)
0.3593
(11.675)
0.3208
(10.688)
0.3236
(1.535)
0.4166
(12.137)
0.3479
(10.525)
0.3020
(9.731)
0.3124
(9.718)
2 - 0.2152(7.736)
0.1864
(7.894)
0.1710
(7.859)
- 0.2111
(7.660)
0.1758
(7.666)
0.1980
(8.414)
3 - - 0.1478(7.707)
0.1359(7.401)
- - 0.1617(7.969)
0.1343(7.426)
4 - - - 0.0786(3.857)
- - - 0.0795
(3.718)
- - - - 0.0465(1.810)
0.0756
(2.353)
0.0804
(2.156)
0.0858
(2.186)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 10: Estimates of ARCH and ARCH in Mean Models: Electrical Sector - Birla
Corporation Ltd.
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
0.0008(1.018)
0.0006
(0.746)
-0.0002
(-0.310)
-0.0000
(-0.005)
-0.0011
(-0.907)
-0.0010
(-0.804)
-0.0007
(-0.536)
-0.0013
(-0.970)
AR (1) 0.1167
(4.182)
0.089
(3.131)
0.0972
(3.351)
0.1040
(3.614)
0.1163
(4.255)
0.0999
(3.247)
0.0905
(2.961)
0.1010
(3.318)
0 0.0010(27.277)
0.0008(22.85)
0.0007(17.738)
0.0005(14.504)
0.0010(25.440)
0.0009(21.633)
0.0007(16.211)
0.0006(13.886)
1 0.2660(6.893)
0.2314
(6.124)
0.2320
(5.889)
0.2358
(6.288)
0.2789
(6.4660)
0.2400
(5.851)
0.2350
(5.633)
0.1932
(5.127)
2 - 0.1477(4.631)
0.1343
(4.363)
0.0963
(3.191)
- 0.1440
(4.239)
0.1298
(3.996)
0.0978
(3.099)
3 - - 0.1462(5.000)
0.1502
(5.122)
- - 0.1441
(4.700)
0.1521
(4.741)
4 - - - 0.1665(4.816)
- - - 0.1653
(4.532)
- - - - 0.1163(4.255) 0.0607(1.335) 0.0441(0.964) 0.0473(3.318)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals
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: Coefficient of the risk factor
Table 11: Estimates of ARCH and ARCH in Mean Models: Machinery Sector -
Thermax Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4) -0.0001
(-0.256)
0.00025
(0.388)
0.00025
(0.390)
0.00019
(0.279)
-0.00032
(-0.336)
-0.00044
(-0.447)
-0.0007
(-0.754)
-0.00072
(-0.701)
0.0162(0.674)
0.0497
(1.982)
0.0621
(2.335)
0.0575
(2.052)
0.0285
(1.141)
0.0453
(1.725)
0.0533
(1.887)
0.0403
(1.360)
0 0.0006(33.418)
0.00058
(27.153)
0.00046
(20.827)
0.0004
(18.647)
0.00067
(32.121)
0.00057
(26.073)
0.0004
(20.409)
0.00041
(17.458)
1 0.3170(8.485)
0.2608
(7.252)
0.2693
(7.524)
0.2468
(6.631)
0.3170
(8.185)
0.2680
(7.308)
0.2583
(7.093)
0.2661
(6.892)
2 - 0.1423(6.534)
0.1304
(6.552)
0.1139
(4.856)
- 0.1508
(6.689)
0.1363
(6.664)
0.1349
(5.545)
3 - - 0.1524(5.378)
0.1267
(4.378)
- - 0.1358
(4.472)
0.1307
(4.406)
4 - - - 0.0743(3.121)
- - - 0.0766
(3.131)
- - - - 0.0136(0.367)
0.0444
(1.101)
0.0599
(1.440)
0.0690
(1.583)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation
i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 12: Estimates of ARCH and ARCH in Mean Models: Machinery Sector -
FAG Bearings India Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
-0.0000(-0.090)
0.0001
(0.2028)
0.0002
(0.305)
0.0004
(0.6087)
-0.0010
(-1.037)
-0.0019
(-1.756)
-0.0015
(-1.288)
-0.0012
(-1.033)
-0.0228(0.025)
-0.0035
(-0.129)
0.0109
(0.387)
0.0267
(0.088)
-0.0081
(-0.297)
0.0072
(0.251)
0.0215
(0.719)
0.3016
(1.013)
0 0.0008(0.000)
0.0007(28.920)
0.0007(25.808)
0.0006(23.380)
0.0008(33.757)
0.0008(27.953)
0.0007(24.123)
0.0006(21.897)
1 0.2033(6.981)
0.1652
(5.306)
0.1488
(4.610)
0.1574
(4.492)
0.1950
(6.010)
0.1579
(4.685)
0.1515
(4.310)
0.1385
(3.898)
2 - 0.1102(4.746)
0.0807
(3.1004)
0.0880
(3.137)
- 0.0882
(3.593)
0.0979
(3.912)
0.0958
(3.213)
3 - - 0.0816(3.717)
0.0745
(3.325)
- - 0.0981
(3.912)
0.0839
(3.422)
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4 - - - 0.0569(2.807)
- - - 0.0684
(3.064)
- - - - 0.0582(1.510)
0.1019
(2.990)
0.1059
(2.470)
0.0965
(2.189)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 13: Estimates of ARCH and ARCH in Mean Models: Machinery Sector -
Kirloskar Oil Enginees Ltd.
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
0.0006(0.878)
0.0013
(1.812)
0.0011
(1.453)
0.0008
(0.982)
-0.0024
(-2.247)
-0.0022
(-2.035)
-0.0023
(-1.999)
-0.0025
(-2.089)
-0.0814(-3.390)
-0.0619
(-2.386)
-0.0587
(-2.082)
-0.0671
(-2.310)
-0.0631
(-2.416)
-0.0564
(-2.043)
-0.0709
(-2.366)
-0.0776
(-2.564)
0 0.0009(30.965)
0.0007
(23.586)
0.0007
(20.192)
0.0006
(18.75)
0.0009
(29.742)
0.0007
(21.794)
0.007
(21.794)
0.0006
(17.664)
1 0.2620(7.674)
0.2545
(0.986)
0.2407
(6.340)
0.2437
(6.205)
0.2566
(7.087)
0.2366
(6.447)
0.2426
(6.140)
0.2393
(5.913)
2 - 0.1493(5.443)
0.1118
(3.818)
0.1012
(3.369)
- 0.1302
(4.277)
0.1037
(3.414)
0.0996
(3.157)
3 - - 0.0532(2.436)
0.0344
(1.590)
- - 0.0441
(2.024)
0.0397
(2.514)
4 - - - 0.0652(2.994)
- - - 0.0682
(2.514)
- - - - 0.1575(4.289)
0.1792
(4.548)
0.1573
(3.708)
0.1533
(3.543)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation
i s: Coefficient of the lagged squared residuals
: Coefficient of the risk factor
Table 14: Estimates of ARCH and ARCH in Mean Models: Machinery Sector -
Cummious India Ltd.
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
0.0002 -0.0000 0.0000 0.0000 -0.0011 -0.0012 -0.0011 -0.0006
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(0.503) (-0.043) (0.112) (0.032) (-1.596) (-1.614) (-1.333) (-0.767)
0.0211(0.989)
0.0288
(1.171)
0.0225
(0.879)
0.0311
(1.151)
0.0220
(1.016)
0.0401
(1.571)
0.0357
(1.336)
0.0454
(1.684)
0 0.0005(47.742)
0.0004
(39.113)
0.0004
(33.489)
0.0004
(30.897)
0.0005
(46.365)
0.0009
(39.169)
0.0004
(35.583)
0.0004
(0.0000)
1 0.2883(11.021)
0.2706(9.796)
0.2405(8.120)
0.2189(6.804)
0.2767(10.357)
0.2044(6.725)
0.2005(6.107)
0.1767(5.660)
2 - 0.0764(4.043)
0.0616
(3.068)
0.0570
(2.665)
- 0.0811
(4.009)
0.0605
(2.762)
0.0585
(3.634)
3 - - 0.0457(2.785)
0.0399
(2.402)
- - 0.0379
(2.294)
0.0409
(2.313)
4 - - - 0.0323(2.065)
- - - 0.0113
(0.751)
- - - - 0.0813(2.465)
0.0944
(2.516)
0.0872
(2.112)
0.0893
(2.138)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 15: Estimates of ARCH and ARCH in Mean Models:
Mining Sector - Aban Loyd Chiles Offshore Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
0.0000(0.084)
0.0004
(0.616)
0.0006
(0.792)
0.0016
(0.821)
-0.0019
(-1.671)
-0.0014
(-1.208)
-0.0009
(-0.728)
-0.0002
(-0.161)
-0.0099(-0.399)
0.0030
(0.1162)
-0.0032
(-0.123)
0.0009
(0.034)
-0.0027
(-0.102)
-0.0119
(-0.447)
0.0032
(0.116)
-0.0174
(-0.579)
0 0.0009(40.047)
0.0008
(27.683)
0.0007
(22.941)
0.0006
(20.943)
0.0010
(37.985)
0.0007
(25.532)
0.0007
(21.536)
0.0006
(19.981)
1 0.2085(7.388)
0.1805
(6.587)
0.1869
(6.429)
0.1686
(5.766)
0.1892
(6.719)
0.1875
(6.455)
0.1719
(6.038)
0.167
(5.518)
2 - 0.1684
(6.456)
0.1329
(4.596)
0.1323
(4.319)
- 0.1484
(5.012)
0.1436
(4.564)
0.1291
(3.990)
3 - - 0.0855(4.259)
0.0673
(3.645)
- - 0.0997
(4.511)
0.0709
(3.609)
4 - - - 0.0820(4.095)
- - - 0.0892
(4.077)
- - - - 0.1149(2.877)
0.0883
(2.168)
0.0866
(1.992)
0.0471
(0.986)
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Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals
: Coefficient of the risk factor
Table 16: Estimates of ARCH and ARCH in Mean Models:
Mining Sector -Avaya Globalconnect Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
-0.0005(-0.737)
0.0001
(0.194)
0.0003
(0.379)
0.0003
(0.442)
-0.0016
(-1.523)
-0.0021
(-1.860)
-0.0012
(-0.955)
-0.0006
(-0.519)
0.0295(1.615)
0.0661
(2.772)
0.0446
(1.702)
0.1596
(2.255)
0.0505
(2.501)
0.0549
(2.153)
0.0654
(2.409)
0.0852
(3.0.45)
0 0.0010
(37.824)
0.0009
(31.920)
0.0008
(28.002)
0.0007
(24.051)
0.0011
(38.051)
0.00097
(30.140)
0.0008
(25.543)
0.0008
(21.850)1 0.3926
(10.874)
0.2904
(7.883)
0.2753
(7.208)
0.2773
(7.111)
0.3643
(9.662)
0.2933
(7.179)
0.2717
(6.793)
0.2574
(6.203)
2 - 0.1878(8.930)
0.1333
(5.431)
0.1299
(5.448)
- 0.1720
(6.450)
0.1413
(5.452)
0.1307
(0.024)
3 - - 0.1194(5.144)
0.0981
(4.000)
- - 0.1332
(5.264)
0.1073
(4.092)
4 - - - 0.0910(3.376)
- - - 0.0741
(2.693)
- - - - - 0.11780(3.147)
0.0793
(1.953)
0.07758
(1.812)
Note:
Figures in the parentheses represent t statistics. : Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 17: Estimates of ARCH and ARCH in Mean Models:Mining Sector -Insilco Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
-0.0017(-1.985)
-0.0018
(-2.119)
-0.0019
(-2.056)
-0.0017
(-1.830)
-0.0037
(-2.915)
-0.0030
(-2.305)
-0.0026
(-1.857)
-0.0029
(-2.010)
0.0318(1.394)
0.0109
(0.422)
0.0033
(0.128)
0.0163
(0.604)
0.0277
(1.188)
0.0015
(0.057)
0.0131
(0.492)
0.0164
(0.613)
0 0.0014(58.818)
0.0012
(48.350)
0.0011
(44.050)
0.0011
(42.175)
0.0013
(50.722)
0.0012
(45.835)
0.0011
(41.297)
0.0011
(40.241)
1 0.2253 0.2006 0.1920 0.1905 0.2219 0.2014 0.1899 0.1756
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(10.017) (7.863) (7.378) (6.965) (9.030) (7.527) (6.822) (6.563)
2 - 0.0911(4.801)
0.0860
(3.836)
0.0871
(3.352)
- 0.1071
(5.039)
0.0938
(3.792)
0.0672
(2.576)
3 - - 0.0802(4.460)
0.0874
(4.285)
- - 0.0904
(4.584)
0.1096
(4.769)
4 - - - 0.0273(1.746)
- - - 0.0421(2.338)
- - - - 0.0885(2.400)
0.0523
(1.359)
0.0349
(0.842)
0.0415
(0.981)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 18: Estimates of ARCH and ARCH in Mean Models:Mining Sector Oil and Natural Gas Corporation Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
-0.0000(-0.074)
0.0003
(0.625)
0.0005
(0.897)
0.0004
(0.634)
0.0001
(0.197)
0.0004
(0.507)
0.0004
(0.540)
0.0005
(0.564)
0.0655(2.908)
0.0595
(2.739)
0.0782
(2.604)
0.841
(2.763)
0.0831
(3.143)
0.0900
(3.085)
0.0859
(2.821)
0.0924
(2.969)
0 0.0006
(36.322)
0.0004
(27.773)
0.0004
(25.011)
0.0004
(24.070)
0.0006
(35.534)
0.0004
(26.952)
0.0004
(24.334)
0.0004
(22.494)1 0.3135
(10.440)
0.2811
(10.551)
0.2744
(9.965)
0.2454
(7.863)
0.3069
(9.917)
0.2892
(9.745)
0.2532
(8.745)
0.2563
(7.526)
2 - 0.2570(7.761)
0.2200
(6.834)
0.2104
(6.448)
- 0.2320
(7.025)
0.2196
(6.611)
0.2158
(6.278)
3 - - 0.0526(2.580)
0.0413
(2.050)
- - 0.0423
(2.114)
0.0364
(1.810)
4 - - - 0.0220(1.196)
- - - -
- - - - -0.0216(-0.576)
-0.0092
(-0.105)
-0.0076
(-0.179)
-0.0099
(-0.230)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
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Table 19: Estimates of ARCH and ARCH in Mean Models:
Non Metalic Sector - Dalmia Cements (Bharat) Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
0.0016(1.843) 0.0007(0.761) 0.0007(0.767) 0.0003(0.331) 0.0003(0.2459) -0.0009(-0.342) -0.0006(-0.403) -0.0020(-1.192)
-0.0512(-1.593)
-0.0566
(-1.600)
-0.0598
(-1.555)
-0.0442
(-1.058)
-0.0552
(-1.681)
-0.0630
(-1.661)
-0.0971
(-1.109)
-0.0400
(-0.872)
0 0.0010(31.189)
0.0008
(24.813)
0.0007
(0.000)
0.0007
(17.135)
0.0009
(28.394)
0.0008
(22.325)
0.0007
(18.267)
0.0007
(16.027)
1 0.2730(8.579)
0.2682
(8.056)
0.2658
(2.673)
0.2438
(6.332)
0.2621
(8.179)
0.2639
(6.854)
0.2442
(6.441)
0.1900
(5.300)
2 - 0.0808(3.201)
0.0657
(2.673)
0.0632
(2.117)
- 0.0663
(2.693)
0.0669
(2.270)
0.0866
(2.536)
3 - - 0.0640(2.746)
0.0687
(2.672)
- - 0.0704
(2.771)
0.0553
(2.125)
4 - - - 0.0084(3.291)
- - - 0.0192
(0.623)
- - - - 0.0331(0.712)
0.0505
(0.984)
0.0472
(0.811)
0.1091
(1.806)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals
: Coefficient of the risk factor
Table 20: Estimates of ARCH and ARCH in Mean Models:
Non Metalic Sector - Gujarat Ambuja Cements Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
0.0006(1.431)
0.0005
(1.162)
0.0003
(0.828)
0.0003
(0.778)
-0.0003
(-0.490)
-0.0004
(-0.606)
-0.0003
(-0.464)
-0.003
(-0.453)
0.0818(4.611)
0.0606
(2.703)
0.0884
(3.703)
0.0805
(3.060)
0.0817
(3.933)
0.0660
(2.745)
0.0919
(3.540)
0.0750
(2.687)
0 0.0004(41.276)
0.0004
(35.024)
0.0003
(27.987)
0.0003
(23.006)
0.0004
(40.160)
0.0004
(34.052)
0.0003
(25.559)
0.0003
(21.862)
1 0.3227(11.045)
0.2467
(8.786)
0.2401
(8.640)
0.2503
(8.160)
0.3171
(10.499)
0.2465
(8.476)
0.2552
(8.585)
0.2639
(7.991)
2 - 0.1714(7.137)
0.1596
(6.577)
0.1531
(6.284)
- 0.1811
(7.019)
0.1678
(6.513)
0.1588
(6.105)
3 - - 0.0865 0.0716 - - 0.0874 0.0772
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(4.142) (3.538) (4.251) (3.522)
4 - - - 0.0798(4.514)
- - - 0.0943
(4.631)
- - - - 0.0637(2.075)
0.0523
(1.489)
0.0500
(1.358)
0.0472
(1.167)
Note: Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 21: Estimates of ARCH and ARCH in Mean Models:
Non Metalic Sector - Gujarat Sidhee Cement Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
-0.0020(-1.871)
-0.0014
(-1.327)
-0.0012
(-1.081)
-0.0010
(-0.905)
-0.0036
(-2.336)
-0.0040
(-2.345)
-0.0034
(-1.925)
-0.0041
(-2.255)
-0.1664(-9.099)
-0.1060
(-5.292)
-0.1338
(-5.523)
-0.1289
(-4.918)
-0.1447
(-6.684)
-0.1115
(-4.940)
-0.1259
(-4.767)
-0.129
(-4.579)
0 0.0021(44.043)
0.0019
(33.924)
0.0019
(31.490)
0.0018
(28.123)
0.0022
(47.418)
0.0020
(33.402)
0.0019
(29.983)
0.0018
(27.143)
1 0.2567(10.690)
0.1653
(6.291)
0.1628
(6.049)
0.1436
(5.213)
0.2272
(10.284)
0.1532
(5.505)
0.1346
(4.768)
0.1230
(4.394)
2 - 0.1768(9.852)
0.0687
(3.429)
0.0553
(2.770)
- 0.1221
(6.380)
0.0630
(3.092)
0.0406
(1.723)
3 - - 0.0712(4.350)
0.0562
(3.304)
- - 0.0758
(4.441)
0.0713
(3.724)
4 - - - 0.0426(2.876)
- - - 0.0475
(3.083)
- - - - 0.0573(1.861)
0.0920
(2.487)
0.7151
(1.771)
0.0986
(2.345)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 22: Estimates of ARCH and ARCH in Mean Models:
Non Metalic Sector -India Cements Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
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-0.0000(-0.066)
-0.0002
(-0.287)
-0.0004
(-0.571)
-0.0006
(-0.772)
-0.0010
(-1.102)
-0.0019
(-1.862)
-0.0012
(-1.1750)
-0.0010
(-0.906)
0.0454(1.955)
0.0541
(2.118)
0.0500
(1.973)
0.029
(0.895)
0.0322
(1.299)
0.0442
(1.624)
0.0304
(1.127)
0.0327
(1.144)
0 0.0009
(43.185)
0.0008
(36.763)
0.0007
(34.944)
0.0006
(24.766)
0.00092
(40.982)
0.0008
(35.117)
0.0006
(25.69)
0.0006
(23.866)
1 0.2792(10.248)
0.2404
(8.783)
0.2253
(8.1009)
0.2268
(7.285)
0.2610
(9.397)
0.2353
(8.415)
0.2486
(8.209)
0.2304
(6.867)
2 - 0.1260(5.215)
0.0943
(4.161)
0.0891
(4.076)
- 0.1151
(4.699)
0.0912
(4.123)
0.0877
(3.842)
3 - - 0.1265(5.407)
0.1148
(4.684)
- - 0.1336
(5.398)
0.1146
(4.431)
4 - - - 0.0736(3.745)
- - - 0.0714
(3.409)
- - - - 0.0322
(1.299)
0.0798
(2.144)
0.0357
(0.929)
0.0312
(0.750)Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 23: Estimates of ARCH and ARCH in Mean Models:
Power Plants - Ahmedabad Electricity Co. Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM
-0.0012(-2.035)
-0.0057
(-0.948)
-0.00035
(-0.542)
0.000623
(-0.084)
-0.0025
(-3.022)
-0.0018
(-2.047)
-0.00081
(-0.785)
-0.0008
(-0.758
-0.0193(-1.078)
-0.0415
(-1.627)
-0.0314
(-1.222)
0.0097
(0.3358)
-0.0025
(-0.1148)
-0.0113
(-0.410)
-0.0031
(-0.108)
0.0268
(0.821
0 0.0007(47.541)
0.00062
(35.716)
0.00052
(32.675)
0.00048
(31.485)
0.00074
(37.347)
0.00059
(33.912)
0.00051
(31.256)
0.0004
(30.522
1 0.4732(16.248)
0.4685
(14.042)
0.4257
(13.053)
0.3975
(11.296)
0.4806
(13.154)
0.4476
(12.382)
0.4061
(11.440)
0.4154
(10.433
2 - 0.1349(6.183)
0.1183
(4.863)
0.1000
(4.114)
- 0.1507
(6.017)
0.1299
(4.820)
0.1055
(3.842
3 - - 0.1150(5.285)
0.1278
(5.196)
- - 0.1368
(5.373)
0.1440
(5.159
4 - - - 0.0575(3.692)
- - - 0.046
(2.649
- - - - 0.1272 0.0966 0.0500 0.0459
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(4.071) (2.402) (1.112) (0.974
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 24: Estimates of ARCH and ARCH in Mean Models:
Power Plants - Gujarat Industries Power Co. Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
-0.0013(-1.935)
-0.0087
(-1.217)
-0.00066
(-0.906)
-0.00081
(-1.080)
-0.0019
(-1.870)
-0.0021
(-2.023)
-0.0021
(-1.982)
-0.0016
(-1.521)
0.0330(1.425)
0.0331(1.332)
0.0466(1.889)
0.0414(1.520)
0.0302(1.240)
0.0296(1.136)
0.0521(2.050)
0.0429(1.521)
0 0.00090(42.437)
0.00080
(32.582)
0.00075
(27.167)
0.00070
(25.389)
0.00092
(40.9007)
0.00080
(31.988)
0.00077
(26.509)
0.00073
(24.765)
1 0.2560(8.578)
0.2300
(7.312)
0.2233
(7.047)
0.2261
(6.557)
0.2521
(8.078)
0.2202
(7.141)
0.2074
(6.577)
0.2087
(6.157)
2 - 0.1306(6.207)
0.1163
(5.614)
0.1002
(4.823)
- 0.1307
(6.179)
0.1153
(5.405)
0.1047
(4.955)
3 - - 0.0585(2.949)
0.0391
(2.122)
- - 0.0618
(3.073)
0.0348
(1.860)
4 - - - 0.0843(6.494) - - - 0.0783(6.240)
- - - - 0.0461(1.312)
0.0684
(1.826)
0.0820
(2.187)
0.0482
(1.225)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 25: Estimates of ARCH and ARCH in Mean Models:
Power Plants - Reliance Energy Ltd
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCH(3) ARCHM(4)
-0.0002(-0.556)
-0.00024
(-0.503)
0.00020
(0.413)
0.00038
(0.708)
-0.00161
(-2.419)
-0.00029
(-0.453)
-0.00098
(-1.341)
-0.00056
(-0.717)
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0.0404(2.506)
0.0789
(4.214)
0.0616
(2.649)
0.0790
(3.196)
0.0293
(1.705)
0.0641
(2.983)
0.0765
(3.132)
0.0642
(2.546)
0 0.00052(43.249)
0.00040
(30.952)
0.0003
(26.011)
0.00034
(24.208)
0.00052
(39.858)
0.00041
(31.298)
0.00037
(27.518)
0.00036
(25-070)
1 0.4513
(19.170)
0.3635
(14.093)
0.3647
(14.090)
0.3020
(13.239)
0.4446
(15.444)
0.3618
(13.708)
0.3193
(13.685)
0.3202
(12.804)
2 - 0.2251(10.053)
0.1380
(6.658)
0.1215
(5.522)
- 0.2091
(8.979)
0.1308
(6.231)
0.0884
(4.0039)
3 - - 0.1631(6.624)
0.1367
(5.561)
- - 0.1500
(5.917)
0.1430
(5.457)
4 - - - 0.0667(3.411)
- - - 0.0513
(2.597)
- - - - 0.1101(4.418)
0.0087
(0.324)
0.0952
(2.659)
0.0669
(1.760)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation AR (1) : Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 26: Estimates of ARCH and ARCH in Mean Models:
Power Plants - Tata Power Co. Ltd.
Coefficient ARCH(1) ARCH(2) ARCH(3) ARCH(4) ARCHM(1) ARCHM(2) ARCHM(3) ARCHM(4)
0.0000
(0.192)
0.0003
(0.5885)
0.00019
(0.358)
0.00020
(0.356)
-0.00065
(-0.897)
-0.00035
(-0.476)
-0.00039
(-0.523)
-0.00022
(-0.287) 0.1105
(5.016)
0.1008
(4.119)
0.1041
(4.190)
0.1188
(4.641)
0.1185
(5.447)
0.1059
(4.432)
0.1256
(5.180)
0.1231
(4.999)
0 0.00059(41.851)
0.00052
(36.808)
0.0004
(34.197)
0.0004
(31.267)
0.00057
(40.276)
0.00051
(36.221)
0.00049
(33.403)
0.00047
(29.977)
1 0.3156(12.306)
0.2773
(10.858)
0.2429
(8.952)
0.2328
(8.435)
- 0.2618
(9.664)
0.2404
(8.772)
0.2159
(7.901)
2 - 0.0956(4.630)
0.0806
(3.829)
0.0597
(2.903)
- 0.1007
(4.560)
0.0637
(2.990)
0.0478
(2.279)
3 - - 0.0627(3.433)
0.0595
(3.2002)
- - 0.0644
(3.365)
0.0739
(3.589)
4 - - - 0.0491(2.562)
- - - 0.0576
(2.613)
- - - - 0.0540(1.759)
0.0404
(1.231)
0.0375
(1.120)
0.0358
(1.055)
Note:
Figures in the parentheses represent t statistics.
: Intercept of the return equation
AR (1) : Coefficient of the lagged value of return equation
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0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor
Table 27: Estimates of GARCH Models:
Aggregate Indices BSE Sensex
CoefficientGARCH
(1,1)
GARCH
(1,2)
GARCH
(2,1)
GARCH
(2,2)
0.0005(2.415)
5.4165e-04
(2.191)
0.00057
(2.314)
0.00050
(2.065)
AR (1) 0.11150
(6.131)
0.1153
(5.914)
0.1141
(5.872)
0.1242
(6.413)
0 0.0001(7.402)
7.2409e-06
(5.860)
0.0001
(6.736)
0.0001
(2.56)
1 0.8399(78.204) 0.8869(86.637) 0.3825(4.643) 1.614(34.828)
2 - - 0.4069(5.496)
-0.6268
(-9.76)
1 0.1260(12.923)
0.1926
(9.427)
0.1657
(11.643)
0.1737
(9.905)
2 - -0.1019(-5.072)
- -0.1629
(-9.621)
Persistence 0.9659 0.9551
Note:
Figures in the parentheses represent t statistics. : Intercept of the return equation
AR (1): Coefficient of the lagged value of return equation
0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals 1 &2 : Coefficient of the lagged conditional variance. Persistence : Measured as the sum of the coefficients of squared residuals and of lagged
conditional variance
Table 28 : Estimates of GARCH Models:
Aggregate Indices BSE 200 Index
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CoefficientGARCH
(1,1)GARCH (1,2)
GARCH
(2,1)
GARCH
(2,2)
0.0003(1.472)
3.1822e-04
(1.346)
0.00032
(1.371)
3.0529e-04
(1.290)
AR (1) 0.1644(8.071)
0.1694(8.195)
0.1667(8.015)
0.1711(8.224)
0 0.0001(10.763)
1.6159e-05
(8.745)
0.00003
(10.540)
2.3331e-05
(8.647)
1 0.6260(31.772)
0.7576
(55.443)
0.3317
(6.872)
0.2917
(6.415)
2 - - 0.2497(5.649)
0.3700
(8.860)
1 0.1273(20.