stock market volatility in india - case of select scripts

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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19

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


0.0004 0.0004 0.0004 0.0005 0.0000 0.0001 -8.9251e- 0.0003


20/54

20

(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:






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)


21/54

21

- - - - 0.0582(1.641)

0.0033

(0.098)

0.0186*

(0.496)

0.020*

(0.506)

Note:





Table 5: Estimates of ARCH and ARCH in Mean Models: Aggregate IndicesS&P CNX 500


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:




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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22

(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:





Table 7: Estimates of ARCH and ARCH in Mean Models: Electrical Sector - Exide

Industries Ltd.


-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:


23/54

23





Table 8: Estimates of ARCH and ARCH in Mean Models: Electrical Sector -

Whirlpool of India Ltd.


-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:





Table 9: Estimates of ARCH and ARCH in Mean Models: Electrical Sector - Blue

Star Ltd.


-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


24/54

24

(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:





Table 10: Estimates of ARCH and ARCH in Mean Models: Electrical Sector - Birla

Corporation Ltd.


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:




0 : Intercept of the volatility equation i s : Coefficient of the lagged squared residuals


25/54

25

: 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:





i s : Coefficient of the lagged squared residuals : Coefficient of the risk factor


FAG Bearings India Ltd


-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)


26/54

26

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:






Kirloskar Oil Enginees Ltd.


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:





i s: Coefficient of the lagged squared residuals



Cummious India Ltd.


0.0002 -0.0000 0.0000 0.0000 -0.0011 -0.0012 -0.0011 -0.0006


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27

(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:






Mining Sector - Aban Loyd Chiles Offshore Ltd


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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28

Note:







Mining Sector -Avaya Globalconnect Ltd


-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



Table 17: Estimates of ARCH and ARCH in Mean Models:Mining Sector -Insilco Ltd


-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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29

(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:





Table 18: Estimates of ARCH and ARCH in Mean Models:Mining Sector Oil and Natural Gas Corporation Ltd


-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:






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30


Non Metalic Sector - Dalmia Cements (Bharat) Ltd


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:







Non Metalic Sector - Gujarat Ambuja Cements Ltd


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


31/54

31

(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.





Non Metalic Sector - Gujarat Sidhee Cement Ltd


-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:






Non Metalic Sector -India Cements Ltd



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32

-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:






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


33/54

33

(4.071) (2.402) (1.112) (0.974

Note:






Power Plants - Gujarat Industries Power Co. Ltd


-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:






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:


: Intercept of the return equation AR (1) : Coefficient of the lagged value of return equation



Power Plants - Tata Power Co. Ltd.


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:





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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.

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