Impact of index futures on indian market volatility-Archana Subramanya-0403

8/7/2019 Impact of index futures on indian market volatility-Archana Subramanya-0403

1/60

1

IImmppaacctt ooffIInnddeexx FFuuttuurreess oonn IInnddiiaann MMaarrkkeett VVoollaattiilliittyy

-- AAnn aapppplliiccaattiioonn ooffGGAARRCCHH

.

AA DDIISSSSEERRTTAATTIIOONN SSUUBBMMIITTTTEEDD IINN PPAARRTTIIAALL FFUULLFFIILLLLMMEENNTT

OOFF TTHHEE RREEQQUUIIRREEMMEENNTTSS FFOORR TTHHEE AAWWAARRDD OOFF

MMBBAA DDEEGGRREEEE OOFF BBAANNGGAALLOORREE UUNNIIVVEERRSSIITTYY..

SSUUBBMMIITTTTEEDDBBYY

MMss..PP..AArrcchhaannaa SSuubbrraammaannyyaa

RREEGG..NNOO0044XXQQCCMM66000077

UUNNDDEERRTTHHEEGGUUIIDDAANNCCEEOOFF

DDrr..TT..VV..NNRRaaoo

FFaaccuullttyy

MMPPBBIIMM

MM..PP..BBIIRRLLAAIINNSSTTIITTUUTTEEOOFFMMAANNAAGGEEMMEENNTT((AASSSSOOCCIIAATTEEBBHHAARRAATTIIYYAAVVIIDDYYAABBHHAAVVAANN))

##4433RRAACCEE CCOOUURRSSEE RROOAADD,,BBAANNGGAALLOORREE556600000011..

22000044--22000066BBaattcchh


2/60

2

DECLARATION

I hereby declare that the dissertation entitled IImmppaacctt ooffIInnddeexx

FFuuttuurreess oonn IInnddiiaann MMaarrkkeett VVoollaattiilliittyy--AAnn aapppplliiccaattiioonn ooff

GGAARRCCHHis theresultofwork undertaken by me, under the

guidance and supervision of Dr.T.V.N.Rao, Associate Professor,

M.P.Birla Institute of Management,Bangalore.

Ialsodeclare that thisdissertationhas notbeen submitted

to any other University/Institution for the award of any Degree

or Diploma.

Place:Bangalore

Date: 16th

June2006 P.Archana Subramanya


3/60

3

Principal Certificate.

I hereby certify that the research work embodied in

this dissertation entitled IImmppaacctt ooffIInnddeexx FFuuttuurreess oonn IInnddiiaann

MMaarrkkeett VVoollaattiilliittyy--AAnn aapppplliiccaattiioonn ooffGGAARRCCHHhas been undertaken

and completed by Ms.P.Archana Subramanya under the

guidance and supervision ofDr.T.V.N.Rao, Faculty, MPBIM,

Bangalore.

Place:Bangalore Dr.N.S. Malavalli

Date:16/06/2006 PrincipalMPBIM, Bangalore


4/60

4

Guide Certificate.

I hereby declare that the research work embodied in

this dissertation entitled IImmppaacctt ooff IInnddeexx FFuuttuurreess oonn IInnddiiaann

MMaarrkkeett VVoollaattiilliittyy--AAnn aapppplliiccaattiioonn ooff GGAARRCCHH has been

undertaken and completed by Ms.P.Archana Subramanya under

my guidance and supervision.

Place:Bangalore Dr.T.V.N.Rao

Date: 16 /06/2006 Faculty Membe


5/60

5

ACKNOWLEDGEMENT

I take this opportunity to sincerely thank Dr.T.V.N Rao

who guided me through out the project through his

valuable suggestions, without which the project would

not have been successful.

I also thank Dr N.S. Malavalli (Principal) for giving me

the opportunity to explore my areas of interest by consistently

lending support in terms of his expertise and also supplying valuable

inputs in terms of resources every step of the way.

My sincere thanks to my parents and friends who out of

hard sweat were able to help me at all time and given

encouragement for successful completion of this project.

P.Archana Subramanya

(04XQCM6007)


6/60

6

TABLE OF CONTENTS

CHAPTERS PARTICULARS PAGE NO.

ABSTARCT

1. INTRODUCTION

1.1 Introduction and Background of the study 4 - 6

2. REVIEW OF LITERATURE

2.1 Theoretical consideration 8 -10

2.2 Survey of empirical literature 11 - 32

3. RESEARCH METHODOLOGY

3.1 Research problem statement 34-34

3.2 Methodology 34-37

3.2 Software packages used 37-37

4. DATA ANALYSIS AND INTERPRETATION

Empirical Results 39-54

5. INFERENCES AND CONCLUSIONS 54-54

BIBLIOGRAPHY 41

ANNEXURES 42 - 58


7/60

7

ABSTRACT

This paper addresses whether, and to what extent, the introduction of

Index Futures contracts trading has changed the volatility structure of

the underlying NSE Nifty Index. Using unit root test it is confirmed

that the data is stationary. The classical F-Test (Variance-Ratio test)

also indicates that the spot volatility has changed, since the inception

of Index Futures trading. Next the GARCH family of technique is

employed to capture the time-varying nature of volatility The results

obtained from the GARCH model indicate that while the introduction

of futures trading has effect on the underlying mean level of the

returns and marginal volatility, it has significantly altered the of spot

market volatility. Specifically, it is found that new information is

assimilated into prices more rapidly than before, and there is a

decline in the persistence of volatility since the onset of futures

trading. These results for NSE Nifty are obtained even after

accounting for world market movements, asymmetric effects and sub-

period analysis, and, contrasting the same with a control index,

namely, NIFTY Junior which does not yet has a derivative segment.

Thus it is concluded that such a change in the volatility structure

appears to be the result of futures trading, which has expanded the

routes over which information can be conveyed to the market.


8/60

8


9/60

9

1.0 INTRODUCTION

In the last decade, many emerging and transition economies have started

introducing derivative contracts. As was the case when commodity futures

were first introduced on the Chicago Board of Trade in 1865, policymakers

and regulators in these markets are concerned about the impact of futures on

the underlying cash market. One of the reasons for this concern is the belief

that futures trading attract speculators who then destabilize spot prices. This

concern is evident in the following excerpt from an article by John Stuart

Mill (1871):

The safety and cheapness of communications, which enable a deficiency in

one place to be, supplied from the surplus of another render the fluctuations

of prices much less extreme than formerly. This effect is much promoted by

the existence of speculative merchant. Speculators, therefore, have a highly

useful office in the economy of society.

Since futures encourage speculation, the debate on the impact of speculators

intensified when futures contracts were first introduced for trading;

beginning with commodity futures and moving on to financial futures and

recently futures on weather and electricity. However, this traditional

favorable view towards the economic benefits of speculative activity has not

always been acceptable to regulators. For example, futures trading was

blamed for some of the stock market crash of 1987 in the USA, thereby

warranting more regulation. However before further regulation is

introduced, it is essential to determine whether in fact there is a causal link

between the introduction of futures and spot market volatility. It therefore


10/60

10

becomes imperative that we seek answers to questions like: What is the

impact of derivatives upon market efficiency and liquidity of the underlying

cash market? To what extent do derivatives destabilize the financial system,

and how should these risks be addressed? Can the results from studies of

developed markets be extended to emerging markets?

This paper seeks to contribute to the existing literature in many ways. This is

the study to examine the impact of financial derivatives introduction on cash

market volatility in an emerging market, India. Further, this study improves

upon the methodology used in prior studies by using a framework that

allows for generalized auto-regressive conditional heteroskedasticity

(GARCH) i.e., it explicitly models the volatility process over time, rather

than using estimated standard deviations to measure volatility. This

estimation technique enables us to explore the link between

information/news arrival in the market and its effect on cash market

volatility. The study also looks at the linkages in ongoing trading activity in

the futures market with the underlying spot market volatility by

decomposing trading volume and open interest into an expected component

and an unexpected (surprise) component. This study looks at the effects of

stock index futures introduction on the underlying cash market volatility.

The results of this study are crucial to investors, stock exchange officials and

regulators. Derivatives play a very important role in the price discovery

process and in completing the market. Their role in risk management for

institutional investors and mutual fund managers need hardly be

overemphasized. This role as a tool for risk management clearly assumes

that derivatives trading do not increase market volatility and risk. The results


11/60

11

of this study will throw some light on the effects of derivative introduction

on the efficiency and volatility of the underlying cash markets.

The study is organized as follows. Section II discusses the theoretical debate

and summarizes the empirical literature on derivative listing effects, Section

III details the model and the econometric methodology used in this study,

Section IV outlines the data used and discusses the main results of the model

and finally Section V concludes the study and presents directions for future

research.


12/60

12


13/60


14/60

14

analysis and Ljung-Box Q-statistics for squared returns provide evidence

about the presence of volatility clustering phenomenon, which calls for

GARCH modeling. To model the conditional variance, Bollerslev (1986)

introduced GARCH models that relate conditional variance of returns as a

linear function of lagged conditional variance and past squared error.

The standard GARCH (p, q) model can be expressed as follows:

t/t-1 ~N(O,ht)

p q

ht= o + i 2

+ ht-j (2)i-1

t=i j=1

where, t is the same error term Ot is the information set till time t, ais are

news coefficients measuring the impact of recent news on volatility and js

are the persistence coefficients measuring the impact of less recent or

old news on volatility. These interpretations of ais & js can be found,

for instance, in Antoniou & Holmes (1995) and Butterworth (2000).

First separate models been fitted for the before and after Nifty time series

using the ARMA-GARCH model of (1) & (2) and it is found that the

ARMA-GARCH orders of the two models are same. This facilitates writing

a single model for the entire series including both before and after

components by introducing a dummy variable, Dt, taking value 0 for before

period and 1 for after. By including individual dummies, instead of additive

or multiplicative dummy, as suggested in Butterworth (2000) and Gulen &

Mayhew (2000), the proposed ARMA-GARCH model allows one to identify

and study the nature of potential impacts of introduction of the futures

contracts on the structure of both mean level and volatility of the spot market

in general terms. By examining the significance of dummy coefficients, one


15/60

15

can test whether there is a change in both the speed and persistence with

which the volatility shocks evolve. Following the onset of futures trading, a

positive significant value of aid would suggest that news is absorbed into

prices more rapidly, while a negative and significant value ofj,d implies

that less recent news have less impact on todays price changes. This

means that the investors attach more importance to recent news leading to a

fall in the persistence of information. Thus, the ARMA-GARCH framework

enables one to model changes that might occur both in the mean level and

structure of volatility, which can be detected by checking the sign and

significance of the coefficients attached to dummy variables.


16/60

16

2.2 SURVEY OF THE EMPIRICAL LITERATURE

The introduction of equity index futures markets enables traders to transact

large volumes at much lower transaction costs relative to the cash market.

The consequence of this increase in order flow to futures markets is

unresolved on both a theoretical and an empirical front. Stein (1987)

develops a model in which prices are determined by the interaction between

hedgers and informed speculators. In this model, opening a futures market

has two effects; (1). The futures market improves risk sharing and therefore

reduces price volatility, and (2). If the speculators observe a noisy but

informative signal, the hedgers react to the noise in the speculative trades,producing an increase in volatility.

In contrast, models developed by Danthine (1978) argue that the futures

markets improve market depth and reduce volatility because the cost to

informed traders of responding to mispricing is reduced. Froot and

Perold(1991) extend Kyles(1985) model to show that market depth is

increased by more rapid dissemination of market-wide information and the

presence of market makers in the futures market in addition to the cash

market. Ross (1989) assumes that there exists an economy that is devoid of

arbitrage and proceeds to provide a condition under which the no-arbitrage

situation will be sustained. It implies that the variance of the price change

will be equal to the rate of information flow. The implication of this is that

the volatility of the asset price will increase as the rate of information flow

increases. Thus, if futures increase the flow of information, than in the

absence of arbitrage opportunity, the volatility of the spot price must change.

Overall, the theoretical work on futures listing effects offer no consensus on

the size and the direction of the change in volatility. We therefore need to


17/60

17

turn to the empirical literature on evidence relating to the volatility effects of

listing index futures and options.

Below are the literature review done by studying four research papers:

2.1.1 IMPACT OF FUTURES INTRODUCTION ON UNDERLYING

INDEX VOLATALITY: AN EVIDENCE FROM INDIA

Kotha Kiran Kumar. & Chiranjit Mukhopadhyay

INTRODUCTION

This paper addresses whether, and to what extent, the introduction of Index

Futures contracts trading has changed the volatility structure of the

underlying NSE Nifty Index.

One of the most recurring themes in empirical financial research is studying

the effect of Derivatives trading on the underlying asset. Special interest is

devoted to studying whether Derivatives markets stabilize or destabilize the

underlying markets. Many theories have been advanced on how the

introduction of Derivatives market might impact the volatility of an

underlying asset. The traditional view against the Derivatives markets is

that, by encouraging or facilitating speculation, they give rise to price

instability and thus amplify the spot volatility. This is called the

Destabilization hypothesis. This has led to call for greater regulation to

minimize any detrimental effect. An alternative explanation for the rise in

volatility is that Derivatives markets provide an additional route by which

information can be transmitted, and therefore, increase in spot volatility may

simply be a consequence of the more frequent arrival, and more rapid

processing of information. Thus Derivatives trading may be fully consistent

with efficient functioning of the markets.


18/60

18

Stock index futures, because of operational and institutional properties, are

traditionally more volatile than spot markets. The close relationship between

the two markets induces the possibility of transferring volatility from futures

markets to the underlying spot markets. There are numerous studies that

have approached the effect of the introduction of Index Futures trading from

an empirical perspective. Majority of the studies compare the volatility of

the spot index or individual component stocks in an index before and after

the introduction of the futures contract using different methodologies

ranging from simple comparison of variances, to linear regression to more

complex GARCH models with different underlying assumptions and

parameters in the models. Most of the studies examined the impact of

introduction of index futures in one market and thus were unable to compare

across markets. Gulen and Mayhew (2000) examine stock market volatility

before and after the introduction of index futures trading in twenty-five

countries, using various GARCH models augmented with either additive or

multiplicative dummy. Their statistical model takes care of asynchronous

data, conditional heteroskedasticity, asymmetric volatility responses, and the

joint dynamics of each countrys index with the world market portfolio.

They found that futures trading are related to an increase in conditional

volatility in the U.S. and Japan, but in nearly every other country, no

significant effect could be found. Most of these studies examined the impact

of introduction of index futures in one market and thus were unable to

compare across markets. Gulen and Mayhew (2000) examine stock market

volatility before and after the introduction of index futures trading in twenty-

five countries, using various GARCH models augmented with either

additive or multiplicative dummy. Their statistical model takes care of


19/60

19

asynchronous data, conditional heteroskedasticity, asymmetric volatility

responses, and the joint dynamics of each countrys index with the world

market portfolio. They found that a futures trading is related to an increase

in conditional volatility in the U.S. and Japan, but in nearly every other

country, no significant effect could be found.

The study in this article improves the earlier studies in five aspects, first two

are in general context and the others are in Indian context. First, the paper

examines closely whether there is any shift in the NSE Nifty volatility in the

period under investigation through a change-point analysis and then

confirms that indeed a change has occurred around the date of introduction

of Index Futures trading. To the authors knowledge no other study has thus

objectively validated the event-study methodology, typically applied in

studying problems of the kind discussed in this paper. Secondly, marginal

volatilities of before and after series are compared apart from the well-

documented comparison of conditional volatility of a series before and after

occurrence of an event. The volatility comparison through GARCH model

gives whether the conditional volatility of the series (which is same as that

of residuals) has changed or not and does not comment on the volatility of

the underlying series as such. Third, this study applies the GARCH model,

which inherently incorporates endogenous information in the expression of

conditional volatility as discussed in Ross (1989), apart from effectively

controlling the temporal dependency phenomena. Following Antoniou &

Holmes (1995), the GARCH model is augmented with individual dummies.

The use of individual dummies is important as one can measure whether

there is a change in the speed and persistence with which volatility shocks

evolve after the futures trading1. Fourth, this paper deviates from the


20/60

20

existing literature on the studies of the Indian markets in using Nifty Junior

index as a proxy for market-wide movements given that it contributes a mere

6% on average, of market capitalization. Instead, MSCI World Index has

been used to control for market-wide movements. Fifth, the entire test

procedure is implemented on Nifty Junior, which does not have

corresponding futures contract and thus may be treated as a control index.

This strengthens the analysis of impact of Index Futures trading on Nifty as

its results differ from that of Nifty Junior.

The study reports that while there is no change in the mean returns and

marginal volatility there is a substantial change in the dynamics by which

the conditional variance evolves. Specifically, the results suggest that a

future trading improves the quality and speed of information flow to spot

market and this trend is not evident in the control index, NSE Nifty Junior.

METHODOLOGY

Any test applied to measure the effects of an intervention, such as the

introduction of futures trading, requires the knowledge of when the

intervention took place, followed by an analysis of the behavior of the spot

market before and after the event. The classic Event-study methodology is

applied to study the impact of introduction of index futures trading on the

volatility of NSE Nifty Index. However before blindly initiating the event-

study methodology, one has to first check whether there is indeed any

change in the series under study, around the event date without using its

prior knowledge, through a Change-Point Analysis. For this purpose an

informal descriptive statistical technique called CUSUM (Cumulative Sum)

chart is employed, which has been widely used in Statistical Process Control


21/60

21

literature for change-point detection, (vide., Ch 7 of Montgomery, 1991) and

as well as a formal Bayesian analysis. If there is any shift in the spot

volatility because of Futures introduction then the date obtained from

CUSUM plot or the Bayesian analysis should approximately coincide with

that of the actual starting date of Futures trading.

CUSUM Chart

A segment of the CUSUM chart with an upward slope indicates a period

where the values tend to be above the overall average. Likewise a segment

with a downward slope indicates a period of time where the values tend to

be below the overall average. Thus a sudden change in direction of the

CUSUM indicates a sudden shift or change in the average. Fig 1 shows the

CUSUM chart with NSE Nifty daily squared returns, as a proxy for

volatility, from June 1999 to June 2001. As is evident from the CUSUM

chart, the NSE Nifty squared returns have taken a sudden turn on 6th June

2000. Incidentally, BSE Sensex Futures started on 5th June 2000 and NSE

Nifty Futures started on 12th June 2000. So around the date of introduction

of Futures there has been a sudden turn in NSE Nifty daily squared returns

and needs further examination to conclusive evidence.

From the CUSUM chart one may suspect that there is an abrupt change in

the volatility of the Nifty series around the futures introduction. However it

may be argued that the spike found around the date of futures introduction

may only be due to the natural variability of the Nifty series. Thus the

change point analysis is also approached from a Bayesian viewpoint to see if

one can statistically infer that there indeed exists a change in the volatility


22/60

22

process of NSE Nifty without utilizing the knowledge of exact date of

introduction of futures trading. The simplest formulation of the change-point

problem in

Bayesian approach

From the CUSUM chart one may suspect that there is an abrupt change in

the volatility of the Nifty series around the futures introduction. However it

may be argued that the spike found around the date of futures introduction

may only be due to the natural variability of the Nifty series. Thus the

change point analysis is also approached from a Bayesian viewpoint to see if

one can statistically infer that there indeed exists a change in the volatility

process of NSE Nifty without utilizing the knowledge of exact date of

introduction of futures trading.

Controlling Other Factors:

The next step is the choice of the length of test period or the length of the

estimation window. The choice of the length of the test period is a critical

question where a balance needs to be struck between the length of the period

for reliable estimation of model parameters, against the possibility of

existence of other events that might affect the series and thus the parameter

estimates. The later is because stock markets are usually affected by a

number of other events over a period of time, which are distinct from the

event in question. Thus there is a problem of confounding by other

intervening variables. The effects of these events on volatility are uncertain


23/60

23

and disentangling these intervening events and extracting a normal model

of expected volatility is not a simple task.

Two methods are used to guard against drawing erroneous conclusion about

the shift in volatility due to introduction of index futures trading, which in

reality might be attributed to other factors. First, the MSCI World index is

used to control for market-wide movements. Second, a control procedure is

undertaken by implementing the entire test procedure on a similar index that

did not have any derivative trading. If the NSE Nifty exhibits a change while

the control index does not, then the conclusions drawn with respect to the

impact of the introduction of the index futures trading on the NSE Nifty are

strengthened. Given that index futures contracts have been introduced on the

most popular and broad measure of Indian stock market, the choice of

control index should typically be the next largest index. Towards this end,

NSE Nifty Junior is chosen as the control index, which does not have futures

trading yet. The theoretical framework of analyzing the change in volatility

is described in the next sub-section.

Using GARCH Model: Analyzing the structure of Volatility

The general approach adopted in the literature to examine the effect of onset

of futures trading is to compare the spot price volatility prior to the event

with that of post-futures. In analyzing the behavior of pre- and post-futures

volatility, one should attempt to explicitly capture the temporal dependency

phenomena and time-varying nature of volatility. In addressing these issues,

following Chan and Karolyi (1991), Lee and Ohk (1992), Antoniou and

Holmes (1995), within the framework of the Generalized Autoregressive


24/60

24

Conditional Heteroskedasticity (GARCH) model is performed. By providing

a detailed specification of volatility, this technique enables one to not only

check whether the volatility has changed but also provides the endogenous

sources of change in volatility.

Marginal Volatility Comparison

Though the GARCH framework explicitly model how the conditional

volatility evolves over time, it does not comment on change in volatility of

the series as a whole, which is the primary objective of the study. Further the

conditional volatility of the series or residuals by definition depends on the

past information and hence unable to conclude on the overall volatility

pattern of the series. This is accomplished by calculating the marginal

volatility of the series, which is derived from the ARMA-GARCH model.

3.0 CONCLUSION:

This paper investigates whether and to what extent the introduction of Index

Futures trading has had an impact on the mean level and volatility of the

underlying NSE Nifty Index. The results reported for the NSE Nifty indicate

that while the introduction of Index Futures trading has no effect on mean

level of returns and marginal volatility, it has significantly altered the

structure of spot market volatility. Specifically, there is evidence of new

information getting assimilated and the effect of old information on

volatility getting reduced at a faster rate in the period following the onset of

futures trading. This result appears to be robust to the model specification,

asymmetric effects, sub-period analysis and market-wide movements. These

results are consistent with the theoretical arguments of Ross (1989).


25/60

25

2.2.2 BEHAVIOUR OF STOCK MARKET VOLATILITY AFTER

DERIVATIVES

Golaka C Nath

INTRODUCTION

The introduction of equity and equity index derivative contracts in Indian

market has not been very old but today the total notional trading values in

derivatives contracts are much ahead of cash market. On many occasions,

the derivatives notional trading values are double the cash market trading

values. Given such dramatic changes, we would like to study the behaviour

of volatility in cash market after the introduction of derivatives. Impact of

derivatives trading on the volatility of the cash market in India has been

studied by Thenmozhi(2002), Shenbagaraman(2003), Gupta and Kumar

(2002) . Gupta and Kumar(2002) did find that the overall volatility of

underlying market declined after introduction of derivatives contracts on

indices. Thenmozhi(2002) reported lower level volatility in cash market

after introduction of derivative contracts. Shenbagaraman(2003) reported

that there was no significant fall in cash market volatility due to introduction

of derivatives contracts in Indian market. Raju and Karande (2003) reported

a decline in volatility of the cash market after derivatives introduction in

Indian market. All these studies have been done using the market index and

not individual stocks. These studies were conducted using data for a smaller

period and when the notional trading volume in the market was not

significant and before tremendous success of futures on individual stocks.

Today derivatives market in India is more successful and we have more than


26/60

26

3 years of derivatives market. Hence the present study would use the longer

period of data to study the behaviour of volatility in the market after

derivatives was introduced. The study would use indices as well as

individual stocks for analys

METHODOLOGY

This study uses the daily stock market data from January 1999 (for IGARCH

data used is from January 1998) to October 2003. Thus the daily returns are

calculated using the following equation:

Rt = Log(Pt / Pt -1) *100 (1)

where Rt is the daily return, Pt is the value of the security on day t and Pt-1

is the value of the security on day t-1.

Standard deviation of returns is calculated using the following methods:

n

S.D =

(Rt -R)

2

/(n -1) (2)t =1

where R is the average return over the period. This study calculates the

rolling standard deviation for 1 year window as well as for a 6 month

window to capture the conditional dynamics. Next volatility is calculated

using Risk Metrics method with l = 0.94 (IGARCH) and the initial volatility

was computed using one year data from January 1998 to December 1998.

Then we have used a GARCH model to estimate the daily volatility. In the

linear ARCH (q) model originally introduced by Engle (1982), the

conditional variance ht is postulated to be a linear function of the past q

squared innovations:


27/60

27

In empirical applications of ARCH (q) models a long lag length and a large

number of parameters are often called for. An alternative and more flexible

lag structure is often provided by the generalized ARCH, or GARCH (p,q)

model proposed independently by Bollerslev (1986) and Taylor (1986). In

many applications especially with daily frequency financial data the estimate

for a1 +a2 + ... +aq + b1 + b2 + ... + b p turns out to be very close to unity.

Engle and Bollerslev (1986) were the first to consider GARCH processes

with a1 + a2 + ... +a q + b1 + b2 + ... + b p = 1 as a distinct class of models,

which they termed integrated GARCH (IGARCH). In the IGARCH class of

models a shock to the conditional variance is persistent in the sense that it

remains important for future forecasts of all horizons.

DATA and DATA CHARACTERISTICS

The study uses two benchmark indices: S&P CNX NIFTY and S&P CNX

NIFTY JUNIOR along with selected few stocks for studying the volatility

behaviour during the period January 1999 to October 2003. 20 stocks have

been considered a from the NIFTY and Junior NIFTY category. Out of the

20 stocks, 13 have single stock futures and options while 7 do not have the

same. Futures and options are available on S&P CNX NIFTY but not on

S&P CNX NIFTY Junior.


28/60

28

CONCLUSION

The paper studies the behaviour of volatility in equity market in pre and post

derivatives period in India using static and conditional variance. Conditional

volatility has been modeled using four different method: GARCH(1,1),

IGARCH with l = 0.94, one year rolling window of standard deviation and a

6 month rolling standard deviation. We have considered 20 stocks randomly

from the NIFTY and Junior NIFTY basket as well as benchmark indices

itself. Also static point volatility analysis has been used dividing the period

under study among various time buckets and justified the creation of such

time buckets. While studying conditional volatility it is observed that for

most of the stocks, the volatility has come down in the post derivative period

while for only few stocks in the sample (details are in Annexure II and III)

the volatility in the post derivatives has either remained more or less same or

has increased marginally. All these methods suggested that the volatility of

the market as measured by benchmark indices like S&P CNX NIFTY and

S&P CNX NIFTY JUNIOR have fallen after in the post derivatives period.

The finding is in line with the earlier findings of Thenmozhi (2002),

Shenbagaraman (2003), Gupta and Kumar (2002) and Raju and Karande

(2003). The earlier studies used shorter period of data and pre single stock

futures and options period

data while we have used data for a longer period that has taken into account

various cyclical trends into consideration.


29/60

29

2.2.3 EFFECT OF INTRODUCTION OF INDEX FUTURES ON

STOCK MARKET VOLATILITY: THE INDIAN EVIDENCE

O.P. Gupta

INTRODUCTION

The Indian capital market has witnessed a major transformation and

structural change during the past one decade or so as a result of on going

financial sector reforms initiated by the Government of India since 1991 in

the wake of policies of liberalization and globalization. The major objectives

of these reforms have been to improve market efficiency, enhancing

transparency, checking unfair trade practices, and bringing the Indian capital

market up to international standards. As a result of the reforms several

changes have also taken place in the operations of the secondary markets

such as automated on-line trading in exchanges enabling trading terminals of

the National Stock Exchange (NSE) and Bombay Stock Exchange (BSE) to

be available across the country and making geographical location of an

exchange irrelevant; reduction in the settlement period, opening of the stock

markets to foreign portfolio investors etc. In addition to these developments,

India is perhaps one of the real emerging markets in South Asianregion that

has introduced derivative products on two of its principal existing exchanges

viz., BSE and NSE in June 2000 to provide tools for risk management to

investors. There had, however, been a considerable debate on the question of

whether derivatives should be introduced in India or not. The L.C. Gupta

Committee on Derivatives, which examined the whole issue in details, had

recommended in December 1997 the introduction of stock index futures in

the first place (1). The preparation of regulatory framework for the

operations of the index futures contracts took another two and a half-year


30/60

30

more as it required not only an amendment in the Securities Contracts

(Regulation) Act, 1956 but also the specification of the regulations for such

contracts. Finally, the Indian capital market saw the launching of index

futures on June 9, 2000 on BSE and on June 12, 2000 on the NSE. A year

later options on index were also introduced for trading on these exchanges.

Later, stock options on individual stocks were launched in July 2001. The

latest product to enter in to the derivative segment on these exchanges is

contracts on stock futures in November 2001. Thus, with the launch of stock

futures, the basic range of equity derivative products in India seems to be

complete.

METHODOLOGY

Following Ibrahim et al. [1999] and Kar et.al. [2000], the study has used

four measures of volatility. The first measure is based upon close-to-close

prices. Therefore, in the first place, the daily returns based on closing prices

were computed using equation

Rt = ln (Ct/Ct-1) (1)

Where Ct and Ct-1 are the closing prices on day t and t-1 respectively; Rt

represents the return in relation to day t. Next, we have computed the

variance of this return series to understand the inter-day volatility. The

second measure of volatility is based upon open-to-open prices.

Analogously, variance of the daily has been computed from returns series

based on open-to-open prices. The third measure of volatility estimates intra-


31/60

31

day volatility. It has been estimated by using Parkinsons [1980] extreme

value estimator, which is considered to be more efficient.

2.1 The Data

The data employed in the study consists of daily prices of two major stock

market indices viz., the S&P CNX Nifty Index (henceforth Nifty Index) and

the BSE Sensex (BSE Index) for a four year period from June 8, 1998 to

June 30, 2002. For each of these indices four sets of prices were used. These

were daily high, low, open, and close prices. Likewise, daily high, low,

open, and close prices were used from June 9, 2000 to March 31, 2002 for

the BSE Index Futures (7) and from June 12, 2000 to June 30, 2001 for the

Nifty Index Futures. The necessary data have from collected from the

Derivative Segments of both of these exchanges.

CONCLUSIONS

This paper has been aimed at examining the impact of index futures

introduction on stock market volatility. Further, it has also examined the

relative volatility of spot market and futures market. The study utilized daily

price data (high, low, open and close) for BSE Sensex and S&P CNX Nifty

Index from June 1998 to June 2002. Similar data from June 9, 2000 to

March 31, 2002 have also been used for BSE Index Futures and from June

12, 2000 to June 30, 2002 for the Nifty Index Futures.

The study has used four measures of volatility: (a) the first is based upon

close-to-close prices, (b) the second is based upon open-to-open prices, (c)

the third is Parkinsons Extreme Value Estimator, and (d) the fourth is

Garman-Klass measure volatility (GKV).


32/60

32

The empirical results reported here indicate that the over-all volatility of the

underlying stock market has declined after the introduction of index futures

on both the indices in terms of all the three measures i.e. ln (Ct/Ct-1) ln

(Ot/Ot-1) and ln (Ht/Lt). It must, however, be noted that since the

introduction of index futures the Indian stock market has witnessed several

changes in its market micro-structure such as the abolition of the traditional

`badla system, reduction in the trading cycle etc. Therefore, these results

should be interpreted in the light of these changes. However, there is no

conclusive evidence, which suggests that, the futures volatility is higher

(lower) in comparison to the underlying stock market for both the indices in

terms of all the four measures of volatility. In fact, there is some evidence

that the futures volatility is lower in some months in comparison to the

underlying stock market for both of these indices. These results are in

contrast to those reported for the other emerging markets. The study, being

first in the Indian context, has several policy implications for regulators,

policy makers, and investors.


33/60

33

2.2.4 DO FUTURES AND OPTIONS TRADING INCREASE STOCK

MARKET VOLATILITY?

Dr. Premalata Shenbagaraman

INTRODUCTION


introducing derivative contracts. As was the case when commodity futures

were first introduced on the Chicago Board of Trade in 1865, policymakers

and regulators in these markets are concerned about the impact of futures on

the underlying cash market. One of the reasons for this concern is the belief

that futures trading attract speculators who then destabilize spot prices. This

concern is evident in the following excerpt from an article by John Stuart

Mill (1871):

The safety and cheapness of communications, which enable a deficiency in

one place to be, supplied from the surplus of another render the fluctuations

of prices much less extreme than formerly. This effect is much promoted by

the existence of speculative merchant. Speculators, therefore, have a highly

useful office in the economy of society.

Since futures encourage speculation, the debate on the impact of speculators

intensified when futures contracts were first introduced for trading;

beginning with commodity futures and moving on to financial futures and

recently futures on weather and electricity. However, this traditional

favorable view towards the economic benefits of speculative activity has not

always been acceptable to regulators. For example, futures trading was


34/60

34

blamed by some for the stock market crash of 1987 in the USA, thereby

warranting more regulation. However before further regulation in

introduced, it is essential to determine whether in fact there is a causal link

between the introduction of futures and spot market volatility. It therefore

becomes imperative that we seek answers to questions like: What is the

impact of derivatives upon market efficiency and liquidity of the underlying

cash market? To what extent do derivatives destabilize the financial system,

and how should these risks be addressed? Can the results from studies of

developed markets be extended to emerging markets?

This paper seeks to contribute to the existing literature in many ways. This is

the first study to examine the impact of financial derivatives introduction on

cash market volatility in an emerging market, India. Further, this study

improves upon the methodology used in prior studies by using a framework

that allows for generalized auto-regressive conditional heteroskedasticity

(GARCH) i.e., it explicitly models the volatility process over time, rather

than using estimated standard deviations to measure volatility. This

estimation technique enables us to explore the link between

information/news arrival in the market and its effect on cash market

volatility. The study also looks at the linkages in ongoing trading activity in

the futures market with the underlying spot market volatility by

decomposing trading volume and open interest into an expected component

and an unexpected (surprise) component. Finally this is the first study to our

knowledge that looks at the effects of both stock index futures introduction

as well as stock index options introduction on the underlying cash market

volatility. The results of this study are crucial to investors, stock exchange

officials and regulators. Derivatives play a very important role in the price

discovery process and in completing the market. Their role in risk


35/60

35

management for institutional investors and mutual fund managers need

hardly be overemphasized. This role as a tool for risk management clearly

assumes that derivatives trading do not increase market volatility and risk.

The results of this study will throw some light on the effects of derivative

introduction on the efficiency and volatility of the underlying cash markets.

METHODOLOGY

One of the key assumptions of the ordinary regression model is that the

errors have the same variance throughout the sample. This is also called the

homoskedasticity model. If the error variance is not constant, the data are

said to be heteroskedastic. Since ordinary least-squares regression assumes

constant error variance, heteroskedasticity causes the OLS estimates to be

inefficient. Models that take into account the changing variance can make

more efficient use of the data. There are several approaches to dealing with

heteroskedasticity. If the error variance at different times is known, weighted

regression is a good method. If, as is usually the case, the error variance is

unknown and must be estimated from the data, one can model the changing

error variance. In the past, studies of volatility have used constructed

volatility measures like estimated standard deviations, rolling standard

deviations, etc, to discern the effect of futures introduction. These studies

implicitly assume that price changes in spot markets are serially uncorrelated

and homoskedastic. However, findings of heteroskedasticity in stock returns

are well documented (Mandelbrot 1963), Fama (1965), Bollerslev (1986).

Thus the observed differences in variances from models assuming

homoscedasticity may simply be due to the effect of return dependence and

not necessarily due to futures introduction.The GARCH model assumes


36/60

36

conditional heteroscedasticity, with homoskedastic unconditional error

variance. That is, the model assumes that the changes in variance are a

function of the realizations of preceding errors and that these changes

represent temporary and random departures from a constant unconditional

variance, as might be the case when using daily data. The advantage of a

GARCH model is that it captures the tendency in financial data for volatility

clustering. It therefore enables us to make the connection between

information and volatility explicit, since any change in the rate of

information arrival to the market will change the volatility in the market.

Thus, unless information remains constant, which is hardly the case,

volatility must be time varying, even on a daily basis.

The impact of stock index futures and option contract introduction in the

Indian market is examined using a unvaried GARCH (1, 1) model. The time

series of daily returns on the S&P CNX Nifty Index is modeled as a

univariate GARCH process. Following Pagan and Schwert (1990) and Engle

and Ng (1993), we need to remove from the time series any predictability

associated with lagged world returns and/or day of the week effects. Further,

it is required to control for the effect of market wide factors, since one is

interested in isolating the unique impact of the introduction of the

futures/options contracts. Fortunately for the Indian stock market there is an

index, the Nifty Junior, which comprises stocks for which no futures

contracts are traded. As such, it serves as a perfect control variable for us to

isolate market wide factors and thereby concentrate on the residual volatility

in the Nifty as a direct result of the introduction of the index derivative

contracts. Therefore the study introduces the return on the Nifty Junior index

as an additional independent variable.


37/60

37

CONCLUSION

In this study one has examined the effects of the introduction of the Nifty

futures and options contracts on the underlying spot market volatility using a

model that captures the heteroskedasticity in returns that characterize stock

market returns. The results indicate that derivatives introduction has had no

significant impact on spot market volatility. This result is robust to different

model specifications. However, futures introduction seems to have changed

the sensitivity of nifty returns to the S&P500 returns. Also, the day-of-the-

week effects seem to have dissipated after futures introduction.

Later the model is estimated separately for the pre and post futures period

and finds that the nature of the GARCH process has changed after the

introduction of the futures trading. Pre-futures, the effect of information was

persistent over time, i.e. a shock to todays volatility due to some

information that arrived in the market today, has an effect on tomorrows

volatility and the volatility for days to come. After futures contracts started

trading the persistence has disappeared. Thus any shock to volatility today

has no effect on tomorrows volatility or on volatility in the future. This

might suggest increased market efficiency, since all information is

incorporated into prices immediately.

Next, using a procedure inspired by Bessembinder and Sequin (1992), it is

found that after the introduction of futures trading, one is unable to pick up

any link between the volume of futures contracts traded and the volatility in

the spot market.


38/60

38


39/60

39

3.1 RESEARCH PROBLEM STATEMENT


introducing the derivatives contracts. As was the case when commodity

trading were first introduced on Chicago Board of Trading in 1865,

policymakers and regulators were worried about impact of future on the

underlying cash market. One of the reason for this concern was futures

trading attracts speculators who then destabilize the spot market.

In India too, Index Futures that were introduced during June 2000 with the

purpose of offering the investors a hedging tool to minimize their risk

aroused mixed feeling amongst the inventors. The general belief was, after

the introduction of Index Futures the market has become more volatile.

Implying there is more return at the cost of more risk. The purpose of this

study is to test whether the market volatility has increased significantly after

the introduction of Index Futures.

3.1.1 SCOPE OF THE STUDY

The limited scope of the study is to find out: Whether the introduction of

stock index futures reduces stock market volatility. Also, if the futures effect

is confirmed, is the effect immediate or delayed. The Study does not intend

to find out whether changes any other international markets affected the

market during the same period.

3.2 METHODOLOGY

3.2.1 OBJECTIVE

The objective of this study is to test, whether the introduction of Index

Futures has had any impact on the volatility of Indian stock market and if

confirmed, is the effect immediate or delayed .


40/60

40

3.2.2 DATA

3.2.2.1 Nature of data

The nature of the data for the above study will be a time series secondary

data showing heteroskedastic nature.

3.2.2.2 Sources of data

The data employed in the study consists of daily prices of the S@P CNX

Nifty Index, NSE500 and Nifty Junior for the period June 9, 1999 to August

1, 2003. The prices used are daily open and close prices. These data will be

collected from National Stock Exchange website.

3.2.2.3 Data Period

The period of data is from June 9, 1999 to August 1, 2003.

3.3. STATISTICAL PROCEDURE

3.3.1 The first objective is to find out whether the data is stationary or non

stationary? This is tested by using Unit Root test.

UUNNIITT RROOOOTT TTEESSTT BBYY AAUUGGMMEENNEETTDD DDIICCKKEEYY FFUULLLLEERR TTEESSTT

The simple Unit root test is valid only if the series as an AR (1) process. If

the series is correlated at high order lags, the assumption of white noise

disturbances is violated. The ADF controls for high- order correlation by

adding lagged difference terms of the dependent variable to the right-hand

side of the regression

yt = C + t-1 + 1 yt-1 + 2 y t-2 + ..+p y t-p + tThis augmented specification is then tested

H0: = 0 Non Stationary

H1: = 0 Stationary


41/60

41

In general, the procedure start with whether the variables X and Y in its level

form is stationary. If the hypothesis is rejected, then the series is transformed

into first difference of the variable and tested for stationarity.

3.3.2 The second objective is to find out whether the data is heteroskedastic

or not. If the data is homoskedastic then there is no need of applying the

GARCH model. The nature of the data is tested by performing ANOVA test.

ANalysis of Variances between groups

Analysis of variance tests the null hypotheses that group means do not differ.

It is not a test of differences in variances, but rather assumes relative

homogeneity of variances. Thus some key ANOVA assumptions are that the

groups formed by the independent variable(s) are relatively equal in size and

have similar variances on the dependent variable ("homogeneity of

variances"). Like regression, ANOVA is a parametric procedure which

assumes multivariate normality (the dependent has a normal distribution for

each value category of the independent(s)).

3.3.3 The third objective of finding out whether the introduction of stock

index futures reduces stock market volatility will be tested by amending the

variance equation of the GARCH model with a dummy variable, which

takes values zero for the pre-futures period and one for the post-futures

period.

3.3 STATISTICAL SSOOFFTTTTWWAARREE PPAACCKKAAGGEESS UUSSEEDD

E views

This software has been used to conduct the Augmented Dickey Fuller

Unit root and GARCH test.


42/60

42

GARCH APPLICATION IN E-Views

There are several reasons that to model and forecast volatility. First, one

may need to analyze the risk of holding an asset or the value of an option.

Second, forecast confidence intervals may be time-varying, so that more

accurate intervals can be obtained by modeling the variance of the errors.

Third, more efficient estimators can be obtained if heteroskedasticity in the

errors is handled properly.

Autoregressive Conditional Heteroskedasticity (ARCH) models are

specifically designed to model and forecast conditional variances. The

variance of the dependent variable is modeled as a function of past values of

the dependent variable and independent or exogenous variables.

ARCH models were introduced by Engle (1982) and generalized as GARCH

(Generalized ARCH) by Bollerslev (1986). These models are widely used in

various branches of econometrics, especially in financial time series

analysis. See Bollerslev, Chou, and Kroner (1992) and Bollerslev, Engle,

and Nelson (1994) for recent surveys.


43/60

43

]


44/60

44

EMPIRICAL RESULTS

Daily closing prices for S & P CNX Nifty, and CNX Nifty Junior were obtained

respectively from www.nseindia.com over the period 1

st

Jan 1999 to 29

th

Aug 2003. Thedata comprises 363 observations related to the period prior to the introduction of futures

trading and the remaining 793 observations to the period after the introduction of futures

trading. Continuously compounded percentage returns are estimated as the log price

relative. That is for an index with daily closing price Pt, its return Rt is defined as log

(Pt/Pt-1). All the return series (before, after and full period) are subjected to Augmented

Dickey Fuller test and the null hypothesis of unit root is rejected in all cases. Fig 1 and

Fig 2 plots the returns of Nifty daily closing price and Nifty Junior daily closing price

respectively. Fig 3 and Fig 4 plot the log data of the returns showing the phenomenon of

volatility clustering. Fig 5 and Fig 6 plot the log price relative for Nifty and Nifty Junior

clearing indicating that the price change volatility is very high. The study of these graphs

provides an initial view of volatility for NSE Nifty and Nifty Junior indices. It can be

observed from the graph that the pre-futures NSE Nifty volatility is greater than that of

post-futures. This broadly suggests that the introduction of index futures has not

destabilized the spot market. However, inferences cannot be drawn from these figures

alone, as they are not supported by any statistical data. The graph 5 and graph 6 displays

the volatility-clustering phenomenon, namely, large (small) shocks of either sign tend to

follow large (small) shocks. These preliminary findings motivate and call for further

investigation by GARCH modeling.
http://www.nseindia.com/


45/60

45

GRAPHICAL EVIDENCES

GRAPH OF CLOSING PRICES

GRAPH SHOWING MOVEMENT OF NIFTY DAILY

CLOSING PRICES

0

200

400

600

800

1000

1200

1400

1600

1800

2000

1 106 211 316 421 526 631 736 841 946 1051 1 156

NO OF OBSERVATIONS

CLOSINGP

RICE

GRAPH SHOWING THE MOVEMENT OF NIFTY JUNIOR

DAILY CLOSING PRICE

0

1000

2000

3000

4000

5000

6000

1 122 243 364 485 606 727 848 969 1090

NO. OF OBSERVATIONS

CLOSINGP

RICE

Series1

Fig 1 (Nifty) Fig 2 (Nifty Junior)

GRAPH OF LOG PRICE DATA

LOG PRICE DATA

0.8

0.85

0.9

0.95

1

1.05

1.1

1 126 251 376 501 626 751 876 1001 1126

NO. OF OBSERVATIONS

LOGP

RICE

Series1

LOG PRICE DATA

0

0.2

0.4

0.6

0.8

1

1.2

1 122 243 364 485 606 727 848 969 1090

NO. OF OBSERVATIONS

LO

G

PRICE

Series1


GRAPH OF LOG PRICE DIFFERRENCE

LOG PRICE DIFFERENCE DATA

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

1 122 243 364 485 606 727 848 969 1090

NO. OF OBSERVATIONS

LOGP

RICED

IFFERENCE

Series1

LOG PRICE DIFFERENCE DATA

-0.1

-0.05

0

0.05

0.1

1 128 255 382 509 636 763 890 1017 1144

NO. OF OBSERVATION

LOGP

RICE

DIFFERENCE

Series1



46/60

46

TEST FOR HETEROSKEDASTICITY

One of the key assumptions of the ordinary regression model is that the

errors have the same variance throughout the sample. This is also called the

homoskedasticity model. If the error variance is not constant, the data are

said to be heteroskedastic. Since ordinary least-squares regression assumes

constant error variance, heteroskedasticity causes the OLS estimates to be

inefficient. Models such as ARCH/ GARCH that takes into account the

changing variance can make more efficient use of the data. In the past,

studies of volatility have used constructed volatility measures like estimated

standard deviations, rolling standard deviations, etc, to discern the effect of

futures introduction. These studies implicitly assume that price changes in

spot markets are serially uncorrelated and homoskedastic. However, findings

of heteroskedasticity in stock returns are well documented. Performing a

DESCRIPTIVE ANALYSIS on the daily stock returns of both S&P CNX

Nifty and Nifty Junior proves the heteroskedastic nature of the above data.

As seen below from the analysis we can conclude that the variance of the ten

periods is different thus proving that the data considered is heteroskedastic.


47/60

47

S&P CNX Nifty

1-Jan-99 to 30-Jun-99 1-Jul-99 to 30-Dec-99

ONE

1220.0

1200.0

1180.0

1160.0

1140.0

1120.0

1100.0

1080.0

1060.0

1040.0

1020.0

1000.0

980.0

960.0

940.0

920.0

900.0

ONE

Frequency

30

20

10

0

Std. Dev = 87.48

Mean = 1041.3

N = 125.00

TWO

1500

.0

1480

.0

1460

.0

1440

.0

1420

.0

1400

.0

1380

.0

1360

.0

1340

.0

1320

.0

1300

.0

1280

.0

1260

.0

1240

.0

1220

.0

1200

.0

1180

.0

TWO

Frequency

30

20

10

0

Std. Dev = 62.74

Mean = 1376.1

N = 129.00

1-Jan-01 to 30-Jun-00 1-Jul-01to 30-Dec-00

P3

1725.0

1675.0

1625.0

1575.0

1525.0

1475.0

1425.0

1375.0

1325.0

1275.0

1225.0

P3

Frequency

14

12

10

8

6

4

2

0

Std. Dev = 147.09

Mean = 1530.0

N = 106.00

P4

1540

.0

1500

.0

1460

.0

1420

.0

1380

.0

1340

.0

1300

.0

1260

.0

1220

.0

1180

.0

1140

.0

P4

Frequency

16

14

12

10

8

6

4

2

0

Std. Dev = 104.56

Mean = 1334.9

N = 144.00


P5

1420.0

1380.0

1340.0

1300.0

1260.0

1220.0

1180.0

1140.0

1100.0

1060.0

1020.0

P5

Frequency

30

20

10

0

Std. Dev = 105.48

Mean = 1215.1

N = 125.00

P6

11

10.0

10

90.0

10

70.0

10

50.0

10

30.0

10

10.0

99

0.0

97

0.0

95

0.0

93

0.0

91

0.0

89

0.0

87

0.0

85

0.0

P6

F

requency

30

20

10

0

Std. Dev = 66.71

Mean = 1026.5

N = 123.00


48/60

48


P7

1190.0

1180.0

1170.0

1160.0

1150.0

1140.0

1130.0

1120.0

1110.0

1100.0

1090.0

1080.0

1070.0

1060.0

1050.0

1040.0

1030.0

P7

Frequency

16

14

12

10

8

6

4

2

0

Std. Dev = 40.86

Mean = 1107.3

N = 126.00

P8

1100.0

1090.0

1080.0

1070.0

1060.0

1050.0

1040.0

1030.0

1020.0

1010.0

1000.0

990.0

980.0

970.0

960.0

950.0

940.0

930.0

920.0

P8

Frequency

20

10

0

Std. Dev = 46.96

Mean = 1004.3

N = 125.00


P9

1120.0

1100.0

1080.0

1060.0

1040.0

1020.0

1000.0

980.0

960.0

940.0

920.0

P9

Frequency

14

12

10

8

6

4

2

0

Std. Dev = 52.80

Mean = 1024.6

N = 124.00

P10

1360.0

1340.0

1320.0

1300.0

1280.0

1260.0

1240.0

1220.0

1200.0

1180.0

1160.0

1140.0

1120.0

1100.0

P10

Frequency

10

8

6

4

2

0

Std. Dev = 69.25

Mean = 1201.7

N = 43.00

JUNIOR NIFTY RESULTS

1-Jan-99 to 30-Jun-99 1-Jul-99 to 30-Dec

J1

2075.0

2025.0

1975.0

1925.0

1875.0

1825.0

1775.0

1725.0

1675.0

1625.0

1575.0

1525.0

J1

Frequency

16

14

12

10

8

6

4

2

0

Std. Dev = 138.52

Mean = 1845.8

N = 125.00

J2

3900.0

3700.0

3500.0

3300.0

3100.0

2900.0

2700.0

2500.0

2300.0

2100.0

1900.0

J2

Frequency

20

10

0

Std. Dev = 489.39

Mean = 2719.1

N = 129.00


49/60

49


J3

5000.0

4800.0

4600.0

4400.0

4200.0

4000.0

3800.0

3600.0

3400.0

3200.0

3000.0

2800.0

2600.0

2400.0

2200.0

J3

F

requency

14

12

10

8

6

4

2

0

Std. Dev = 912.89

Mean = 3689.2

N = 106.00

J4

2950.0

2900.0

2850.0

2800.0

2750.0

2700.0

2650.0

2600.0

2550.0

2500.0

2450.0

2400.0

2350.0

2300.0

2250.0

2200.0

2150.0

2100.0

J4

F

requency

20

10

0

Std. Dev = 191.04

Mean = 2499.9

N = 144.00


J5

2500.0

2400.0

2300.0

2200.0

2100.0

2000.0

1900.0

1800.0

1700.0

1600.0

1500.0

1400.0

J5

Frequency

30

20

10

0

Std. Dev = 388.51

Mean = 1854.3

N = 125.00

J6

1420.0

1400.0

1380.0

1360.0

1340.0

1320.0

1300.0

1280.0

1260.0

1240.0

1220.0

1200.0

1180.0

1160.0

1140.0

1120.0

1100.0

1080.0

1060.0

1040.0

J6

Frequency

16

14

12

10

8

6

4

2

0

Std. Dev = 108.07

Mean = 1263.4

N = 123.00


J7

1660.0

1640.0

1620.0

1600.0

1580.0

1560.0

1540.0

1520.0

1500.0

1480.0

1460.0

1440.0

1420.0

1400.0

1380.0

1360.0

1340.0

1320.0

1300.0

1280.0

J7

Frequen

cy

30

20

10

0

Std. Dev = 109.26

Mean = 1525.6

N = 126.00

J8

1680.0

1640.0

1600.0

1560.0

1520.0

1480.0

1440.0

1400.0

1360.0

1320.0

1280.0

1240.0

J8

Frequency

16

14

12

10

8

6

4

2

0

Std. Dev = 123.57

Mean = 1396.3

N = 125.00


50/60

50


J9

1750.0

1700.0

1650.0

1600.0

1550.0

1500.0

1450.0

1400.0

1350.0

1300.0

1250.0

J9

Frequency

30

20

10

0

Std. Dev = 134.81

Mean = 1441.5

N = 124.00

J10

2300.0

2250.0

2200.0

2150.0

2100.0

2050.0

2000.0

1950.0

1900.0

1850.0

1800.0

J10

Frequency

10

8

6

4

2

0

Std. Dev = 118.22

Mean = 2000.6

N = 43.00

From the above analysis it is very clear that the variance of the 10 periods

are different, thus proving the data to be heteroskedastic.

STATISTICAL EVIDENCES

Further to prove the heteroskedastic nature of the stock returns statistically,

ANOVA TEST is carried out.

The F is named in the honour of the great statistician R.A. Fisher. The

object of the F test is to find out whether the two independent estimates of

population variance differ significantly, or whether the two samples may be

regarded as drawn from normal populations having the same variances.

The analysis of variance frequently referred to by the contractionANOVA,

is a statistical technique specially designed to test whether the means of

more than two quantitative populations are equal.

Each index is broken down to ten equal periods (10) and ANOVA test is

done verify whether the data is heteroskedastic (varying variances) or

homoskedastic (equal variances)


51/60

51

ANOVA: Results for S & P CNX NIFTY

The results of a ANOVA statistical test performed

Source of Sum of d.f. Mean FVariation Squares Squares

Between 1.4899E-03 9 1.6555E-04 0.7565

Error 0.3053 *** 2.1884E-04

Total 0.3068 ***

The probability of this result, assuming the null hypothesis, is 0.66

In the above test F calculated (0.7865) is more than the table value (0.66). Hence the

hypothesis is rejected and it is proved that the 10 populations or the 10 periods are of

different variances.

ANOVA: Results for NIFTY JUNIOR

The results of a ANOVA statistical test performed at 12:23 on 12-JUN-2006

Source of Sum of d.f. Mean F

Variation Squares Squares

Between 1.1544E-02 9 1.2826E-03 2.989

Error 0.4931 *** 4.2917E-04

Total 0.5047 ***

The probability of this result, assuming the null hypothesis, is 0.0016

In Nifty Junior also it is very clear that the null hypothesis is rejected as F calculated

(2.989) is higher than F table. Thus the data is heteroskedastic.

AUGMENTED DICKEY FULLER TEST

UNIT ROOT TEST

H0: There is unit root in the series-------------- Non Stationary

H1: There is no unit root in the series --------- Stationary


52/60

52

SERIES NAME ADF STATISTICS CRITICAL

VALUE 1%

CRITICAL

VALUE 5%

CRITICAL

VALUE 10%

INTERPRETATION FOR

1%, 5%, AND 10%

NIFTY INDEX -32.07324 -2.5675 -1.9396 -1.6158 STATIONARY

NIFTY JUNIOR -29.37228 -2.5675 -1.9396 -1.6158 STATIONARY

APOLLO -32.70965 -2.5675 -1.9396 -1.6158 STATIONARY

RELIANCE ENERGY

-32.14360 -2.5675 -1.9396 -1.6158 STATIONARY

SIEMENS

-31.86540 -2.5675 -1.9396 -1.6158 STATIONARY

GE

-30.91421 -2.5675 -1.9396 -1.6158 STATIONARY

BHARAT FORGE

-31.99583 -2.5675 -1.9396 -1.6158 STATIONARY

ASHOK LEYLAND

-31.24009 -2.5675 -1.9396 -1.6158 STATIONARY

BANK INDIA

-32.94337 -2.5675 -1.9396 -1.6158 STATIONARY

IFCI

-33.88069 -2.5675 -1.9396 -1.6158 STATIONARY

UTI

-37.69565 -2.5675 -1.9396 -1.6158 STATIONARY

BOB

-32.07729 -2.5675 -1.9396 -1.6158 STATIONARY

AUROBINDO PHARM

-66.87823 -2.5675 -1.9396 -1.6158 STATIONARY

ASIAN PAINTS

-33.33692 -2.5675 -1.9396 -1.6158 STATIONARY

CORPORATIONBANK

-31.28189 -2.5675 -1.9396 -1.6158 STATIONARY

LICH

-31.67365 -2.5675 -1.9396 -1.6158 STATIONARY

PUNJAB TRACTORS

-31.11023 -2.5675 -1.9396 -1.6158 STATIONARY

BONG

-40.74248 -2.5675 -1.9396 -1.6158 STATIONARY

RAYMONDS-32.08536 -2.5675 -1.9396 -1.6158 STATIONARY

CONCOR

-35.66869 -2.5675 -1.9396 -1.6158 STATIONARY

NICHOLAS

-30.67899 -2.5675 -1.9396 -1.6158 STATIONARY

PFIZER

-33.61204 -2.5675 -1.9396 -1.6158 STATIONARY

NIRMA

-28.20883 -2.5675 -1.9396 -1.6158 STATIONARY

INGERAND

-35.62704 -2.5675 -1.9396 -1.6158 STATIONARY

COCHIN

-29.27522 -2.5675 -1.9396 -1.6158 STATIONARY

ABB

-32.40998 -2.5675 -1.9396 -1.6158 STATIONARY

BAJAJ-33.61912 -2.5675 -1.9396 -1.6158 STATIONARY

BHEL

-33.55707 -2.5675 -1.9396 -1.6158 STATIONARY

BPCL

-31.55388 -2.5675 -1.9396 -1.6158 STATIONARY

CIPLA

-32.18889 -2.5675 -1.9396 -1.6158 STATIONARY

DABUR

-33.66047 -2.5675 -1.9396 -1.6158 STATIONARY

REDDY -32.89738 -2.5675 -1.9396 -1.6158 STATIONARY


53/60

53

GLAXO

-34.41562 -2.5675 -1.9396 -1.6158 STATIONARY

HDFC

-32.77667 -2.5675 -1.9396 -1.6158 STATIONARY

HERO HONDA

-33.11789 -2.5675 -1.9396 -1.6158 STATIONARY

HLL

-33.73247 -2.5675 -1.9396 -1.6158 STATIONARY

ICICI

-29.71351 -2.5675 -1.9396 -1.6158 STATIONARY

ITC

-33.17538 -2.5675 -1.9396 -1.6158 STATIONARY

IPCL

-31.76127 -2.5675 -1.9396 -1.6158 STATIONARY

INFOSYS

-30.88505 -2.5675 -1.9396 -1.6158 STATIONARY

LARSEN AND TUBRO

-31.68402 -2.5675 -1.9396 -1.6158 STATIONARY

ONGC

-30.40827 -2.5675 -1.9396 -1.6158 STATIONARY

OBC

-33.56244 -2.5675 -1.9396 -1.6158 STATIONARY

RANBAXY

-32.47195 -2.5675 -1.9396 -1.6158 STATIONARY

RELIANCE

-31.08694 -2.5675 -1.9396 -1.6158 STATIONARY

SATYAM

-32.57036 -2.5675 -1.9396 -1.6158 STATIONARY

SBI

-33.98794 -2.5675 -1.9396 -1.6158 STATIONARY

SUN PHARMA

-30.47760 -2.5675 -1.9396 -1.6158 STATIONARY

TATA CHEMICALS

-32.47730 -2.5675 -1.9396 -1.6158 STATIONARY

TATA MOTOR

-31.01780 -2.5675 -1.9396 -1.6158 STATIONARY

TATA POWER

-31.30019 -2.5675 -1.9396 -1.6158 STATIONARY

TATA STEEL

-33.69769 -2.5675 -1.9396 -1.6158 STATIONARY

WIPRO

-32.22066 -2.5675 -1.9396 -1.6158 STATIONARY

ZEE

-33.68494 -2.5675 -1.9396 -1.6158 STATIONARY

Table 1

From table 1 we can conclude that the data under consideration is a

stationary data and there exist no unit root.

GARCH TEST

The GARCH model assumes conditional heteroskedasticity, with

homoskedastic unconditional error variance. That is, the model assumes that

the changes in variance are a function of the realizations of preceding errors

and that these changes represent temporary and random departures from a


54/60

54

constant unconditional variance, as might be the case when using daily data.

The advantage of a GARCH model is that it captures the tendency in

financial data for volatility clustering. It therefore enables us to make the

connection between information and volatility explicit, since any change in

the rate of information arrival to the market will change the volatility in the

market. Thus, unless information remains constant, which is hardly the case,

volatility must be time varying, even on a daily basis

Thus GARCH MODEL used for the study of impact on the market volatility.

It is observed that the volatility as measured by variance for the period

(1999-2003) has come down for most of the stocks. The period (1999-2003)

is broken down to ten bi-annual periods and variance for each period is

calculate and shown below in table-2

Table showing the variances for Nifty and Nifty JuniorPERIOD NIFTY NIFTY JU

1-Jan-99

30-JUN-99

0.053760197 0.058425979

1-Jul-99

30-DEC-99

0.031600144 0.657133781

1-Jan-0030-JUN-00

0.065039571 0.14173093

1-Jul-00

30-DEC-00

0.034736971 0.06862588

1-Jan-01

30-JUN-01

0.040223739 0.062930514

1-Jul-00

30-DEC-01

0.025396778 0.030082506

1-Jan-02

30-JUN-02

0.018053329 0.030082506

1-Jul-02

30-DEC-02

0.00997472 0.017579076

1-Jan-03

30-JUN-03

0.013078324 0.020111077

1-Jul-03

30-DEC-03

0.0069779 0.010076804

Table-2


55/60

55

To determine the impact of index futures on the volatility of the underlying

stock market GARCH (1,1) model has been used. It determines the

conditional volatility of the benchmark indices as well as stocks in question.

It can be seen that for almost all stocks as well as the benchmark indices, the

static volatility for the period before introduction of derivatives was higher.

S&P CNX NIFTY

Dependent Variable: NNEWMethod: ML - ARCH

Date: 06/10/06 Time: 19:48Sample(adjusted): 2 1130Included observations: 1129 after adjusting endpointsConvergence achieved after 13 iterationsBollerslev-Wooldrige robust standard errors & covarianceBackcast: 1

Coefficient Std. Error z-Statistic Prob.AR(1) -0.173768 0.316736 -0.548620 0.5833MA(1) 0.271653 0.308591 0.880299 0.3787

Variance EquationC 7.11E-05 2.35E-05 3.028840 0.0025

ARCH(1) 0.166509 0.042064 3.958499 0.0001GARCH(1) 0.705074 0.061467 11.47076 0.0000

D1 -4.94E-05 1.92E-05 -2.566697 0.0103R-squared -0.000516 Mean dependent var -0.000221

Adjusted R-squared -0.004971 S.D. dependent var 0.016268S.E. of regression 0.016309 Akaike info criterion -5.597555Sum squared resid 0.298687 Schwarz criterion -5.570828Log likelihood 3165.820 Durbin-Watson stat 2.101752Inverted AR Roots -.17Inverted MA Roots -.27

Table -3


56/60

56

JUNIOR NIFTYDependent Variable: SER04Method: ML - ARCHDate: 06/10/06 Time: 19:59Sample(adjusted): 2 1130Included observations: 1129 after adjusting endpoints

Convergence achieved after 6 iterationsBollerslev-Wooldrige robust standard errors & covarianceBackcast: 1

Coefficient Std. Error z-Statistic Prob.AR(1) 0.052898 0.313498 0.168735 0.8660MA(1) 0.053009 0.317348 0.167036 0.8673

Variance EquationC 8.35E-05 2.76E-05 3.026120 0.0025

ARCH(1) 0.203384 0.044021 4.620161 0.0000GARCH(1) 0.671995 0.060347 11.13548 0.0000

D1 -5.40E-05 2.29E-05 -2.355464 0.0185R-squared 0.017999 Mean dependent var 0.000198Adjusted R-squared 0.013627 S.D. dependent var 0.021031

S.E. of regression 0.020888 Akaike info criterion -5.149255Sum squared resid 0.489955 Schwarz criterion -5.122529Log likelihood 2912.755 Durbin-Watson stat 1.930473Inverted AR Roots .05Inverted MA Roots -.05

Table- 4

In Table-3, the estimates of ARCH (1), GRACH (1) and D. D among the

GARCH parameters are of interest.

ARCH (1) represents news about volatility from the previous period,

measured as the lag of the squared residual from the mean equation.

GARCH (1) represents last periods forecast variance. There is a substantial

increase in news incorporation coefficient ARCH (1), GARCH (1) which are

positive, implying increase in market efficiency, measured by its ability to

quickly incorporate new information. The results of Nifty Junior which acts

as the control for the Nifty where the futures index are not introduced shows

GRACH (1) are less than that in Nifty, thus proving that the introduction of

the index futures trading led to a more rapid absorption of news into prices.

The sum of ARCH(1) and GARCH(1) coefficients is very close to one,

indicating that volatility shocks are quite persistent (as observed in the fig. 5

and fig. 6). As the sum ofC, ARCH (1), GARCH (1), and D approaches


57/60

57

one or equal to one the Mean reversion is a slow process. This means that

the shocks tend to cause a very high degree of volatility. The sum C, ARCH,

GRACH and D in Nifty (0.87) is lesser than that of Nifty Junior (0.88)

marginally thus suggesting that introduction of Index futures does impact the

underlying spot volatility and has reduced it. Hence on the whole, the

volatility of the Nifty series has decreased but the change is marginal. The

above can be better explained with the help of a dummy variable introduced

during the GARCH test. This variable takes value 0 before the introduction

of the Index Futures and 1 after the introduction of Index Futures.

VALUE OF THE DUMMY VARIABLE

INDICES DUMMY VARIABLE

NIFTY -4.94E-05

NIFTY JUNIOR -5.40E-05

Table -5

From the table-5 it is clear that introduction of Index Futures has had aneffect on the underlying cash market. The volatility of the market has

reduced (-4.94E-05>-5.40E-05) significantly. The same results were observed for

the individual stocks too.

NIFTY NIFTY JUNIOR

COMPANY D1 COMPANY D1

ABB -0.00022

RELIANCE

ENERGY -0.000224BAJAJ -0.0000196 SIEMENS -0.000121

BHEL -0.0000462 GE -8.23E-05

BPCL -0.0002 BHARAT FORGE -1.53E-06

CIPLA -0.00062

ASHOK

LEYLAND -3.56E-05


58/60

58

DABUR 0.002679 BANK INDIA 6.62E-06

REDDY -3.50E-05 IFCI 0.000163

GLAXO -0.00018 UTI -0.000353

HDFC -0.00018 BOB -4.90E-05

HERO HONDA -1.34E-05 AUROBINDOPHARM -0.000649

HLL 0.003218 ASIAN PAINTS -0.000129

ICICI -2.62E-05 APOLLO -9.71E-05

ITC -1.07E-05

CORPORATION

BANK -5.99E-05

IPCL -9.61E-05 LICH -1.06E-06

INFOSYS -0.00021

PUNJAB

TRACTORS -0.002953

LARSEN AND

TUBRO -5.93E-05 BONG

-0.000634

ONGC -2.25E-05 RAYMONDS -0.000139

OBC -4.85E-05 CONCOR -0.000227

RANBAXY -0.00018 NICHOLAS -4.76E-05

RELIANCE -6.48E-05 PFIZER -0.000212

SATYAM -0.00105 NIRMA -0.000165

SBI -4.42E-05 INGERAND -1.24E-05

SUN PHARMA -0.00054 COCHIN 0.001287

TATA

CHEMICALS -5.50E-05 MOSER -0.000302TATA MOTOR -2.21E-05

TATA POWER -1.53E-05

TATA STEEL -9.50E-05

WIPRO -9.93E-05

ZEE -0.00287

Thus table shows that the results of NSE Nifty have reduced

Impact of index futures on indian market volatility-Archana Subramanya-0403

Documents

Transcript of Impact of index futures on indian market volatility-Archana Subramanya-0403