Document Sample

Impact of Index Futures on Indian Market Volatility - An application of GARCH . A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE AWARD OF MBA DEGREE OF BANGALORE UNIVERSITY. SUBMITTED BY Ms.P.Archana Subramanya REG. NO – 04XQCM6007 UNDER THE GUIDANC E OF Dr . T. V. N R ao F acul t y M PBI M M . P. BI RLA I N STI T U TE O F M AN AG EM E N T (ASSOCIA TE B HA R ATIY A VID YA BH A VA N) # 4 3 RACE COURSE ROAD, BANGALORE – 560001. 2004-2006 Batch 1 DECLARATION I hereby declare that the dissertation entitled “Impact of Index Futures on Indian Market Volatility-An application of GARCH” is the result of work undertaken by me, under the guidance and supervision of Dr.T.V.N.Rao, Associate Professor, M.P.Birla Institute of Management, Bangalore. I also declare that this dissertation has not been submitted to any other University/Institution for the award of any Degree or Diploma. Place: Bangalore Date: 16th June 2006 P.Archana Subramanya 2 Principal Certificate. I hereby certify that the r e s e a r c h work embodied in this dissertation entitled “Impact of Index Futures on Indian Market Volatility-An application of GARCH” has been undertaken and completed by Ms.P.Archana Subramanya under the guidance and supervision of Dr.T.V.N.Rao, Faculty, MPBIM, Bangalore. Place: Bangalore Date: 16/06/2006 Dr. N. S. Malavalli Principal MPBIM, Bangalore 3 Guide Certificate. I hereby declare that the research work emb o di ed in t h is dissertation entitled “Impact of Index Futures on Indian Market Volatility-An application of GA R C H ” has been undertaken and completed by Ms.P.Archana Subramanya under my guidance and supervision. Place: Bangalore Date: 16/06/2006 Dr.T.V.N.Rao Faculty Member. 4 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) 5 TABLE OF CONTENTS CHAPTERS ABSTARCT 1. INTRODUCTION 1.1 Introduction and Background of the study 2. REVIEW OF LITERATURE 2.1 Theoretical consideration 2.2 Survey of empirical literature 3. RESEARCH METHODOLOGY 3.1 Research problem statement 3.2 Methodology 3.2 Software packages used 4. DATA ANALYSIS AND INTERPRETATION Empirical Results 5. INFERENCES AND CONCLUSIONS BIBLIOGRAPHY PARTICULARS PAGE NO. 4-6 8 -10 11 - 32 34-34 34-37 37-37 39-54 54-54 41 42 - 58 ANNEXURES 6 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 subperiod 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. 7 8 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 9 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 10 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. 11 12 2.1 THEORITICAL CONSIDERATION 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 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. Following Pagan and Schwert (1990) and Engle and Ng (1992), the first step in GARCH modeling of daily returns series, which does not possess a unit root, is to remove any predictability associated with lagged returns and holiday / week-end effects by accommodating sufficient number of (AR, MA) terms and holiday/weekend dummies in the mean equation respectively. Thus for NSE Nifty logarithmic daily returns, the conditional mean equation is specified as: l m n Rt = Ö + Ó ÖRt-i + Ó èj åt-j + vHOLt +ÓãkRWt-k + åt (1) i=1 j=1 k=1 Where Rt is the daily logarithmic return on the NSE Nifty index, HOLt corresponds to week-end/ holiday dummy. Graphical analysis and the computation of some basic statistical measures like the kurtosis, descriptive 13 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: åt /Ùt-1 ~N(O,ht) p ht = áo + Óái å + Óht-j i-1 t=i j=1 2 q (2) where, åt is the same error term Ot is the information set till time t, ai’s are news coefficients measuring the impact of recent news on volatility and ßj’s are the persistence coefficients measuring the impact of “less recent” or “old” news on volatility. These interpretations of ai’s & ßj’s 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 14 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 of ßj,d implies that “less recent news” have less impact on today’s 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. 15 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 Kyle’s(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 16 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. 17 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 country’s 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 twentyfive countries, using various GARCH models augmented with either additive or multiplicative dummy. Their statistical model takes care of 18 asynchronous data, conditional heteroskedasticity, asymmetric volatility responses, and the joint dynamics of each country’s 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 welldocumented 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 19 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 eventstudy 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 20 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 21 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 22 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 23 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). 24 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 25 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 =Ó (Rt -R)2 /(n -1) t =1 (2) 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: 26 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. 27 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. 28 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 29 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- 30 day volatility. It has been estimated by using Parkinson’s [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 Parkinson’s Extreme Value Estimator, and (d) the fourth is Garman-Klass measure volatility (GKV). 31 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. 32 2.2.4 DO FUTURES AND OPTIONS TRADING INCREASE STOCK MARKET VOLATILITY? Dr. Premalata Shenbagaraman 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 33 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 34 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 35 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. 36 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-theweek 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 today’s volatility due to some information that arrived in the market today, has an effect on tomorrow’s 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 tomorrow’s 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. 37 38 3.1 RESEARCH PROBLEM STATEMENT In the last decade, many emerging and transition economies have started 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 “. 39 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. UNIT ROOT TEST BY AUGMENETD DICKEY FULLER TEST 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 + t This augmented specification is then tested H0: H1: = 0 Non Stationary = 0 Stationary 40 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 SOFTTWARE PACKAGES USED E views This software has been used to conduct the Augmented Dickey Fuller Unit root and GARCH test. 41 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. 42 ] 43 EMPIRICAL RESULTS Daily closing prices for S & P CNX Nifty, and CNX Nifty Junior were obtained respectively from www.nseindia.com over the period 1st Jan 1999 to 29th Aug 2003. The data 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. 44 GRAPHICAL EVIDENCES GRAPH OF CLOSING PRICES GRAPH SHOWING MOVEMENT OF NIFTY DAILY CLOSING PRICES 2000 1800 GRAPH SHOWING THE MOVEMENT OF NIFTY JUNIOR DAILY CLOSING PRICE 6000 CLO SIN G PRICE 5000 4000 3000 2000 1000 0 1 122 243 364 485 606 727 848 969 1090 NO. OF OBSERVATIONS Series1 1600 CLOSING PRICES 1400 1200 1000 800 600 400 200 0 1 106 211 316 421 526 631 736 841 946 1051 1156 NO OF OBSERVATIONS Fig 1 (Nifty) GRAPH OF LOG PRICE DATA LOG PRICE DATA 1.1 1.05 1 0.95 0.9 0.85 0.8 1 126 251 376 501 626 751 876 1001 1126 NO. OF OBSERVATIONS Series1 Fig 2 (Nifty Junior) LOG PRICE DATA 1.2 1 LO G P R IC E 0.8 0.6 0.4 0.2 0 1 122 243 364 485 606 727 848 969 1090 NO. OF OBSERVATIONS Series1 LOG PRICE Fig 3 (Nifty) GRAPH OF LOG PRICE DIFFERRENCE LOG PRICE DIFFERENCE DATA 0.1 0.08 0.06 0.04 0.02 0 -0.02 1 -0.04 -0.06 -0.08 -0.1 Fig 4 (Nifty Junior) LOG PRICE DIFFERENCE DATA LOG PRICE DIFFERENCE 0.1 0.05 0 1 -0.05 -0.1 NO. OF OBSERVATION 128 255 382 509 636 763 890 1017 1144 Series1 LO G PR ICE D IFFER ENC E Series1 122 243 364 485 606 727 848 969 1090 NO. OF OBSERVATIONS Fig 5 (Nifty) Fig 6 (Nifty Junior) 45 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. 46 Std. Dev = 104.56 Std. Dev = 66.71 Std. Dev = 62.74 Mean = 1334.9 Mean = 1026.5 Mean = 1376.1 N = 129.00 1-Jul-01to 30-Dec-00 N = 144.00 1-Jul-01 to 30-Dec-01 1-Jul-99 to 30-Dec-99 TWO TWO P4 P6 P4 30 20 10 16 14 12 10 8 6 4 2 30 20 10 0 0 Std. Dev = 105.48 Mean = 1215.1 Std. Dev = 147.09 Std. Dev = 87.48 Mean = 1530.0 N = 125.00 Mean = 1041.3 N = 125.00 N = 106.00 1-Jan-01 to 30-Jun-00 1-Jan-99 to 30-Jun-99 S&P CNX Nifty ONE ONE P3 P3 .0 20 12 .0 00 12 .0 80 11 0.0 6 11 .0 40 11 0.0 2 11 .0 00 11 0.0 8 10 .0 60 10 0.0 4 10 .0 20 10 .0 00 10 .0 0 98 .0 0 96 .0 0 94 0 0. 92 .0 0 90 30 20 10 0 17 16 16 15 15 14 14 13 13 12 12 . 25 . 75 . 25 . 75 . 25 . 75 . 25 . 75 . 25 . 75 . 25 0 0 0 0 0 0 0 0 0 0 0 1-Jan-01 to 30-Jun-01 P5 30 20 10 14 12 10 8 6 4 2 0 Frequency 0 P5 F requency 0 .0 20 14 .0 80 13 .0 40 13 .0 00 13 .0 60 12 .0 20 12 .0 80 11 .0 40 11 .0 00 11 .0 60 10 .0 20 10 P6 .0 00 15 .0 80 14 0 .0 6 14 0 .0 4 14 0 .0 2 14 .0 00 14 0 .0 8 13 0 .0 6 13 .0 40 13 0 .0 2 13 0 .0 0 13 .0 80 12 0 .0 6 12 0 .0 4 12 0 .0 2 12 .0 00 12 0 .0 8 11 .0 40 15 .0 00 15 .0 60 14 .0 20 14 .0 80 13 .0 40 13 .0 00 13 .0 60 12 .0 20 12 .0 80 11 .0 40 11 N = 123.00 .0 10 11 .0 90 10 .0 70 10 .0 50 10 .0 30 10 .0 10 10 0 0. 99 0 0. 97 0 0. 95 0 0. 93 0 0. 91 0 0. 89 0 0. 87 0 0. 85 47 Frequency Frequency Frequency Frequency 1-Jan-02 to 30-Jun-02 P7 16 14 12 10 8 6 1-Jul-02 to 30-Dec-02 P8 20 10 Frequency Std. Dev = 40.86 2 0 Mean = 1107.3 N = 126.00 F requency 4 Std. Dev = 46.96 Mean = 1004.3 0 N = 125.00 P7 1-Jan-03 to 30-Jun-03 P9 14 12 8 10 .0 90 11 0 .0 8 11 0 .0 7 11 0 .0 6 11 0 .0 5 11 0 .0 4 11 0 .0 3 11 0 .0 2 11 0 .0 1 11 0 .0 0 11 0 .0 9 10 0 .0 8 10 0 .0 7 10 0 .0 6 10 0 .0 5 10 0 .0 4 10 0 .0 3 10 P8 1-Jul-03 to 30-Dec-03 P10 .0 00 11 0 . 0 9 108 0 . 0 10 0 . 0 7 106 0 . 0 10 0 . 0 5 104 0 . 0 10 0 . 0 3 102 0 . 0 10 0 . 0 1 10 0 . 0 0 1 0 .0 0 9 9 0 .0 9 8 .0 0 9 7 0 .0 9 6 .0 0 9 5 0 .0 9 4 .0 0 9 3 0 .0 92 10 8 6 4 6 4 Frequency F requency 2 0 92 94 0 0. 96 0 0. 98 10 10 10 10 10 11 11 0 0. 0 0. 00 .0 20 .0 40 .0 60 .0 80 .0 00 .0 20 Std. Dev = 52.80 Mean = 1024.6 N = 124.00 2 Std. Dev = 69.25 Mean = 1201.7 N = 43.00 1100.0 1140.0 1180.0 1220.0 1260.0 1300.0 1340.0 1120.0 1160.0 1200.0 1240.0 1280.0 1320.0 1360.0 0 .0 P9 P10 JUNIOR NIFTY RESULTS 1-Jan-99 to 30-Jun-99 J1 16 14 12 10 8 6 10 20 1-Jul-99 to 30-Dec J2 Frequency Std. Dev = 138.52 2 0 15 15 16 16 17 17 18 18 19 19 20 . 25 0 . 75 . 25 . 75 . 25 . 75 . 25 . 75 . 25 . 75 . 25 Frequency 4 Mean = 1845.8 N = 125.00 20 . 75 Std. Dev = 489.39 Mean = 2719.1 0 N = 129.00 .0 00 39 .0 00 37 .0 00 35 .0 00 33 .0 00 31 .0 00 29 .0 00 27 .0 00 25 .0 00 23 .0 00 21 .0 00 19 0 0 0 0 0 0 0 0 0 0 0 J1 J2 48 Std. Dev = 108.07 Std. Dev = 123.57 Mean = 1263.4 Mean = 1396.3 N = 123.00 Std. Dev = 191.04 1-Jul-00 to 30-Dec-00 J4 J4 16 14 12 10 8 6 4 2 16 14 12 10 8 6 4 2 20 10 0 0 Std. Dev = 388.51 Std. Dev = 109.26 Mean = 1854.3 Mean = 1525.6 Std. Dev = 912.89 N = 125.00 N = 126.00 Mean = 3689.2 1-Jan-00 to 30-Jun-00 J5 J7 J3 J3 J5 22 30 20 10 30 20 10 14 12 10 8 6 4 2 0 0 Frequency 0 J7 .0 00 50 .0 00 48 .0 00 46 0 .0 0 44 .0 00 42 0 .0 0 40 .0 00 38 .0 00 36 0 .0 0 34 .0 00 32 .0 00 30 0 .0 0 28 .0 00 26 0 .0 0 24 .0 00 1-Jan-01 to 30-Jun-01 1-Jan-02 to 30-Jun-02 .0 00 25 0 . 00 24 0 . 00 23 0 . 00 22 0 . 00 21 0 . 00 20 0 . 00 19 0 . 00 18 0 . 00 17 0 . 00 16 0 . 00 15 0 . 00 14 N = 106.00 Frequency 0 .0 50 29 0 .0 0 29 0 .0 5 28 0 .0 0 28 0 .0 5 27 0 .0 0 27 0 .0 5 26 0 .0 0 26 0 .0 5 25 0 .0 0 25 0 .0 5 24 0 .0 0 24 0 .0 5 23 0 .0 0 23 0 .0 5 22 0 .0 0 22 0 .0 5 21 0 .0 0 21 J6 J8 J6 .0 60 1 6 0 .0 4 1 6 0 .0 2 0 16 0 . 0 1 6 0 .0 8 1 5 0 .0 6 0 15 0 . 4 1 5 0 .0 2 1 5 0 .0 0 0 15 0 . 8 1 4 0 .0 6 1 4 0 .0 4 0 14 0 . 2 1 4 0 .0 0 1 4 0 .0 8 0 13 0 . 6 1 3 0 .0 4 1 3 0 .0 2 0 13 0 . 0 1 3 0 .0 8 12 J8 .0 20 1 4 0 .0 0 1 4 0 .0 8 0 1360 . 1 3 0 .0 4 1 3 0 .0 2 0 1300 . 1 3 0 .0 8 1 2 0 .0 6 0 1240 . 1 2 0 .0 2 1 2 0 .0 0 0 1280 . 1 1 0 .0 6 1 1 0 .0 4 0 1120 . 1 1 0 .0 0 1 1 0 .0 8 0 1060 . 1 0 0 .0 4 10 Mean = 2499.9 N = 125.00 1-Jul-01 to 30-Dec-01 1-Jul-02 to 30-Dec-02 .0 80 16 0 . 40 16 0 . 00 16 0 . 60 15 0 . 20 15 0 . 80 14 0 . 40 14 0 . 00 14 0 . 60 13 0 . 20 13 0 . 80 12 0 0. N = 144.00 4 12 49 Frequency Frequency F req ue ncy F re q ue n cy 1-Jan-02 to 30-Jun-02 J9 30 1-Jul-02 to 30-Dec-02 J10 10 8 20 6 4 10 Frequency F req uen cy Std. Dev = 134.81 Mean = 1441.5 0 N = 124.00 2 Std. Dev = 118.22 Mean = 2000.6 N = 43.00 1800.0 1900.0 2000.0 2100.0 2200.0 2300.0 1850.0 1950.0 2050.0 2150.0 2250.0 0 J9 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 contraction ANOVA, 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) 50 12 50 13 00 .0 13 50 .0 14 00 .0 14 50 .0 15 00 .0 15 50 .0 16 00 .0 16 50 .0 17 00 .0 17 50 .0 .0 J10 ANOVA: Results for S & P CNX NIFTY The results of a ANOVA statistical test performed Source of Sum of Variation Squares d.f. Mean Squares F 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 Variation Squares d.f. Mean Squares F Between 1.1544E-02 9 1.2826E-03 Error 0.4931 *** 4.2917E-04 Total 0.5047 *** 2.989 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 51 SERIES NAME ADF STATISTICS CRITICAL VALUE 1% CRITICAL VALUE 5% CRITICAL VALUE 10% INTERPRETATION FOR 1%, 5%, AND 10% NIFTY INDEX NIFTY JUNIOR APOLLO -32.07324 -29.37228 -32.70965 -32.14360 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY RELIANCE ENERGY -31.86540 SIEMENS -30.91421 GE -31.99583 BHARAT FORGE -31.24009 ASHOK LEYLAND -32.94337 BANK INDIA -33.88069 IFCI -37.69565 UTI -32.07729 BOB -66.87823 AUROBINDO PHARM -33.33692 ASIAN PAINTS CORPORATION BANK LICH -31.11023 PUNJAB TRACTORS -40.74248 BONG -32.08536 RAYMONDS -35.66869 CONCOR -30.67899 NICHOLAS -33.61204 PFIZER -28.20883 NIRMA -35.62704 INGERAND -29.27522 COCHIN -32.40998 ABB -33.61912 BAJAJ -33.55707 BHEL -31.55388 BPCL -32.18889 CIPLA -33.66047 DABUR REDDY -32.89738 -31.28189 -31.67365 52 -34.41562 GLAXO -32.77667 HDFC -33.11789 HERO HONDA -33.73247 HLL -29.71351 ICICI -33.17538 ITC -31.76127 IPCL -30.88505 INFOSYS -31.68402 LARSEN AND TUBRO -30.40827 ONGC -33.56244 OBC -32.47195 RANBAXY -31.08694 RELIANCE -32.57036 SATYAM -33.98794 SBI -30.47760 SUN PHARMA -32.47730 TATA CHEMICALS -31.01780 TATA MOTOR -31.30019 TATA POWER -33.69769 TATA STEEL -32.22066 WIPRO -33.68494 ZEE -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -2.5675 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.9396 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 -1.6158 STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY STATIONARY 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 53 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 Junior PERIOD 1-Jan-99 30-JUN-99 1-Jul-99 30-DEC-99 1-Jan-00 30-JUN-00 1-Jul-00 30-DEC-00 1-Jan-01 30-JUN-01 1-Jul-00 30-DEC-01 1-Jan-02 30-JUN-02 1-Jul-02 30-DEC-02 1-Jan-03 30-JUN-03 1-Jul-03 30-DEC-03 NIFTY 0.053760197 0.031600144 0.065039571 0.034736971 0.040223739 0.025396778 0.018053329 0.00997472 NIFTY JU 0.058425979 0.657133781 0.14173093 0.06862588 0.062930514 0.030082506 0.030082506 0.017579076 0.013078324 0.0069779 0.020111077 0.010076804 Table-2 54 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: NNEW Method: ML - ARCH Date: 06/10/06 Time: 19:48 Sample(adjusted): 2 1130 Included observations: 1129 after adjusting endpoints Convergence achieved after 13 iterations Bollerslev-Wooldrige robust standard errors & covariance Backcast: 1 Coefficient Std. Error z-Statistic Prob. AR(1) -0.173768 0.316736 -0.548620 0.5833 MA(1) 0.271653 0.308591 0.880299 0.3787 Variance Equation C 7.11E-05 2.35E-05 3.028840 0.0025 ARCH(1) 0.166509 0.042064 3.958499 0.0001 GARCH(1) 0.705074 0.061467 11.47076 0.0000 -4.94E-05 D1 1.92E-05 -2.566697 0.0103 R-squared -0.000516 Mean dependent var -0.000221 Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Inverted AR Roots Inverted MA Roots -0.004971 0.016309 0.298687 3165.820 -.17 -.27 S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat 0.016268 -5.597555 -5.570828 2.101752 Table -3 55 JUNIOR NIFTY Dependent Variable: SER04 Method: ML - ARCH Date: 06/10/06 Time: 19:59 Sample(adjusted): 2 1130 Included observations: 1129 after adjusting endpoints Convergence achieved after 6 iterations Bollerslev-Wooldrige robust standard errors & covariance Backcast: 1 Coefficient Std. Error z-Statistic AR(1) 0.052898 0.313498 0.168735 MA(1) 0.053009 0.317348 0.167036 Variance Equation C 8.35E-05 2.76E-05 3.026120 ARCH(1) 0.203384 0.044021 4.620161 GARCH(1) 0.671995 0.060347 11.13548 -5.40E-05 D1 2.29E-05 -2.355464 R-squared 0.017999 Mean dependent var Adjusted R-squared 0.013627 S.D. dependent var S.E. of regression 0.020888 Akaike info criterion Sum squared resid 0.489955 Schwarz criterion Log likelihood 2912.755 Durbin-Watson stat Inverted AR Roots .05 Inverted MA Roots -.05 Prob. 0.8660 0.8673 0.0025 0.0000 0.0000 0.0185 0.000198 0.021031 -5.149255 -5.122529 1.930473 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 of ‘C’, ARCH (1), GARCH (1), and ‘D’ approaches 56 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 NIFTY NIFTY JUNIOR DUMMY VARIABLE -4.94E-05 -5.40E-05 Table -5 From the table-5 it is clear that introduction of Index Futures has had an effect 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 D1 -0.00022 -0.0000196 -0.0000462 -0.0002 -0.00062 NIFTY JUNIOR COMPANY RELIANCE ENERGY SIEMENS GE BHARAT FORGE ASHOK LEYLAND COMPANY ABB BAJAJ BHEL BPCL CIPLA D1 -0.000224 -0.000121 -8.23E-05 -1.53E-06 -3.56E-05 57 DABUR REDDY GLAXO HDFC HERO HONDA HLL ICICI ITC IPCL INFOSYS LARSEN AND TUBRO ONGC OBC RANBAXY RELIANCE SATYAM SBI SUN PHARMA TATA CHEMICALS TATA MOTOR TATA POWER TATA STEEL WIPRO ZEE 0.002679 -3.50E-05 -0.00018 -0.00018 -1.34E-05 0.003218 -2.62E-05 -1.07E-05 -9.61E-05 -0.00021 -5.93E-05 -2.25E-05 -4.85E-05 -0.00018 -6.48E-05 -0.00105 -4.42E-05 -0.00054 -5.50E-05 -2.21E-05 -1.53E-05 -9.50E-05 -9.93E-05 -0.00287 BANK INDIA IFCI UTI BOB AUROBINDO PHARM ASIAN PAINTS APOLLO CORPORATION BANK LICH PUNJAB TRACTORS BONG RAYMONDS CONCOR NICHOLAS PFIZER NIRMA INGERAND COCHIN MOSER 6.62E-06 0.000163 -0.000353 -4.90E-05 -0.000649 -0.000129 -9.71E-05 -5.99E-05 -1.06E-06 -0.002953 -0.000634 -0.000139 -0.000227 -4.76E-05 -0.000212 -0.000165 -1.24E-05 0.001287 -0.000302 Thus table shows that the results of NSE Nifty have reduced in comparison with those of Nifty Junior, the control index. As the coefficients of the dummies in the variance equation of NSE Nifty Junior higher than the Nifty, we can say that the volatility has reduced after the introduction of the Index Futures. 58 CONCLUSION This paper intends to studies the behavior of volatility in equity market in pre and post derivatives period in India using conditional variance. Conditional volatility is modeled using GARCH (1, 1). Twenty-Seven stocks are considered randomly from the NIFTY and Junior NIFTY basket as well as benchmark indices itself. 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 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 in the post derivatives period. 59 BIBLIOGRAPHY REFERNCE BOOKS Basic Econometrics - Damodar N.Gujarati, (fourth edition) Econometrics –John Stewart and Len Gill WEBSITES www.nseindia.com www.finance.yahoo.com www.google.com www.investorpedia.com REFERNCE ARTICLES Impact of futures introduction on underlying index volatality: evidence from India - kotha kiran kumar. & chiranjit mukhopadhyay Behaviour of stock market volatility after derivatives - golaka c nath Do futures and options trading increase stock market volatility? Dr. premalata shenbagaraman Effect of introduction of index futures on stock market volatility: the indian evidence - o.p. gupta 60

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 1277 |

posted: | 5/18/2009 |

language: | English |

pages: | 60 |

OTHER DOCS BY sathis0290

How are you planning on using Docstoc?
BUSINESS
PERSONAL

By registering with docstoc.com you agree to our
privacy policy and
terms of service, and to receive content and offer notifications.

Docstoc is the premier online destination to start and grow small businesses. It hosts the best quality and widest selection of professional documents (over 20 million) and resources including expert videos, articles and productivity tools to make every small business better.

Search or Browse for any specific document or resource you need for your business. Or explore our curated resources for Starting a Business, Growing a Business or for Professional Development.

Feel free to Contact Us with any questions you might have.