Impact of Individual Stock Derivatives Introduction in India on Its Underlying Spot Market Volatility

Abstract

This study has made an attempt to examine the impact of the introduction of derivative trading in individual stocks of different market capitalisations that are listed in NSE representing different industrial sectors of the Indian economy using the generalised autoregressive conditional heteroscedastic (GARCH)(p, q) model. This article contributes to existing literature first, by examining the effect of derivative introduction on return volatility of stocks of different market capitalisations. Second, while in earlier studies effect of derivative introduction on return volatility has been examined only on derivative related stocks, in this article it is examined both on derivative-related and derivative-unrelated stocks. Third, the article also examines the impact of derivative trading on stocks of different industrial sectors of the Indian economy. From the result of the study, we find that volatilities of stock returns have declined due to the introduction of derivatives trading on most of the individual large-cap stocks considered in the study, which are all derivative-related stocks. Though we find decrease in return volatilities of all the derivative-unrelated mid-cap stocks in our study, the results of the derivative-related mid-cap stocks are found to be mixed. In case of small-cap stocks, the results indicate a decrease in return volatilities of most of the derivative-related and derivative-unrelated stocks considered in the study. Moreover, there is evidence of volatility reduction for almost all the derivative-unrelated stocks. We find no significant sectoral differences while examining the impact of derivatives trading on return volatilities of stocks representing different sectors of the Indian economy.

Keywords

Volatility derivative market capitalisation heteroscedasticity persistence volatility clustering GARCH(p,q)

Introduction

Volatility is an important phenomenon for any type of asset market, particularly, for stock markets. Stock markets with its primary and secondary segments assist the corporate and the government to raise funds and if efficient, they are able to allocate capital to its highest-value users so that returns are maximised subject to their tolerance for risk. Stock markets encourage savings, capital formation and investment, which are essential for economic development. They help investors to diversify their assets and thus reduce the risk the investors have to bear, reduce also the cost of capital and facilitate investment and economic growth. However, the effectiveness of the stock market in economic development is ultimately determined by its volatility and market efficiency. Inefficiency in the stock market may arise due to operational inefficiency and also due to the opportunistic activities of the cash as well as derivative market players leading to pricing inefficiency. In the event of lack of efficiency in a stock market, investors face difficulty in choosing the optimal investment and the resulting uncertainty may induce investors either to withdraw from the market till this uncertainty prevails or make them reluctant to invest funds for long term. On the other hand, volatile security markets lower the investors’ confidence and disturb also the primary market resulting into reduced collection of new funds by the issuers, implying capital market inefficiency in raising and collecting funds. All these will dishearten the investors to invest their savings in the stock market, and hence deter economic growth. Therefore, increasing stock market volatility is not desirable since it unfavourably affects growth of firms, generation of employment and eventually, economic prosperity of a country.

The Security and Exchange Board of India (SEBI) allowed the trading on individual stock options in July 2001 and trading on individual stock futures in November 2001. Investors of equity stock options can enjoy more leverage than their counterparts who invest in the underlying stock market itself in form of greater exposure by paying a small amount as premium. Investors can also use options in specific stocks to hedge their holding positions in the underlying (i.e., long in the stock itself), by buying a protective put. Thus, they can insure their portfolio of equity stocks by paying premium. On the other hand, investors can take long-term view on the underlying stock using stock futures. Stock futures offer high leverage. This means that one can take large position with less capital. Single-stock futures offer arbitrage opportunity between stock futures and the underlying cash market. It also provides arbitrage opportunity between synthetic futures (created through options) and single-stock futures. When used efficiently, single-stock futures can be an effective risk management tool. For instance, an investor with position in cash segment can minimise either market risk or price risk of the underlying stock by taking reverse position in an appropriate futures contract. The price of stock futures is affected mainly by the prices of the underlying stock whereas in case of stock options, volatility of the underlying stock affects the price along with the prices of the underlying stock (www.bseindia.com). The objective of introducing trading on individual stock options and individual stock futures in Indian stock market was to curb the increasing volatility of the asset prices in financial markets and bring about sophisticated risk management tools leading to higher returns by reducing risk and transaction costs as compared to individual financial assets. If the efficiency of information transmission improves due to derivative trading, it is expected to have positive impact on spot market volatilities by narrowing down volatility clustering. But in the presence of speculators as information disseminators, attracted by the lower transaction cost in the derivative market, the spot price volatility may be intensified. This is a major reason of concerns to the fund managers and market regulators. Whether derivative trading has actually increased or decreased, the volatility of spot prices in India is a debated issue, which could be solved empirically. This study has made an attempt to examine the impact of the introduction of derivative trading in individual stocks of different market capitalisations that are listed in NSE representing different industrial sectors of the Indian economy. This article contributes to existing literature first, by examining the effect of derivative introduction on return volatility of stocks of different market capitalisations. Second, while in earlier studies effect of derivative introduction on return volatility has been examined only on derivative-related stocks, in this article, it is examined both on derivative-related and derivative-unrelated stocks. Third, the article also examines the impact of derivative trading on stocks of different industrial sectors of the Indian economy.

Brief Literature Survey

In the relevant literature, there are mainly two types of theory explaining the impact of derivative trading on the underlying stock market. Some argue that the introduction of derivative trading increases the spot market volatility and thereby destabilises the underlying market, while there are others who argue that the introduction of derivatives reduces the spot market volatility and thereby stabilises the market.

Comparing daily return volatilities during the pre-futures and post-futures period between S&P 500 and non S&P 500 group of stocks, Harris (1989) has argued that increase in post-future volatility in cash market may not be due to index futures by themselves but due to other index-related phenomena such as the growth in foreign ownership of equities and the growth in index funds. Using both parametric and nonparametric tests, Kamara, Miller and Siegel (1992) examined whether there were any changes in volatility of S&P 500 index due to futures trading introduction for the period 1976–1987. Along with F-tests, the authors used Kolmogorov–Smirnov two-sample test and Wilcoxon Rank sum test to examine whether dispersion was significantly higher in the post-futures period. They noticed higher daily return volatility in the post-futures period, though monthly return volatility was found to be unchanged. Antoniou and Holmes (1995) examined the impact of trading in the FTSE-100 stock index futures on the volatility of the underlying spot market in UK utilising generalised autoregressive conditional heteroscedastic (GARCH) family of econometric techniques. They observed that spot market was more volatile in the post-futures period which, according to them, was the result of an increase in the rate of information flow to the spot market and not due to speculators having adverse destabilising effects. Chang, Cheng and Pinegar (1999) examined the consequence of index futures listing on the underlying stocks by dividing portfolio volatility into two parts, namely, the average volatility of constituent stocks and the cross-sectional dispersion of returns. The authors found that after the listing of Nikkei 225 futures in Japan, there was a decreasing cross-sectional dispersion of return across stocks in the index, though the index volatility was found to increase proportionally more than the average individual stock volatility. However, no similar impact was found for stocks outside the index and no impact was found for the off-shore listing of Nikkei 225 futures in Singapore market. Benilde and Armada (2001) in their paper used daily closing price data of Portuguese Stock Index PSI-20 for the period December 1992–December 1998 applying the GARCH model to measure the impact of futures trading on spot market volatility. The authors found increased Portuguese stock market volatility due to the introduction of PSI-20 index futures, though they argued not to generalise their derived result as their study had the limitations of not controlling for other influences on the volatility. Investigating the impact of Universal Stock Futures introduction on the underlying market dynamics, Chau, Holmes and Paudyal (2008) found lesser impact and persistence of news and greater asymmetry in the post-futures period, though from the control stock result they opined that those changes were not due to futures introduction.

T.W. James (1993) examined the impact of price discovery by futures market on the volatility of the underlying cash market. For estimating the price discovery function of the futures market, the author has used the Garbade and Silber model and from the estimated results the author has confirmed that futures market has been beneficial to cash market since it has not only offered better efficiency and liquidity to the cash market but also reduced its long-term cash volatility. Chatrath, Ramchander and Song (1995) evidenced a stabilising effect of trading of S&P 100 stock index options on the underlying stock index. Galloway and Miller (1997) examined the effect of introduction of futures contract on the Midcap 400 stocks and observed declining impact on the volatility of the underlying spot market.

Thenmozhi (2002) found that in India volatility of Nifty in the post-futures period had been in the declining trend which, according to the author, might be due to increased cash market liquidity resulting from faster dissemination of information, shifting of speculators from cash to futures market for lower transaction cost, high leverage, low margins, standardised contracts and trading conditions prevalent in the futures market. Shenbagaraman (2003) showed that futures and options trading in India had not led to any significant change in the volatility of the underlying stock index though she observed changes in the nature of volatility during the post-futures period. Raju and Karande (2003) found reduced volatility in the cash market after the introduction of stock index futures in India. Nath (2003) showed that volatility of Indian stock market represented by Nifty, Nifty Junior and few individual stocks had reduced in the post-derivative period. Vipul (2006) found reduced volatility of the underlying stocks in the post-derivative period which according to the author was because of the reduction in persistence of volatility of previous day. Ray and Panda (2011) investigated the impact of derivatives introduction on the underlying stock volatility and observed changes in the structure of volatility and longer persistence of volatility in some of their sample stocks in post-derivative period.

Research GAP

From the survey of a good number of different existing studies, we have identified the following research gaps:

The impact of derivatives introduction in trading of individual stocks on their return volatility using control variables has not been comprehensively studied in India with wider time coverage.

The studies related to impact measurement of stock derivatives introduction on volatility of underlying stock return where stocks are classified according to different industrial sectors, different market capitalisations and derivative-related and derivative-unrelated stocks are rarely found in India.

The results of the study may be useful for fund managers adopting suitable strategies and can guide market regulators to adopt appropriate regulatory policies.

Objectives of the Study

Our main objective is to examine the following issues with respect to the Indian stock market for the period spanning from 1 April 1996 (or from which date data are available for some stocks) to 31 March 2012.

To examine whether the introduction of derivative trading on individual stocks has been successful in reducing their return volatility irrespective of whether they are large-cap, mid-cap or small-cap companies.

To examine whether the introduction of derivative trading on individual stocks/stock market has similar influence on volatility of stock return of both derivative-related stocks and derivative-unrelated stocks under same market capitalisation.

To examine whether there is any sectoral difference regarding the influence of introduction of derivative trading on individual stocks/stock market on the volatility of the stock return corresponding to different sectors.

Plan of the Article

The remaining portion of the study is organised as follows. The sixth section outlines the data used in the study along with the study period. The seventh section details the econometric and statistical techniques to be applied in the study. The eighth section enumerates the analysis of the data and findings of the study and finally the ninth section concludes the study and presents directions for future research.

Study Period and Database

To examine the impact of derivative instruments introduction on the return volatility of different individual stocks, we have collected their daily closing price data from the website http://nseindia.com for the period spanning from 1 April 1996 (or from which date data are available for some stocks) to 31 March 2012. When we have found any gap in the data set of any stock, we have omitted the observations of the same date from the control variable (Nifty is used as a control variable for individual stocks) data set also. So we have in many cases different number of observations for the same span of time period. We have selected 41 stocks representing different sectors (specifically, 12 sectors, viz., Automobile, Bank, Cement, Computer Software, Construction, Engineering, Finance, FMCG, Energy, Metal, Pharmaceutical and Telecom) of the economy and different market capitalisations (namely, large-cap, mid-cap and small-cap). It should be mentioned that all the selected large-cap stocks (12) are derivative-related stocks. Only for 4 out of 16 selected mid-cap stocks and 4 out of 13 selected small-cap stocks, no derivative instruments have been introduced during the study period. We have examined the effect of derivatives introduction in Indian stock market by comparing the return volatilities of derivative-related stocks with derivative-unrelated counterparts and also with derivative-related stocks of that period when no derivatives were introduced on them. Thus, the study compares the impact of derivatives introduction on stocks of different sectors, different market capitalisations and between derivatives-related and derivatives-unrelated stocks. We have collected the information regarding date of derivative instrument introduction on each stock from the circular archive of NSE India. For those stocks which have no derivative instruments till our study period, we have examined the effect of derivative introduction in the Indian stock market as a whole (i.e., 12 June 2000 as the cut-off date) on their return volatility. Span of the period of analysis of different stocks, the sectors they represent, the number of observations and date of derivative instruments (stock options and stock futures) introduction on each stock and the stock index are presented in Table 1.

Table 1.

Selected Stocks under Study with their Study Periods, Numbers of Observations and Derivative Introduction Dates

Sector	Stock/Index	Span of the Period	No of Observations	Date of Derivative Introduction
Automobile	Tata Motors	1 April 1996 to 31 March 2012	3,994	2 July 2001
	Ashok Leyland	1 April 1996 to 31 March 2012	3,994	19 April 2005
	Escorts	1 April 1996 to 31 March 2012	3,994	27 May 2005
	#Eicher Motors	1 April 1996 to 31 March 2012	3,984	–––
Bank	State Bank of India	1 April 1996 to 31 March 2012	3,994	2 July 2001
	Oriental Bank	1 April 1996 to 31 March 2012	3,994	29 August 2003
	#ING Vysya Bank	1 April 1996 to 31 March 2012	3,994	–––
	#Lakshmi Vilas Bank	1 April 1996 to 31 March 2012	3,978	–––
Cement	ACC	1 April 1996 to 31 March 2012	3,994	2 July 2001
	India Cement	1 April 1996 to 31 March 2012	3,994	27 May 2005
	#Madras Cement	1 April 1996 to 31 March 2012	3,974	–––
	Prism Cement	1 April 1996 to 31 March 2012	3,807	21 August 2008
Computer Software	Infosys	1 April 1996 to 31 March 2012	3,992	2 July 2001
	Mphasis	4 July 2001 to 31 March 2012	2,682	12 May 2005
	Polaris Software	24 November 1999 to 31 March 2012	3,084	31 January 2003
Construction	Jai Prakash Associate	14 June 2004 to 31 March 2012	1,942	29 December 2006
	Unitech	1 April 1996 to 31 March 2012	3,920	14 May 2007
Engineering	L&T	1 April 1996 to 31 March 2012	3,972	2 July 2001
	Voltas	1 April 1996 to 31 March 2012	3,993	29 December 2006
	RIIL	1 April 1996 to 31 March 2012	3,966	21 August 2008
Finance	HDFC	1 April 1996 to 31 March 2012	3,994	2 July 2001
	LIC Housing Finance	1 April 1996 to 31 March 2012	3,994	19 April 2005
	#Bajaj Finance	1 April 1996 to 31 March 2012	3,917	–––
	SREI Infrastructure Finance	1 April 1996 to 31 March 2012	3,632	21 August 2008
FMCG	ITC	1 April 1996 to 31 March 2012	3,994	2 July 2001
	#P&G	1 April 1996 to 31 March 2012	3,661	–––
	Glaxo Smith	1 April 1996 to 31 March 2012	3,993	19 April 2005
	Balrampur Chini Mill	1 April 1996 to 31 March 2012	3,993	29 December 2006
Energy	Tata Power	1 April 1996 to 31 March 2012	3,994	2 July 2001
	Hindustan Petroleum	1 April 1996 to 31 March 2012	3,994	2 July 2001
	Gujarat Fluorochem	1 April 1996 to 31 March 2012	3,897	5 August 2011
Metal	Tata Steel	1 April 1996 to 31 March 2012	3,994	2 July 2001
	Bhushan Steel	21 November 2003 to 31 March 2012	2,081	6 September 2007
	#Prakash Industries	1 April 1996 to 31 March 2012	3,185	–––
Pharmaceutical	Ranbaxy	1 April 1996 to 31 March 2012	3,994	2 July 2001
	Piramal Health Care	2 April 1996 to 31 March 2012	3,986	19 April 2005
	#Aventis	1 April 1996 to 31 March 2012	3,948	–––
	Orchid	1 April 1996 to 31 March 2012	3,672	12 May 2005
Telecom	Bharti Airtel	18 February 2002 to 31 March 2012	2,525	19 April 2005
	MTNL	1 April 1996 to 31 March 2012	3,994	2 July 2001
	Tulip Telecom	5 January 1996 to 31 March 2012	1,546	6 September 2007
	Nifty	1 April 1996 to 31 March 2012	3,994	12 June 2000

Source: Authors’ own.

Note: #Stocks with no derivative product. For those stocks which have no derivative instrument till our study period, we have examined the effect of derivative introduction in the stock market on their return volatility by considering 12 June 2000 (i.e., the date of derivative introduction in Indian stock market) as the cut-off date. ▯➜ Large-cap, ▮➜ Mid-cap and ▮➜ Small-cap stocks.

Methodology

Volatility has been estimated on return (R_i,t) which is represented as

R_{i, t} = \log_{e} (P_{i, t} / P_{i, t - 1})

(1)

where R_i,t is the continuous daily return for the ith stock at time t, and P_i,t_–1 and P_i,t are two successive daily closing prices of the ith stock.

Stationarity of all the return series has been checked using augmented Dickey–Fuller (ADF) test (1979) statistic. We have graphically plotted the daily return series over time so that volatility clustering can be checked. Observing the presence of few outliers in almost all the return series, we have searched for the reasons of their existence and have found that the reasons were stock split or/and bonus issue or/and rights issue. We have collected information on all such corporate actions and have adjusted the stock prices in the following manner:

In case of stock split: adjusted share price = $P \times \frac{X}{Y}$ , where X (existing shares) is subdivided into Y (sub-divided shares);

In case of rights issue: adjusted share price = $\frac{P \times Y + X (F a c e V a l u e + \Pr e m i u m)}{X + Y}$ , where X:Y is the rights ratio.

In case of bonus issues: adjusted share price = $P \times \frac{Y}{X + Y}$ , where X:Y is the bonus ratio.

We have calculated the coefficients of skewness and kurtosis to understand whether the return series is skewed and leptokurtic or not. To test the null hypothesis of normality, Jarque–Bera (JB) statistic has been applied. In the past studies, findings of heteroscedasticity in stock returns are well documented. If the error variance is not constant, that is, heteroscedastic, then OLS estimation is inefficient. Moreover, the tendency in financial data for volatility clustering can be well captured in a GARCH framework. Therefore, we have modelled the time-varying conditional variance in our study as a GARCH process.

To be sure about the appropriateness of the GARCH-type model for a given data set, we have performed Autoregressive Conditional Heteroscedastic (ARCH) LM test (Engle, 1982) which is a Lagrange multiplier test for the presence of ARCH effect in the residuals. Further we use Akaike information criterion (AIC) to determine the order of the GARCH model when AIC = (–2L/n + 2k/n); here k denotes the number of estimated parameters, n is the number of observations, L is the the value of the log-likelihood function (LLF) using k estimated parameters [EViews 3.1 help system]. Akaike information criterion suggests us to choose that lag length which leads to minimisation of the value of the information criterion.

To represent the time-varying volatility and to examine the impact of derivative introduction on individual stock, we model the time series of stock return as a GARCH(p, q) process following Bollerslev (1986), where p is the order of ARCH term and q is the order of GARCH term. The order of p and q is chosen by the AIC criterion. We consider 2 as the maximum lag length. According to AIC, we find that GARCH(1, 2) is suitable for 31 stocks and GARCH(1, 1) is suitable for 10 stocks. Therefore, we estimate the following conditional mean equation:

R_{i, t} = a_{0} + a_{1} R_{i, t - 1} + ε_{t} ε_{t} ~ N (0, h_{t})

(2)

where R_i,t and R_i,t_–1 are daily return and lagged daily return of the ith individual stock, respectively. The residual [ε_t] in equation (2) is assumed to be distributed N(0, h_t) where the conditional variance h_t is represented as

h_{t} = α_{0} + α_{1} ε_{t - 1}^{2} + \sum_{j = 1}^{q} β_{j} h_{t - j} j = 1, o r 1 t o 2

(3)

The values of parameters α₁ and ∑β_j determine the short-run dynamics of the resulting volatility of time series. If the value of GARCH lag coefficient ∑β_j is significantly large, the volatility is persistent in nature, whereas a large value of GARCH error coefficient α₁ indicates quite intensive reaction of volatility to market movements. If the value of α₁ + ∑β_j is close to unity, a shock at time t will persist for many future periods implying a long memory.

To be sure whether the introduction of derivative instrument is the sole responsible factor behind the changing nature of volatility, we have introduced a control variable to take care of the market-wide factors. For this, we use S&P CNX Nifty to take care of the market fluctuations as it is the most popular stock index in India and it occupies a major part of the Indian stock market. The augmented mean equation with control variable thus becomes

R_{i, t} = a_{0} + a_{1} R_{i, t - 1} + b_{1} R_{N i f, t - 1} + ε_{t}

(4)

To address the issue of how the initial introduction of derivative instruments does have impact on cash market volatility, we introduce a dummy variable D_f into the conditional variance equation which takes on a value of 0 before the derivatives on individual stocks were introduced and a value of 1 after that. If the coefficient of the dummy γ is statistically significant, derivatives introduction has an impact on the spot market volatility. Moreover, if this co- efficient is statistically significantly positive (negative), it implies that the derivative introduction leads to increasing (declining) volatility in associated spot market. Equation (3) then becomes

\begin{matrix} h_{t} = α_{0} + α_{1} ε_{t - 1}^{2} + \sum_{j = 1}^{q} β_{j} h_{t - j} + γ D_{f} \\ j = 1, o r 1 t o 2 \end{matrix}

(5)

where D_f is a dummy variable taking a value of 0 prior to the introduction of derivative and a value of 1 in the post-derivative introduction period.

To estimate the GARCH(p, q) model, the maximum likelihood method is employed which can find the most likely values of the parameters given the actual data with T observations. After specifying mean and variance equation as mentioned above, the LLF is specified to maximise under a normality assumption for the disturbances as

\ln L = - T / 2 \ln (2 π) - 0.5 \sum_{t = 1}^{T} \ln h_{t} - 0.5 \sum_{t = 1}^{T} ε_{t}^{2} / h_{t}

With the help of EViews software, the above LLF has been maximised to generate the parameter values along with constructing their standard errors (Brooks, 2008; pp. 394–399; Enders, 2008, pp. 138–140).

Data Analysis and Findings

After adjustment for aforementioned corporate actions, volatility clustering of the daily return series over time of 12 large-cap stocks is depicted in Figure 1, that of 4 derivative-unrelated and 12 derivative-related mid-cap stocks is depicted in Figures 2 and 3, respectively, and that of 4 derivative-unrelated and 9 derivative-related small-cap stocks is depicted in Figures 4 and 5, respectively. The visual inspection of the plots of daily return series of all these stocks reveals that returns continuously fluctuate around a mean value that is close to zero. The movements are in both positive and negative territories and large fluctuations tend to cluster together with relatively low fluctuations that are separated by periods showing volatility clustering.

Figure 1.

Source: Authors’ own.

Figure 2.

Source: Authors’ own.

Figure 3.

Source: Authors’ own.

Figure 4.

Source: Authors’ own.

Figure 5.

Source: Authors’ own.

The descriptive statistics and the result of ADF unit root test of stationarity on returns of all the selected largecap, mid-cap, small-cap stocks and S&P CNX Nifty are summarised in Table 2. The coefficient of skewness for each of the return series is observed to be different from zero which indicates that return distribution is not symmetric. The coefficient of kurtosis for each of the stock return series is fairly high suggesting that the underlying data are leptokurtic or heavily tailed and sharply peaked about the mean compared to normal distribution. These observed skewness and kurtosis coefficients indicate that the distributionss of daily return series of all the selected stocks are individually non-normal. The Jarque–Bera normality test also supports this non-normality feature of return distribution as we find from Table 2 that the estimated values of Jarque–Bera statistic of all the return series are separately statistically significant at 1 per cent level. We can find from Table 2 that all the estimated values of ADF test statistic are statistically significant at 1 per cent level which implies that all the return series are stationary.

To test for the presence of ‘ARCH’ effect in the residuals of the estimated model, the ARCH LM test (Engle, 1982) is applied, the results of which are presented in Table 3. From Table 3, we find that both the F-statistic and the ARCH LM statistic are statistically significant at 1 per cent level for all the selected stocks, thereby rejecting the null hypothesis of no heteroscedasticity. The results of the ARCH LM test confirm the presence of ARCH effect in all the return series which are also consistent with the graphical presentations of the return series showing volatility clustering.

Table 2.

Result of ADF Test and Descriptive Statistics of Return Series of Selected Stocks

Sector	Stock/Index	ADF Test Statistic²	Coefficient of Skewness	Coefficient of Kurtosis	Jarque–Bera Test Statistic³	No. of Observations
Automobile	Tata Motors	–27.92472	–0.091515	5.310297	893.8190	3,994
	Ashok Leyland	–27.51787	0.194101	5.772630	1,304.403	3,994
	Escorts	–27.55275	0.122186	5.529417	1,074.664	3,994
	¹Eicher Motors	–28.63624	0.624414	10.28817	9,076.389	3,984
Bank	State Bank of India	–28.93409	0.019568	5.704048	1,217.073	3,994
	Oriental Bank	–28.00442	–0.195208	8.649073	5,336.059	3,994
	¹ING Vysya Bank	–27.80706	0.671343	7.680820	3,946.219	3,994
	¹Lakshmi Vilas Bank	–29.97908	0.647451	8.630469	5,532.561	3,978
Cement	ACC	–27.75037	–0.109230	5.866290	1,375.158	3,994
	India Cement	–27.90883	0.096397	5.527411	1,069.223	3,994
	¹Madras Cement	–25.92552	0.195401	7.021694	2,703.437	3,974
	Prism Cement	–26.14091	0.580201	6.962773	2,704.572	3,807
Computer Software	Infosys	–29.21417	–0.352920	9.633224	7,401.480	3,992
	Mphasis	–21.37447	–0.143763	12.43139	9,949.532	2,682
	Polaris Software	–24.41782	–0.145437	7.672532	2,816.356	3,084
Construction	Jai Prakash Associate	–20.54575	–0.388984	8.204047	2,240.367	1,942
	Unitech	–25.59982	–1.240005	33.11629	149,146.4	3,920
Engineering	L&T	–27.34874	0.263563	7.217688	2,990.048	3,972
	Voltas	–27.43403	0.389389	5.509329	1,148.524	3,993
	RIIL	–24.48997	1.193857	11.19299	12,034.53	3,966
Finance	HDFC	–31.96679	0.311547	7.254817	3,077.330	3,994
	LIC Housing Finance	–28.45152	0.298760	8.976669	6,003.915	3,994
	¹Bajaj Finance	–26.95304	0.507239	8.037361	4,309.381	3,917
	SREI Infrastructure Finance	–29.66726	0.154456	15.96187	25,439.95	3,632
FMCG	ITC	–29.02965	0.019354	5.698365	1,211.958	3,994
	¹P&G	–26.93659	0.495701	7.575624	3,343.594	3,661
	Glaxo Smith	–28.95464	0.401426	8.639990	5,399.544	3,993
	Balrampur Chini Mill	–27.74819	0.127038	6.507084	2,057.092	3,993
Energy	Tata Power	–27.85105	–0.038762	8.624817	5,266.185	3,994
	Hindustan Petroleum	–29.05999	0.011239	9.089554	6,171.259	3,994
	Gujarat Fluorochem.	–26.09922	0.270652	5.110863	771.0788	3,897
Metal	Tata Steel	–27.52918	–0.182893	5.633639	1,176.541	3,994
	Bhushan Steel	–20.48045	1.411788	18.01426	20,237.78	2,081
	¹Prakash Industries	–27.16851	0.762282	20.38863	40,434.72	3,185
Pharmaceutical	Ranbaxy	–27.28558	–0.123449	8.633881	5,292.313	3,994
	Piramal Health Care	–27.76240	0.165456	6.117818	1,632.648	3,986
	¹Aventis	–27.84655	0.203030	6.581521	2,137.213	3,948
	Orchid	–25.21437	–0.615497	15.87367	25,588.75	3,672
Telecom	Bharti Airtel	–23.64125	0.455256	7.408027	2,131.493	2,525
	MTNL	–28.26907	0.052059	5.871684	1,374.170	3,994
	Tulip Telecom	–18.72008	1.066241	10.55407	3,968.803	1,546
	Nifty	–28.23677	–0.171204	9.259931	6,540.838	3,994

Source: Authors’ own.

Notes: ¹Stocks with no derivative product. ² ADF test statistic is estimated by fitting the equation in the form: $Δ y_{t} = φ + δ y_{t - 1} + \sum_{j = 1}^{4} θ_{j} Δ y_{t - j} + μ_{t};$

³ Jarque–Bera (JB) test statistic $= \frac{N - k}{6} [s^{2} + \frac{1}{4} {(K - 3)}^{2}]$ , where N is the number of observations, S is the coefficient of skewness, K is the coefficient of kurtosis, k is the number of estimated coefficients used to create the series and JB follows the chi-square distribution with 2 d.f. ▯➜ Large-cap, ▮➜ Mid-cap and ▮➜ Small-cap stocks.

The results of the maximum likelihood estimates of the GARCH(p, q) model to daily return series of selected individual stocks are presented in Tables 4 and 5. Parameters of the mean equation are presented in Table 4 and that of the variance equation are presented in Table 5. From Table 4, we find that out of 41 stocks, parameter a₀ in the mean equation is significant in the case of only 17 stocks, namely, Tata Motors, Eicher Motors, State Bank of India, ACC Cement, Infosys, Mphasis, Unitech, L&T, Voltas, HDFC, Bajaj Finance, ITC, Glaxo Smith, Tata Power, Tata Steel, Prakash Industries and Bharti Airtel. Parameter a₁ is significant in the case of only 17 stocks, namely, Lakshmi Vilas Bank, Madras Cement, Infosys, Polaris Software, Voltas, RIIL, LIC Housing Finance, Bajaj Finance, SREI Infrastructure Finance, P&G, Glaxo Smith, Hindustan Petroleum, Bhushan Steel, Prakash Industries, Ranbaxy, Aventis and Orchid Chemicals. Except Polaris Software, ITC and Bharti Airtel, the estimated parameter b₁ in the mean equations is significant for all the stocks either at 1 per cent level or at 5 per cent level. When we look at the parameters of variance equation in Table 5, we find that coefficients α₀ are significant at 1 per cent level for all the stocks. ARCH coefficients α₁ are all significant at 1 per cent level. In addition, all the GARCH coefficients at lag 1, that is, β₁ are significant at 1 per cent level. Except for ITC, GARCH coefficients at lag 2, that is, β₂ are significant at 1, 5 or 10 per cent level for the relevant stocks. For all the stocks, we find the individual values of (α₁ + ∑β_j) < 1, implying that there is no unit root and the return series of all the individual stocks are stationary. In addition, α₁ + ∑β_j in all the series are very close to unity implying shocks to the conditional variance are highly persistent. Except Mphasis, HDFC, ITC, P&G and Bharti Airtel, we find a significant F-statistic for all other stocks implying that there is heteroscedasticity in return variance for each of these stocks. So there is GARCH effect in return volatility throughout the period for those stocks.

We have estimated the impact of introduction of derivatives trading on individual stocks’ return volatility by introducing a dummy variable in the conditional variance equation of the GARCH(p, q) model. Except for one large-cap stock of the construction sector (Jaiprakash Associate) and five derivative-related midcap stocks representing five sectors (namely, India Cement [cement sector], Mphasis [computer software sector], Voltas [engineering sector], LIC Housing Finance [finance sector] and Glaxo Smith [FMCG sector]), we find that for all the other return series of individual stocks (35 stocks), the estimated coefficients of the derivative dummy γ_{are significantly different from zero indicating that the introduction of derivative trading on individual stocks does have an impact on volatility of the corresponding stock return though these impacts are not found to be negative in all the cases.}

Table 3.

Result of ARCH Test on Return Series of Selected Stocks

Sector	Stock/Index	F-Statistic	Prob. F	ARCH LM Statistic²	Prob. Chi-square
Automobile	Tata Motors	246.4346	0.000000	232.2158	0.000000
	Ashok Leyland	168.0609	0.000000	161.3490	0.000000
	Escorts	220.2516	0.000000	208.8342	0.000000
	¹Eicher Motors	388.1840	0.000000	353.8653	0.000000
Bank	State Bank of India	270.8126	0.000000	253.7272	0.000000
	Oriental Bank	547.6664	0.000000	481.8080	0.000000
	¹ING Vysya Bank	267.6578	0.000000	250.9572	0.000000
	¹Lakshmi Vilas Bank	231.4834	0.000000	218.8519	0.000000
Cement	ACC	220.7058	0.000000	209.2422	0.000000
	India Cement	229.8091	0.000000	217.4027	0.000000
	¹Madras Cement	304.4224	0.000000	282.8840	0.000000
	Prism Cement	91.21006	0.000000	89.12058	0.000000
Computer Software	Infosys	219.4460	0.000000	208.1048	0.000000
	Mphasis	127.6356	0.000000	121.9202	0.000000
	Polaris Software	361.8112	0.000000	323.9870	0.000000
Construction	Jai Prakash Associate	24.12359	0.000001	23.85159	0.000001
	Unitech	307.3841	0.000000	285.1578	0.000000
Engineering	L&T	183.6130	0.000000	175.5808	0.000000
	Voltas	142.2738	0.000000	137.4431	0.000000
	RIIL	675.7713	0.000000	577.5959	0.000000
Finance	HDFC	106.5273	0.000000	103.8091	0.000000
	LIC Housing Finance	232.6971	0.000000	219.9842	0.000000
	¹Bajaj Finance	117.7281	0.000000	114.3479	0.000000
	SREI Infrastructure Finance	170.7874	0.000000	163.1990	0.000000
FMCG	ITC	228.4395	0.000000	216.1773	0.000000
	¹P&G	110.8502	0.000000	107.6479	0.000000
	Glaxo Smith	152.7439	0.000000	147.1846	0.000000
	Balrampur Chini Mill	254.5263	0.000000	239.3798	0.000000
Energy	Tata Power	759.9759	0.000000	638.7030	0.000000
	Hindustan Petroleum	72.81247	0.000000	71.54339	0.000000
	Gujarat Fluorochem.	187.9302	0.000000	179.3679	0.000000
Metal	Tata Steel	391.1826	0.000000	356.4337	0.000000
	Bhushan Steel	61.22561	0.000000	59.52975	0.000000
	¹Prakash Industries	88.19972	0.000000	85.87414	0.000000
Pharmaceutical	Ranbaxy	289.5750	0.000000	270.1164	0.000000
	Piramal Health Care	187.6273	0.000000	179.2743	0.000000
	¹Aventis	272.2601	0.000000	254.8084	0.000000
	Orchid	15.25121	0.000096	15.19634	0.000097
Telecom	Bharti Airtel	47.70336	0.000000	46.85460	0.000000
	MTNL	296.7182	0.000000	276.3184	0.000000
	Tulip Telecom	23.98488	0.000001	23.64816	0.000001
	Nifty	169.7328	0.000000	162.8887	0.000000

Source: Authors’ own.

Notes: ¹Stocks with no derivative product. ²ARCH LM Statistic (at lag 1) is the LM test statistic for examining the presence of ARCH effect in the residuals of the estimated model. If the value of ARCH LM statistic is greater than the critical value from the chi-square distribution, the null hypothesis of no heteroscedasticity is rejected.

Table 4.

Maximum Likelihood Estimates of GARCH(p, q) Model of Return Series of Selected Stocks

Large-cap Stocks	Parameters of Mean Equation¹
	a₀	a₁	b₁
Tata Motors	0.000688***[1.673286](0.0943)	0.022232[1.063198](0.2877)	0.125049*[3.860938](0.0001)
State Bank of India	0.000827**[2.408832](0.0160)	0.012616[0.586854](0.5573)	0.096247*[3.270595](0.0011)
ACC	0.000902**[2.562884](0.0104)	–0.028549[–1.609273](0.1076)	0.144868*[5.692902](0.0000)
Infosys	0.001586*[4.647558](0.0000)	0.087113*[4.086996](0.0000)	–0.092547*[–3.824132](0.0001)
Jai Prakash Associate	0.001067[1.409710](0.1586)	–0.024148[–0.799795](0.4238)	0.312527*[4.898941](0.0000)
L&T	0.001177*[3.320430](0.0009)	–0.016216[–0.778911](0.4360)	0.202081*[6.577837](0.0000)
HDFC	0.000889*[2.800727](0.0051)	0.006966[0.368051](0.7128)	0.052769**[2.326101](0.0200)
ITC	0.001084*[3.715550](0.0002)	–0.012816[–0.669101](0.5034)	0.032657[1.566343](0.1173)
Tata Power	0.000743**[2.207724](0.0273)	0.016853[0.869201](0.3847)	0.107133*[4.355027](0.0000)
Tata Steel	0.000824**[2.137432](0.0326)	0.015001[0.692934](0.4884)	0.092293*[2.603452](0.0092)
Ranbaxy	0.000376[1.292811](0.1961)	0.061837*[3.502385](0.0005)	0.063623*[3.330695](0.0009)
Bharti Airtel	0.001248*[2.651068](0.0080)	–0.000832[–0.033131](0.9736)	0.040340[1.162338](0.2451)
Mid-cap Derivative-unrelated Stocks	Parameters of Mean Equation¹
	a₀	a₁	b₁
ING Vysya Bank	4.20E–05[0.095480](0.9239)	–0.013554[–0.702602](0.4823)	0.191244*[7.571125](0.0000)
Madras Cement	0.000320[0.873878](0.3822)	–0.087542*[–4.605841](0.0000)	0.223580*[10.10966](0.0000)
P&G	0.000347[1.208395](0.2269)	–0.087913*[–4.025800](0.0001)	0.097294*[5.819129](0.0000)
Aventis	0.000311[1.014329](0.3104)	–0.060738*[–3.193187](0.0014)	0.123132*[6.518592](0.0000)
Mid-cap Derivative-related Stocks	Parameters of Mean Equation¹
	a₀	a₁	b₁
Ashok Leyland	0.000688***[1.673286](0.0943)	0.022232[1.063198](0.2877)	0.125049*[3.860938](0.0001)
Oriental Bank	0.000238[0.656029](0.5118)	0.000781[0.040466](0.9677)	0.180433*[8.581170](0.0000)
India Cement	–0.000350[–0.724341](0.4689)	–0.008741[–0.445424](0.6560)	0.156334*[4.468983](0.0000)
Mphasis	0.001185**[2.410113](0.0159)	–0.020139[–0.788883](0.4302)	0.115457*[3.576242](0.0003)
Unitech	0.000964***[1.903163](0.0570)	–0.019271[–1.053411](0.2922)	0.154689*[4.964758](0.0000)
Voltas	0.000857***[1.772038](0.0764)	0.033385***[1.896942](0.0578)	0.156303*[4.974376](0.0000)
LIC Housing Finance	0.000640[1.587019](0.1125)	0.054350*[2.798145](0.0051)	0.102668*[3.670886](0.0002)
Glaxo Smith	0.000794*[2.766307](0.0057)	–0.064937*[–3.222519](0.0013)	0.124933*[7.466996](0.0000)
Hindustan Petroleum	0.000131[0.329507](0.7418)	0.046431*[2.588923](0.0096)	0.074090*[3.104576](0.0019)
Bhushan Steel	0.000889[1.535981](0.1245)	0.080003*[3.118632](0.0018)	0.110288*[3.039551](0.0024)
Piramal Health Care	0.000414[1.250617](0.2111)	0.019623[1.036913](0.2998)	0.105436*[4.621037](0.0000)
MTNL	–0.000470[–1.129547](0.2587)	0.006874[0.364910](0.7152)	0.156680*[5.409228](0.0000)
Small-cap Derivative-unrelated Stocks	Parameters of Mean Equation¹
	a₀	a₁	b₁
Eicher Motors	0.001315*[2.569885](0.0102)	0.000306[0.015945](0.9873)	0.146575*[5.046423](0.0000)
Lakshmi Vilas Bank	0.000226[0.513402](0.6077)	–0.043481**[–2.216013](0.0267)	0.170867*[6.543130](0.0000)
Bajaj Finance	0.000742***[1.749613](0.0802)	–0.048930**[–2.519445](0.0118)	0.158806*[5.869837](0.0000)
Prakash Industries	–0.001441**[–1.962496](0.0497)	–0.038807***[–1.843750](0.0652)	0.394350*[9.054526](0.0000)
Small-cap Derivative-related Stocks	Parameters of Mean Equation¹
	a₀	a₁	b₁
Escorts	1.69E–05[0.034613](0.9724)	0.029325[1.462451](0.1436)	0.175490*[4.851612](0.0000)
Prism Cement	0.000288[0.508774](0.6109)	–0.020393[–1.139328](0.2546)	0.240886*[6.748040](0.0000)
Polaris Software	0.000694[1.096469](0.2729)	0.061490**[2.511764](0.0120)	0.001031[0.022310](0.9822)
RIIL	–0.000566[–1.217012](0.2236)	0.040556**[2.030539](0.0423)	0.193560*[5.662675](0.0000)
SREI Infrastructure Finance	0.000845[1.267645](0.2049)	–0.094360*[–5.444274](0.0000)	0.384063*[9.864243](0.0000)
Small-cap Derivative-related Stocks	Parameters of Mean Equation¹
	a₀	a₁	b₁
Balrampur Chini Mill	0.000695[1.499786](0.1337)	–0.001316[–0.069513](0.9446)	0.177922*[5.940959](0.0000)
Gujarat Fluorochem.	0.000680[1.402355](0.1608)	0.009589[0.514597](0.6068)	0.206939*[7.097385](0.0000)
Orchid	0.000767[1.561839](0.1183)	0.059764*[2.912789](0.0036)	0.143637*[5.141612](0.0000)
Tulip Telecom	0.000453[0.603345](0.5463)	–0.018746[–0.727151](0.4671)	0.229494*[5.261378](0.0000)

Source: Authors’ own.

Notes: †Mean Equation: R_t = a₀ + a₁ R_{t – 1} + b₁ R_{Nif,t – 1} + ε_t; ε_t ~ N(0, h_t);

*, **, *** indicate the significance of the parameter respectively at 1%, 5%, 10% significance level.

Table 5.

Maximum Likelihood Estimates of GARCH(p, q) Model of Return Series of Selected Stocks

Large-cap Stocks	Parameters of Variance Equation¹					GARH Statistic
	α₀	α₁	β₁	β₂	γ	R² value²
Tata Motors	3.72E–05*[5.434181](0.0000)	0.106180*[7.939802](0.0000)	0.517488*[3.228011](0.0012)	0.344744**[2.310019](0.0209)	–1.33E–05*[–3.184664](0.0014)	0.009071*{5.212302}(0.000006)
State Bank of India	3.50E–05*[6.341497](0.0000)	0.121651*[10.96891](0.0000)	0.396578*[4.025930](0.0001)	0.443126*[4.849650](0.0000)	–1.25E–05*[–3.409409](0.0007)	0.005097*{2.917244}(0.004802)
ACC	6.98E–05*[6.920634](0.0000)	0.132103*[10.09693](0.0000)	0.552534*[4.421456](0.0000)	0.264991**[2.377538](0.0174)	–4.32E–05*[–5.882475](0.0000)	0.004475**{2.559600}(0.012484)
Infosys	3.45E–05*[6.816114](0.0000)	0.157007*[8.706003](0.0000)	0.654845*[6.036954](0.0000)	0.165264***[1.774865](0.0759)	–1.26E–05*[–3.673916](0.0002)	0.012240*{7.052874}(0.000000)
Jai Prakash Associate	3.56E–05*[5.869665](0.0000)	0.101071*[7.329899](0.0000)	0.879065*[62.57263](0.0000)		–5.15E–06[–0.963423](0.3353)	0.011764*{3.839205}(0.000823)
L&T	4.49E–05*[8.429554](0.0000)	0.116558*[13.17015](0.0000)	0.845976*[79.42263](0.0000)		–2.37E–05*[–6.080103](0.0000)	0.010565*{7.056387}(0.000000)
HDFC	4.14E–05*[8.527041](0.0000)	0.139883*[10.53151](0.0000)	0.490960*[4.918570](0.0000)	0.320468*[3.668993](0.0002)	–1.59E–05*[–5.440556](0.0000)	0.001249{0.711894}(0.662005)
ITC	5.55E–05*[6.844846](0.0000)	0.113106*[8.612401](0.0000)	0.681452*[5.114332](0.0000)	0.136622[1.170232](0.2419)	–3.03E–05*[–5.958935](0.0000)	–0.000468
Tata Power	4.98E–05*[8.944940](0.0000)	0.152228*[15.16125](0.0000)	0.319232*[4.103402](0.0000)	0.490565*[6.962479](0.0000)	–2.82E–05*[–7.409866](0.0000)	0.008643*{4.964454}(0.000013)
Tata Steel	4.21E–05*[7.327377](0.0000)	0.102735*[12.49393](0.0000)	0.862039*[82.76929](0.0000)		–1.70E–05*[–4.646177](0.0000)	0.003530**{2.353922}(0.028478)
Large-cap Stocks	Parameters of Variance Equation¹					GARH Statistic
	α₀	α₁	β₁	β₂	γ	R² value²
Ranbaxy	8.59E–06*[7.681352](0.0000)	0.158981*[13.32337](0.0000)	0.379817*[4.546968](0.0000)	0.444423*[5.851121](0.0000)	1.02E–05*[5.927247](0.0000)	0.008669*{4.979540}(0.000013)
Bharti Airtel	0.000130*[7.137906](0.0000)	0.153330*[10.59225](0.0000)	0.721718*[25.41266](0.0000)		–5.44E–05*[–5.563259](0.0000)	–0.000677
Mid-cap Derivative-unrelated Stocks	Parameters of Variance Equation¹					GARH Statistic
	α₀	α₁	β₁	β₂	γ	R² value²
ING Vysya Bank	0.000184*[11.38606](0.0000)	0.208919*[16.47644](0.0000)	0.184453*[4.538206](0.0000)	0.430502*[11.84856](0.0000)	–3.69E–05*[–3.311094](0.0009)	0.011219*{6.460624}(0.000000)
Madras Cement	9.06E–05*[10.13058](0.0000)	0.162681*[10.54933](0.0000)	0.511933*[5.321881](0.0000)	0.194038**[2.447626](0.0144)	–1.14E–05**[–2.383026](0.0172)	0.012130*{6.956777}(0.000000)
P&G	0.000123*[11.43374](0.0000)	0.224508*[18.42864](0.0000)	0.412994*[8.406005](0.0000)	0.213900*[5.178825](0.0000)	–7.17E–05*[–8.895759](0.0000)	0.001036{0.541387}(0.803585)
Aventis	0.000122*[10.22371](0.0000)	0.147065*[14.71021](0.0000)	0.747174*[53.01827](0.0000)		–8.30E–05*[–8.317996](0.0000)	0.003847**{2.536758}(0.018765)
Mid-cap Derivative-related Stocks	Parameters of Variance Equation¹					GARH Statistic
	α₀	α₁	β₁	β₂	γ	R² value²
Ashok Leyland	2.89E–05*[7.408490](0.0000)	0.075925*[11.47689](0.0000)	0.898957*[108.9366](0.0000)		–6.53E–06*[–2.803144](0.0051)	0.007869*{5.270561}(0.000020)
Oriental Bank	3.50E–05*[9.248443](0.0000)	0.169436*[16.29435](0.0000)	0.257003*[4.212326](0.0000)	0.524735*[9.045426](0.0000)	1.46E–05*[3.710784](0.0002)	0.012739*{7.347390}(0.000000)
India Cement	8.02E–05*[8.150314](0.0000)	0.172595*[11.80446](0.0000)	0.365607*[4.725938](0.0000)	0.398469*[5.900582](0.0000)	–2.28E–06[–0.439004](0.6607)	0.003954**{2.260399}(0.026994)
Mphasis	0.000119*[9.098822](0.0000)	0.274808*[19.81167](0.0000)	0.323845*[4.704641](0.0000)	0.299982*[5.272267](0.0000)	–5.04E–06[–0.512676](0.6082)	–0.001497
Unitech	7.70E–05*[7.805217](0.0000)	0.167270*[15.75130](0.0000)	0.365936*[4.020255](0.0001)	0.404745*[4.928840](0.0000)	3.25E–05*[2.826151](0.0047)	0.005385*{3.025717}(0.003573)
Voltas	1.76E–05*[5.733142](0.0000)	0.086788*[10.90893](0.0000)	0.334190*[3.222530](0.0013)	0.566485*[5.741051](0.0000)	–1.75E–06[–0.759060](0.4478)	0.010261*{5.902074}(0.000001)
LIC Housing Finance	5.67E–05*[8.975989](0.0000)	0.148147*[9.826233](0.0000)	0.576771*[4.658499](0.0000)	0.212341***[1.959294](0.0501)	–2.52E–07[–0.084156](0.9329)	0.010030*{5.769148}(0.000001)
Glaxo Smith	4.06E–05*[14.20020](0.0000)	0.188957*[14.40163](0.0000)	0.374606*[6.019537](0.0000)	0.358175*[6.309377](0.0000)	–3.31E–06[–1.540283](0.1235)	0.005023*{2.874116}(0.005398)
Hindustan Petroleum	2.61E–05*[6.727091](0.0000)	0.135156*[12.43699](0.0000)	0.240441*[4.544919](0.0000)	0.586195*[11.40064](0.0000)	1.32E–05*[4.821385](0.0000)	0.004312**{2.465762}(0.015949)
Bhushan Steel	0.000174*[12.34258](0.0000)	0.429173*[22.24396](0.0000)	0.306258*[5.725617](0.0000)	0.162784*[4.006853](0.0001)	5.40E–05*[4.949211](0.0000)	0.010347*{3.096184}(0.002992)
Piramal Health Care	5.45E–05*[10.13365](0.0000)	0.194260*[12.89878](0.0000)	0.328483*[5.287839](0.0000)	0.391650*[7.344801](0.0000)	8.59E–06**[2.247628](0.0246)	0.003436***{1.959214}(0.056791)
Mid-cap Derivative-related Stocks	Parameters of Variance Equation¹					GARH Statistic
	α₀	α₁	β₁	β₂	γ	R² value²
MTNL	7.84E–05*[8.844966](0.0000)	0.122129*[14.65196](0.0000)	0.808609*[65.39162](0.0000)		–2.65E–05*[–4.946693](0.0000)	0.004198**{2.801321}(0.010123)
Small-cap Derivative-unrelated Stocks	Parameters of Variance Equation¹					GARH Statistic
	α₀	α₁	β₁	β₂	γ	R² value²
Eicher Motors	0.000290*[10.57452](0.0000)	0.166299*[12.42406](0.0000)	0.150232*[4.123816](0.0000)	0.533837*[14.94833](0.0000)	–0.000148*[–7.451390](0.0000)	0.006808*{3.893228}(0.000310)
Lakshmi Vilas Bank	0.000129*[12.05707](0.0000)	0.202067*[15.77917](0.0000)	0.376164*[7.952912](0.0000)	0.302755*[8.303361](0.0000)	–1.89E–05**[–2.483610](0.0130)	0.003341***{1.900922}(0.065293)
Bajaj Finance	0.000131*[8.637705](0.0000)	0.180457*[11.44712](0.0000)	0.595071*[7.011413](0.0000)	0.126790***[1.886140](0.0593)	–4.39E–05*[–4.076081](0.0000)	0.004375**{2.453684}(0.016460)
Prakash Industries	3.07E–05*[3.730665](0.0002)	0.193145*[17.35259](0.0000)	0.305154*[7.095912](0.0000)	0.510085*[13.51573](0.0000)	3.90E–05*[4.587759](0.0000)	0.023197*{10.77793}(0.000000)
Small-cap Derivative-related Stocks	Parameters of Variance Equation¹					GARH Statistic
	α₀	α₁	β₁	β₂	γ	R² value²
Escorts	8.48E–05*[10.00397](0.0000)	0.148275*[11.68394](0.0000)	0.531594*[4.683245](0.0000)	0.240717**[2.346264](0.0190)	3.44E–05*[4.888825](0.0000)	0.011538*{6.646996}(0.000000)
Prism Cement	5.13E–05*[12.67874](0.0000)	0.079299*[15.28734](0.0000)	0.891195*[158.3532](0.0000)		–2.33E–05*[–8.142675](0.0000)	0.003756**{2.387679}(0.026392)
Polaris Software	0.000333*[9.001660](0.0000)	0.179104*[12.12204](0.0000)	0.461927*[5.031272](0.0000)	0.257270*[3.261072](0.0011)	–0.000197*[–6.920872](0.0000)	0.004408***{1.945788}(0.058741)
RIIL	0.000137*[15.53542](0.0000)	0.211117*[15.54332](0.0000)	0.271044*[5.433328](0.0000)	0.413444*[9.476573](0.0000)	–2.49E–05*[–3.757716](0.0002)	0.027960*{16.26438}(0.000000)
SREI Infrastructure Finance	5.76E–05*[9.374427](0.0000)	0.124613*[12.61025](0.0000)	0.353723*[4.709410](0.0000)	0.506653*[7.333394](0.0000)	–1.66E–05*[–2.830629](0.0046)	0.033800*{18.11110}(0.000000)
Balrampur Chini Mill	0.000117*[9.309308](0.0000)	0.184141*[12.05789](0.0000)	0.356394*[4.594926](0.0000)	0.330473*[4.906655](0.0000)	5.22E–05*[4.667500](0.0000)	0.007559*{4.336058}(0.000085)
Gujarat Fluorochem.	8.81E–05*[8.856160](0.0000)	0.171081*[12.20115](0.0000)	0.309466*[4.395729](0.0000)	0.448201*[6.972606](0.0000)	–2.47E–05**[–1.986070](0.0470)	0.014110*{7.951408}(0.000000)
Orchid	8.44E–05*[11.33830](0.0000)	0.193807*[22.56399](0.0000)	0.751703*[62.66285](0.0000)		1.64E–05*[2.764468](0.0057)	0.011377*{7.029120}(0.000000)
Tulip Telecom	1.93E–05*[4.043325](0.0001)	0.042981*[9.956242](0.0000)	0.947214*[198.5704](0.0000)		–9.81E–06**[–2.436196](0.0148)	0.019075*{4.987819}(0.000045)

Source: Authors’ own.

Notes: (i)¹Variance equation: $h_{t} = α_{0} + \sum_{i = 1}^{p} α_{i} ε_{t - i}^{2} + \sum_{j = 1}^{q} β_{j} h_{t - j} + γ D_{f}$ , where D_f represents the dummy variable, which takes the value zero for the pre-derivative period and one for the post-derivative period.

²Coefficient of GARCH model determination; terms within square brackets represent Z-statistic, terms within braces represent F values and terms within parentheses denote probability.

(ii) *, ** and *** indicate the significance of the parameter, respectively, at 1%, 5% and 10% significance level. ▯➜ GARCH (1,2); ▮➜ GARCH (1,1).

Specifically, we find a significant negative sign of the coefficient of the derivative dummy γ for all the large- cap stocks in our study except Jaiprakash Associate in construction sector and Ranbaxy in pharmaceuticals sector indicating that volatility of stock return has declined due to the introduction of derivative trading on most of the individual large-cap stocks considered in the study. It is to be noted that the estimated coefficient of the derivative dummy γ is not significantly different from zero for Jaiprakash Associate but significantly positive for Ranbaxy (indicating increase in its return volatility).

We have selected 16 mid-cap stocks in our study, representing 12 sectors of the Indian economy for examining the impact of derivatives trading on their return volatility. For four stocks (ING Vysya Bank, Madras Cement, P&G and Aventis Pharmaceuticals) out of these 16 stocks, no derivatives trading have been introduced till the end of our study period. For these stocks, we, therefore, have considered the effect of derivative introduction in the Indian stock market on their return volatility considering 12 June 2000 (i.e., the date of derivative introduction in Indian stock market) as the cut-off date. It is observed from Table 5 that the coefficients of the derivative dummy for all the four derivative-unrelated mid-cap stocks are negative and statistically significant at 1 or 5 per cent level, indicating that volatility of stock return has declined due to the introduction of derivative trading in the Indian stock market for each of the derivative-unrelated mid-cap stocks examined in the study. We also observe a mixed type of impact of derivatives introduction on the derivative-related mid-cap stocks from the results of Table 5. For stocks related to banking sector (Oriental Bank of Commerce), construction sector (Unitech), energy sector (Hindustan Petroleum), metal sector (Bhushan Steel) and pharmaceuticals sector (Piramal Health Care), the derivative dummy coefficient γ is significant and positive. implying that derivative introduction has actually increased their return volatilities. However, for stocks related to automobile sector (Ashok Leyland) and telecom Sector (MTNL), we find a significant negative sign of the coefficient of the derivative dummy γ indicating that volatility of stock return has actually declined due to the introduction of derivative trading on these derivative-related mid-cap stocks. For stocks related to cement sector (India Cement), computer software sector (Mphasis), engineering sector (Voltas), finance sector (LIC Housing Finance) and FMCG sector (Glaxo Smith), we find no significant impact of derivatives introduction on their return volatilities.

We have selected 13 small-cap stocks representing 11 sectors of the Indian economy in our study out of which for four stocks (Eicher Motors, Lakshmi Vilas Bank, Bajaj Finance and Prakash Industries), no derivatives trading has been introduced till the end of our study period. For those stocks, we, therefore, have considered the effect of derivative introduction in the Indian stock market as a whole on their return volatility considering 12 June 2000 (i.e., the date of derivative introduction in Indian stock market) as the cut-off date. From Table 5, we observe a significant negative sign of the coefficient of the derivative dummy γ for Eicher Motors, Lakshmi Vilas Bank and Bajaj Finance and a significantly positive sign for that of Prakash Industries indicating that derivatives introduction in the Indian stock market is able to reduce return volatility of almost all the without derivative small-cap stocks considered in our study (except Prakash Industries). We have examined the impact of derivatives introduction on the return volatility of nine selected derivative-related small-cap stocks (viz., Escorts, Prism Cement, Polaris Software, Reliance Industrial Infrastructure Limited [RIIL], SREI Infrastructure Finance, Balrampur Chini Mill, Gujarat Fluorochemicals, Orchid Chemicals and Tulip Telecom) representing nine important sectors of the Indian economy. It is to be noted that we have not been able to find derivative-related small-cap stocks for all the 12 sectors considered in our study as data of many of the small-cap stocks were not found to be adequate, that is, not covering the study period in compliance with the objective of the study. We find a significant negative sign of the coefficient of the derivative dummy γ for almost all the stocks and thus decrease in their return volatility due to the derivatives introduction (except Escorts in automobile sector, Balrampur Chini Mill in FMCG sector and Orchid Chemicals in the pharmaceuticals sector; for these stocks, we have actually found a significant positive sign of the coefficient of the derivative dummy γ implying increase in their return volatility in the post-derivative introduction period). Therefore, derivatives introduction in the Indian stock market is able to reduce volatility of stock return for most of the derivative-related small-cap stocks considered in our study.

We find mixed types of impact of derivatives introduction on return volatilities of stocks belonging to different sectors in our study except for telecom sector (where we find exclusively declining impact), indicating no significant sectoral differences regarding the impact of derivatives introduction, at least during our period of analysis.

Thus, the results of the study show that volatilities of stock returns have declined due to the introduction of derivatives trading on most of the individual large-cap stocks considered in the study, which are all derivative-related stocks. Though we find a decrease in return volatilities of all the derivative-unrelated mid-cap stocks in our study, the results of the derivative-related mid-cap stocks are found to be mixed. In the case of small-cap stocks, the results indicate a decrease in return volatilities of most of the derivative-related and derivative-unrelated stocks considered in the study. Therefore, it can be concluded that the introduction of derivatives trading on individual stocks is successful in reducing the return volatility of most of the large-cap, small-cap and all the derivative-unrelated mid-cap stocks selected for the study. Moreover, there is evidence of volatility reduction for almost all the derivative-unrelated stocks. We find a mixed type of impact of derivatives introduction on return volatilities of stocks belonging to different sectors in our study except for telecom sector (where we find exclusively declining impact) indicating no significant sectoral difference regarding the impact of derivatives introduction, at least during our period of analysis.

Conclusions

In this article, we have tried to examine the impact of the introduction of derivatives trading on the individual stocks representing different market capitalisations and different sectors of the economy on their underlying spot market volatility using daily closing price data from 1 April 1996 (or from which date data are available for some stocks) to 31 March 2012 in a GARCH(p, q) framework. The results of the study show that volatilities of stock returns have declined due to the introduction of derivatives trading on most of the individual large-cap stocks considered in the study which are all derivative-related stocks. Though we find a decrease in return volatilities of all the derivative-unrelated mid-cap stocks in our study, the results of the derivative-related mid-cap stocks are found to be mixed. In the case of small-cap stocks, the results indicate a decrease in return volatilities of most of the derivative-related and derivative-unrelated stocks considered in the study. Therefore, it can be said that the introduction of derivatives trading on individual stocks is successful in reducing the return volatility of most of the large-cap, small-cap and all the derivative-unrelated mid-cap stocks selected for the study. There is evidence of volatility reduction for almost all the derivative-unrelated stocks. We find no significant sectoral difference while examining the impact of derivatives trading on return volatilities of stocks representing different sectors of the Indian economy. The policy implications of these findings are that (i) more and more derivative instruments are to be introduced on individual stock as well as stock index underlying in India so that Indian stock market become stable and more efficient and (ii) no sectoral bias should be there regarding the introduction of derivative instruments. As a policy measure, government may undertake further reforms in the form of introduction of sophisticated financial instruments in the domestic stock market.

It should be noted that this study is based on data of selected stocks. Results may be different for other stocks of the same category. Moreover, scope of further research is there on examining the impact of different company- specific, industry-specific and market-specific information on stock market volatility in India.

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