Impact of futures and asymmetric effect on the volatility of Indian stock market.
Author:
Padhi, Puja
Pub Date:
12/01/2008
Publication:
Name: Indian Journal of Economics and Business Publisher: Indian Journal of Economics and Business Audience: Academic Format: Magazine/Journal Subject: Business; Economics Copyright: COPYRIGHT 2008 Indian Journal of Economics and Business ISSN: 0972-5784
Issue:
Date: Dec, 2008 Source Volume: 7 Source Issue: 2

Accession Number:
190889677
Full Text:
Abstract

The purpose of this article is to investigate the effect of the introduction of stock index futures on the volatility of the spot equity market and to test the impact of the introduction of the stock index futures contracts, a GARCH model is modified along the lines of GJR-GARCH and EGARCH model, especially to take into account the link between information and volatility. This paper provides the evidence that there is not much change in the volatility pattern after the introduction of futures in the Indian stock market. The impacts of futures trading for the post futures period can be captured by the asymmetric coefficient (d), suggest that there is a statistically significant and positive asymmetric effect. Thus the introduction of futures trading has impact on the asymmetric coefficient. It shows the similar pattern for the pre and post futures period. Empirical research can be further expanded by selecting and analyzing high frequency intraday data and the inclusion of additional economic variables in the conditional variance equation.

Keywords: Index Futures, volatility, asymmetric effect, futures market

JEL Classification: G14 G32

I. INTRODUCTION

The issue of the impact of futures trading on stock market volatility has received considerable and increasing attention in the recent years, after the introduction of futures in the Indian stock market. Examining the impact of futures trading on the stock market volatility in a way that allows for consideration of volatility clustering and asymmetric responses to news not only provides important guidance yield insights into the reasons why asymmetric exist. If the market dynamics are the cause of asymmetries, than innovations, such as introduction of futures, may be expected to impact not only the level of volatility in the underlying market, but also on the structure and characteristics of that volatility. This article seeks to address the issue of the impact that the existence of futures trading has on market volatility. The rest of the article is organized as follows. The next section discusses some theoretical issues and develops the arguments as to the role of futures markets and their potential effects on stock price volatility. The third section presents the empirical design. The data and results are provided in the forth section and final section concludes.

II. IMPACT OF FUTURES ON VOLATILITY

From the literature on stock market volatility, it is known that a multitude of factors influence return volatility. Of them asymmetry is one. Asymmetry volatility refers to a situation in which a negative shock to financial time series is likely to cause volatility to rise by more than a positive shock of the same magnitude. In the case of equity returns, such asymmetries are typically attributed to "leverage effects", whereby a fall in the value of a firm's stock causes the firm's debt to equity ratio to rise. This leads shareholders, who bear the residual risk of the firm, to perceive their future cash flow stream as being relatively riskier. Asymmetric or leverage volatility models explain that good news and bad news have different predictability on future volatility. An asymmetry reaction of conditional volatility to the arrival of news is induced both by the sign of past shocks and the size of unexpected volatility (Engle and Ng 1993). There are factors other than the sign of past shocks that are responsible for the asymmetric behavior of volatilities. To examine this, Fornari and Mele (1997) proposed the Volatility--Switching ARCH model that captures asymmetries via the impact of past shocks on the level of volatility, rather than through the unexpected returns. Not only shocks and noise trading but seasonality in asset behavior also affects stock return. Antoniou et. al (1998) explained to fully understand the impact of futures trading on the volatility of the underlying market and whether such an impact is desirable or undesirable, it is necessary to model volatility pre- and post futures by using a technique that takes into account of possible asymmetric responses to news. Even if it is found that spot market volatility has increased post futures, this is not necessarily an undesirable consequence of derivative trading, because there may, simultaneously, be a change in the spot market dynamics that removes asymmetries and improve the transmission mechanism for news. Alexakis (2007) examined the impact of stock index futures trading, on the volatility of the underlying FTSE/ASE-20 stock index market in ATHEX, is investigated by estimating a model for a period which covers the time before and after the introduction of stock index futures contracts. He argued that futures lead the cash index returns, by responding more rapidly to economic events than stock prices. Thus, new market information may be disseminated faster in the futures market compared to the stock market and that futures volatility spills some information over to cash market volatility.

III. METHODOLOGY AND THEORETICAL APPROACH ON ARCH AND EGARCH MODEL

In the context of the impact of derivatives market on spot market volatility, if derivatives trading do increase the rate of flow of information, then spot prices may exhibit increased volatility. Thus, it is important to use a model to take into account the link between information and volatility and possible asymmetric responses to news, so as to seen whether the introduction of stock index futures trading has increased or decreased spot price volatility and to investigate the extent to which the introduction if stock index futures contracts also affected the nature of volatility in the underlying spot market.

The ARCH model of Engle (1982) and the GARCH model of Bollerslev (1986) can capture time variation in return distributions. The GJR model is a simple extension of GARCH model, with an additional term added to account for possible asymmetries. The conditional variance is now given by

[[sigma].sub.t.sup.2] = [[alpha].sub.0] + [[alpha].sub.1] [[epsilon].sub.t-1.sup.2] + [[beta].sub.1] [[epsilon].sub.t-1.sup.2] [I.sub.t-1] + [gamma] [[sigma].sub.t-1.sup.2] (1)

where, [I.sub.t-1] = 1 if [[epsilon].sub.t-1] < 0

= 0 otherwise

For a leverage effect, [beta] > 0. The condition for non negativity will be [[alpha].sub.0] > 0, [[alpha].sub.1] [greater than or equal to] 0, [beta] [greater than or equal to] 0, and [[alpha].sub.1] + [beta] [greater than or equal to] 0.

While the GARCH models successfully capture thick tail returns and volatility clustering, they are not well-suited to capture the "leverage effect", since the conditional variance is a function only of magnitude of the lagged residuals and not their signs. In the exponential GARCH (EGARCH) model of Nelson (1991), the conditional variance ([[sigma].sub.t.sup.2]) is formulated to depend on both the size and sign of lagged residuals. More formally, the conditional variance equation is written as

ln [[sigma].sub.t.sup.2] = [[alpha].sub.0] + [[SIGMA].sub.i=1.sup.q] [[alpha].sub.i] g ([Z.sub.t-i]) + [[SIGMA].sub.i=1.sup.p] [[beta].sub.i] ln([[sigma].sub.t-j.sup.2]) (2)

where [z.sub.t] = [[epsilon].sub.t] / [[sigma].sub.t] is the normalized residual series.

In the above equation, the value of g([z.sub.t]), depends on several elements. Nelson (1991) notes that, "to accommodate the symmetric relation between stock returns and volatility changes the value of g([z.sub.t]) must be a function of both the magnitude and sign of [z.sub.t]". That is why he suggested to express the function of g(x) as

g([z.sub.t]) = [[theta].sub.1] [z.sub.t] + [[theta].sub.2] [[absolute value of [z.sub.t]] - E [absolute value of [z.sub.t]]] ... (3)

The first term ([[theta].sub.1] [z.sub.t]) shows the sign effect, the second term [[theta].sub.2] [[absolute value of [z.sub.t]] - E [absolute value of [z.sub.t]]] shows the magnitude effect.

The model has some advantages over the pure GARCH specification. First, since log ([[sigma].sub.t.sup.2]) is modelled, then even if the parameters are negative [[sigma].sub.t.sup.2] will be positive. There is thus no need to artificially impose non-negativity constraints on the model parameters. Second, asymmetries are allowed under the EGARCH formulation, since if the relationship between volatility and return is negative, [[theta].sub.1] will be negative.

IV. DESCRIPTION OF DATA AND PRELIMINARY STATISTICS

The impact of stock index future trading, on the volatility of the underlying Nifty and Nifty Junior stock index market, is investigated by estimating a model for a period which covers the time before and after the introduction of stock index futures contracts. In the analysis, 12th June 2000 will be threshold point that separates pre- and post-stock index futures trading in order for robust inferences to be made. The data set comprises daily closing observations of the spot index rates for the aforementioned market. It covers the periods 1st June 1995 to 26th September 2006 for nifty index. The particular period and the set of data for the empirical investigation are chosen in order to give emphasis on the introduction of future how it affect the stock market volatility. The stock index prices are obtained from National Stock Exchange. All prices are transformed to natural logarithms.

The descriptive statistics of logarithmic first-differences of the daily nifty and nifty junior spot index prices are reported in Table i and Table 2 respectively, which is divided into two periods. The first period (panel A) correspond to the pre future period (1/06/ 1995-1/12/2000) of the analysis. The second (panel B) correspond to the post futures period (1/14/2000-9/26/2006) of the analysis for Nifty index. In Table 2 panel A and B correspond to pre and post futures period of Nifty Junior. The results indicate excess skewness and kurtosis in the price series, departure from normality for the spot prices, while all the variable in the first difference stationary, all having a unit root on their log-levels presentation. The figures obtained for the standard deviation estimates, provide an initial view of volatility, where by comparing two periods (pre- and post-derivatives) it seems that volatility has decreased for nifty index and it remains same for nifty junior over time.

Table 2, reports the Ljung-Box (1976) statistics, where the results indicate significant linear and non-linear temporal dependencies in the adjusted residual series respectively.

V. EMPIRICAL RESULTS

To assess whether there has been a change in volatility after the inception of futures trading, a GARCH (1,1) and GJR-GARCH (1,1) model of conditional volatility is estimated.

GARCH (1,1) refers to the first order ARCH term and first order GARCH term in the conditional variance equation. '[alpha]' (ARCH 1) is the 'news' coefficient, with a higher value implying that recent news has a greater impact on price changes. It relates to the impact of yesterday's news on today's price changes. In contrast [beta] (GARCH) reflects the impact of "old news" on price changes. It indicates the level of persistence in information and it effects on volatility.

In the GARCH (1, 1) model [beta] = 0.8 and [[alpha].sub.1] = 0.12, this seems to suggest that past conditional variance has a greater impact on volatility of spot market returns than recent news announcements. A high [beta] shows persistence of volatility due to old news. The log likelihood value is high (8186.031), which is an indication that the GARCH (1, 1) model is a good fit. We did the ARCH LM test on residual to see if there was any ARCH effect left. It shows there is no significant ARCH effect in the residual series. [alpha] + [beta] shows the persistence of the series it's close to one.

We studied the impact of introduction of index Futures on the stock market by restricting the period of study to a year before and after introduction of Futures. During this time no other derivative contracts like index options, futures and option on individual shares etc were traded in the Indian market. Since this period is restricted to one year before and after futures, we can get a better insight onto the impact of other stock market reforms. The ARCH 1 (0.127) and GARCH 1. (0.746) terms are significant and their sum is close to one indicating a high level of persistence of volatilities. (See table 4). This shows that the market has a long memory and that impact of a shock persists for a long time to come. The dummy variable for the future (-2.17E-05) is negative and significant, which would have implied a decline in volatility. The value is significant at conventional levels (see Table 4).

The estimates of the GJR-GARCH model of the spot stock index prices for the two sub period pre-futures Period (7/06/2C03-7/6/2005) and post-futures period (8/6/2005-1/6/2007) analysis are represented in table 5. The diagnostic tests, on the standardized residuals and squared residuals, indicate absence of linear and non-linear dependencies, respectively. Thus the estimated model fits the data very well. The standard diagnostic tests of the residuals from the model confirm the absence of any further ARCH effects. The results of the coefficients of the lagged variance [[alpha].sub.1] and [[beta].sub.1] indicate that the conditional volatility is time varying, with no ARCH effects and it is significant for the pre-futures period. The [[alpha].sub.1] coefficient is not significant for the pre futures period for nifty and nifty junior and post futures period for nifty junior. This means that news about the volatility for the previous period does not have much importance. The lagged error term, [??], relates to changes in the spot price on the previous day, can be viewed as a new news coefficient. Hence a higher value in the post futures period implies that recent news have a greater impact on price changes. The results, from Table 5, indicate that this holds, suggesting that information is being impounded in prices more quickly due to the introduction of futures trading. The results of the asymmetric coefficient ([gamma]) suggest that there is a statistically significant and positive asymmetric effect, which implies that negative shocks elicit a larger response than positive shocks of an equal magnitude.

The impacts of futures trading for the post futures period can be captured by the asymmetric coefficient ([gamma]) suggest that there is a statistically significant and positive asymmetric effect. Thus the introduction of futures trading have impact on the asymmetric coefficient. It shows the similar pattern for the pre and post futures period.

The issue of the impact of futures trading on the spot market volatility is further investigated by estimating the EGARCH model, The results are reported in Table 6. The results of the impact of futures introduction on asymmetric market responses may be assessed via consideration of the asymmetric coefficient ([gamma]) that captures the nature of bias in the pre and post future period. Whether the asymmetric coefficient behaves the same way as it was in the GJR-GARCH model. The results indicate that the pre-futures asymmetric coefficient is statistically insignificant whereas the post futures asymmetric coefficient is negative and statistically insignificant. This shows that during the post futures period the negative shocks elicit a larger response than positive shocks of an equal magnitude.

V. CONCLUSION

The study examined the impact of stock index future trading, on the volatility of the underlying Nifty and Nifty Junior stock index market, is investigated by estimating a model for a period which covers the time before and after the introduction of stock index futures contracts. In the analysis, 12th June 2000 will be threshold point that separates pre-and post-stock index futures trading in order for robust inferences to be made. The data set comprises daily closing observations of the spot index rates for the aforementioned market. It covers the periods 1st June 1995 to 26th September 2006 for nifty index. The results suggest that there is the decrease in volatility in the case of nifty where as there is the increase of volatility in the case of nifty junior after the introduction of futures in the derivative market. A desirable impact on the asymmetry of volatility. This implies that negative shocks elicit a larger response than positive shocks of an equal magnitude. Certainly, other economic variables could be added and checked, leading possibly to stronger results.

References

Antoniou A., P. Holmes and R. Priestlet (1998), "The Effects of Stock Index Futures Trading on Stock, Index Volatility: An Analysis of the Asymmetric Response of Volatility to News", The Journal of Futures Markets, 18 (2), pp. 151-166.

Alexakis P. (2007), "On the Effect of Index Futures Trading on Stock Market Volatility", International Research Journal of Finance and Economics, 11, pp. 7-29.

Bollerslev, T. (1986), "Generalized Autoregressive Conditional Heteroscedasticity", Journal of Econometrics, 31, 307-327.

Engle R. F. (1982), "Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U. K. Inflation", Econometrica, 50, 987-1008.

Engle, R. F. and V. Ng (1993), "Measuring and Testing the Impact of News on Volatility", Journal of Finance, 43, 1749-77.

Fabio Fornari and A. Mele (1997), "Sign and Volatility-switching ARCH Models: Theory and Applications to International Stock Markets", Journal of Applied Econometrics, 12, 49-65.

Nelson D. B. (1991), "Conditional Heteroskedasticity in Asset Returns: An New Approach", Econometrica, 59, 347-70.

PUJA PADHI

Pondicherry Central University
Table 1
Descriptive Statistics of Logarithmic First-Differences of
Spot Nifty Index Prices (1/06/1995-9/26/2006)

Statistic          Panel A: Pre futures   Panel B: Post futures

Mean                       -2.77E-05                  0.0008
Std. Deviation                0.0172                  0.0139
Skewness                      0.0414                 -0.9768
Kurtosis                      5.8980                 10.8183
Jarque-Bera                 558.6266                4110.347
ADF (lags) Level     -34.128 (0.000)         -22.462 (0.000)

Notes: All series are measured in logarithmic first differences.
Figures in the parenthesis (.) indicate Z-statistics. Skew and kurt
are the estimated centralized third and fourth moments of the data.
J-B is the Jarque-Bera (1980) for the normality. ADF is the Augmented
Dicket Fuller (1981) test. Level and 111 difference corresponding
to price series in log levels and log first-differences, respectively.
The 5% critical value for the ADF (1981) test is -2.89.

Table 2
Ljung-Box Statistics for Linear & Non-Linear Temporal Dependence in
Autoregressive Models Pre & Post Futures Period for Nifty Index

Index               Q[1]      [12]      Q[24]    [Q.sup.2][1]

Pre-Nifty Index     0.412    19.520    39.245       0.406
                   (0.521)   (0.077)   (0.026)     (0.524)
Post-Nifty Index    0.010    18.500    26.392       0.024
                   (0.920)   (0.101)   (0.334)     (0.876)

Index              [Q.sup.2][12]   [Q.sup.2][24]

Pre-Nifty Index        6.005          20.743
                      (0.916)         (0.654)
Post-Nifty Index      15.829          55.873
                      (0.199)         (0.000)

Notes: Figures in the parenthesis (.) indicate exact significance
levels. Q(L) and [Q.sup.2](L) are the Ljung Box (1978). Q statistics
on the first L lags of the sample autocorrelation function of the
series and of the squared series; these series are distributed as
chi- squared The order of the most parsimonious autoregressive
models are in squared brackets.

Table 3
Estimates of GARCH (1,1) Model for twelve years on Nifty
(1995 to 2007)

Variables         Description   Coefficient   Z-statistics

[[alpha].sub.0]   Intercept       2.28E-05       7.371922
[[alpha].sub.1]   ARCH (1)        0.127449       15.14601
[[beta].sub.1]    LARCH (1)       0.809336       68.91760
[[gamma].sup.2]   Dummy          -1.11E-05      -5.263318

Variables         Probability

[[alpha].sub.0]     0.0000
[[alpha].sub.1]     0.0000
[[beta].sub.1]      0.0000
[[gamma].sup.2]     0.0000

Table 4
Estimates of GARCH (1,1) with One Year before and After
Introduction of Futures in Nifty (1999 to 2001)

Variables         Description   Coefficient   Z-statistics   Probability

[[alpha].sub.0]   Intercept       5.45E-05       2.485027       0.0130
[[alpha].sub.1]   ARCH (1)        0.127584       3.311698       0.0009
[[beta].sub.1]    GARCH (1)       0.746672       10.01378       0.0000
[[gamma].sup.2]   Dummy          -2.17E-05      -1.804849       0.0711

Table 5
GJR-GARCH Model Estimates of Nifty for the Pre & Post Futures Period

Panel A: Coefficients Estimates, Nifty-Alt (1)
Mean Equation:

Coefficients                   Pre-Futures Period

                               (1/06/1995-1/12/2000)
[[PHI].sub.0]                  0.0001(0.242) [0.808]
[[PHI].sub.1]                  0.1124(3.635) [0.000]
Variance Equation:
[a.sub.0]                      1.64E-05 (5.465) [0.000]
[[alpha].sub.1]                0.067 (4,560) [0.000]
[[beta].sub.1]                 0.855 (66.827) [0.000]
[gamma]                        0.055 (2.592) [0.009]

Panel B: Residual Diagnostic

Skewness                       0.0853
Kurtosis                       6.6008
J-B                            708.223
Q(24)                          33.153 (0.101)
[Q.sup.2](24)                  22.680 (0.031)
ARCH(4)                        0.8674 [0.4827]

Panel A: Coefficients Estimates, Nifty-Alt (1)
Mean Equation:

Coefficients                   Post-Futures Period

                               (1/14/2000-9/26/2006)
[[PHI].sub.0]                  0.0006 (2.2291) [0.025]
[[PHI].sub.1]                  0.129 (5.009) [0.000]
Variance Equation:
[a.sub.0]                      2.16E-05 (7.805) [0.000]
[[alpha].sub.1]                0.0004 (0.2160) [0.828]
[[beta].sub.1]                 0.7258 (29.757) [0.000]
[gamma]                        0.293 (7.960) [0.000]

Panel B: Residual Diagnostic

Skewness                       -0.463
Kurtosis                       3.936
J-B                            126.3566
Q(24)                          39.245 (0.026)
[Q.sup.2](24)                  20.743 (0.654)
ARCH(4)                        0.3345 [0.854]

Notes: Figures in the parenthesis(.) and in squared brackets [.]
indicate Z-statistics and exact significance levels. J-B is the
Jarque-Bera (1980) normality test. Q(24) and Q2(24) are the
Ljung-Box (1978) tests for 24th, order serial correlation and
Heteroskedasticity. ARCH(4) is the Engel's (1982) F- test.

Table 6
EGARCH Model Estimates of Nifty for the Pre & Post Futures Period

Panel A: Coefficient Estimates, Nifty AR (1)

Coefficients      Pre-Futures Period         Post-Futures Period

                  (1/06/1995-1/12/2000)      (1/14/2000-9/26/2006)
[[PHI].sub.1]     4.354 (0.1293) [0.000]     0.146 (5.915) [0.000]
[a.sub.0]         -0.690 (-3.3488) [0.000]   -1.247 (-7.311) [0.000]
[[alpha].sub.1]   0.227 (5.514) (0.000)      0.262 (6.561) [0.000]
[[beta].sub.1]    0.936 (40.059) [0.000]     0.879 (47.924) [0.000]
[gamma]           -0.039 (-1.651) [0.098]    -0.1950 (-7.767) [0.000]
T-Distribution    5.878 (7.590) [0.000]      11.530 (4.402) [0.000]

Notes: See notes in Table 5.
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