Chapter- 7. Relation Between Volume, Open Interest and Volatility

Chapter- 7 Relation Between Volume, Open Interest and Volatility

CHAPTER-7 Relationship between Volume, Open Interest and Volatility 7.1 Introduction The literature has seen a chunk of studies dedicated to explore the relationship between the volatility of future contract prices and their trading volume and open interest. A widely documented phenomenon is the positive contemporaneous correlation between price volatility and trading volume. Karpoff (1987) reviews previous studies on price volume relation on various financial markets, in which he cites 18 studies that document the positive correlation between volatility and volume. Several theories predict a contemporaneous relation between price volatility and trading volume. The Mixture of Distribution hypothesis (Clark (1973), Epps and Epps (1976), Tauchen and Pitts (1983), and Harris (1986)) assumes that the variance per transaction is monotonically related to the volume of that transaction. Consequently, price changes are sampled 105

from a mixture of normal distributions with either the volume per transaction, number of transactions, or number of information arrivals per observation unit acting as the mixing variable. Copeland (1976),(1977), Morse (1981), Jennings, Starks, and Fellingham (1981), and Jennings and Barry (1983) develop and extend Sequential Arrival of Information models where new information is disseminated sequentially to traders, and traders not yet informed can not perfectly infer the presence of informed trading. Consequently, the sequential arrival of new information to the market generates both trading volume and price movements, with both increasing during periods characterized by numerous information shocks. A third explanation is found in Admati and Pfleiderer (1988), who show that traders with trade timing discretion choose to trade when recent volume is large. Therefore, transactions and price movements are bounced in time, and the effect of volume on price movements depends on recent volume levels (Admati and Pfleiderer, Hypothesis 3). As far as futures markets are concerned, open interest is considered to be another important variable, being used as a proxy for market depth, which Kyle (1985) defines as the order flow required to move prices by one unit. His model implies that larger volumes support more informed traders, and that depth varies with the level of non- informational trading activity. Further, as noted by Bessembinder and Seguin (1993), a bi-directional causality relationship between volatility and trading volume (or open 106

interest) would support the mixture of distribution hypothesis (see Clark 1973). The sequential arrival of information theory of Copeland (1976, 1977) would hold if volatility is dependent upon the lagged volume and/or lagged open interest. Also Admati and Pfleiderer (1988) s traders with trade timing discretion tend to trade in heavy liquidity theory would apply if trading volume affects volatility. Open interest represents the number of future contracts outstanding at any point in time, where as trading volume captures the number of contracts traded during a specific time period. Open interest supplements the information provided by trading volume. Open interest can proxy the potential for a price change, while trading volume assesses the strength of a price level. The change in the level of open interest can also measure the direction of capital flows relative to that contract. In this chapter, the purpose of the study is to empirically examine the dynamics of GARCH effect in relation to trading activity variables like trading volume and open interest in the CNX Nifty Index Futures market. We have followed the methods developed by Girma and Mougoue (2002) to investigate, whether by adding the current/ the first lag open interest and trading volume in the variance equation helps the GARCH model better explain the volatility in CNX Nifty Index Futures market. Further in contrast to Girma and Mougoue (2002) we have used the open interest and volume 107

series after adjusting for Time to Maturity (TTM) effect which is popularly known as Samuelson s Effect (1965). Most studies of volatility have reiterated the empirical findings that volatility in financial time series is highly persistent with clearly demonstrated volatility clustering behavior. See, for example, Mandelbrot (1963), Bollerslev et al (1994) and Brooks (2002). Numerous models have been proposed to describe the phenomena of heteroskedasticity and volatility clustering. Among these models the Autoregressive Conditional Heteroskedasticity (ARCH) and Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process developed by Engle (1982) and Bollerslev (1986) respectively, appear to be appropriate models for the daily returns of many financial time series. The GARCH (1,1) model is one of the most successful such parameterization for characterizing high frequency financial market volatility. One of the common findings in many empirical applications of this model is a high degree of persistence within the estimated conditional variance process (see Bollerslev et al. 1992). The objective of this chapter is to examine the relationship between volatility, trading volume and/or open interest in an attempt to uncover the sources of variability in the Nifty Index Future market, in addition to studying whether volume and/or open interest data help improve the accuracy of GARCH-type model. A good understanding of the sources of variability in the Nifty Index Future contract could lead to superior trading 108

and hedging strategies. The findings of the study have practical implications for hedgers such as institutional investors and also individual investors dealing in equity future market. These findings also could be of interest to speculators and market regulators fearful of potentially destabilizing excess volatility in equity futures market. 7.2 Literature Survey The literature on modeling the relationship amongst volatility, volume and open interest has seen three main streams of development as discussed in chapter 2.3. Taking clues from literature survey (as discussed chapter 2.3), in this chapter, the study explores the effect of volume and open interest on Nifty Index Future Return volatility. First, it investigates the effect of volume and open interest on Nifty Index Future return volatility taken one at a time. Then, it explores the effect of volume and open interest on nifty index future return volatility taking both the variables simultaneously in the conditional variance equation. 7.3 Data and Methodology The data used are the daily closing prices, trading volume (turnover) of the contracts, between 12/06/2000 (the date on which future contract on CNX Nifty Index started trading in NSE) and 29/09/2009 closest to expiration (i.e. near month contract) for CNX Nifty Future. We have taken the daily closing prices, volume and open interest of the near month (M) 109

future index contract that is deliverable in the same trading month (M). After the expiration of the (M) month contracts on the last Thursday of that month, and on the first day of the next trading month (M+l) the data for the contract which will be deliverable in the month (M+l) is taken. For example, if the calendar trading month is January, the daily closing prices, volume and open interest are collected for the contract that is deliverable on the last Thursday of January. On the day after the closing date of the January, it is rolled over to February month contract that are deliverable on the last Thursday of February. The choice of near month contract provides high degrees of liquidity. In total we have 2324 observations of closing price and trading volume obtained from nseindia.com the official website NSE (National Stock Exchange of India). CNX Nifty is a bellwether index of NSE il representing 50 stocks across 22 sectors. NSE is the world s 4 largest exchange in number of trades in equity as on June 09 (source: ISMR). Also one of the largest equity derivatives volume globally as on Dec 08 (source: WFERFIA). Nifty represents 52% of the traded volume of NSE (source NSE) and 63% of market capitalization of NSE (source: NSE; data as of 31.12.2009). Assuming continuous compounding, the daily return series are calculated as the first difference of the logarithms of the daily closing prices on future index contract. no

R, = ln(p,/pa (7.1) Table: 7.1 presents the various descriptive statistics for the daily Nifty Future Index return, volume and open interest. The mean daily Index Future return is 0.000531%, with a standard deviation of 0.018%. The return series is fat-tailed as reported by excess kurtosis of 11.53 and negatively skewed as reported by skewness is -0.48. Applying the Jarque-Bera test for normality, we find strong support for the hypothesis that the time series for future index returns don t correspond to a normal distribution. The existing literature shows that excess kurtosis and skewness are evidence of possible heteroseedastieity (see, e.g., Akgiray et al., 1991; Hall et al., 1989; Harvey & Siddique, 1999). ill

Tabie:7.1 Summary Statistics of Future Index Return, Volume & Open Interest RETURN VOLUME OI Mean 0.000531 546122.1 14619450 Median 0.001045 318188.8 10897000 Maximum 0.161947 3091293 44400050 Minimum -0.162581 51.87 5000 Std. Dev. 0.01844 573910.8 12970229 Skewness -0.486002 0.940613 0.396376 Kurtosis 11.53451 3.166897 1.729823 Jarque-Bera 7138.467 345.0944 216.8949 Probability 0 0 0 ARCH LM (10) 244.2308 (0.0000) Sum 1.233276 1.27E+09 3.39E+10 Sum Sq. Dev. 0.789245 7.64E+14 3.90E+17 Observations 2322 2322 2322 Therefore, we conducts ARCH LM test using Engle s (1982) methods for arch effect. The test results show that the LM statistic is significant at better than the 1% level, implying that the Nifty Index Future return series are heteroscedastic. In fact, the p value given below the parameter estimate is well below 0.01, strongly rejecting the null hypothesis of homoskedasticity. Open interest can take on rich time to maturity pattern. Milonas.B (1986) considers time to maturity pattern in open interest for various markets. He finds that for liquid future contract of immediate maturity, there can be different time to maturity patterns, with more distant contracts having more or less open interest than nearer to expiration. Thus we might expect to see a time to maturity effect in volume series. 112

In order to adjust for this documented shift in both mean and variance of the volume and open interest series we run regression on time to expiration. The time to maturity variable is simple decreasing factor. In our sample data, 25 days is the maximum days to expiration and it decreases to 0 (zero) days, being the day of expiration. Following Campbell. J.Y, Grossman. S. J and Wang. J.C (1993) we measure the turnover (volume) and open interest series in logs rather than in absolute units to remove low frequency variation from the level and variance of both the series. Also following Gallant. A. R; Rossi. P. E and Tauchen. G; (1992) we introduce t and t2 time trend variables to remove the liner and quadratic trend in volume and open interest series. We run the following regression models to bring stationarity in volume and open interest series for further analysis in the study.1 LogOIt = a0 + ajt + a2t2 + a3ttei + yt (7.2) /=0 LogVt = ao + a}t + a3t2 + a3ttei + vt (7.3) i=0 Where, 1 The volume and open interest series are tested for unit root in their levels using Augmented Dicky Fuller (ADF) test; the results can not reject the null hypothesis of a unit root. Again the residual of the equation (7.2) and (7.3), taken as volume and open interest series respectively for further analysis, are tested for unit root; reject the null hypothesis of a unit root. 113

t (linear trend variable) = {t/2324) t2 (Quadratic trend variable) = {t/2324)2 LogOl= log open interest at time t LogVt = log volume at time t TTEi = Time to Maturity effect from 25days to expiration to zero day (the day of expiration. yt = the residual of equation (7.2) represents the detrended open interest adjusted for time to maturity effect. vt = the residual of the equation (7.3) represents the detrended volume adjusted for time to maturity effect. (We have tested stationarity of both the residual series of equation (7.2) and (7.3) by applying Augmented Dickey Fuller test. The results of the test are presented in Table-7.3. Both y, and v, represent open interest and volume series respectively are stationary as per the result of the test and used in our study for further analysis. However we use the return series without any seasonal adjustment because we find so such significant effect of time to maturity. In the Table-7.2, we present the regression statistics of the equation (7.2) and (7.3). 114

Table-7.2 Regression Statistics R2 F-statistic Prob(F-statistic) Equation (7.2) 0.966109 2310.003 0.00* Equation (7.3) 0.957206 1812.59 0.00* * Accepted at 1% level of significance that betas are significant and not equal to zero. That means iogoi and logv series has some seasonal tendency as far as TTE is concerned. Panel A Table-7.3 Test of Unit Root Null Hypothesis: NEWOI has a unit root Exogenous: Constant Lag Length: 0 (Automatic based on SIC, MAXLAG=26) t-statistic Prob. Augmented Dickey-Fuller test statistic -10.1579 0* Test critical values: 1% level -3.433001 5% level -2.862597 10% level -2.567378 Panel B Null Hypothesis: NEWVOL has a unit root Exogenous: Constant Lag Length: 6 (Automatic based on SIC, MAXLAG=26) Augmented Dickey-Fuller test statistic -5.925845 0* Test critical values: 1% level -3.433009 5% level -2.8626 10% level -2.56738 * The null hypothesis that open interest series (Yt) an<j volume series (Vt) are stationary can not be rejected at 1% level. The descriptive statistics in the Table-7.1 suggests that, Nifty Index Future Return series are not normally distributed and are characterized by excess kurtosis. Also, the return series exhibited significant heteroscedasticity, suggesting the use of the Generalized ARCH (GARCH) model Bollerslev 115

(1986) is appropriate. Therefore, in order to study the relation between future index return volatility, volume and open interest, we use augmented GARCH framework. The GARCH (1,1) model has been shown to be adequate for examining the relation between return volatility and volume (Bollerslev, 1986,1987); Lamoureux & Lastrapes, 1990; Najand & Yung, 1991, etc). Finally, we estimate the GARCH (1, 1) model using the adjusted volume and open interest series and the level of the return series as appropriate. We specifically use the following GARCH (1,1) models. Rt- fi + Rt.i+ st (7.4) et/it.j-n&hj (7.5) ht = ao + ais2t-i + a2ht.j (7.6) ht = a0 + aje2^ + a2ht.1+ yivh (j = 0, 1) (7.7) ht = a0 + a,s2t.]+ a2ht.]+ @I(OI)t_j + 2VH (j = 0, 1) (7.8) In equation (7.7) and (7.8),y will take 0 for current volume and open interest and 1 for lagged volume and open interest. For equation (7.8) we have followed Girma and Mougoue (2002).Further, Bessembinder and Seguin (1993) states that, open interest measures are pertinent along with volume. Since many speculators are day traders, who don t hold open positions over night, open interest as of the close of the trading likely reflects primarily hedging activity and,thus, proxies for the 116

amount of uninformed trading. Using open interest in conjunction with volume data may provide insights into the price effects of market activity generated by informed versus uninformed traders or hedgers and speculators. Where, Rt is the nifty future index return series, V or OI are the adjusted volume or open interest of the nifty index future contract on a given day and (y, the coefficient) their respective parameter estimate. < / and 02 in equation (7.8) are parameter estimates for open interest and volume when both volume and open interest are entered simultaneously in the conditional variance equation. Note that equation (7.7) is also used to model the relation between open interest and volatility by simply substituting open interest (OI) for volume (V). As Table-7.1 shows that nifty index future return series are non-normally distributed, the model given by equation (7.4) to (7.8) is estimated under the assumption that et follows a conditional normal distribution which is conditioned on the available information (/,_/) at time t-1. The empirical findings are presented and discussed in the next section. 117

7.4 Empirical Results Table-7.4 GARCH (1,1) Estimate for Nifty Index Future Return Coefficient Std. Error z-statistic Prob. F 0.001264 0.000275 4.591327 0 ao 0.000009780 1.08E-06 9.055034 0 ai 0.166674 0.011824 14.09654 0 02 0.811876 0.012033 67.47172 0 0.97855 ai+02 The results of simple GARCH (1, 1) model [Equation-(7.6)] parameter estimates of Nifty Index Future Return are presented in the Table-7.4. The index return volatility shows high level of persistence as U]+a2 =.97855. 118

Table-7.5 GARCH (1,1) Estimate for Nifty Index Future Return with Volume Coefficient Std. Error z-statistic Prob. Panel A: GARCH (1,1) Estimate for Nifty Index Future Return with Current Volume p 0.001265 0.000291 4.344016 0 do 2.00E-05 1.77E-06 11.26785 0 ai 0.173495 0.014893 11.64928 0 m 0.769878 0.014934 51.55146 0 Y 1.98E-05 2.19E-06 9.024093 0 ai+q2 0.943373 Panel B: GARCH (1,1) Estimate for Nifty Index Future Return with Lagged Volume F 0.001185 0.000292 4.060099 0 do 1.33E-05 1.45E-06 9.155124 0 ai 0.158279 0.012232 12.94012 0 02 0.806935 1.28E-02 63.10163 0 Y 8.47E-06 2.00E-06 4.235588 0 ai+02 0.96521 Using volume as an explanatoiy variable in the conditional variance function [Equation (7.7)], Table-4 shows the GARCH (1,1) estimates for the Nifty Index Future Return. Panel A of the Table-7.5 shows that current volume has a significant explanatoiy power for Nifty Index Future return volatility. Because there is a greater reduction in volatility persistence from 0.97855 to 0.9433. Also the coefficient of the contemporaneous average volume in the conditional variance equation, y, is statistically significant at 1% level. Panel B of the Table-7.5 shows that lagged volume has a significant explanatory power for nifty index future return volatility when it is used as an explanatory variable. The coefficient of the lagged volume in 119

the conditional variance equation [Equation (7.7)], is statistically significant at the 1% level. Furthermore, the introduction of lagged volume in the conditional variance equation reduces the observed persistence, as measured by (ai+a2), from 0.97855 to 0.9652. In summary, when entered separately, the contemporaneous and lagged volume variables have a significant explanatory power for the volatility of returns for nifty index future. However, the persistence of volatility remains high thereby, suggesting that volatility shocks to nifty index future return tend to persist and affect future volatility for longer period of time. Table-7.6 GARCH (1,1) Estimate for Nifty Index Future Return with Open Interest Coefficient Std. Error z-statistic Prob. Panel A: GARCH (1,1) Estimate for Nifty Index Future Return with Current Open Interest p 0.001218 0.000281 4.32927 0 do 9.86E-06 1.18E-06 8.374932 0 ai 0.16571 0.011657 14.21601 0 ai 8.13E-01 1.20E-02 67.57853 0 Y ai+q2 4.29E-06 0.9789 1.57E-06 2.739914 0.0061 Panel B: GARCH (1,1) Estimate for Nifty Index Future Return with Lagged Open Interest F 0.001217 0.000281 4.332944 0 do 9.76E-06 1.16E-06 8.405276 0 ai 0.165279 0.011615 14.22996 0 <X2 0.813967 0.011972 67.9872 0 Y ai+a2 3.43E-06 0.9792 1.47E-06 2.33159 0.0197 120

(y is the coefficient of current open interest in Panel A and of lagged open interest in Panel B) Table-7.6 shows the estimates of the GARCH (1, 1) model for the nifty index future return using open interest as an explanatory variable in the conditional variance function [Equation (7.7)]. Panel A of the Table-7.6 shows that current open interest has marginal or no explanatory power for the nifty index future return volatility. The coefficient of the contemporaneous open interest in the conditional variance equation, y, is statistically significant at 1% level. Panel B of the Table-7.6 shows the impact of the lagged open interest variable on the volatility of the returns for Nifty Index Future. The coefficient of the lagged open interest in the conditional volatility equation, y, is statistically significant at 1% level. The findings show that, the inclusion of lagged open interest as explanatory variable in the conditional variance equation leads to marginal increase in volatility persistence. In summary, when entered separately, the contemporaneous and lagged open interest variables have marginal explanatory power for the volatility of returns for Nifty Index Future Return. Akin to in the case of volume, the persistence of volatility for nifty index future returns and open interest (current or lagged) reduces GARCH effect in return volatility marginally. 121

The persistence of return volatility suggests that volatility shocks to nifty index return persist and affect future volatility for a longer period of time. Table-7.7 shows the result of estimating the GARCH (1,1) model for the Nifty Index Future Return using volume and open interest simultaneously as explanatory variables. In particular, Table-7.7 presents the results of exploring the explanatory power of volume and open interest when they are entered simultaneously in the conditional variance equation [Equation (7.8)]. 122

Table-7.7 GARCH (1,1) Estimate for Nifty Index Future Return with Volume and Open Interest Coefficient Std. Error z-statistic Prob. Panel A: GARCH (1,1) Estimate for Nifty Index Future Return with Current Volume and Open Interest p 0.00126 0.000293 4.300088 0 do 1.98E-05 1.75E-06 11.29331 0 ai 0.173258 0.014846 11.67066 0 d2 7.71E-01 1.49E-02 51.59022 0 01-1.65E-06 3.29E-06-0.503499 0.6146 02 1.99E-05 2.26E-06 8.807273 0 ai+02 0.9440 Panel B: GARCH (1,1) Estimate for Nifty Index Future Return with Lagged Volume and Open Interest P 0.000548 0.00062 0.88316 0.3771 do 2.10E-04 9.40E-06 22.35035 0 d1 0.131048 0.021187 6.185272 0 02 0.496913 0.027513 18.06126 0 01 0.00005970000 5.09E-06 11.72933 0 02 0.00008530000 2.03E-05 4.208263 0 dl+q2 0.62796100000 Panel A of the Table-7.7 reveals that when current volume and open interest are entered in the conditional variance equation simultaneously, only current volume achieves statistical significance at the 1% level. In this case the persistence of volatility, as measured by (ai+a2) also declines from 0.97855 to 0.9440. However, the persistence of volatility of nifty index future return remains and past volatility can explain current volatility. Thus, current volume and open interest don t remove the GARCH effect. 123

Panel B of the Table-7.7 shows that, when lagged volume and lagged open interest are included as explanatory variable in the conditional variance equation, the coefficients of both the lagged open interest ( i) and lagged volume (<X>2) are significant at 1% level. Furthermore, the results in the Panel B of the Table-7.7 show that, the persistence of volatility as measured by (<Xi+a2) decreases dramatically from 0.97855 in Table-7.4 to 0.6279 for the Nifty Index Future Return. Thus, it appears that including lagged volume and lagged open interest in the conditional variance equation has greater power of reducing the persistence in volatility for the Nifty Index Future return than the current volume and open interest either separately or jointly. These findings seem to support the Sequential Information Arrival hypothesis of Copeland (1976). Finally, these findings also suggest a degree of market inefficiency for nifty index future and are consistent with previous research on price variability and volume and/or open interest (see, e.g., Foster, 1995; Fujihara and Mougoue, 1997). 124

7.5 Conclusion The study of this chapter finds that contemporaneous volume provide significant explanation for Nifty Index Future Return volatility than open interest when entered separately. Similarly, the lagged volume has significant explanatory power than lagged open interest for volatility of Nifty Index Future Return. Furthermore, the study also finds that lagged volume and lagged open interest when entered in the conditional variance, equation simultaneously, provide significant explanatory power than contemporaneous volume and open interest and reduce the persistence of volatility dramatically. These findings are consistent with previous research on price variability and volume and/or open interest and seem to support the Sequential Information Arrival hypothesis of Copeland (1976). Finally, these findings also suggest a degree of market inefficiency for the Nifty Index Future. As far as source(s) of uncertainty (volatility) for Nifty Index Future return is concerned, the empirical results show that contemporaneous and lagged volume and open interest are significantly related to the volatility of the Nifty Index Future return. The findings of the study in the current chapter have practical implication for speculators, hedgers as it is well known that successful hedging and speculative activities in the future market depends critically on the ability to predict price movements. As per the findings that current and lagged volume and open interest affect volatility implies that a 125

short-term improvement in predicting future price movements can be achieved using these variables. This improvement of short term future price predictability should lead to the construction of more accurate hedge ratios and different investment and trading strategies. 126