Volatility Analysis of Commodity Futures and Common Stocks Market: An Example of India
^{1}Lecturer, Department of Economics, Vivekananda College, Thakurpukur, Kolkata 713104, India
ABSTRACT:
The paper investigates the pattern of volatility in daily return from select Commodity Futures and Stock market in India. One Commodity Future from each group of futures is chosen for the study and they are  Potato, Gold, Crude oil and Mentha Oil. S&P CNX Nifty is selected as a representative of stock market. This study uses several econometrics techniques and in particular, GARCH family models are used for examining the volatility aspects of commodity futures and Nifty Index. The results obtained point to the fact that Crude Oil and Gold futures market is almost similar to the functioning of the stock market in India.
KEYWORDS: Commodity Futures, Nifty, Volatility, GARCH.
INTRODUCTION:
Uncertainty plays a crucial role in economic and finance theory. Volatility refers to the amount of uncertainty about the size of changes in a security’s worth. Modeling volatility of a financial time series has become an important area over the last few years. Commodity futures markets have become more visible nowadays in India as well as across the world. A small change in price could have vast effects on the trading in futures market.
The present paper is an attempt to examine the crosssectional volatility among two financial assets, namely common stock and commodity futures in India. We examine the volatility of daily returns of few select commodity futures and compare them with the volatility of S&P CNX Nifty index.
Such an exercise is imperative to locate the commodity futures market in India visàvis the advanced counterpart in the financial market, that is, the well developed and mature stock market. For the purpose of the analysis, this paper deals with the volatility of daily returns of Nifty visàvis four select commodity futures as Potato, Gold, Crude Oil and Mentha Oil. Moreover, for analytical simplicity, we take into consideration only the far month contracts of the said commodity futures. The choice of the far month contracts is based on the observation that, generally, the randomness of fluctuations in daily returns tends to be less for far month contracts compared to other expiry contract cycles.
The daily return series of the select commodity futures with their specified contract cycles and the Nifty index are plotted graphically to get an idea of volatility clustering. This is followed by descriptive statistics of the return series which are further tested for stationarity in it. Then we examined the possible outcomes of the different GARCH family models for the assets. The study takes into account two symmetric model of volatility, as GARCH and GARCHM along with two asymmetric models of volatility EGARCH and TGARCH.
The present paper derives its motivation from the following facts: First, The spontaneous growth of commodity futures market in India was witnessed in the post 2003. The following data which bears testimony to the ever increasing market of commodity futures point to the importance of commodity futures among the investors. The volume of commodity futures has increased from about Rs 1.29 lakh crore in 2003–04 to a peak of Rs 181 lakh crore in 2011–12, and settled at Rs 170.5 lakh crore in 2012–13(Data source: www.fmc.gov.in). These data prompted us to fix up our research agenda on commodity futures. Second, in India, while the volatility issues related to dominant financial assets, like stocks, options have been well researched but very few researches had been carried out with the trend and pattern of volatility in daily returns from commodity futures. For this reason it is the research gap that the present paper would explore. Finally, any work on the cross sectional examination on volatility pattern of Commodity futures market and Stock market is very hard to find in India. So, filling this research gap is another vital agenda of our paper. The rest of the paper is organized as follows. The second section presents the literature review. The third section and fourth section deals with the relevant data source and the methodology used in this paper respectively. The result and discussion of the analysis is carried out in the fifth section. Finally the sixth section concludes the paper.
LITERATURE REVIEW:
There are plenty of works on volatility with respect to stock market. But, very few literatures are available on volatility aspect of futures in the Indian commodity futures market. Some significant literatures on volatility for commodity futures and also few prominent literatures on stock market volatility are in order.
Notable among them are  Premalata Shenbagaraman (2003) explains the impact of introducing Index Futures and Option contracts on the Stock Index in India. In this paper, the author explores the impact of the introduction of derivative trading on cash market volatility. Amita Batra (2004) analyzes the time variation in volatility in the Indian stock market during the study period of 19792003. She examined the possibility of an increase in volatility persistence in the Indian stock market during the process of financial liberalization in India. Madhusudan Karmakar (2005) examined the conditional volatility models to capture the features of stock market volatility of India. Brajesh Kumar (2009) examined the relationship between future trading activity and spot price volatility for different commodity groups as agricultural, metal, precious metals and energy commodities in the perspective of Indian Commodity derivatives market. Brajesh Kumar and Ajay Pandey (2010) examined the relationship between volatility and trading activity including trading volume and open interest, for different categories of Indian commodity derivatives market. Brajesh Kumar and Ajay Pandey (2011) examined the cross market linkages of Indian commodity futures with futures markets outside India. They analyze the cross market linkages in terms of return and volatility spillovers. P. Srinivasan (2012) examined the price discovery process and volatility spillovers in Indian spotfutures commodity markets. Sanjay Sehgal, Namita Rajput and Rajeev Kumar Dua (2012) examined the futures trading activity on spot price volatility. Ajay Kumar Chouhan, Shikha Singh and Anchal Arora (2013) examined the market efficiency of the Indian commodity market and volatility spillover effects between the spot and future market with the example of agri commodities guar seed and chana. The result indicates that the commodity futures markets effectively serves the price discovery function in the spot market and shows that the volatility spillovers from future to the spot market are dominant, however in case of Agricultural commodities the volatility in spot market may influences volatility in future market. Mantu Kumar Mahalik, Debashis Acharya and M. Suresh Babu (2014) examine the price discovery and volatility spillovers in Indian spotfutures commodity market. Karunanithy Banumathy and Ramachandran Azhagaiah (2015) examined the volatility pattern of Indian stock market. Meenakshi Malhotra and Dinesh Kumar Sharma (2016) investigate about the information transmission process i.e, volatility spillover between spot and futures market and examined the impact of futures trading activity on the volatility of physical market prices.
It is hard to find any literature on the analysis of comparison of commodity futures market and stock market in India. Here, only, Brajesh Kumar and Priyanka Singh (2008) examined the volatility, risk premium and seasonality in risk and return relation of the Indian Commodity market and Stock market. The result shows that the returns of commodity market and stock market have persistence as well as clustering and asymmetric properties.
So, the analysis of comparison of inter asset daily return’s volatility is the notable research gap that we identified in the context of Indian Derivative and Stock Market. Thus the present paper aims to fill up this research gap and it examines the volatility comparison between the stock market and commodity futures market.
Data Source:
For this study we have selected 4 (four) commodity futures as Potato, Crude Oil, Gold, Mentha Oil from four different categories of commodity futures as Agricultural Commodity Futures, Energy, Metal and Oil & Oil Related Product respectively. This choice of the commodity futures satisfies two basic criterions of (i) high frequency of futures contracts and (ii) large volume/value of such futures within the study period. The required data related to commodity futures have been taken from the official website of Multi Commodity Exchange (MCX), Mumbai, from 2004 to 2012.
Data on Nifty is collected from NSE website over the period of nine years from 1st January 2004 to 31st December 2012.
METHODOLOGY:
Generally, trading of the commodity futures occurs in onemonth, twomonth, and threemonth expiry cycles. For simplicity, we consider only the three month holding contracts of futures.
Daily returns from futures are calculated as the value of continuously compounded rate of return multiplied by100.
That is,
Log return of the price series = ln(F_{t }/ F_{t1}) *100, (1)
where F_{t } and F_{t1} are contract expiring closing prices on day t and (t1) of a futures three month holding contract.
We selected the Nifty Index as a proxy of Indian stock market. The daily closing prices of Nifty indices over the period of nine years from 1st January 2004 to 31st December 2012 were collected and used for analysis.
In case of Nifty Index, daily returns are also calculated as:
Log return of the price series = ln (F_{t }/ F_{t1}) *100, (2)
where F_{t } and F_{t1} are closing prices on day t and (t1).
To begin with, we test the presence of unit root in the daily returns series in terms of ADF and PP test. The volatility clustering effect of daily return series is examined using the descriptive statistics, correlogram and ARCHLM test.
Then we examine with the GARCH models for the assets under consideration. The GARCH model assumes conditional heteroskedasticity with homoscedastic unconditional error variance. In other words, the GARCH model assumes that the changes in variance are a function of the realizations of the preceding errors and that these changes represent temporary and random departures from a constant unconditional variance. The advantage of a GARCH model is that it can capture the tendency in financial data for volatility clustering which enables us to make the connection between information and volatility explicitly, since any change in the rate of information arrival to the market will change the volatility in the market. Thus if information does not remain constant volatility must be time varying.
GARCH (1, 1) model as a symmetric measure of volatility is examined for the select commodity futures and Nifty index, along with the diagnostic residual test for the presence of further ARCH effect. Another symmetric measurement of volatility GARCHM (1, 1) is also examined. Using the asymmetric models of volatility, that is, EGARCH and TGARCH models, the presence of leverage effect in daily returns are identified.
Descriptive Statistics:
To analyze the characteristics of the daily return series of the commodity futures market during the study period, the descriptive statistics show the mean (X), standard deviation (σ), Skewness (S), Kurtosis (K), and JarqueBera statistics results.
We calculated the coefficients of Skewness and Kurtosis to verify whether the return series is skewed or leptokurtic. To test the null hypothesis of normality, the JarqueBera statistic (JB) has been applied, as follows:
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 a Chisquare distribution with 2 degrees of freedom (d. f.). We perform a joint test of normality where the joint hypothesis of s=0 and k=3 is tested. If the JB statistic is greater than the table value of chisquare with 2 d. f., the null hypothesis of a normal distribution of residuals is rejected.
Test for Stationarity:
For testing whether the data are stationary or not, we performed the Augmented DickeyFuller (Dickey and Fuller 1979) and PhilipsPerron Test (PP) (Phillips and Perron 1988). The stationarity of the return series has been checked by ADF test by fitting a regression equation based on a random walk with an intercept, or drift term (φ), as follows:
where is a disturbance term with white noise. Here the null hypothesis is (with alternative hypothesis). If this hypothesis is accepted, there is a unit root in the y_{t }sequence, and the time series is nonstationary. If the magnitude of the ADF test statistic exceeds the magnitude of Mackinnon critical value, the null hypothesis is rejected, and there is no unit root in the daily return series.
Phillips and Perron (1988) suggested an alternative (nonparametric) method to control for serial correlation when testing for the presence of a unit root. The PP method estimates the non augmented DF test equation, and it can be seen as a generalization of the ADF test procedure, which allows for fairly mild assumptions concerning the distribution of errors. The PP regression equation is as follows:
where the ADF test corrects for higher order serial correlation by adding lagged differenced terms on the righthand side, while the PP test corrects the t statistic of the coefficient obtained from the AR(1) regression to account for the serial correlation _{t }. The null hypothesis is (with alternative hypothesis).
Test for Heteroskedasticity:
The presence of heteroskedasticity in asset returns has been well documented in the existing literature. If the error variance is not constant (heteroskedastic), then, the OLS estimation is inefficient. The tendency of volatility clustering in financial data can be well captured by a Generalized Autoregressive Conditional Heteroskedastic (GARCH) model. Therefore, we modeled the timevarying conditional variance in our study as a GARCH process.
t
To identify the type of GARCH model that is more appropriate
for our data, we performed the ARCH LM test (Engle 1982). This is a Lagrange Multiplier
test for the presence of an ARCH effect in the residuals. We first regressed the
return series on their oneperiod lagged return series and obtained the residuals
(^{ˆ2 }). Then, the residuals have been squared and regressed
on their own lags of order one to four to test for the ARCH effect. The estimated
equation is:
Where K_{t} is the error term. We, then, obtained the coefficient of determination (R^{2}). The null hypothesis is the absence of ARCH error, against the alternative hypothesis. Under the null hypothesis, the ARCH LM statistic is defined as TR^{2}, where T represents the number of observations. The LM statistic converges to a ^{2}^{ }distribution. Hence, we use the Lagrange Multiplier (LM) test for Autoregressive Conditional Heteroskedasticity (ARCH) to verify the presence of heteroskedasticity in the residuals of the daily return series for all commodity futures. If the ARCH LM statistic is significant, we confirm the presence of an ARCH effect.
The ARCH model as developed by Engel (1982) is an extensively used timeseries models in the financerelated research. The ARCH model suggests that the variance of residuals depends on the squared error terms from the past periods. The residual terms are conditionally normally distributed and serially uncorrelated. A generalization of this model is the GARCH specification. Bollerslev (1986) extended the ARCH model based on the assumption that forecasts of the timevarying variance depend on the lagged variance of the variable under consideration. The GARCH specification is consistent with the return distribution of most financial assets, which is leptokurtic and it allows long memory in the variance of the conditional return distribution.
The Generalized Arch Model (GARCH):
The GARCH model (Bollerslev 1986) assumes that the volatility at time t is not only affected by q past squared returns but also by p lags of past estimated volatility. The specification of a GARCH (1, 1) is given as:
mean equation:
variance equation:
where ω > 0, α ≥ 0, β ≥ 0, and r_{t} is the return of the asset at time t, μ is the average return, and ε_{t} is the residual return. The parameters α and β capture the ARCH effect and GARCH effect, respectively, and they determine the shortrun dynamics of the resulting time series. If the value of the GARCH term β is sufficiently large, the volatility is persistent. On the other hand, a large value of α indicates an insensitive reaction of the volatility to market movements. If the sum of the coefficients is close to one, then, any shock will lead to a permanent change in all future values. Hence, the shock is persistent in the conditional variance, implying a long memory.
The GARCHinMean (GARCHM) model:
The GARCHinmean (GARCHM) model was developed by Engle, Lilien and Robins (1987). This model is based on the GARCH (1, 1) model by Bollerslev (1986). In this model, the return of an asset may depend on its volatility. So, a simple GARCHM (1, 1) model can be written as:
mean equation:
variance equation:
_{ }
_{ }
_{where in the return equation}
_{} are the parameters to be estimated. _{} is the return, _{}is the conditional variance and _{}stands for the error term for a Gaussian innovation with zero mean. The parameter λ is the most important as it describes the nature of relationship between the return and volatility of the concerned asset. If the parameter λ in the mean equation is positive and statistically significant, increase in conditional variance, (a proxy of increased risk), means increase in the mean return. Hence, a positive λ means the return of an asset is positively related to its volatility. So, the λ is also called the risk premium.
The Exponential GARCH model (EGARCH):
This model was proposed by Nelson (1991) and is based on the logarithmic expression of the conditional variability such that even if the parameters are negative, _{} will be positive. Hence there is no need to impose any non negativity constraints on model parameters. The EGARCH equation is:
The lefthand side of the equation implies the log of the conditional variance. The coefficient γ is known as the leverage or asymmetric parameter. If γ < 0, then it is said that there is leverage effect and the impact is symmetric if γ≠ 0.
Threshold GARCH Model (TGARCH):
To confirm the result obtained through EGARCH model, TGARCH model has been used by the study. The generalized specification of the TGARCH model for the conditional variance (Zakoian 1994) is given by:
The γ is known as the asymmetry or leverage term. In this model, good news (ε_{t−1 }> 0) has an impact of α_{i} and the bad news (ε _{t−1} < 0) has impact on α_{i}+γ_{i}. So, if γ is significant and positive, then it can be said that, negative shocks have a larger effect on σ^{2} _{t} than the positive shocks.
The result of the study is set out in the following section.
RESULT AND DISCUSSION:
Descriptive statistics on daily return series are summarized here.
Table 1: Simple Statistics

Mean 
Median 
Maximum 
Minimum 
Std. Dev. 
Skewness 
Kurtosis 
Jarque – Ber 
Probability 
Potato 
0.000579 
0.002266 
0.47847 
0.557147 
0.037906 
2.45975 
121.0494 
449624.1 
0.000000 
Mentha oil 
0.002403 
0.000000 
0.669725 
0.591267 
0.046594 
3.34316 
83.00441 
525838.3 
0.000000 
Crude oil 
0.000574 
0.000362 
0.33352 
0.242462 
0.024035 
0.12481 
48.82034 
180300.2 
0.000000 
Gold 
0.000434 
0.000511 
0.08112 
0.08509 
0.010107 
1.02644 
17.93436 
12290.4 
0.000000 
Nifty 
0.000503 
0.001093 
0.163343 
0.13.539 
0.01693 
0.23968 
11.89702 
7416.041 
0.000000 
It is observed that the average daily returns from all commodity futures and also from Nifty are either close to zero or negative throughout the study period. The descriptive statistics shows that the returns are negatively skewed since the estimated coefficients of Skewness for the return series are observed to be different from zero indicating that underlying return distributions are not symmetric. The estimated coefficients of Kurtosis for the daily return series are found to be fairly high suggesting that the underlying distributions are leptokurtic or heavily tailed and sharply peaked about the mean compared to the normal distribution. These observed Skewness and Kurtosis indicate that the distribution of daily return series is nonnormal. The JarqueBera normality test also supports this nonnormality of return distributions as the estimated values of JarqueBera statistic of all the return series are statistically significant at 1% level.
Figure 1 : Daily returns series graph for potato
Figure 2 : Daily returns series graph for Mentha Oil
Figure 3 : Daily returns series graph for Crude Oil
Figure 4 : Daily returns series graph for Gold
Figure 5 : Daily returns series graph for Nifty
The correlogram test is conducted to check for serial correlation in residuals. We observe no serial correlation in the residuals up to 24 lags for Mentha oil, Crude oil, Gold futures and Nifty.
Table 2 :Correlogram Test (upto 24 lags)
Commodity Futures with Far month contract cycles and Nifty → 
Potato 
Mentha Oil 
Crude Oil 
Gold 
Nifty 
Residuals are serially correlated 
Yes 
No 
No 
No 
No 
The ADF and PP test are performed to test the stationarity of the series and is presented in Exhibit 7. The p values of ADF and PP are less than 0.05, which lead to conclude that the data for the entire study period is stationary. Both the test statistics mentioned in Table 3 reject the hypothesis at 1% level with the critical value of –3.43 for both ADF and PP tests of the unit root in the daily return series. So, these results confirm that the daily return series are stationary.
The graphs shown earlier confirm that there is no clustering effect for Potato futures. The graph for Mentha Oil futures exhibits small clustering effect for some periods. The graphs of Crude Oil and Gold futures daily return series exhibit clustering effect or volatility. The graph for Nifty indices also exhibit clustering effect. Hence, we leave out the potato futures from the ARCHLM test and report the results of ARCHLM test for other commodity futures and Nifty.
Table 4 presents the result of ARCHLM test (Engel, 1982) of heteroskedasticity. This test is applied to find out the presence of ARCH effect in the residuals of the daily return series. From the Table 4, we see that the ARCHLM test statistics is significant for Gold futures and Nifty index.
Table 3 : Result of Unit Root Test
Commodity Futures and Nifty→ 
Potato 
Mentha Oil 
Crude Oil 
Gold 
Nifty 
ADF Test Statistic 
27.875 
44.308 
43.860 
34.323 
44.630 
Prob.* 
0.000 
0.000 
0.0001 
0.000 
0.0001 
Philips Perron Test Statistic 
27.875 
44.315 
43.860 
34.331 
44.563 
Prob.* 
0.000 
0.0001 
0.0001 
0.000 
0.0001 
Test critical value 

1% 
3.438 
3.433 
3.433 
3.435 
3.433 
5% 
2.865 
2.862 
2.862 
2.863 
2.862 
10% 
2.568 
2.567 
2.567 
2.567 
2.567 
Note: ADF Test Statistic is estimated by fitting the equation of the form: _{}and PP test statistic is estimated by the equation: _{}
Table 4 :Result of ARCHLM Test for Residuals

Mentha Oil 
Crude Oil 
Gold 
Nifty 
Obs*Rsquared 
0.037136 
0.099779 
142.6915 
76.16686 
Prob. ChiSquare 
0.8472 
0.7521 
0.0000 
0.0000 
Note: ARCH LM Statistic (at lag1) is the Lagrange Multiplier test statistic to examine 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 Chisquare distribution, the null hypothesis of no heteroskedasticity is rejected
Table 5 : Estimated result of GARCH (1,1) Model
Mentha Oil 
Crude Oil 
Gold 
Nifty 

Coefficients 

Mean 

μ (constant) 
0.002299** 
0.00044*** 
5.84E05*** 
0.001094* 

Variance 

ω (constant) 
0.000315^{*} 
5.14E05^{*} 
4.82E06^{*} 
4.70E06^{*} 

α (arch effect) 
0.003595^{*} 
0.00364^{*} 
0.217631^{*} 
0.125560^{*} 

β (garch effect) 
0.856938^{*} 
0.9111^{*} 
0.775297^{*} 
0.862083^{*} 

α + β 
0.853343 
0.90746 
0.992928 
0.987643 

Log likelihood 
3241.84 
4778.326 
4295.068 
6363.459 

Akaike info. criterion (AIC) 
3.307962 
4.6343 
6.61537 
5.674662 

Schwarz info. criterion (SIC) 
3.293707 
4.62063 
6.59545 
5.661912 

Residual Diagnostics for GARCH (1, 1):ARCHLM (1) test for heteroskedasticity 

Obs*Rsquared 
0.025106 
0.003309 
0.617633 
0.229526 

Prob. ChiSquare(1) 
0.8741 
0.9541 
0.4319 
0.6319 

* Significant at 1% level, **Significant at 5% level, ***Significant at 10% level
The result confirms the presence of ARCH effects in the residuals as the test statistics are significant at 1% level. However, in case of Crude Oil and Mentha oil futures we find no ARCH effect in the residuals and this is in conformity with negligible amount of volatility clustering exhibited by the daily returns’ volatility graph of it. Hence the results confirms for the analysis of the GARCH effect (Although the result of ARCHLM test implies no ARCH effect for Mentha oil and Crude oil futures, there remains a trace of volatility clustering in its daily return graph. Hence, we also consider Mentha oil and Crude oil futures for GARCH analysis).
Now, the GARCH model is used for modeling the volatility of daily return series for the Crude oil, Gold and Mentha oil commodity futures and also for Nifty. The result of GARCH (1, 1) model is shown in Table 5, which shows that the parameter of GARCH is statistically significant.
In other words, the coefficients like, constant (ω), ARCH term (α), GARCH term (β) are highly significant at 1% level. In the variance equation, we see the estimated β coefficient is considerably greater than α coefficient which implies that the volatility is more sensitive to its lagged value. It shows that the volatility is persistent. The sum of these coefficients (α and β) are close to unity which indicates that the shock persist for many periods. It is to be noted that the persistence of shock is relatively more for Gold futures and Nifty index and the shock persistence is least for Mentha oil futures, which is in tune with the volatility clustering graphs depicted earlier. To check for the robustness of GARCH (1, 1) model, we employed the ARCHLM test (Engel, 1982) to test the presence of any further ARCH effect. As shown in the above table, the ARCHLM test statistic for GARCH (1, 1) model does not show the presence of any additional ARCH effect in the residuals of the model, which implies that the variance equation is well specified for the said commodity futures and Nifty index.
To measure the conditional volatility here we use another model, that is, the GARCHinmean model.
The result of GARCHM model is presented in Table 7 and it is observed that, for Crude oil, Mentha oil and Nifty far month contracts, the GARCHM coefficient is positive, but it is negative for only Gold contracts. For Crude Oil and Nifty, we see that, the coefficient is significant at 10% level and 15% level respectively.
Table 7: Estimated result of GARCHM (1,1) Model
Mentha Oil 
Crude Oil 
Gold 
Nifty 

Coefficients 

Mean 

μ (constant) 
0.005792*** 
0.020018*** 
0.002455*** 
0.001772*** 
Risk premium λ 
1.642291*** 
0.002761*** 
0.000244*** 
7.57E05*** 
Variance 

ω (constant) 
0.000317* 
8.21E05* 
4.79E06* 
4.70E06* 
α (arch effect) 
0.003650* 
0.005315* 
0.219070* 
0.125608* 
β (garch effect) 
0.856000* 
0.866337* 
0.774650* 
0.862047* 
α + β 
0.85235 
0.861022 
0.99372 
0.987655 
Log likelihood 
3241.888 
4778.143 
4295.243 
6363.472 
Akaike info. criterion (AIC) 
3.306989 
4.633149 
6.614098 
5.673782 
Schwarz info. criterion (SIC) 
3.289883 
4.616750 
6.590191 
5.658481 
Residual Diagnostics for GARCHM (1, 1):ARCHLM (1) test for heteroskedasticity 

Obs*Rsquared 
0.016132 
0.055949 
0.626897 
0.232053 
Prob. ChiSquare(1) 
0.8989 
0.8130 
0.4285 
0.6300 
*Significant at 1% level, ***Significant at 10% level
Table 8 :Estimated result of EGARCH (1,1) Model
Mentha Oil 
Crude Oil 
Gold 
Nifty 

Coefficients 

Mean 

μ (constant) 
0.002905* 
3.44E05*** 
0.000389** 
0.000770* 
Variance 

ω (constant) 
4.405515^{*} 
0.013023^{*} 
0.656394^{*} 
0.495841^{*} 
α (ARCH effect) 
0.112604^{*} 
0.009979^{*} 
0.307133^{*} 
0.239519* 
β (GARCH effect) 
0.293699^{*} 
0.997690^{*} 
0.952569^{*} 
0.963387^{*} 
γ (leverage effect) 
0.358569^{*} 
0.013756^{*} 
0.118048^{*} 
0.100116^{*} 
α + β 
0.406303 
0.987711 
1.259702 
1.202906 
Log likelihood 
3261.249 
4970.083 
4334.158 
6379.259 
Akaike info. criterion (AIC) 
3.326097 
4.818130 
6.670506 
5.686225 
Schwarz info. criterion (SIC) 
3.311848 
4.804470 
6.650596 
5.673480 
Residual Diagnostics for EGARCH (1, 1):ARCHLM (1) test for heteroskedasticity 

Obs*Rsquared 
0.002758 
0.060122 
13.01368 
0.131421 
Prob. ChiSquare(1) 
0.9581 
0.8063 
0.0003 
0.7170 
*Significant at 1% level, ** Significant at 5% level, ***Significant at 10 % level
This in turn implies that increased risk leads to an increase in mean return for crude oil far month contracts and Nifty. But, in case of Mentha Oil, the coefficient is positive but not significant. That is, there is no feedback from the conditional variance to the conditional mean. For the Gold futures, it is observed that, although the coefficient for GARCHM is negative, it is not significant. An explanation for this might be that investment in gold futures in India is an alternative avenue for putting barren wealth irrespective of its riskreturn feature. Further, for all three commodity futures contracts and Nifty index, the coefficients of constant term, ARCH term and GARCH term are significant at 1% level and the sum of α and β is close to 1, which suggests that the shock will continue in the future periods. To check for the robustness of GARCHM (1, 1) model, we employed the ARCHLM test (Engel, 1982) to test the absence of any further ARCH effect. As shown in the above table, the ARCHLM test statistic for GARCHM (1, 1) model does not show any additional ARCH effect in the residuals of the model, which implies that the variance equation is well specified for the said commodity futures and Nifty index.
To capture the asymmetries in volatility of the return series, two models as EGARCH (1, 1) and TGARCH (1, 1) have been used.
Table 8 estimate the EGARCH (1, 1) model and the result reveals that the sum of ARCH and GARCH coefficients are greater than one in case of Gold and Nifty while it is near to one in case of Crude oil. That means the conditional variance is explosive for Gold futures and Nifty index. Interestingly, the conditional variance for Mentha oil futures is dampening (α + β = 0.406303) and thereby confirming the earlier findings on it. Here we see that the estimated coefficients are statistically significant at 1% level. In the conditional variance equation, it is observed that, α is the coefficient for latest news which is statistically significant at 1% level for the three commodity futures and Nifty returns. So, the findings indicate that the recent news has an effect on the volatility. Similarly, the β coefficient is also significant at 1% level for all assets and suggests that old news too has an impact on the market volatility. The EGARCH model also takes leverage effect into account. We know that, leverage effect is a negative correlation between the past return and future volatility of the return. Higher leverage effect means greater risk of the asset. Leverage effect exists where positive shock has less impact on conditional variance compared to a negative shock. As we see here the leverage coefficient (γ) is not equal to zero, which implies that the impact is asymmetric. The leverage coefficient is negative and statistically significant at 1% level in the case of Nifty and Crude Oil. This in turn implies that the volatility increases lead to fall in the asset’s price of Nifty and Crude oil futures. But in the case of Gold and Mentha Oil futures, there exist positive leverage coefficient which means the asset’s price will be rise as volatility increases. To check for the robustness of EGARCH (1, 1) model, we employed the ARCHLM test (Engel, 1982) to test the presence of any further ARCH effect. As seen from the above table the ARCHLM tests indicate that no serial dependence persists in the squared residuals except Gold commodity futures. Hence, the results suggest that the EGARCH (1, 1) model is reasonably well specified and appropriate model to capture the timevarying volatility effects in the time series analyzed for Mentha Oil, Crude Oil futures and Nifty futures. So, for the Gold futures we estimate further level of EGARCH model and find that EGARCH (2,1) model is well specified as any further ARCH effect is not present in the ARCHLM test.
To test the asymmetric volatility in daily returns, we use an alternative model, that is, the TGARCH model.
Table 9: Estimated result of TGARCH (1,1) Model
Mentha Oil 
Crude Oil 
Gold 
Nifty 

Coefficients 

Mean 

μ (constant) 
0.002613*** 
0.001084* 
0.000239*** 
0.000793* 
Variance 

ω (constant) 
0.002149^{*} 
1.73E07^{*} 
3.31E06^{*} 
5.92E06^{*} 
α (ARCH effect) 
0.171807^{*} 
0.002462^{*} 
0.318234^{*} 
0.051308^{*} 
β (GARCH effect) 
0.205083^{*} 
1.000315^{*} 
0.821309^{*} 
0.861024^{*} 
γ (leverage effect) 
0.179408^{***} 
0.001325^{*} 
0.270643^{*} 
0.132179^{*} 
α + β 
0.37689 
0.997853 
1.139543 
0.912332 
Log likelihood 
3208.238 
4961.046 
4322.658 
6381.567 
Akaike info. criterion (AIC) 
3.271949 
4.809361 
6.652785 
5.688284 
Schwarz info. criterion (SIC) 
3.257701 
4.795700 
6.632876 
5.675539 
Residual Diagnostics for TGARCH (1, 1):ARCHLM(1) test for heteroscedastisity 

Obs*Rsquared 
0.091923 
0.017686 
10.96784 
0.586488 
Prob. ChiSquare(1) 
0.7617 
0.8942 
0.0009 
0.4438 
Table 9 reveals that the leverage coefficient for Crude Oil commodity futures and Nifty returns are positive and significant at 1% level which implies that the bad news (negative shocks) have greater impact on the conditional variance than the good news (positive shocks). The leverage coefficient is negative for Mentha Oil and Gold futures.
The diagnostic test is performed for TGARCH (1, 1) model to test whether the residuals are normally distributed. As shown in the above table, the ARCHLM test statistic for TGARCH (1, 1) model does not show any additional ARCH effect present in the residuals of the model(except Gold), which implies that the variance equation is well specified for the said two commodity futures Mentha Oil & Crude Oil for far month contracts cycles and Nifty index. So, for the Gold futures we estimate further level of TGARCH model and find TGARCH (2,1) model is well specified as any further ARCH effect is not present in the ARCHLM test.
CONCLUSION:
Comparison of daily returns’ volatility between Nifty index and far month contract cycles of four commodity futures was explored in this chapter in a phased manner. Firstly, a descriptive statistics of daily return series from the assets were conducted along with graphical presentation of volatility clustering. The ADF and PP test are performed to test the stationarity of the series and the results suggested that the said series are stationary. However, in this first phase of analysis, far month contracts of Potato futures did not exhibit any volatility clustering and was thus left out from the subsequent volatility analysis. In the second phase, we conducted the ARCHLM test to find out the presence of ARCH effect in the residuals of the daily return series. The ARCHLM test statistics is significant for Gold futures and for Nifty index. The result confirms the presence of ARCH effects in the residuals as the test statistics are significant at 1% level. However, in case of Crude Oil and Mentha oil futures we find no ARCH effect in the residuals and this is in conformity with negligible amount of volatility clustering exhibited by the daily returns’ volatility graph of it. Then we proceeded for GARCH (1, 1) model where the coefficients like, constant (ω), ARCH term (α), GARCH term (β) are highly significant at 1% level. Moreover, the sum of the coefficients (α and β) are close to unity which indicates that the shock persist for many periods. Then we apply the GARCHM (1,1) model. Here we see that, for Mentha oil the risk premium is positive, but insignificant. That implies that higher risk given by higher conditional variance may not lead to higher returns. The risk premium is positive and significant in case of Crude oil and Nifty which implies increased risk leads to increased return. In case of Gold, the parameter of GARCHM is negative and not significant. An explanation for this might be that investment in gold futures in India is an alternative avenue for putting barren wealth irrespective of its riskreturn feature. Subsequently, we run the EGARCH (1, 1) model where the result reveals that the sum of ARCH and GARCH coefficients are greater than one in case of Gold futures and Nifty index while it is near to one in case of Crude oil. That means the conditional variance is explosive for Gold futures and Nifty index. Furthermore, the conditional variance for Mentha oil was found to be dampening in accordance with the previous findings of negligible volatility clustering of its daily return series. From the EGARCH (1, 1) and TGARCH (1, 1) model, we also observe that the leverage coefficient (γ) is not equal to zero, which implies that the impact is asymmetric. Therefore the findings of this exercise suggests that the Crude Oil and Gold futures market is almost similar to the functioning of the stock market in India as in the stock market, volatility clustering is observed and hence GARCH (1,1), GARCHM(1,1), EGARCH(1,1) and TGARCH(1,1) are applicable (The result confirms the previous research studies by Banumathy and Azhagaiah (2015), Karmakar (2007). This is amenable to easy economic interpretation: Crude oil futures market is largely dependent on the global market situations which are highly volatile. Naturally, this spillover effect of global volatility has its impact on the Indian Crude oil futures market. On the other hand, other significant macroeconomic variables(like rate of interest, exchange rate and so on, that are fluctuating in nature) have its impact on Gold futures market in India and thereby explains its volatility.
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Received on 14.09.2018 Modified on 25.09.2018
Accepted on 20.10.2018 ©AandV Publications All right reserved
Res. J. Humanities and Social Sciences. 2019; 10(1):105114.
DOI: 10.5958/23215828.2019.00018.4