DOI: 10.17492/focus.v5i2.14383 www.journalpressindia.com/fjib
© 2018 Journal Press India
Price Discovery Mechanism in Spot and Futures Market of Agricultural Commodities: The Case of India
Minakshi*
ABSTRACT
There has been increasing focus by emerging market researchers, policymakers and regulators for investigating price discovery, relationship between future and physical market and accessible trading and risk management instruments for the benefit of various stakeholders and thus contributing to the development of literature. The central question of this paper is examining the role of influence of one market on the other and the role of each market segment in price discovery in the Indian context.
Johansen Vector Error Correction Model (VECM) has been employed to examine the relationship between the spot and futures prices. The co-integration results do not confirm the existence of long-run relationship between spot and futures prices. It is thus, implied that futures prices unlikely serve as market expectations of subsequent spot prices of selected agri-commodities in India and do not help in price discovery process.
Keywords: Price discovery; Agri-commodities; VECM; Spot and Futures Market.
1.0 Introduction
India is known to be one of the largest consumers as well as producer of many agri-commodities. It’s time for India to take a central role in price leadership at international level. In this backdrop, the importance of examining price discovery mechanism of selected agri-commodities has been established. According to Gonzalo and Figueroa-Ferretti (2010) futures market contribute in two important manners to the organization of economic activity. Firstly, futures markets facilitate price discovery and secondly, they offer way of risk transfer and hedging. An efficient agricultural commodity market is one in which the spot market ‘fully reflects’ available information (Malkiel & Fama, 1970), i.e. an efficient futures market should send price signals to the spot market immediately to eliminate supernormal profit from arbitraging on price differences or at
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*Associate Professor, Department of Commerce, Dyal Singh College, New Delhi, India. (Email:
minakshi.du@gmail.com)
maturity; the future prices become equivalent to spot prices except for some transaction costs. Easwaran and Ramasundaram (2008) propounded that price discovery is highly useful to all segments of the economy where a producer gets an idea of the price likely to prevail at a future point of time and therefore can decide between various competing commodities and choose the best that suits him whereas a consumer simply gets an idea of the price at which the commodity would be available in the future and thus, guiding him in buying decisions.
Many scholars through application of different methodologies, have studied one market’s dominant role on the other for the purpose of price discovery such as Tan and Lim (2001). Chan (1992) rightly concluded that futures market is the main source of market-wide information and there is a price discovery in the futures market. Garbade and Silber (1983) concluded that risk transfer and price discovery is considered as two major contributions of futures market towards organization of economic activity.
The seminal study by Garbade and Silber (1983) used daily spot and futures prices for four storable agricultural commodities to understand the price discovery process in storable agricultural commodities. Although their findings were not clear enough for oats, they did conclude that spot markets are dominated by futures market prices in the case of orange juice wheat and corn. Schroeder and Goodwin (1991) in their study reported about live hogs and Oellermann et al. (1989) in their study about feeder cattle studied price discovery in livestock contracts and concluded that the information flow is from the futures market to the spot market i.e. the futures market captures the information in the beginning and then the transfer happens to the spot market. Brockman and Tse (1995) in their study of the Canadian cash and futures market of agricultural commodities used econometric techniques such as cointegration and vector error correction model (VECM) and concluded that for all four commodities the spot market is led by the futures market and hence futures market drives the price discovery.
Fortenbery and Zapata (1997) used cointegration techniques to study the lead-lag relationships between spot and futures market in the US for anhydrous ammonia, diammonium phosphate and cheddar cheese and concluded that the cheddar cheese spot and futures markets are not cointegrated whereas the anhydrous ammonia and diammonium phosphate futures and spot markets are cointegrated. Koutmos and Tucker (1996) in a study regarding S&P 500 spot index and stock index future inspected the existence of dynamic interactions and temporal relationships by applying the VECM and ECM-EGARCH.
Yang et al. (2001) studied the futures market for non-storable (hogs, live cattle, feeder cattle) and storable (corn, oats, soybean, wheat, cotton, and pork bellies) commodities for price discovery performance by applying cointegration procedures and
vector error correction models (VECM) and concluded that spot markets are led by the futures market both in case of storable and non-storable commodities. Moosa (2002) studied the crude oil futures market to determine whether they performed the important functions of risk transfer and price discovery by using daily data of spot and one-month future prices of WTI crude oil covering from January 1985 to July 1996 and concluded in their study that 60% of the price discovery function is performed in futures market.
Mattos and Garcia (2004) studied the Brazilian Agri-commodities market for the existence of any lead-lag relationship between futures and spot market. Their study included futures of spot prices of the following commodities namely corn, cotton, live cattle, soybeans, sugar and coffee (Arabica) and this study concluded with mixed results.
For commodities with thinly traded markets such as corn, cotton and soybeans, there was absence of cointegrating relationship and in the case of coffee markets and live cattle, futures and spot prices were cointegrated.
Tse and Xiang (2005) in a study found that although crude and gas futures contracts account for less than one percent of the volume of standard contracts on the NYNEX E-Mini futures, they chip in for more than 30% of the price discovery. In a study by Zapata and Armstrong (2005) on the eleven futures prices traded in New York and world cash prices of exported sugar, with observations from January 1990 to January 1995, found out that futures market of sugar leads the cash market in price discovery mechanism. Azizan et al. (2007) examined the Malaysian crude palm oil futures market by using daily price data of crude palm oil futures and spot markets. They investigated for the return and volatility spillovers in the Malaysian crude palm oil futures market using bivariate ARMA (p, q)-EGARCH (p, q) model specifications and found bidirectional information transmission between futures and spot markets for both returns and volatility. Ge et al. (2008) studied the interaction between cotton markets in the US and China and found cointegration between that cotton futures in US and China. The study further showed that the American and Chinese cotton futures market share price transmissions.
Thomas and Karande (2001) investigated the castor seed futures market traded on the regional exchanges in Ahmedabad and Mumbai for the presence of price discovery process and concluded that each regional market reacted differently to information in the price discovery of castor seed. They found that although there was no lead-lag relationship found between the spot and futures market in Ahmedabad market, the futures market in Mumbai heavily dominated the spot market. Kumar (2004) employed the Johansen (1988) cointegration technique to examine the price discovery phenomena of five Indian agricultural commodities futures market and concluded that
futures market has been unable to incorporate information from the spot market and further confirmed the Indian agricultural commodities futures markets to be inefficient.
By employing the co-integration test to examine the linkages between Indian castor seeds futures and spot market, Karande (2006) study concluded that the Indian futures markets of Ahmedabad and Mumbai are cointegrated and there exists unidirectional causality from futures to spot market. Praveen and Sudhakar (2006) studied the Nifty futures traded on National Stock Exchange (NSE) and gold futures on Multi Commodity Exchange of India (MCX). In case of the commodity markets, they found a unidirectional causal relationship between the gold futures price and the spot gold price, meaning that gold futures price influenced the spot gold price, but the opposite was not true. In case of stock markets, the result concluded that Nifty futures had no effect on the spot Nifty. Roy and Kumar (2007) also employed the Johansen co- integration test to study the lead lag relationship between spot and futures market of wheat in India. Roy and Kumar’s (2007) study, where he investigated thirty-two wheat futures contracts in India concluded that wheat futures market is well cointegrated with their spot market and observed bidirectional causality in most of the wheat futures contracts. Iyer and Pillai (2010) used two-regime threshold vector auto regression (TVAR) for six commodities to investigate whether futures markets play a dominant role in the price discovery process and concluded that futures market prices play a vital role in the price discovery process.
Shihabudheen and Padhi (2010) studied six Indian commodity markets, namely, Castor seed, Jeera, Sugar, Gold, Silver and Crude Oil for price discovery mechanism and volatility spillovers effect. The findings of the study concluded that futures price acts as an efficient price discovery vehicle for five of the six commodities except for sugar.
Pavabutr and Chaihetphon (2010) investigated the gold futures contracts in the Multi Commodity Exchange of India (MCX) over the period 2003 to 2007 for price discovery by employing vector error correction model (VECM) to demonstrate that futures prices of both standard and mini contracts lead spot price. Srinivasan and Ibrahim (2012) employed Johansen VECM and the bivariate EGARCH model to study the price discovery process and volatility spillovers in Indian spot-futures commodity markets.
The results of the study demonstrated that spot markets of MCXCOMDEX, MCXAGRI, MCXENERGY and MCXMETAL serve as effective price discovery vehicle.
Furthermore, volatility spillovers to futures from sport market are dominant in case of all MCX commodity markets.
Studies of several Indian authors including Chakrabarty and Sarkar (2010), Mahalik et al. (2009) have also found futures market is an efficient vehicle for price discovery process. Whereas results of Naik and Jain (2002), Easwaran and
Ramasundaram (2008), Chandrasekhar (2006) found to the contrary. Thus, this study aims at investigating the relationship between spot and futures markets and exploring whether futures market acts as an efficient price discovery vehicle for the selected agricultural commodities. The following analysis is expected to find new dimensions for unexplored Agri-commodities.
2.0 Research Methodology
The required daily price data on spot and futures market prices are collected from the NCDEX website for the period 1st February, 2009 to 31st December, 2014. The corresponding contracts were considered for the study. However for Cotton, corresponding contracts were available from October 2013 to December 2014 (Table 1).
In total, fifty-two contracts have been analysed for finding meaningful conclusions.
Table 1: Description of Contracts for Chilly and Cotton
Commodity Contract (No of Months) No of Observations Correlation SP &FP
Chilly
Feb-09 114 -0.33
Mar-09 95 -0.022
Apr-09 73 -0.12
Jun-09 61 0.43
Aug-09 85 0.22
Oct-09 102 0.36
Dec-09 124 0.86
Feb-10 109 0.77
Mar-10 96 0.8
Apr-10 72 0.5
Jun-10 63 0.22
Jul-10 66 0.18
Aug-10 72 0.014
Sep-10 69 0.93
Oct-10 68 0.56
Nov-10 66 0.79
Dec-10 65 0.89
Feb-11 82 0.98
Mar-11 82 0.97
Apr-11 78 0.87
Jun-11 69 0.11
Jul-11 73 -0.23
Aug-11 76 0.082
Sep-11 69 0.74
Oct-11 65 0.56
Nov-11 61 0.82
Dec-11 62 0.96
Feb-12 58 0.6
Mar-12 77 0.53
Apr-12 77 0.64
Jun-12 57 0.41
Jul-12 59 -0.29
Aug-12 61 0.32
Sep-12 66 0.81
Oct-12 65 0.73
Nov-12 60 0.8
Dec-12 64 0.76
Mar-13 98 0.75
Apr-13 115 0.73
Jun-13 117 0.01
Jul-13 121 -0.17
Aug-13 84 0.07
Sep-13 85 -0.27
Oct-13 78 0.26
Nov-13 93 0.24
Dec-13 92 0.79
Cotton
Oct-13 156 0.996
Nov-13 177 0.24
Dec-13 203 0.79
Oct-14 32 0.94
Nov-14 48 0.996
Dec-14 69 0.93
Source: Author’s data compilation
The methodological approach adopted for this study is on the lines of earlier studies as documented in the research findings where Vector Error Correction Mechanism (VECM) has been employed. For effectively carrying out this, Johansen cointegration technique was employed to access the long-run relationship between the variables.
Generally, the presence of co-integration ensures long term relationship of spot and futures prices and the absence of co-integration shows that spot and futures prices drift apart without bound or the futures price provides little information about the movement of the spot price.
The Johansen co-integration technique uses following steps as per the methodology:
a) test for stationarity,
b) selection of the optimal length to incorporate in the test of cointegration,
c) test for no. of cointegrating relations through Johansen log-likelihood VECM and d) estimation of suitable VECM and identification of cointegrating vectors
2.1 Test of non-stationarity
Prior to estimating VECM equations, it should be known whether variables are stationary or not. (a) If they are stationary, then there is no need of doing VECM analysis as OLS gives better results in terms of efficiency of the model and (b) if they are not stationary, then it should be known whether variables are integrated of same order.
Integrated of x order means it takes x number of differences to make the series stationary. If variables are not integrated of same order, then VECM cannot be estimated.
Augmented Dickey-Fuller (ADF) test has been carried out to test the stationarity of price series. The ADF approach controls for higher-order correlation by adding lagged difference terms of the dependent variable to the right-hand side of the regression. The ADF test is specified here as follows:
ΔYt = b0 + βYt-1 + μ1ΔYt-1 + μ2ΔYt-2 + …….. + μpΔYt-p + εt …..(1) where, Yt represents time series to be tested, b0 is the intercept term, β is the coefficient of interest in the unit root test, μi is the parameter of the augmented lagged first difference of Yt to represent the pth order autoregressive process, and εt is the white noise error term. In carrying out the unit root test, it is required to test the following hypothesis:
H0: α=0 (non-stationary) H1: α≠0 (stationary)
If the null hypothesis is rejected, this means that the time series data is stationary. The decision criteria involve comparing the computed values of Augmented Dickey-Fuller ‘T’ statistic with the critical values for the rejection of a hypothesis for a unit root. If the computed ADF statistic is less relative to the critical values, then the null hypothesis of non-stationarity in time series variables cannot be rejected.
2.2 Selection of optimal lag to incorporate in the test of cointegration
In order to run the model successfully, the optimal length of lags should be known to be used in the equations. Optimal length is determined looking at values of log-likelihood, likelihood ratio, final prediction error and various information criteria estimates in various vector equations of fp and sp with different lags. By theory, a model is better when LL and LR are higher and FPE and ICs are lower.
2.3 Test for number of cointegrating relations through Johansen log-likelihood VECM
Now using optimal lags obtained above, it can be examined if the two variables are cointegrated. Two variables would be cointegrated if the maximum rank in the Johansen test for cointegration is greater than zero and not zero. By rule in case of n variables, the maximum rank can be n-1 i.e. there can be maximum n-1 cointegrating relationship.
Johansen’s co-integration tests have been used to assess the long-run relationship among spot and futures prices, using maximum likelihood technique. The Johansen’s co-integration test, assuming an n-dimensional vector Xt with integration of an order I(1), estimates a vector autoregressive model. Johansen and Juselius (1990) further improved the model by incorporating an error correction as:
𝑋𝑡 = 𝑐 + ∑𝑘𝑖=1⨅𝑖 𝑋𝑡−1+ 𝜖𝑡 …..(2)
𝑋𝑡 = µ + ∑µ−1𝑖=1𝑟𝑖 ∆𝑖 𝑋𝑡−1+ ⨅𝑖 𝑋𝑡−1+ 𝜖𝑡 …..(3) where Xt is an n x 1 vector of the I(1) variables representing spot (St) and futures (Ft-n) prices, respectively, μ is a deterministic component which may include a linear trend term, an intercept term or both, denotes the first difference operator, ⨅𝑖 is an n x r matrix of parameters indicating α and β , c is a vector of constants, k is lag length based on the Hannan-Quinn criterion and 𝜖𝑡 is error term, indicating how many linear combinations of Xt are stationary. The co-integration model asserts that if the coefficient matrix has reduced rank r < k, then co-integrating relationship can be determined by examining the rank of the coefficient matrix , which is based on the number of co- integrating vectors. The rank of thus defines the number of co-integrating vectors. For the two variables (St and F0, t) in this study, the maximum rank of will be 2, indicating that St and F0, t are jointly stationary. A rank of one (1) will indicate a single co- integration and a zero (0) rank would indicate lack of co-integration between St and F0, t. Johansen suggested that the trace and maximum eigen value likelihood tests to determine the rank of . These are presented in equations (3) and (4) respectively:
𝐽𝑡𝑟𝑎𝑐𝑒= −𝑇 ∑𝑛𝑖=𝑟+1In(1 − λ̂i) …...(4)
𝐽𝑚𝑎𝑥= −𝑇 In(1 − λ̂r+1 ) …...(5)
where T is the sample size and λ̂ is the ith largest canonical correlation.
Asymptotic critical values have been provided by Johansen and Juselius (1990) as test statistics.
Here we test for each rank in a sequence. First, the test for rank zero is run with the null hypothesis ‘the maximum rank is zero’. If it is rejected (if trace statistics>5%
critical value) then, the test for rank one is examined with the null hypothesis ‘the maximum rank is one’ and so on till n-1 rank. If the result shows that the maximum rank is more than zero, then it ensures existence of long-term market efficiency in Indian commodity futures markets.
2.4 Estimation of suitable VECM and identification of cointegrating vectors
If variables are cointegrated then cointegrating vectors are estimated using VECM. In case of two variables, if we get one cointegrating relationship, then we can exactly determine the nature of relationship between two variables, sp and fp in an equation form.
3.0 Summary Results and Findings
Whether available data of sp and fp helps in highlighting price discovery can be determined by cointegration analysis and whether sp and fp are cointegrated can be assessed by looking at the trend of two variables together. For example the trend of future prices and spot prices of Chilly contract of April, 2009 involving 73 observations depicts that the two variables move in different direction specially before t=45. So, it is not likely that sp and fp would be cointegrated (Figure 1). Now to conduct formal test of cointegration, it is tested whether two variables are stationary, non-stationary but integrated of the same order or there is no integration between variables. Trend of two variables again gives some hint on this. For the same contract variables are non- stationary (Figure 1). The STATA is used for the econometric analysis.
Figure 1: Trend of Future and Spot Prices for Chilly (April, 2009)
fp: future price and sp: spot price Source:NCDEX
Further, last column of Table 1 presents correlation between sp and fp. If correlation is low, then it is highly likely that two variables are not cointegrated but vice versa is not always true. In the case of above contract, correlation is -0.12 i.e. very low.
So, sp and fp should not be cointegrated which we would examine through the procedure adopted for empirical testing.
In the formal test as the first step i.e. the test for stationarity, we have applied Augmented Dickey-Fuller (ADF) test with null hypothesis of unit root (or variable is non-stationary). Summarized results are given below in Table 2 for the all the 52 contracts. The computed values of ADF ‘T’ statistics for all the contracts of Chilly and Cotton are presented below at 5% level of significance. In Table 2, fourth and seventh columns represent the number of times we have taken the difference of the variables to make it stationary because it is evident from the Table that t statistics of the variable is always greater than the critical values implying that null hypothesis is rejected and so variable at specified level of difference is stationary.
Table 2: ADF Test Results
Commodity Contract Spot Price Future Price
40004500500055006000
0 20 40 60 80
t
fp sp
Spot 't' statistics
level of difference
for test
critical 't' value at 5% LOS
Future 't' statistics
level of difference
for test
critical 't' value at 5% LOS
Chilly
Feb-09 -4.14 1 -2.89 -3.224 0 -2.89
Mar-09 -3.366 1 -2.9 -3.765 1 -2.9
Apr-09 -5.139 2 -2.919 -5.37 2 -2.919
Jun-09 -4.219 2 -2.928 -4.93 2 -2.928
Aug-09 -3.099 1 -2.908 -3.576 1 -2.908
Oct-09 -3.866 1 -2.985 -3.252 1 -2.985
Dec-09 -3.573 1 -2.889 -3.957 1 -2.889
Feb-10 -3.26 1 -2.89 -4.064 1 -2.89
Mar-10 -3.041 1 -2.9 -3.255 1 -2.9
Apr-10 -3.49 1 -2.919 -5.515 2 -2.92
Jun-10 -4.357 2 -2.927 -4.022 2 -2.927
Jul-10 -4.518 2 -2.924 -3.135 1 -2.924
Aug-10 -4.75 2 -2.92 -2.974 2 -2.92
Sep-10 -3.956 2 -2.922 -3.687 1 -2.921
Oct-10 -2.992 1 -2.922 -3.121 1 -2.922
Nov-10 -3.304 2 -2.924 -4.346 1 -2.924
Dec-10 -4.357 2 -2.925 -3.059 1 -2.924
Feb-11 -3.802 1 -2.911 -5.233 2 -2.912
Mar-11 -3.731 1 -2.911 -5.444 2 -2.912
Apr-11 -3.651 1 -2.914 -4.958 2 -2.915
Jun-11 -3.511 1 -2.921 -2.951 1 -2.921
Jul-11 -3.607 1 -2.918 -4.46 2 -2.919
Aug-11 -3.094 1 -2.916 -2.964 0 -2.915
Sep-11 -3.491 2 -2.922 -3.354 1 -2.921
Oct-11 -3.598 2 -2.925 -3.894 1 -2.924
Nov-11 -3.143 2 -2.928 -3.512 1 -2.928
Dec-11 -3.69 2 -2.928 -5.409 2 -2.928
Feb-12 -4.26 2 -2.933 -4.608 2 -2.933
Mar-12 -3.197 1 -2.915 -3.688 1 -2.915
Apr-12 -3.06 1 -2.915 -3.645 1 -2.915
Jun-12 -3.645 2 -2.936 -4.216 2 -2.936
Jul-12 -4.178 2 -2.93 -4.219 2 -2.93
Aug-12 -4.501 2 -2.928 -4.537 2 -2.928
Sep-12 -5.112 2 -2.924 -5.128 2 -2.924
Oct-12 -4.813 2 -2.925 -6.346 2 -2.925
Nov-12 -3.86 2 -2.929 -4.178 2 -2.929
Dec-12 -4.097 2 -2.926 -4.393 2 -2.926
Mar-13 -3.188 1 -2.898 -3.296 1 -2.898
Apr-13 -3.136 1 -2.89 -3.272 1 -2.89
Jun-13 -3.677 1 -2.889 -3.483 1 -2.889
Jul-13 -3.887 1 -2.889 -3.799 1 -2.889
Aug-13 -3.506 1 -2.909 -3.427 1 -2.909
Sep-13 -3.959 1 -2.908 -2.922 1 -2.908
Oct-13 -3.731 1 -2.914 -4.155 1 -2.914
Nov-13 -2.989 2 -2.903 -3.381 1 -2.909
Dec-13 -4.096 1 -2.903 -4.817 1 -2.903
Cotton
Oct-13 -3.193 1 -2.887 -3.163 1 -2.887
Nov-13 -2.989 2 -2.903 -3.381 1 -2.902
Dec-13 -4.096 1 -2.903 -4.817 1 -2.903
Oct-14 -3.391 4 -3 -3.832 3 -3
Nov-14 -4.596 3 -2.964 -3.247 2 -2.961
Dec-14 -3.704 2 -2.922 -4.721 2 -2.922
Source: Author’s data compilation
The process of knowing the order of integration is given in detail below.
Suppose, the obtained test statistics for variables (sp and fp) at original level are within the range of critical values then the null hypothesis of ‘unit root’ is not rejected. So, both sp and fp variable are non-stationary. Then we test for the stationarity of first difference of both variables (d.sp and d.fp). If the obtained test statistics results for the variables are within the range of critical values, then the null hypothesis of ‘unit root’ is not rejected.
In this case also, both d.sp and d.fp variable are non-stationary. Similarly we test for the stationarity of second difference of both variables (d2.sp and d2.fp). If the obtained results for the second degree of difference between sp and fp for each variable are outside the range of critical values, then the null hypothesis of ‘unit root’ is rejected.
Thus, both d2.sp and d2.fp variables are stationary. Thus, in this case both variables are integrated of same order (2). So, we can go for test of cointegration and VECM estimation. In Table 2, examples are contracts of April 09 to March 10 for chilly and so on.
Whereas, results of contracts of February 09, April 10 in chilly etc. show that variables are not integrated. So, here we cannot go for next step and conclude that variables can’t be cointegrated.
3.1 Selection of optimal lag to incorporate in the test of cointegration
In order to run the model successfully, we need to know the optimal length of lags to be used in the equations. Optimal length is determined looking at values of log- likelihood, likelihood ratio, final prediction error and various information criteria
estimates. By theory, a model is better when LL and LR are higher and FPE and ICs are lower. The following Table 3 shows the obtained optimal lag, log-likelihood, likelihood ratio, final prediction error and various information criteria estimates from the models estimated with different lags.
In Table 3, *symbol shows the best result for each category among various lags.
For example, in the contract of March 09 of chilly lag 2 occupies the * mark for all categories. So, in this case optimal lag length of sp and fp variables in the estimation of VECM should be 2. Whereas, in June 09 of chilly results do not indicate unanimity but majority of * marks are obtained by lag 3. So, here we select optimal lag length as 3.
Table 3: Selection of Optimal Lag
Commodity Contract lag LL LR df p FPE AIC HQIC SBIC
Chilly
Feb-09
Mar-09
0 -1237.2 2.30E+09 27.2352 27.2575 27.2904
1 -985.457 503.49 4 0 1.00E+07 21.7903 21.8571 21.9558
2 -973.29 24.334* 4 0 8.3e+06* 21.6108* 21.7221* 21.8867*
Apr-09 0 -423.671 5.50E+10 30.4051 30.4342 30.5003
1 -356.677 133.99* 4 0 6.1e+08* 25.9055* 25.9928* 26.191*
Jun-09
0 -804.363 6.60E+09 28.2934 28.3213 28.3651
1 -679.076 250.57 4 0 9.40E+07 24.0378 24.1213* 24.2528*
2 -675.941 6.2714 4 0.18 9.70E+07 24.0681 24.2074 24.4265 3 -670.826 10.229* 4 0.037 9.4e+07* 24.029* 24.224 24.5308
Aug-09
0 -1162.98 1.10E+10 28.7649 28.7886 28.824
1 -968.656 388.64 4 0 9.70E+07 24.0656 24.1367 24.2429*
2 -961.428 14.457* 4 0.006 9.0e+07* 23.9859* 24.1045* 24.2815
Oct-09 0 -1371.61 5.10E+09 28.0328 28.0541 28.0856
1 -1145.09 453.04* 4 0 5.5e+07* 23.4916* 23.5556* 23.6499*
Dec-09
0 -1657.12 3.50E+09 27.6519 27.6708 27.6984
1 -1334.43 645.37 4 0 1.70E+07 22.3405 22.3971 22.4799
2 -1323.41 22.05 4 0 1.50E+07 22.2234 22.3178* 22.4557*
3 -1317.44 11.936* 4 0.018 1.5e+07* 22.1906* 22.3227 22.5159
Feb-10
0 -1406.24 1.50E+09 26.8237 26.8442 26.8742
1 -1146.74 519.01 4 0 1.20E+07 21.9569 22.0183 22.1085
2 -1134.82 23.822 4 0 1.00E+07 21.8062 21.9086* 22.0589*
3 -1129.36 10.932* 4 0.027 9.80E+06 21.7783 21.9217 22.1321 4 -1124.93 8.863 4 0.065 9.8e+06* 21.77* 21.9544 22.225
Mar-10
0 -1304.83 7.50E+09 28.4094 28.4315 28.4642
1 -1013.6 582.47 4 0 1.40E+07 22.1652 22.2315 22.3296
2 -1002.52 22.154* 4 0 1.2e+07* 22.0113* 22.1219* 22.2854*
Apr-10
Jun-10 0 -812.154 3.30E+09 27.5984 27.6259 27.6689
1 -677.467 269.37* 4 0 4.0e+07* 23.1684* 23.2508* 23.3797*
Jul-10
Aug-10 0 -925.521 2.40E+09 27.28 27.3059 27.3453
1 -732.541 385.96* 4 0 9.3e+06* 21.7218* 21.7994* 21.9176*
Sep-10
Oct-10
0 -807.825 3.40E+08 25.307 25.3336 25.3745
1 -645.652 324.35 4 0 2.40E+06 20.3641 20.4439 20.5665*
2 -641.461 8.382 4 0.079 2.40E+06 20.3582 20.4911 20.6955 3 -634.305 14.313 4 0.006 2.20E+06 20.2595 20.4456 20.7318 4 -628.527 11.554* 4 0.021 2.0e+06* 20.204* 20.4432* 20.8112 Nov-10
Dec-10
Feb-11 Mar-11 Apr-11
Jun-11
0 -1006.15 1.00E+11 31.02 31.0464 31.0869
1 -839.846 332.61 4 0 6.90E+08 26.026 26.1052 26.2267
2 -828.537 22.617 4 0 5.50E+08 25.8011 25.9331* 26.1357*
3 -823.624 9.8261* 4 0.043 5.4e+08* 25.773* 25.9578 26.2414 Jul-11
Aug-11 Sep-11 Oct-11 Nov-11
Dec-11
0 -839.995 1.40E+10 29.0343 29.062 29.1054
1 -677.37 325.25 4 0 5.90E+07 23.5645 23.6475 23.7776
2 -663.434 27.872 4 0 4.2e+07* 23.2219* 23.3602* 23.5771*
3 -662.007 2.8539 4 0.583 4.60E+07 23.3106 23.5043 23.8079 4 -656.895 10.225* 4 0.037 4.40E+07 23.2722 23.5213 23.9117
Feb-12
0 -801.967 2.90E+10 29.7766 29.805 29.8502
1 -648.406 307.12 4 0 1.20E+08 24.2372 24.3225 24.4582
2 -638.464 19.882* 4 0.001 9.2e+07* 24.0172* 24.1592* 24.3855*
Mar-12
0 -1081.92 2.70E+10 29.6963 29.7213 29.7591
1 -871.953 419.93 4 0 9.60E+07 24.0535 24.1285 24.2418
2 -859.439 25.028* 4 0 7.6e+07* 23.8203* 23.9453* 24.134*
Apr-12
0 -1100.09 4.40E+10 30.1941 30.2191 30.2569
1 -876.31 447.55 4 0 1.10E+08 24.1729 24.2479 24.3611
2 -865.656 21.308* 4 0 9.0e+07* 23.9906* 24.1156* 24.3043*
Jun-12 0 -772.089 1.70E+10 29.2109 29.2395 29.2853
1 -653.71 236.76* 4 0 2.2e+08* 24.8947* 24.9805* 25.1178*
Jul-12 0 -806.244 2.00E+10 29.3907 29.4189 29.4637
1 -660.367 291.76* 4 0 1.1e+08* 24.2315* 24.3162* 24.4505*
Aug-12 0 -803.426 6.40E+09 28.2605 28.2884 28.3322
1 -683.791 239.27* 4 0 1.1e+08* 24.2032* 24.2868* 24.4183*
Sep-12
0 -810.751 8.30E+08 26.2178 26.2447 26.2864
1 -688.184 245.13 4 0 1.80E+07 22.393 22.4739 22.5989*
2 -682.109 12.15* 4 0.016 1.7e+07* 22.3261* 22.4608* 22.6692
Oct-12
0 -839.39 3.30E+09 27.5866 27.6137 27.6558
1 -678.779 321.22* 4 0 1.90E+07 22.4518 22.5331* 22.6594*
2 -674.585 8.3868 4 0.078 1.90E+07 22.4454 22.581 22.7915 3 -670.502 8.1672 4 0.086 1.9e+07* 22.4427* 22.6325 22.9271
Nov-12
0 -760.602 2.30E+09 27.2358 27.2638 27.3081
1 -612.585 296.03 4 0 1.30E+07 22.0923 22.1765 22.3093
2 -604.532 16.106* 4 0.003 1.2e+07* 21.9476* 22.0878* 22.3093*
Dec-12
0 -750.39 2.70E+08 25.0797 25.107 25.1495
1 -643.697 213.39 4 0 8.70E+06 21.6566 21.7385* 21.866*
2 -638.128 11.139* 4 0.025 8.3e+06* 21.6043* 21.7408 21.9533
Mar-13
0 -1371.63 1.70E+10 29.2261 29.248 29.2802
1 -1078.33 586.6 4 0 3.60E+07 23.0708 23.1364 23.2332
2 -1068.92 18.811* 4 0.001 3.2e+07* 22.9558* 23.0651* 23.2264*
Apr-13
0 -1629.16 2.00E+10 29.3903 29.4101 29.4392
1 -1270.74 716.85 4 0 3.40E+07 23.0043 23.0637 23.1507*
2 -1262.57 16.328* 4 0.003 3.1e+07* 22.9293* 23.0283* 23.1734
Jun-13
0 -1719.96 5.90E+10 30.4772 30.4968 30.5254
1 -1347.63 744.66* 4 0 8.70E+07 23.9581 24.0169* 24.1029*
2 -1342.95 9.3595 4 0.053 8.6e+07* 23.9461* 24.044 24.1874
Jul-13 0 -1807.06 9.20E+10 30.9241 30.9432 30.9713
1 -1394.84 824.43* 4 0 8.6e+07* 23.946* 24.0036* 24.0877*
Aug-13 0 -1174.97 2.10E+10 29.4242 29.4481 29.4837
1 -949.661 450.61* 4 0 8.1e+07* 23.8915* 23.9632* 24.0702*
Sep-13
0 -1147.56 7.30E+09 28.3842 28.408 28.4434
1 -998.568 297.99 4 0 2.0e+08* 24.8041* 24.8753* 24.9815*
2 -997.662 1.8113 4 0.77 2.20E+08 24.8806 24.9992 25.1762 3 -997.251 0.82266 4 0.935 2.40E+08 24.9692 25.1352 25.383
4 -991.599 11.305* 4 0.023 2.30E+08 24.9284 25.1418 25.4605
Oct-13
0 -981.088 1.20E+09 26.5699 26.5948 26.6322
1 -802.499 357.18 4 0 1.10E+07 21.8513 21.9258 22.0381*
2 -796.486 12.026* 4 0.017 1.0e+07* 21.7969* 21.9211* 22.1083 Nov-13
Dec-13
0 -1282.45 1.60E+10 29.192 29.2147 29.2483
1 -1033.03 498.85 4 0 6.20E+07 23.6142 23.6823 23.7832
2 -1020.72 24.612* 4 0 5.1e+07* 23.4255* 23.5389* 23.707*
Cotton
Oct-13
0 -2314.08 5.90E+10 30.4748 30.4909 30.5146
1 -1922.68 782.8 4 0 3.60E+08 25.3774 25.4259 25.4967*
2 -1915.7 13.963* 4 0.007 3.5e+08* 25.3381* 25.419* 25.5371 Nov-13
Dec-13
0 -1282.45 1.60E+10 29.192 29.2147 29.2483
1 -1033.03 498.85 4 0 6.20E+07 23.6142 23.6823 23.7832
2 -1020.72 24.612* 4 0 5.1e+07* 23.4255* 23.5389* 23.707*
Oct-14 Nov-14
Dec-14 0 -963.98 2.80E+10 29.7225 29.7489 29.7894
1 -798.346 331.27* 4 0 1.9e+08* 24.7491* 24.8283* 24.9498*
Source: Author’s data compilation
3.2 Test for no. of cointegrating relations through Johansen log-likelihood VECM Now the two variables are examined to be cointegrated. Two variables would be cointegrated if the maximum rank in the Johansen test for cointegration is greater than zero and not zero. By rule in case of n variables, the maximum rank can be n-1 i.e. there can be maximum n-1 cointegrating relationship. Johansen’s Cointegration test is performed to examine the long-run relationship between spot and future market prices of selected agricultural commodities and its result are presented in Table 4.
In Table 4, * indicates the null hypothesis of maximum rank at specified level is accepted. For example, the maximum rank is 0 in the case of contracts from March 09 to December 09 for chilly, but the maximum rank is 1 in the case of contract of Feb 10 of chilly. The tabulated results of Johansen’s maximum Eigen value and trace statistic reveal the presence of cointegrating relations in 6 contracts between the futures and spot market prices of Chilly and Cotton respectively. Whereas, for others (besides in grey color and blank in Table 5) there is no cointegration between sp and fp.
Table 4: Test of Cointegration
Commodity Contract Maximum Rank Parameters LL Eigen-value trace statistics critical value
Chilly
Feb-09
Mar-09 0 6 -1012.93 . 12.1918* 15.41
Apr-09 0 6 -776.238 . 2.5330* 15.41
Jun-09 0 10 -684.7 . 6.0486* 15.41
Aug-09 0 10 -974.902 . 5.9369* 15.41
Oct-09 0 2 -1183.57 . 6.9500* 15.41
Dec-09 0 10 -1333.87 . 10.1416* 15.41
Feb-10 0 6 -1168.3 . 26.0372 15.41
1 9 -1156.25 0.20158 1.9487* 3.76
Mar-10 0 6 -1024.81 . 3.8019* 15.41
Apr-10
Jun-10 0 2 -715.336 . 10.1524* 15.41
Jul-10
Aug-10 0 2 -765.071 . 4.6556* 15.41
Sep-10
Oct-10 0 14 -632.491 . 7.9276* 15.41
Nov-10 Dec-10 Feb-11 Mar-11 Apr-11
Jun-11 0 10 -838.767 . 6.1084* 15.41
Jul-11 Aug-11
Sep-11 Oct-11 Nov-11
Dec-11 0 6 -693.614 . 17.3485 15.41
1 9 -684.996 0.24969 0.1123* 3.76
Feb-12 0 6 -665.895 . 2.7378* 15.41
Mar-12 0 6 -891.031 . 12.3761* 15.41
Apr-12 0 6 -893.011 . 7.1379* 15.41
Jun-12 0 2 -700.281 . 5.4089* 15.41
Jul-12 0 2 -698.893 . 8.8015* 15.41
Aug-12 0 2 -726.839 . 9.7906* 15.41
Sep-12 0 6 -708.314 . 9.7754* 15.41
Oct-12 0 2 -714.295 . 6.5175* 15.41
Nov-12 0 6 -634.134 . 8.6653* 15.41
Dec-12 0 6 -664.465 . 13.9227* 15.41
Mar-13 0 6 -1098.68 . 16.7796 15.41
1 9 -1090.84 0.15081 1.0868* 3.76
Apr-13 0 6 -1293.53 . 19.5020* 20.04
Jun-13 0 2 -1384.82 . 7.5868* 15.41
Jul-13 0 2 -1432.42 . 7.3632* 15.41
Aug-13 0 2 -992.425 . 6.3867* 15.41
Sep-13 0 2 -1040.76 . 14.0145* 15.41
Oct-13 0 6 -830.16 . 16.9015 15.41
1 9 -821.98 0.19368 0.5411* 3.76
Nov-13
Dec-13 0 6 -1046.5 . 8.7211* 15.41
Cotton
Oct-13 0 6 -1975.55 . 26.3148 15.41
1 9 -1962.82 0.15245 0.8419* 3.76
Nov-13
Dec-13 0 6 -1046.5 . 8.7211* 15.41
Oct-14 Nov-14
Dec-14 0 2 -861.066 . 32.0667 20.04
1 5 -847.817 0.32273 5.5684* 6.65 Source: Author’s data compilation
The Johansen cointegration test result confirms that there exists a long-run relationship between spot and futures prices of selected respective agricultural commodities for these 6 contracts. Besides, the analysis indicates the spot and futures prices of each selected stocks stand in a long-run relationship between them, thus justifying the use of a VECM for showing short-run dynamics. By using the definition of cointegration, the Granger Representation Theorem (Engle & Granger, 1987) which states that if a set of variables are cointegrated, then there exist valid error correction representations of the data.
3.3 Estimation of suitable VECM and identification of cointegrating vectors
Table 5 presents the results for the cointegrating equations in respect of those 6 contracts having cointegration. For the Feb 10 of Chilly contract result may be interpreted as an increase of 1 unit in spot prices results in increase of future prices by 1.5 units.
Table 5: Co-Integrating Equations
Commodity Contract variable coefficient Std. Err. P value Cointegrating Equation
Chilly
Feb-10
sp 1 . . 1*fp -1.5*sp + 3125.85= error
fp -0.67 0.078 0 Or
constant -2082.62 . . fp = -3125.85 + 1.5*sp + error Dec-11
sp 1 . . 1*fp -0.76*sp -1318.9= error
fp -1.32 0.073 0 Or
constant 1736.176 . . fp = 1318.9+ 0.76*sp + error
Mar-13
sp 1 . . 1*fp -0.211*sp - 5195.88= error#
fp -4.73 0.98 0 Or
constant 24561.83 . . fp = 5195.88+ 0.21*sp + error
# note that equation and coefficient of sp are not significant Oct-13
sp 1 . . 1*fp +1.15*sp – 12867.19= error
fp 0.872 0.389 0.025 Or
constant -11219.5 . . fp = 12867.19 – 1.15*sp + error
Cotton
Oct-13
sp 1 . . 1*sp -1.13*fp +3232.95= error
fp -1.13213 0.016 0 Or
constant 3232.96 . . sp = - 3232.95 + 1.13*fp + error Dec-14
sp 1 . . 1*sp -2.36*fp +21669.67= error
fp -2.35884 0.166 0 Or
constant 21669.67 . . sp = 2.36*fp -21669.67+ error Source: Author’s data compilation
Table 6 summarizes the extent of cointegration between the two variables for all the 52 contracts. The results show that 13 contracts of spot and future prices are not integrated at all, thus proving not driving one over the other. The next level finds that there is no visibility of cointegration in case of 33 studied contracts. However, six contracts for the two studied commodities are proved to be cointegrated indicating future prices driving spot or vice versa and farmers may look for these prices for price discovery of their produce.
Table 6: Level of Cointegration
Commodity Month Not Integrated Not Cointegrated Cointegrated
Chilly
Feb-09 y
Mar-09 y
Apr-09 y
Jun-09 y
Aug-09 y
Oct-09 y
Dec-09 y
Feb-10 Y
Mar-10 y
Apr-10 y
Jun-10 y
Jul-10 y
Aug-10 y
Sep-10 y
Oct-10 y
Nov-10 y
Dec-10 y
Feb-11 y
Mar-11 y
Apr-11 y
Jun-11 y
Jul-11 y
Aug-11 y
Sep-11 y
Oct-11 y
Nov-11 y
Dec-11 Y
Feb-12 y
Mar-12 y
Apr-12 y
Jun-12 y
Jul-12 y
