Relationship between Futures and Spot Market for selected Spices in India
Vijayakumar. N, (Corresponding Author) Assistant Professor, PSG Institute of Management, Coimbatore- 641 004 Tamilnadu, India. +91-94433-82134 Email:
[email protected]
Parvadavardini Soundarrajan Research Scholar, PSG Institute of Management, Coimbatore- 641 004 Tamilnadu, India. +91- 9500914567 Email:
[email protected]
M. Dharani Ph.D. Research Fellow Department of Commerce (School of Management) Pondicherry University Puducherry – 605014, India Mobile: 91-944-3194968 Mail:
[email protected]
Abstract: We examine the relationship between spot and futures prices for selected five agricultural commodities, namely, Chilli, Coriander, Jeera, Pepper and Turmeric. We considered all the contracts of the above commodities over a period of 36 months, from Jan 2008 to Dec 2010. The study examined the existence of unit root in the data series by employing Augmented Dickey -Fuller (ADF) test and we found the existence of long run relationship between selected spot and futures market using Johansen co-integration test and the presence of disequilibrium between markets in short run by employing Vector Error Correction Model (VECM). Key words: Commodity market, Spices, Co-integration, Vector error correction
1. Introduction This study highlights the association and integration between futures and spot markets in terms of pricing market information over the trading period. As there were no previous studies about the price linkages on futures and spot market for spices in India, this study would provide a base for similar research studies with reference to other agriculture and non agriculture products sold in the National Commodities Derivatives Exchange (NCDEX) platform or any other commodity exchanges. This study would also contribute to the commodity exchanges to show the implications of the information flow between the two markets i.e. futures and spot and to determine which market serves as a price discovery center.
Derivatives as a tool for managing risk first originated in the commodities markets. The first central exchange for commodity trading was established in 1848 in Chicago under the name Chicago Board of Trade. The emergence of the derivatives markets as the effective risk management tools in 1970s and 1980s has resulted in the rapid creation of new commodity exchanges and expansion of the existing ones. Commodity futures markets have a long history in India. Cotton was the first commodity to attract futures trading in the country
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leading to the setting up of the Bombay Cotton Trade Association Ltd in 1875. The Bombay Cotton Exchange Ltd. was established in 1893 following the widespread discontent amongst leading cotton mill owners and merchants over the functioning of Bombay Cotton Trade Association. Subsequently, many exchanges came up in different parts of the country for futures trading on various commodities.
Commodity exchanges are centers where futures trading is organized in a wider sense; Exchanges facilitate price discovery as players get to set futures prices which are also made available to all participants. Hence, a farmer in the southern part of India knowing the best price prevailing in the country and enables him to take informed decisions. For this to happen, the concept of commodity exchanges must percolate down to the villages. These exchanges also enable actual users (farmers, agro processors, industry where the predominant cost is commodity input/output cost) to hedge their price risk given the uncertainty of the futures - especially in agriculture where there is uncertainty regarding the monsoon and hence prices. This holds good also for non-agro products like metals or energy products as well where global forces which could exert considerable influences.
By involving the group of investors and speculators, commodity exchanges provide liquidity and buoyancy to the system. Finally, the arbitrageurs play an important role in balancing the market as arbitrage conditions, where they exist, are ironed out as arbitrageurs trade with opposite positions on different platforms and hence generate opposing demand and supply forces which ultimately narrows down the gaps in prices. It must be pointed out that while the monsoon conditions affect the prices of agro-based commodities, the phenomenon of globalization has made prices of other products such as metals, energy products, etc., vulnerable to changes in global politics, policies and growth paradigms, etc. Thus, the commodity exchanges would provide a valuable hedge through the price discovery process while catering to the different kind of players in the market.
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This study attempts to examine the existence of relationship between the spot and futures prices of spices using Chilli, Coriander, Jeera, Pepper and Turmeric traded in India. As well as, we expect that the spice futures contract would drive and contribute for price discovery in the spices spot market. Therefore, we analyse to what extent the spot and futures market for spices are placing similar values on new market information.
This study is organized into five sections including the present one. The review of earlier studies is discussed in section 2. The data and methodological issues are described in section 3. The empirical results are presented in section 4. Summary and concluding remarks are given in section 5.
2. Literature Survey This section discusses the previous studies pertaining to commodity spot and futures and assists to develop a theoretical background of the study.
Dewbre (1981) proposed an econometric model by recognizing the role of rational expectation formation in joint determination of commodity cash and futures prices to explore the implications of such an approach by addressing the issues like the direction and magnitude of changes in the cash and futures prices occurring in response to changes in the economic information. From the analysis, they observed the persistence of ‘rational expectation’ and working of equally redundant efficient market hypothesis.
Garbade and Silber (1983) examined the characteristics of price movement in cash and futures market for storable commodities. They employed the simultaneous price dynamics model and found that over short intervals of time, the correlation of price changes become a function of elasticity of arbitrage between the physical commodity and its counterpart futures contract. Basically, the two price series exhibits stochastic behavior while pricing identical assets and exhibit a deterministic linear relationship between them.
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Ollerman and Farris (1985) and Brorsen, Ollerman, Farris (1989) investigated the lead-lag relationship between live cattle futures contract prices and cash prices and observed that futures prices tend to lead live cattle cash prices; they also found that cash prices tend to respond to changes in futures prices within one business day. Brorsen, Ollerman and Farris (1989) employed regression techniques to measure the effects of futures trading on the variability and volatility of cash cattle prices and found that the futures trading impacting cash markets. Moreover, futures trading increases cash market pricing efficiency also increases short run spot price risk.
Garcia, Leuthold, Fortenbery and Sarassoro (1988) and Leuthold (1988) evaluated the pricing efficiency of the live cattle futures and cash market by employing ARIMA model and Composite forecasting procedures, in terms of the mean-squared error criterion, a necessary condition for market efficiency and found the most accurate forecast with generation of large risk-return ratio. Thus, these results do not show strong evidence of inefficiency and call into question the use of only mean-squared errors to examine a market’s pricing efficiency.
Koontz, Garcia and Hudson (1990) researched the dominant satellite relationship between live cattle cash and futures market. They employed Granger causality test to identify the lead/lag relationship and casual flows between series and observed that the results are consistent with the idea that the futures market is interacting much closely with the more dominant cash market. Bessler and Covey (1991) employed cointegration methods on daily data and shows the evidence of cointegration between nearby futures (i.e. those closest to expiration) and cash prices, but no evidence of cointegration when more distant futures contracts were considered. Further, this result was rationalized by Fortenbery and Zapata (1993) and suggested a possible reason for inconsistent result of Bessler and Covey might be the lack of explicit storage relationship between cash and futures market for livestock. Bessembinder and Senguin (1992) examined contemporaneous relationship through augmented GARCH model. They also decomposed futures trading volume and open interest
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series into expected and unexpected component. The lead-lag relationship between spot price volatility and futures trading volume and open interest is investigated through VAR model. Granger causality test, forecast error variance decompositions and impulse response function confirm that the lagged unexpected volatility causes spot price volatility for all commodities.
Baharumshah and Habibullah (1994), Sinharoy and Nair (1994) and Chopra and Blesser (2005) analyzed the existence of long run relationship among pepper prices. They employed cointegration and found that regional and world pepper markets were highly cointegrated and prices of pepper tended to move uniformly across spatial markets by indicating competitive pricing behavior.
Zapata (2005) examined the relationship between selected sugar futures prices traded in New York and the world cash prices for export sugar and found the unidirectional relationship from futures to cash. The finding of cointegration between futures and cash prices suggests that the sugar futures contract is a useful vehicle for reducing overall market price risk faced by cash market participants selling at the world price.
Brajesh (2009) investigated the relationship between futures trading activity and spot market volatility for agricultural, metal, precious metals and energy commodities in Indian commodity derivatives market.
The studies of long run relationship provide mixed results. Research results differ according to the methodology used, model, the data, the sample, and the time period. For futures market to provide efficient price discovery they must exhibit a close relationship with the prices recorded in the cash market. Tests of the futures/cash price relationships for various commodities have been numerous. In recent times, the focus tends to be on whether futures and cash market price new information the same, and whether futures lead or follow cash price changes. Research focuses on measuring directional causality between futures and cash market, and speed of price adjustment in the trailing market.
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3. Data and Methodology We estimate the relationship between cash and futures market of selected spices that are traded in the NCDEX exchange of India. The daily prices of spot and futures of selected spices viz Chilli, Coriander, Jeera, Pepper and Turmeric are obtained from the NCDEX website from January 1, 2008 to December 31, 2010. The daily prices obtained for 36 months are arranged with respect to their expiration date provided in the futures market segment of NCEDX.
We employed the Augmented Dickey -Fuller (ADF) Test to trace the existence of unit root on the daily data set of the selected spices. The ADF Test includes extra lagged terms of the dependent variables in order to eliminate autocorrelation. The lag length on these extract term is determined by the Akaike Information Criterion (AIC) and Schwartz Criterion (SC). The ADF Test is given in the following regression equation.
t -1 0 t 1 2 t
i
t 1
t
i 1
(1)
The ADF test for the existence of unit root of Yt, is in the logarithm format for the variables Spot and Futures at time t. The variable ∆Yt-1 expresses the first differences with p lags and the εt is the variable that adjusts the errors of autocorrelations. The null and the alternative hypothesis for the existence of unit root in variable Yt is: H0 : δ2 = 0 Hε : δ2 < 0 The results of the ADF Test for the variables Spot and Futures for the alternative models of constant and constant with trend for their logarithmic levels and their differences are presented in Table-1. The results for the selected products indicate that the series is non- stationary when the variables are defined at levels with constant. While, the first differencing of series removes the non- stationary components in all cases (constant and constant with trend) and the null hypothesis of non- stationarity is clearly rejected at the 5%
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significance level. This confirms that the spot and futures are integrated in order one and reflects the existence of long run relationship between them. Thus, the robustness of the result guides us to treat the variables as I (1) to proceed with Co-integration analysis.
The pioneering work on co-integration analysis was done by Engle and Granger (1987). After this, the researchers like Stock and Watson (1988) and Johansen (1988) tried to extend the work. This study tests the presence of co-integrating relationship between spot market prices and futures market prices using the Johansen and Juselius (1990) Maximum Likelihood Method within a Vector Auto Regressive (VAR) framework. The Johansen (1988) model estimated to capture the co-integration between the variable using the following equation: Zt = ∏ 1 Z t-1 + ∏ 2 Z t-2 + Λ + ∏k Z t-k + deterministic components + ε1t The notation Zt denote a p x 1 vector of variables which are not integrated in order higher than one, then Z t can be formulated as a VAR model of order k.
Where ε1t is independently and normally distributed and ∏ 1, ∏ 2, Λ, ∏t-k are coefficient matrices. The model can be reparameterized to yield a Vector Correction Model as: ΔΖt = Γ1 ΔΖ t- 1 + Λ + Γ k-1 ΔZ t-(k-1) + Γ Z t-1 + deterministic components + ε2t Where ε2t, is independently and normally distributed and Γ1, Γ2 , Λ,Γ1-(k-1) and Γ are coefficient matrices. Let r = rank (Γ), then if 0 < r < p the matrix Γ can be portioned into p x r matrices α and β such that ∏ = Γβ’ and β’ is I (0) (Johansen and Juselius,1990). r is the number of co- integrating relationships and β in each column is the co- integrating vector. In this study we used Johansen (1995) Trace statistics and Maximal Eigen value Tests to determine the number of co-integrating relationships between the variables in the bi-variate model. After detecting the long-run relationship between two variables or equilibrium it is also required to understand the existence of short-run relationship between the variables in
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the given data series. This problem can be better resolved by the Error Correction Model (ECM).
The Error Correction Model detects the Long run co-integration relationship in the following form:
t 0 1 t et 1 t
(2)
This model will include both long run and short run information where β1 is the impact multiplier (the short run effect) and π is the feed back effect (adjustment effect and shows
number
of
e t 1 t 1 1
2
disequilibrium
t 1 ,
being
corrected).
The
β2
in
the
equation
however includes the long run response. The coefficient of Error
Correction Model includes information about whether the past values of variables affect the current value of the variables under study. The size and statistical significance of the coefficient of the Error Correction Model measures the tendencies of each variable to return to equilibrium. For example π in equation (2) is statistically significant means that yt responds to disequilibrium in relation with exogenous variables. According to Choudry (1995), even if the co-efficient of the lagged changes of the independent variables are not statistically significant, Granger Causality can still exist as long as π is significantly different from zero. The short run dynamics are captured through individual co-efficient of the different terms.
4. Empirical results This section describes the empirical results of the study. The results of ADF test to check the stationarity of the futures prices and spot prices of the selected spices are presented in Table 1. The ADF test indicates that the futures prices and spot prices of chilli, coriander, jeera, pepper and turmeric series are non stationary at levels. While the first differencing of the series are non stationary, they are converted into stationary series by removing the non stationary components in the data series. For constant and constant with trend cases, null
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hypothesis of the series in unit root is summarily rejected at 5% level of significance and it confirmed that the futures and spot prices are integrated in order one. Which means they are made stationary in order one or in the first difference.
Further, we estimate Co-integration test for examining the existence of long run relationship between spot and futures prices for selected spices. This estimate confirmed that the variable under the study are integrated at order one (1st difference) and it suggests to continue with cointegration test. We perform Johansen cointegration test (1988) in the study and its result is presented in Table 2. This test rejects the null hypothesis that the spot and futures prices of selected spices are not co-integrated and clearly depicts the two integrated variables having a long run relationship at 5% level of significance, which is confirmed by the lower critical values than the estimated Max rank values and Trace rank values. Thus the futures and spot price series are serially correlated and hold the long run relationship. For all the spices the results suggests to proceed with vector error correction model (VECM) to further detect the equilibrium of the data series; since, the relationship between spot futures commodities may diverge from equilibrium path in the short run. Therefore, the disequilibrium between short- run and long- run values in the lagged time series would be adjusted over the time by the changes in spot and futures prices due to changes in the market micro and macro structures.
The estimated result of VECM is presented in the Table 3 (i) and 3 (ii). This model takes the null hypothesis in which the errors are co-integrated in short run. The result indicate the short run deviations from the long run equilibrium. In order one (at significant at 5% level), it is confirmed that the spot and futures prices are having long run relationship and the disequilibrium happens in short run for all the spices in the selected period of study. The result also shows that the coefficient of error correction term in commodity futures equation is statistically significant and negative for all the selected prices of spice futures. While, the coefficient of error correction term in selected prices of spot spices is not statistically
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significant except the pepper prices (positively significant with coefficient of 0.0009). this implies that when futures prices and spot prices deviate from the equilibrium, the spot prices will tend to make corrections in the market to restore equilibrium immediately. It means that the spot price seems to drive the futures prices in case of all the spices except pepper. Thus, in the case of spice commodities, spot leads the futures and generally indicating that all the informations relating to commodities first reflect on the spot prices and get transformed into futures.
5. Summary and Conclusion We examined whether spot and futures markets for spices have established a long run equilibrium relationship in terms of pricing behaviour, and whether the market information flow systematically from spot to futures or vice versa. In this study we used daily prices of spot and futures of selected spices viz Chilli, Coriander, Jeera, Pepper and Turmeric are obtained from the NCDEX website from January 1, 2008 to December 31, 2010. Initially we check stationarity of the data series and proceeded to find the existence long-run relationship and the dynamic relationship in short-run between spot and futures market for the study period by employing co- integration test and VECM test respectively. We found the evidence of a stable long-run relationship between spot and futures market for spice commodities and obtain equilibrium immediately whenever any deviations between the markets exist. This infers that spot market driving the futures market by systematically incorporating the market information and also infers that both the markets have gained sufficient trading experience through long-run equilibrium relationship. If the same results is the common phenomena for the other commodities in these markets then it would imply that both the markets potentially can form prices and design the unique institutional structure.
Since, the spot and futures market for spices exhibit an identifiable long run equilibrium relationship, hedging opportunities using the spices futures contract appears limited. Therefore, the price bases for spices behave in a predictable and stationary way. It is
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also clear that trading price risk for basis risk in the spices market would results in an overall risk reducing exercise. As a result, the spot market prices will drive the futures market in most of the spices. Thus, there is a scope of future study based on the relationship between the two markets.
References Baharumshah A. Z and Habibullah M. S (1994), “Price efficiency in pepper markets in Malaysia: A co-integration analysis”, Indian Journal of Agricultural Economics, 49 (2), 205216. Bessembinder H and Seguin P.J (1992), “Futures-Trading Activity and Stock Price Volatility”, Journal of Finance, Vol. 47, pp. 2015-2034. Bessler D and Covey T (1991), “Co-integration: Some results on U.S Cattle prices”, The Journal of Futures Market, Vol. 11, pp. 461-474. Brajesh K (2009), “Effect of Futures Trading on Spot Market Volatility: Evidence from Indian Commodity Derivatives Markets”, Working Paper Series 1364231, Social Science Research Network, IIM Ahmedabad. Brorsen B.W, Ollerman C.M and Farris P.L (1989), “The Live cattle futures market and daily cash price movements”, The Journal of Futures market, Vol. 9, pp. 273-282. Chopra A and Bessler D. A (2005), “Price Discovery in the Black Pepper Market in Kerala”, India, Indian Economic Review, Vol. XXXX, No. (1), pp. 1-21. Choudry T (1995), “Long-run money demand function in argentina during 1935-1962: Evidence from cointegration and error correction models”, Applied Economics, Vol. 27, pp. 661-667. Dewbre J.H (1981), “Interrelationship between spot and futures market: Some Implications of rational expectation”, American Journal of Agricultural Economics, pp. 926-933. Engle R.F and Granger C.W.J (1987), “Cointegration and error correction: representation, estimation and testing”, Econometrica, Vol. 55, pp. 251-76. Fortenbery T.R and Zapata H.O (1993), “An Examination of Cointegration between futures and local grain markets”, The journal of Futures markets, Vol. 13, pp. 921-932. Garbade K.D and Silber W.L (1983), “Price movements and price discovery in futures and cash market”, Review of economics and statistics, Vol. 65, pp. 289-297. Garcia P, Leuthold R.M, Fortenbery T.R and Sarassoro G.F (1988), “Pricing Efficiency in the live cattle futures market”, American journal of agricultural economics, Vol. 70, pp. 162169. Johansen S (1988), “Statistical Analysis of Cointegration Vectors,” Journal of Economic Dynamics and Control, Vol. 12 (2–3), pp. 231–254.
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Johansen S (1995), “Likelihood-Based Inference in Cointegrated Vector Autoregressive Models”, New York: Oxford University Press. Johansen S and Juselius K (1990), “Maximum likelihood estimation and inference on cointegration with application to the demand of money”, Oxford Bulletin of Economics and Statistics, Vol. 52, pp. 169-210. Koontz S.R, Garcia P and Hudson M.A (1990), “Dominanat-satellite relationships between live cattle cash and futures market”, The Journal of Futures Market, Vol. 10, pp. 123-136. Leuthold R. M (1988), “An analysis of the futures-cash price basis for live beef cattle”, North Central Journal of Agricultural Economics, Vol. 1, pp. 47-52. Ollerman C.O and Farris P. L (1985), “Futures or cash: which market leads live beef cattle process”, The Journal of Futures Market, Vol. 5, pp. 529-538. Sinharoy S and Nair S. R (1994), “International trade and pepper price variations : A cointegration approach”, Indian Journal of Agricultural Economics, Vol. 49 (3), pp. 417- 425. Stock H.J and Watson W (1988), “Variable trends in economic time-series”, Journal of Economic Perspectives, Vol. 2 (3), pp. 147-174. Zapata H O, Fortenbery T.R and Armstrong D (2005), “Price discovery in the world sugar futures and cash markets: implications for the Dominican Republic”, Staff Paper 469, Agricultural and Applied Economics University of Wisconsin Madison.
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Table - 1 Augmented Dicky Fuller Test Results Commodity Futures Difference Product Chilli
Coriander
Jeera
Pepper
Turmeric
C
C&T
-22.34
-22.33
(-2.86)*
(-3.41)*
-29.75
-29.74
(-2.86)*
(-3.41)*
-22.00
-22.00
(-2.86)*
(-3.41)*
-33.79
-33.79
(-2.86)*
(-3.41)*
-26.99
-26.98
(-2.86)*
(-3.41)*
Commodities Spot Difference Product Chilli
Coriander
Jeera
Pepper
Turmeric
Note:
C
C&T
-54.47
-54.46
(-2.86)*
(-3.41)*
-47.31
-47.31
(-2.86)*
(-3.41)*
-52.97
-52.97
(-2.86)*
(-3.41)*
-71.44
-71.44
(-2.86)*
(-3.41)*
-49.49
-49.49
(-2.86)*
(-3.41)*
a. C is the constant, C&T is Constant and Trend b. Figures in the parenthesis are T-Statistics and * denotes significant at 5% level which is the rejection of the null hypothesis of non-stationary. Acritical value at 5% level of significance for the constant is -2.86 and and trend is -3.41
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Table - 2 Johansen Cointegration Test between Commodities Futures and Spot Product
Chilli
Coriander
Jeera
Pepper
Turmeric
Ho
Ha
λMax rank
λMax CV
r=0
r=1
491.42*
12.32
373.93*
11.22
r≤1
r=2
117.49*
4.12
117.49*
4.12
r=0
r=1
343.18*
12.32
254.55*
11.22
r≤1
r=2
88.62*
4.12
88.62*
4.12
r=0
r=1
612.44*
12.32
437.20*
11.22
r≤1
r=2
175.24*
4.12
175.24*
4.12
r=0
r=1
968.99*
12.32
700.98*
11.22
r≤1
r=2
268.00*
4.12
268.00*
4.12
r=0
r=1
612.06*
12.32
431.30*
11.22
r≤1
r=2
180.75*
4.12
180.75*
4.12
Note: r is the co-integrating vector. CV is the critical value at 5% level. *denotes rejection of null hypothesis at 5% level of significance.
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λTrace rank
λTrace CV
Table- 3 (i) Vector Error Correction Model Commodity Futures Products Variables
Chilli
Coriander
Jeera
Pepper
Turmeric
-0.46
-0.33
-0.88
-0.55
-1.01
(-19.27)*
(-13.74)*
(-28.76)*
(-29.24)*
(-29.38)*
-0.37
-0.45
-0.07
-0.31
-0.02
(-15.97)*
(-17.82)*
(-3.03)*
(-18.00)*
(-1.008)
-0.16
-0.22
-0.014
-0.15
-0.025
(-8.75)*
(-10.41)*
(-0.75)
(-11.46)*
(-1.29)
1.95
1.90
0.26
2.38
2.01
(1.90)
(1.73)
(0.35)
(3.70)*
(3.58)*
0.26
0.88
0.72
4.59
1.12
(0.25)
(0.80)
(0.96)
(7.14)*
(1.99)*
2.51
-3.01
9.11
2.51
1.98
(0.00099)
(-0.05)
(0.001)
(0.03)
(0.109)
R2
0.41
0.39
0.48
0.44
0.52
Adj R2
0.41
0.39
0.48
0.44
0.52
S.E Equation
0.001
0.002
0.0004
0.0005
0.0009
F-Statistics
408.72
276.23
534.71
842.66
581.46
14698.45
9674.48
18036.97
32452.62
14696.18
CointEql
Futures (-1)
Futures (-2)
Spot (-1)
Spot (-2)
C
Log Likelihood
Note: Figures in parenthesis are T-statistics * denotes the rejection of null hypothesis 5% level of significance.
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Table- 3 (ii) Vector Error Correction Model Commodities Spot Products Variables
Chilli
Coriander
Jeera
Pepper
Turmeric
-0.0001
0.0002
-0.0002
0.0009
0.001
(-0.24)
(0.46)
(-0.33)
(2.37)*
(1.06)
0.0002
0.0002
0.0009
-0.0005
-0.0005
(0.62)
(0.54)
(1.40)
(-1.34)
(-0.59)
0.0002
0.0005
0.0009
-0.0003
-0.001
(0.61)
(1.20)
(1.99)*
(-1.16)
(-2.11)*
-0.02
-0.03
0.01
0.02
0.03
(-1.24)
(-1.70)
(0.68)
(1.52)
(2.01)*
0.004
-0.02
-0.03
0.01
0.01
(0.25)
(-1.29)
(-1.92)
(0.87)
(0.55)
-1.75
8.07
-6.78
-4.45
-8.61
(-0.37)
(0.78)
(-0.31)
(-0.28)
(-1.37)
R2
0.0007
0.003
0.003
0.001
0.004
Adj R2
-0.0009
0.0008
0.001
0.0007
0.002
S.E Equation
2.48
4.67
1.16
1.15
3.21
F-Statistics
0.43
1.36
1.93
1.80
2.30
26015.21
17828.61
28669.01
52892.99
23577.81
CointEql
Futures (-1)
Futures (-2)
Spot (-1)
Spot (-2)
C
Log Likelihood
Note: Figures in parenthesis are t-statistics * denotes the rejection of null hypothesis 5% level of significance.
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