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\title{Co-Integration and Causality between Equity and Commodity Futures: Implications for Portfolio Diversification}
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\begin{document}

             \author[1]{Y.  Bansal}

             \author[2]{S.  Kumar}

             \author[3]{P.  Verma}

             \affil[1]{  Thapar University, Patiala}

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\date{\small \em Received: 10 December 2013 Accepted: 5 January 2014 Published: 15 January 2014}

\maketitle


\begin{abstract}
        


This paper examines the long term statistical relationship of commodity future prices with equity prices using various tools including Augmented Dickey Fuller Test, Vector Auto Regression and Johansen?s Cointegration technique. The paper also investigates the short term dynamics of prices by testing for the existence and direction of inter-temporal Granger-causality between the indices. The analysis shows that there is no long term cointegration between the commodity future prices and equity prices therefore, an investor with long term investment horizon would benefit by including commodity futures to a traditional portfolio.

\end{abstract}


\keywords{causality, cointegration, commodity futures, equity, portfolio diversification.}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
trategic asset allocation is one of the most important set of decisions for a portfolio manager. Asset allocation is the amount of exposure (positive or negative) to a certain class of asset in the portfolio. Before doing the asset allocation the first step is to decide on the types of asset to be included in the portfolio. The theory says that an asset that has low or negative correlation with other assets existing in the portfolio should be included. But correlation being a short term estimate; the key issue for an investor is how to consider the long term movements between the asset prices \hyperref[b11]{(Kasa, 1992)}. In standard risk -return models, any long term trends in the data is removed by differencing the prices of the assets. Although these trends are implicit in the returns data, but then these risk-return models does not include the decisions based on long term common trends in the price data \hyperref[b0]{(Alexander, 1999)}. To incorporate this long term impact in portfolio construction, the paper uses cointegration technique developed by  {\ref Johansen (1988} {\ref Johansen ( , 1991} {\ref Johansen ( , 1992b) )} and \hyperref[b16]{Johansen and Juselius (1990)} to test the long term comovement of commodity future prices with equity prices.\par
Correlation and cointegration although related, are two different concepts. Correlation having a short term implication reflects comovements that are liable to instabilities over time. So, correlation based portfolio strategies require frequent re-balancing. In contrast, cointegration measures long run co-movements in prices that may occur even through periods when static correlations appear low. The high correlation of returns does not essentially imply high cointegration in the prices \hyperref[b0]{(Alexander, 1999)}. Thus, diversification decisions based on cointegrated assets may be more effective in the long term. By including the assets that are not cointegrated would result in a more effective portfolio that does not require frequent re-balancing of the portfolio. While constructing a portfolio, high correlation among assets cannot be taken as a sufficient measure for long term diversification benefits, there is a need to enhance the standard risk-return modeling methodologies to take account of common long term trends among the asset prices. To complement this, the paper extends the traditional models by including a preliminary stage in which the asset prices are analyzed, and then augments the correlation analysis to include both short term and long term dynamics.\par
The aim of the paper is to estimate the long and short run relation of asset prices applying the principle of cointegration, vector error correction approach and granger causality to time series analysis. ) and these studies concluded that the return of an equal weight commodity futures portfolio was comparable to a stock portfolio. Following, \hyperref[b2]{Ankrim \& Hensel (1993)},  {\ref Lummer \& Seigel (1993)}, \hyperref[b14]{Satyanarayan \& Varangis (1996)}, have shown that commodity futures provide a good diversification to the portfolio of equity \& bond. \hyperref[b3]{Anson (1999)} found out that commodity futures can prove to be a valuable asset for risk-averse investor, but the amount of investment in commodity futures depends upon certain factors like utility functions, level of risk tolerance \& portfolio composition. \hyperref[b15]{Simon (2013)} has modeled the conditional relationships between the Goldman Sachs Total Return Commodity Index and Sub-Indexes and the S\&P 500 
\section[{II.}]{II.} 
\section[{Review of Literature}]{Review of Literature} 
\section[{S}]{S} 
\section[{Global Journal of Management and Business Research}]{Global Journal of Management and Business Research}\par
Volume XIV Issue V Version I Year ( ) index using the bivariate GARCH framework and the results indicate that while the diversification benefits of commodities have diminished over the sample period, the estimated conditional correlations remain low enough for commodities to provide meaningful diversification benefits to equity investors. \hyperref[b6]{Buyuksahin et al.(2010)} empirically investigated the relationship between ordinary, as well as extreme, returns on passive investments in commodity and equity markets using Johansen's Cointegration technique and identified that commodities provide substantial diversification to opportunities to passive equity investors.\par
Perhaps one of the more important contributions to the literature is that of \hyperref[b10]{Gorton and Rouwenhorst (2006)}. They construct their own commodity futures index for the period 1959 -2004 and examine how this compares with returns from stock and bond indices. They concluded that the average annualized return on the collateralized futures index was very similar to that on the S\&P 500 over the whole period and both assets outperformed corporate bonds. They also found that the relative performance varied over time and that "the diversification benefits of commodities work well when they are needed most". Hence, one conclusion reached was that commodity futures are useful in creating diversified portfolios with respect to the idiosyncratic component of returns.\par
Becker and Finnerty (2000) stated, with reference to the period from 1970 to 1990, that the risk and return of a portfolio composed of stocks and bonds had increased with the inclusion of commodities in asset allocation. They specify that this increase had been more valid in the 1970s compared to the following decade, due to high inflation in the first part of the study period. \hyperref[b5]{Bodie and Rosansky (1980)} analyzed the returns of an equal weight commodity futures portfolio, and showed that the results obtained with medium and long-term portfolios were comparable to stock portfolios. \hyperref[b11]{Kasa (1992)} is one of the first ones to use the multivariate cointegration method proposed by \hyperref[b16]{Johansen and Juselius (1990)} to analyze co-movements in stock markets and found a common stochastic trend for the period 1974 -1990 between the U.S., Japan, England, Germany and Canada. \hyperref[b1]{Arshanapalli and Doukas (1993)} had used cointegration techniques to test the linkage and dynamic interactions among stock market movements and reported that The U.S. stock market has a considerable influence on the French, German and English markets in the post-crash period. On the same line of research, \hyperref[b13]{Meric and Meric (1997)} analyzed changes in the co-movements of the 12 largest equity markets in Europe and the U.S. after the 1987 market crash and found that the benefits of international diversification decreased considerably in these developed markets after the crash. \hyperref[b17]{Wong et al. (2005)} investigated the long run equilibrium relationship and short run dynamics between the Indian market and 3 developed countries (U.S., U.K. and Japan) for the period 1991-2003 and found that the Indian market follows these markets and is therefore integrated with them in the long run.\par
In essence, we are not interested in finding or explaining relationships between economies, but we are rather trying to find assets that move on their own in the long term, so that they can increase the portfolio performance. 
\section[{III.}]{III.} 
\section[{Research Methodology}]{Research Methodology}\par
The paper provides detailed empirical evidence on the extent to which the prices of commodity futures and equity market move in sync so that the investor is able to take better investment decisions. We take the perspective of a passive investor when analyzing the relationship between commodity future and equity investments. Modern portfolio theory suggests that the relevant information matrix for such an investor includes the expected asset returns, the variability of these returns, as well as cross-asset correlations (Buyuksahin et al., 2010).\par
Additionally, leads or lags in the time series make correlations almost useless. For example, if we lag by one or two days some of the daily time series, that we will be using in the empirical part of the paper, the effect on the correlation between the series will be significant, the correlation might even turn from positive to negative. On the other side, the effect on the common long term relationship between the series will be minimal. Cointegration allows for short term divergence between two different time series, meaning that in a day to day basis, the series does not necessarily have to go up or down at the same time, one might go up while the other goes down, thus there is no need for the two series to move in daily synchrony at all. In the long run, however the two price series cannot wander off in opposite directions for very long without coming back to their long term equilibrium.\par
The distinction between stationary and non stationary time series is extremely important because stationarity is a precondition to make statistical inferences. If the mean or variance of our time series change with time, then it is impossible to generalize results from regressions made for a specific period of time into a different period of time. So, it is necessary to identify if our time series is stationary or not before any statistical inference can be made.\par
If we perform regression analysis on time series where the dependent, independent, or both variables have a unit root process, then the results will have no economic significance, in particular, the estimates will 2 Global Journal of Management and Business Research C Volume XIV Issue V Version I Year ( ) be biased and hypothesis tests will be invalid. This is the problem of spurious regression which was first reported back in 1926 by Yule. In order to confirm the (stationary) nature of the series, we perform the Augmented Dickey-Fuller test under the unit root test to identify whether or not the series is stationary. To analyze long-term cointegration, we use the daily settlement prices for all the indices.\par
Our study of testing whether there is a long-run statistical relationship between commodity futures and equity markets depend on the methods of Johansen's cointegration analysis. The idea for the analysis is that if two series each follow upward trend, then, in general, they will diverge in the long run. Our approach will comprise of four parts: (1) testing for a unit root in each price indices, (2) testing for the number of cointegrating vectors in the systems of asset prices, provided the null hypothesis of a unit root for every price index is not rejected, (3) testing the vector autoregression between the assets, and (4) testing the causality effect among the two assets. where ?0 is constant, t is a deterministic trend, and enough lagged differences (p) are included to ensure that the error term becomes white noise. If the autoregressive representation of Yt contains a unit root, the t-ratio for a1 should be consistent with the hypothesis, a1=0. However, the ADF test loses power for sufficiently large values of p. 
\section[{Cointegration Test: To investigate the existence of a}]{Cointegration Test: To investigate the existence of a}\par
long-term relationship between real and financial variables, we explore existence of any significant long-run relationships among the variables in our model. If the real and financial variables are cointegrated with one another, then this will provide statistical evidence for the existence of a long-run relationship. Though, a set of economic series are not stationary, there may exist some linear combination of the variable which exhibit a dynamic equilibrium in the long run \hyperref[b8]{(Engle and Granger 1987)}. We employ the maximum-likelihood test procedure established by Johansen and Juselius (1990) and  {\ref Johansen (1991)}. Specifically, if Yt is a vector of n stochastic variables, then there exists a p-lag vector auto regression with Gaussian errors of the following form: where Î?"1, .. ... Î?"p-1 and ? are coefficient matrices, zt is a vector of white noise process and k contains all deterministic elements.\par
The focal point of conducting Johansen's cointegration tests is to determine the rank (r) of matrix Î?" k. In the present application, there are three possible outcomes. First, it can be of full rank, (r = n), which would imply that the variables are stationary processes, which would contradict the earlier finding of nonstationarity. Second, the rank of k can be zero (r = 0), indicating that there is no long-run relationship among the variables. In instances when Î?" k is of either full rank or zero rank, it will be appropriate to estimate the model in either levels or first differences, respectively. Finally, in the intermediate case when there are at most r cointegrating vectors 0 ? r ? n (i.e., reduced rank), it suggests that there are (n -r) common stochastic trends.\par
The number of lags used in the vector autoregression is chosen based on the evidence provided by Akaike's Information Criterion. The cointegration procedure yields two likelihood ratio test statistics, referred to as the maximum eigenvalue (?-max) test and the trace test, which will help determine which of the possibilities is supported by the data. 3. VAR and Granger Causality: If the variables are found to be not cointegrated in long run, then the next step is to employ vector autoregression followed by the granger causality. The vector auto regression (VAR) is commonly used for forecasting systems of interrelated time series and for analyzing the dynamic impact of random disturbances on the system of variables. The optimum lag length is identified using Akaike Information Criteria (AIC).\par
The VAR approach sidesteps the need for structural modelling by treating every endogenous variable in the system as a function of the lagged values of all of the endogenous variables in the system. Generalizing the discussion about dynamic relationships to these two interrelated variables yields a system of equations: 
\section[{??}]{??}\par
The equations describe a system in which each variable is a function of its own lag, and the lag of the other variable in the system. 
\section[{IV.}]{IV.} 
\section[{Data \& Empirical Analysis}]{Data \& Empirical Analysis}\par
The daily prices for asset classes from Indian Capital market, viz., Equity (S\&P CNX Nifty), and Commodity futures (MCX COMDEX) are examined for the period June 2005 to December 2011. Daily data was preferred because any transmission mechanism between the stock markets in the ECM (Error Correction Model) is most likely to occur within few days. Monthly data was our backup option. A drawback in using daily data is that we will most likely face Autoregressive Conditional heteroskedastic (ARCH) residuals -the variance of the residuals in one period is dependent on their variance in the previous period. It is possible that monthly data will correct or eliminate the ARCH residuals; therefore, we performed cointegration analysis using monthly data, however, the ARCH processes of the residuals were not eliminatedalthough decreased slightly for some series. The estimation results from monthly data were generally the same as the results obtained from daily data. 
\section[{a) Correlation Test}]{a) Correlation Test}\par
The short term estimation of the relationship between the variables can be studied using the crosscorrelation coefficients (as shown in Table  {\ref 1}). For the asset to be included in a portfolio, it should have low or negative correlation with other assets existing in the portfolio.\par
The MCX COMDEX also demonstrates a significant low correlation with the equity during the analyzed period. Thus, commodity futures have the potential to reduce risk in a portfolio of stocks.  
\section[{b) Unit Root Tests}]{b) Unit Root Tests}\par
To analyse the long term relation among the variables we use Johansen Cointegration Analysis. But, before running this analysis the data is checked for stationarity. As discussed in the above section, Figure \hyperref[fig_0]{1} depicts the line graph for Equity and Commodity Futures at level, showing that the two indices are not stationary. Figure \hyperref[fig_3]{2}   Further, the study tests the stationarity by running Augmented Dickey Fuller test (ADF) on log of price indices. The optimal lag length is determined using minimum Akaike Information Criteria (AIC). The null hypothesis in case of ADF test is that the series under reference has a unit root, which implies that the series are not stationary in nature. A probability value of below 0.05 does not accept the null hypothesis at 5\% level of significance and implies that the series under reference are stationary at 5\% level of significance.\par
The probability value of less than 0.05 for log of commodity futures D (CF) and log of Equity, D(Equity) as presented in Table \hyperref[tab_3]{2A} and 2B, implying that the null hypothesis is not accepted and the variable does not have a unit-root, which confirms that the series is stationary meaning that both the indices are integrated of the order 1, I(1). The stationarity is verified at all the three conditions, i.e.,no intercept -no trend, intercept but no trend, no intercept but trend. Since the series are observed to be stationary in nature after the first     {\ref (15.495}) is more than the trace statistic(13.739), therefore we accept the null hypothesis that there is no cointegration equation among the variables. On the similar lines, Max-eigen value also indicates no cointegration by accepting the null hypothesis that there is zero cointegration equations among the variables, with p-value 0.3823 more than 0.05 and critical value  {\ref (14.264}) is more than the max eigen statistics (7.964). Therefore, both the tests indicate that there is no cointegration among equity and commodity futures. 
\section[{d) Vector Autoregression}]{d) Vector Autoregression}\par
Since the above results show that there is no cointegration among the two variables, therefore we run the vector autoregression among CF and Equity to identify the cause and effect relationship. The results are shown in Table \hyperref[tab_7]{4A and 4B}.    {\ref 10}), the coefficients C6 and C7 are significant with 0.0012 and 0.0009 being less than 0.05, thereby meaning that CF does cause Equity. These results confine to the results given by cointegration analysis. e) Granger Causality Test Further, we run the Granger Causality among the variables, to identify the direction of causality in the variables. Results of Granger Causality test are reported in Table \hyperref[tab_8]{5}. We test the null hypothesis that one series does not Granger Cause another series at the conventional levels of significance. As in the below table, p-value of 0.1565 > 0.05, accepts the null hypothesis that equity doesnot granger cause commodity future. For the next hypothesis, we accept the alternate hypothesis that commodity futures granger cause equity as p-value of 0.0029 <0.05. We can say that there is a unidirectional relationship between commodity futures-equity. So for the given data it is identified that there is no long run relation between commodity future prices and equity prices and that there is a unidirectional relation between CF and Equity.\par
V. 
\section[{Concluding Remarks}]{Concluding Remarks}\par
The paper has undertaken an examination of cause and effect between equity and commodity futures so that commodity futures could be considered as a diversification tool for investors to earn an extra return by using the data across 2005-2011. This is done by evaluating the short and long run relationship between the two variables. Since the introduction of commodity futures in India is of late  {\ref (2003)}, therefore the data available for analysis is not very large. The analysis shows that there is a very low correlation among the two variables and no cointegration between equity and commodity futures results in no long term relation between the two variables meaning that the two series do not share a common stochastic drift. So if a passive investor includes commodity futures to the traditional portfolio mix of equity and bond, he would be able to \begin{figure}[htbp]
\noindent\textbf{1}\includegraphics[]{image-2.png}
\caption{\label{fig_0}1 .}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-3.png}
\caption{\label{fig_1})}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{21}\includegraphics[]{image-4.png}
\caption{\label{fig_2}2 GlobalFigure 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2}\includegraphics[]{image-5.png}
\caption{\label{fig_3}Figure 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{}\includegraphics[]{image-6.png}
\caption{\label{fig_4}}\end{figure}
  \begin{figure}[htbp]
\noindent\textbf{I} \par 
\begin{longtable}{P{0.25396341463414634\textwidth}P{0.23323170731707318\textwidth}P{0.16067073170731708\textwidth}P{0.010365853658536586\textwidth}P{0.10884146341463415\textwidth}P{0.08292682926829269\textwidth}}
\tabcellsep S\&P CNX\tabcellsep NSE\tabcellsep G-\tabcellsep \\
Asset Class\tabcellsep Nifty\tabcellsep Sec\tabcellsep \tabcellsep NSE TB\tabcellsep MCXCOMDEX\\
S\&P CNX Nifty\tabcellsep 1.00000\tabcellsep \tabcellsep \tabcellsep \\
NSE G-Sec\tabcellsep -0.01138\tabcellsep 1.00000\tabcellsep \tabcellsep \\
NSE TB\tabcellsep -0.18278\tabcellsep -0.02050\tabcellsep \tabcellsep 1.00000\\
MCXCOMDEX\tabcellsep 0.36436**\tabcellsep \multicolumn{2}{l}{-0.35956**}\tabcellsep -0.12306\tabcellsep 1.00000\end{longtable} \par
  {\small\itshape [Note: ** denotes significance at the 1\% level(2-tailed)    ]} 
\caption{\label{tab_1}Table I :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2A} \par 
\begin{longtable}{}
\end{longtable} \par
 
\caption{\label{tab_3}Table 2A :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2B} \par 
\begin{longtable}{P{0.5707900207900207\textwidth}P{0.04948024948024948\textwidth}P{0.20852390852390854\textwidth}P{0.021205821205821207\textwidth}}
\multicolumn{3}{l}{Null Hypothesis: D(EQUITY) has a unit root}\\
Exogenous: Constant\tabcellsep \tabcellsep \\
\multicolumn{3}{l}{Lag Length: 0 (Automatic -based on SIC, maxlag=23)}\\
\tabcellsep \tabcellsep t-Statistic\tabcellsep Prob.*\\
\multicolumn{2}{l}{Augmented Dickey-Fuller test statistic}\tabcellsep -36.92791\tabcellsep 0.0000\\
Test critical values:\tabcellsep 1\% level\tabcellsep -3.434307\\
\tabcellsep 5\% level\tabcellsep -2.863175\\
\tabcellsep 10\% level\tabcellsep -2.567688\\
\multicolumn{2}{l}{*MacKinnon (1996) one-sided p-values.}\tabcellsep \\
c) Cointegration Test\tabcellsep \tabcellsep \multicolumn{2}{l}{of cointegrating relations, r. The results are shown in}\\
\multicolumn{2}{l}{We applied Johansen and Juselius (1990)}\tabcellsep Table 3A and 3B.\\
\multicolumn{2}{l}{multivariate cointegration tests to determine the number}\tabcellsep \end{longtable} \par
 
\caption{\label{tab_4}Table 2B :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3A} \par 
\begin{longtable}{P{0.06707031249999999\textwidth}P{0.6939453125\textwidth}P{0.033203125\textwidth}P{0.02125\textwidth}P{0.03453125\textwidth}}
\tabcellsep \multicolumn{2}{l}{1 Cointegrating Equation(s):}\tabcellsep Log likelihood\tabcellsep -16563.05\\
\tabcellsep \multicolumn{3}{l}{Normalized cointegrating coefficients (standard error in parentheses)}\\
\tabcellsep CF\tabcellsep EQUITY\\
\tabcellsep 1.000000\tabcellsep -1.178339\\
\tabcellsep \tabcellsep (0.30654)\\
2014\tabcellsep \tabcellsep \\
Year\tabcellsep \tabcellsep \\
2 40\tabcellsep \tabcellsep \\
( ) ( ) Global Journal of Management and Business Research C Volume XIV Issue V Version I\tabcellsep \multicolumn{3}{l}{Series: CF EQUITY Lags interval (in first differences): 1 to 4 Unrestricted Cointegration Rank Test (Trace) Hypothesized Trace No. of CE(s) Eigenvalue Statistic None 0.005067 13.73898 At most 1 * 0.003676 5.774479 Trace test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegration Rank Test (Maximum Eigenvalue) 0.05 Critical Value 15.49471 3.841466 Hypothesized Max-Eigen 0.05 No. of CE(s) Eigenvalue Statistic Critical Value None 0.005067 7.964500 14.26460 At most 1 * 0.003676 5.774479 3.841466 Max-eigenvalue test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I): CF EQUITY -0.001071 0.001262}\tabcellsep Prob.** 0.0904 0.0163 Prob.** 0.3823 0.0163\\
\tabcellsep 0.002539\tabcellsep -0.000612\\
\tabcellsep \multicolumn{3}{l}{Unrestricted Adjustment Coefficients (alpha):}\\
\tabcellsep D(CF)\tabcellsep 1.569698\tabcellsep -1.278129\\
\tabcellsep D(EQUITY)\tabcellsep -3.062121\tabcellsep -3.749438\end{longtable} \par
 
\caption{\label{tab_5}Table 3A :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3B} \par 
\begin{longtable}{P{0.0804054054054054\textwidth}P{0.12635135135135137\textwidth}P{0.1722972972972973\textwidth}P{0.09763513513513514\textwidth}P{0.11486486486486487\textwidth}P{0.1608108108108108\textwidth}P{0.09763513513513514\textwidth}}
Lag: 2\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
Ho\tabcellsep ?trace\tabcellsep CV (trace,5\%)\tabcellsep Prob.\tabcellsep ?max\tabcellsep CV (max,5\%)\tabcellsep Prob.\\
r=0\tabcellsep 13.73898\tabcellsep 15.49471\tabcellsep 0.0904\tabcellsep 7.964500\tabcellsep 14.26460\tabcellsep 0.3823\\
r?1\tabcellsep 5.774479\tabcellsep 3.841466\tabcellsep 0.0163\tabcellsep 5.774479\tabcellsep 3.841466\tabcellsep 0.0163\end{longtable} \par
 
\caption{\label{tab_6}Table 3B :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4A} \par 
\begin{longtable}{P{0.03639253921153031\textwidth}P{0.6867740568037304\textwidth}P{0.03891479440440865\textwidth}P{0.05440864773208987\textwidth}P{0.03350996184824078\textwidth}}
\tabcellsep \multicolumn{3}{l}{Co-Integration and Causality between Equity and Commodity Futures: Implications for Portfolio}\\
\tabcellsep \multicolumn{2}{l}{Diversification}\tabcellsep \\
\tabcellsep R-squared\tabcellsep 0.997015\tabcellsep 0.995221\\
\tabcellsep Adj. R-squared\tabcellsep 0.997007\tabcellsep 0.995209\\
\tabcellsep Sum sq. resids\tabcellsep 1458921.\tabcellsep 8889045.\\
\tabcellsep S.E. equation\tabcellsep 30.52250\tabcellsep 75.34105\\
\tabcellsep F-statistic\tabcellsep 130765.8\tabcellsep 81530.88\\
\tabcellsep Log likelihood\tabcellsep -7597.055\tabcellsep -9016.550\\
\tabcellsep Akaike AIC\tabcellsep 9.677983\tabcellsep 11.48510\\
\tabcellsep Schwarz SC\tabcellsep 9.695040\tabcellsep 11.50216\\
\tabcellsep Mean dependent\tabcellsep 2529.031\tabcellsep 4367.760\\
\tabcellsep S.D. dependent\tabcellsep 557.9515\tabcellsep 1088.462\\
2014\tabcellsep \multicolumn{2}{l}{Determinant resid covariance (dof adj.) Determinant resid covariance}\tabcellsep 5163154. 5130341.\tabcellsep 2014\\
Year\tabcellsep Log likelihood Akaike information criterion\tabcellsep \tabcellsep -16594.82 21.13917\tabcellsep Year\\
\tabcellsep Schwarz criterion\tabcellsep \tabcellsep 21.17328\\
2 42\tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \multicolumn{3}{l}{Table 4B : OLS for CF and Equity}\\
( ) ( ) Global Journal of Management and Business Research C Volume XIV Issue V Version I\tabcellsep \multicolumn{3}{l}{Vector Autoregression Estimates Standard errors in ( ) \& t-statistics in [ ] CF EQUITY 1.054101 0.204671 (0.02556) (0.06309) [ 41.2393] [ 3.24394] -0.058845 -0.210345 (0.02553) (0.06302) [-2.30501] [-3.33800] EQUITY(-1) CF(-1) CF(-2) 0.007831 1.052822 (0.01031) (0.02545) [ 0.75965] [ 41.3748] EQUITY(-2) -0.005175 -0.054759 (0.01034) Estimation Method: Least Squares Coefficient Std. Error t-Statistic 1.054101 0.025561 41.23928 -0.058845 0.025529 -2.305007 0.007831 0.010309 0.759652 -0.005175 0.010340 -0.500521 1.717696 3.651948 0.470351 0.204671 0.063093 3.243942 -0.210345 0.063015 -3.338005 1.052822 0.025446 41.37481 -0.054759 0.025522 -2.145576 24.03004 9.014388 2.665743 Determinant residual covariance C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) C(10) 5130341. Equation: CF = C(1)*CF(-1) + C(2)*CF(-2) + C(3)*EQUITY(-1) + C(4) *EQUITY(-2) + C(5) Observations: 1571 R-squared 0.997015 Mean dependent var Adjusted R-squared 0.997007 S.D. dependent var S.E. of regression 30.52250 Sum squared resid Durbin-Watson stat 1.996879 Equation: EQUITY = C(6)*CF(-1) + C(7)*CF(-2) + C(8)*EQUITY(-1) + C(9) Prob. 0.0000 0.0212 0.4475 0.6167 0.6381 0.0012 0.0009 0.0000 0.0320 0.0077 2529.031 557.9515 1458921. *EQUITY(-2) + C(10) Observations: 1571 R-squared 0.995221 Mean dependent var 4367.760 Adjusted R-squared 0.995209 S.D. dependent var 1088.462 S.E. of regression 75.34105 Sum squared resid 8889045. (0.02552) [-0.50052] [-2.14558] Durbin-Watson stat 2.002214}\tabcellsep Global Journal of Management and Business Research Volume XIV Issue V Version I ( ) C\\
\tabcellsep C From the table 3B, we can identify that for the\tabcellsep 1.717696\tabcellsep 24.03004\\
\tabcellsep \tabcellsep (3.65195)\tabcellsep (9.01439)\\
\tabcellsep \tabcellsep {}[ 0.47035]\tabcellsep {}[ 2.66574]\end{longtable} \par
 
\caption{\label{tab_7}Table 4A :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.5074626865671641\textwidth}P{0.031716417910447756\textwidth}P{0.044402985074626866\textwidth}P{0.15858208955223882\textwidth}P{0.10783582089552239\textwidth}}
Null Hypothesis:\tabcellsep Lags\tabcellsep Obs\tabcellsep F-Statistic\tabcellsep Prob.\\
EQUITY does not Granger Cause CF\tabcellsep 4\tabcellsep 1569\tabcellsep 1.66108\tabcellsep 0.1565\\
CF does not Granger Cause EQUITY\tabcellsep \tabcellsep \tabcellsep 4.04775\tabcellsep 0.0029\end{longtable} \par
 
\caption{\label{tab_8}Table 5 :}\end{figure}
 			\footnote{© 2014 Global Journals Inc. (US)} 			\footnote{© 2014 Global Journals Inc. (US) 1} 		 		\backmatter  			 \par
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