Correlation dynamics of crude oil with agricultural commodities: A comparison between energy and food crops

Economic Modelling 82 (2019) 453–466

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Economic Modelling journal homepage: www.journals.elsevier.com/economic-modelling

Correlation dynamics of crude oil with agricultural commodities: A comparison between energy and food crops Debdatta Pal a, *, Subrata K. Mitra b a b

Indian Institute of Management Lucknow, India Indian Institute of Management Raipur, India

A R T I C L E I N F O

A B S T R A C T

JEL classification: C32 Q11 Q41

This study elucidates plausible correlation between crude oil and agricultural commodities. We assess whether the conditional correlation of crude oil with energy crops (e.g., corn and soybeans) is different from that of food crops (e.g., oats and wheat). We find a stronger correlation of about 20 percent between returns of crude oil and energy crops. However, the correlation coefficient value for oil-oats and oil-wheat is as low as eight percent. We add to the literature by exploring correlation in a dynamic context using three different GARCH models and found that conditional correlation between crude oil and energy corps is relatively high. In order to reduce risk associated with crude oil price fluctuations, this study also examined hedging possibilities against crude oil by investment in agricultural commodities. Although hedging effectiveness is low with all underlying agricultural commodities, soybeans provide relatively better hedging possibilities compared to other agricultural crops.

Keywords: Conditional correlation Hedging Crude oil Agricultural commodities Multivariate GARCH

1. Introduction Energy and agriculture markets are conventionally interconnected on the supply side as natural gas and diesel contribute a major portion of input costs for agricultural production (Hanson et al., 1993; Du and McPhail, 2012). However, Renewable Fuel Programme under the Energy Policy Act of 2005 that mandated ethanol usage seemed to have connected the crude oil and agricultural commodity prices, more specifically, corn and soybeans, the feed stocks of biofuel, on the demand side as well (Roberts and Schlenker, 2013). The correlation among crude oil and agricultural commodity prices is fairly evident in the scatterplot of crude oil returns and agricultural commodity returns as presented in Fig. 1. Although the difference in the degree of dispersion is not clearly noticeable from the plots, the Pearson correlation measures reveal that returns of crude oil have better correlation properties (r is about 20 percent) with returns of energy crops, i.e., corn and soybeans. Whereas the correlation coefficient value of crude oil with two major food crops, i.e., oats and wheat, is at around eight percent. This static correlation measure gives a clue that returns from energy crops display a stronger relationship with crude oil returns as compared to the food crops. Our study explores the correlation of crude oil with both energy and food crops in a dynamic setting. Investors in both energy and agricultural commodity markets are

interested in commodities that would offer counter-cyclic profits, i.e., when performance of conventional assets, such as treasuries and stocks, is relatively poor (Brooks and Prokopczuk, 2013; Ordu et al., 2017; Aït-Youcef, 2018). Return from investment in energy and agricultural commodities usually carry low correlation with financial assets and hence, has drawn the attention of investors usually in search of newer avenues for the diversification of their portfolios. However, any plausible interdependence among energy and agricultural commodities may enlarge the common stochastic discount factor. Any shock in the energy market is expected to transmit to the feed stocks of bioenergy, then even to food commodity (e.g., oats and wheat) markets if all agricultural commodities are considered under single asset class by the investment community (Tang and Xiong, 2012). In parallel, shocks in macroeconomic environment impacting the business cycle and aggregate demand would transmit to agricultural commodity returns through price shocks in crude oil market (Kilian, 2008). A large number of commodities across energy and agricultural markets have witnessed synchronized business cycle of peak and trough over the last decade (Cabrera and Schulz, 2016). The transmission mechanism suggests that a significant shock in one market (asset) not only enhances the correlations of returns in that market but also spills over to other markets (assets). This spill over is likely to intensify during the crisis periods, with a further ramification of

* Corresponding author. Indian Institute of Management Lucknow, India. E-mail address: [email protected] (D. Pal). https://doi.org/10.1016/j.econmod.2019.05.017 Received 5 October 2018; Received in revised form 2 April 2019; Accepted 15 May 2019 Available online 21 May 2019 0264-9993/© 2019 Elsevier B.V. All rights reserved.

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Fig. 1. Correlation plots: X axis contains return of crude oil, whereas Y axis contains corresponding return of agricultural crops. It can be observed that scatterplot of Oil-Oats and Oil-Wheat are more dispersed compared to plots of Oil-Corn and Oil-Soybeans. Daily data over the period from January 3, 2000 to January 4, 2018.

To fill this gap in the existing literature, the objective of our study is to broaden understanding of the conditional correlation and hedge ratios of crude oil with both energy crops (e.g., corn and soybeans) and food crops (oats and wheat). The justification for exploring the potential of agricultural commodities to hedge against crude oil are as follows: First, as the fundamental causes behind price movement of agricultural commodities (i.e., weather fluctuations or restricted supplies of land) are entirely different from those affecting crude oil prices (i.e., augmented economic activity or supply shock as suggested by Kilian, 2009), there lies increasing scope to hedge crude oil with agricultural commodities. Second, triggered by the U.S. ethanol mandate, corn and soybeans, two major feedstocks for ethanol and biodiesel, have been vulnerable to spiraling price rises along with the excess co-movement of oil prices during the post-crisis period (Roberts and Schlenker, 2013; Serra et al.,

both return and volatility remaining correlated over a longer time period. As correlation emerges as a crucial indicator of financial market integration (Forbes and Rigobon, 2002), for benefiting from the financialization of commodities, one requires a deeper understanding of how energy (more specifically oil) and agricultural commodity markets are correlated. While the available literature has examined volatility spillover across oil and agricultural commodities in some detail (e.g., Du et al., 2011; Serra, 2011; Mensi et al., 2013; Nazlioglu et al., 2013; Abdelradi and Serra, 2015; Ahmadi et al., 2016; de Nicola et al., 2016; Jebabli and Roubaud, 2018), little is known about the conditional correlation and hedging between oil and agricultural commodities. However, accurate estimation of conditional correlations and hedge ratios is of paramount importance for pricing derivatives, optimizing an investment portfolio, and managing risk.

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2. Literature review

2011; Pal and Mitra, 2017a, 2017b, 2018). Third, the rapid expansion of corn and soybeans (i.e., energy crop) cultivation is likely to limit the allocation of land to oats and wheat, two major food crops; thus, such changes are expected to push up the price of both oats and wheat. This close interconnection among the prices of oil and the underlying agricultural commodities makes a strong case for exploring the conditional correlation and hedging potential of energy crops as compared to food crops in more detail. We contribute to the existing literature in the following ways: First, in contrast to the work of Sadorsky (2014) who has examined the conditional correlation of crude oil with only one crop, i.e., wheat, we opt for a wider crop choice, comparing oats and wheat (food crop) with corn and soybeans (energy crops) that are more relevant in the post-ethanol mandate era. Second, from a methodological perspective, empirical investigations to date on the conditional correlation between crude oil and agricultural commodities have employed multivariate generalized autoregressive conditional heteroscedasticity (M-GARCH) models, such as the vector error correction (VEC) model and the Baba-Engle-Kraft-Kroner (BEKK) approach employed by Baba et al. (1990). It should be noted that the large number of free parameters in VEC specification as well as the poorly performing likelihood function in a BEKK framework may lead to estimation challenges for M-GARCH models with more than two variables. In light of these factors, the dynamic conditional correlation (DCC) model proposed by Engle (2002) could overcome the challenges faced by the VEC and BEKK models. However, the prime issues with DCC models are: (a) they do not capture nonlinearity; and (b) their estimation is restricted by a specific model or broader dynamics. To capture the possible nonlinear relationship between oil and agricultural commodities as envisaged by Balcombe and Rapsomanikis (2008), we have used the asymmetric dynamic conditional correlation GARCH (ADCC-GARCH) model proposed by Cappiello et al. (2006). Furthermore, we have addressed the issue of model-specificity by using the generalized orthogonal GARCH (GO-GARCH) approach advanced by van der Weide (2002). The novelty of the GO-GARCH model used in this study lies in its ability to relax the conditions of model-specificity along with its strength in overcoming the estimation challenge on large data sets with multiple variables. Guided by the work of Basher and Sadorsky (2016), we have also computed the optimal hedge ratios between crude oil and agricultural commodity return series by using DCC-GARCH, ADCC-GARCH, and GO-GARCH approaches. We also provide a comparison between the models based on hedging effectiveness which is likely to offer a clearer understanding of how hedge ratios vary across different M-GARCH specifications. Finally, our results suggest that the dynamic conditional correlations of crude oil with both the energy crops (i.e., corn and soybeans) across DCC-, ADCC-, and GO-GARCH models are positive, and the correlation values are 0.20 and 0.25, respectively. However, the dynamic conditional correlations between crude oil and oats oscillated between negative and positive values. Based on the GO-GARCH model, the mean values of the hedge ratios of crude oil with corn and soybeans were estimated to be 0.3656 and 0.4792, respectively. This indicates that a U.S.$1 long position in oil can possibly hedge for either 36 cents in the corn market or 47 cents in the soybeans market. Although hedging effectiveness is low with all underlying agricultural commodities, soybeans provide relatively better hedging possibilities compared to other agricultural crops. Our results are fairly robust for alternate specifications. For investors, our outof-sample hedge ratios between crude oil and underlying agricultural commodities as calculated from a rolling window analysis would be helpful for portfolio optimization. In the following section, we review the previous literature. In section 3, we elaborate on the empirical approach. Section 4 includes an explanation of the data. In section 5, we discuss the results of our analysis, and conclude the study in Section 6.

We understand that a wide array of literature has been devoted to examine the conditional correlation and hedging of crude oil with other asset classes that include stock indices, precious metals, and biofuels as well as agricultural commodities. Since we are exploring the conditional correlation of oil with agricultural commodities in this particular paper, we restrict our review of the literature to those works that deal with volatility transmission, dynamic correlations, and hedging between crude oil and agriculture markets. Du et al. (2011) have explored the volatility linkage between oil to agricultural commodity markets in the U.S. They followed a stochastic volatility approach when considering weekly future prices spreading over November of 1998 to January of 2009. Their results demonstrated evidence of considerable volatility spillover from crude oil to wheat and corn markets. Along similar lines, Serra (2011) examined the possible volatility transmission from oil to the ethanol market in Brazil. She used the BEKK model employed by Baba et al. (1990) for the estimation of weekly price series covering July of 2000 until November of 2009. Her results suggest that there was a strong volatility linkage among the oil, sugar, and ethanol markets. Wu et al. (2011) also examined whether volatility in oil prices spilled over onto the U.S. corn market. They used GARCH specification to estimate weekly data series covering a period from January of 1992 to June of 2009. Their results signified considerable volatility transmission from crude oil to the corn market after 2005. Taking a different approach, Ji and Fan (2012) examined the volatility spillover from crude oil to the crop-Commodity Research Bureau (CRB) index. The CRB is a commodity price index covering commodities from energy, metals, and the agricultural sector. More specifically, the crop-CRB index is a sub-index of the CRB that includes only agricultural crops. Ji and Fan (2012) used a bivariate exponential GARCH model to estimate daily data ranging between July 7, 2006 and June 30, 2010. They ascertained that the volatility transmission from oil to the crop-CRB index was significant enough during both the pre- and post-financial crisis. Their results also show that the dynamic conditional correlation of crude oil with the crop-CRB index oscillates between 0.2 (during September 2007) and 0.6 (during November 2008). Gardebroek and Hernandez (2013) also studied volatility spillover across crude oil, ethanol, and corn markets in the U.S. They used both the BEKK and DCC models in the GARCH framework for estimations based on weekly data ranging from September of 1997 to October of 2011. However, they did not find any evidence of volatility transmission from crude oil or ethanol to the U.S. corn market. Nazlioglu et al. (2013) also assessed the volatility linkage of crude oil with select agricultural commodities (e.g., soybeans, wheat, corn, and sugar) in the U.S. market. The causality to variance test suggested by Hafner and Herwartz (2006) was employed on daily spot prices from January 1, 1986 to March 21, 2011. Interestingly, they uncovered a strong volatility spillover effect from oil to the corn, soybeans, and wheat markets since 2006. Along similar lines, Wu and Li (2013) employed the BEKK model within the multivariate GARCH framework to explore volatility transmission across oil, ethanol, and corn markets in China. The weekly data series ranged from September of 2003 to August of 2012. Their results also revealed significant volatility spillover from crude oil to both the ethanol and corn markets. In the similar line, Mensi et al. (2014) also performed both BEKK-GARCH and DCC-GARCH specifications to explore volatility transmission among crude oil, corn, barley, sorghum, and wheat markets in the U.S. They used daily spot closing prices over the period ranging from January of 2000 to January of 2013. They also found evidence of strong volatility spillover from crude oil to the corn market. In contrast, Sadorsky (2014) also modeled volatility and dynamic conditional correlations between the U.S. oil and wheat markets by employing the vector autoregressive moving average asymmetric GARCH (VARMA-AGARCH) approach proposed by McAleer et al. (2009) along with the DCC-GARCH model. He used daily price data from 2000 to 2012. The mean optimal hedge ratio between crude oil and wheat computed from the VARMA-AGARCH and DCC-GARCH models were 455

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process comprised of two steps. The first step estimates the GARCH parameters, followed by the estimation of the conditional correlations in the second step. In this case:

reported to be 0.63 and 0.56, respectively. Broadening the focus of research in a different way, Ahmadi et al. (2016) examined the impact of various oil price shocks, namely, supply shock, aggregate demand shock, speculative shock, residual shock, and volatility shock, on the price volatility of corn, wheat, soybeans, sugar, and coffee in the U.S. They used the structural vector autoregressive modeling approach on real daily future closing prices covering the time span of April of 1983 to May of 2014. Ultimately, they discovered that the volatility of each underlying commodity varied significantly depending on the causes of the oil shocks. Furthermore, the price volatility of agricultural commodities in response to different oil shocks was found to have increased significantly after 2006. In a recent investigation, Lopez Cabera and Schulz (2016) used both constant and dynamic conditional correlation models within a GARCH framework to assess volatility spillover from energy to the agriculture market in Germany. The weekly data series covered the period between 2003 and 2012. This particular study unraveled a positive long-run correlation between the volatility of oil and biodiesel during the post-financial crisis period. Along similar lines of interest but with a different approach, Teterin et al. (2016) integrated trigonometric functions in a M-GARCH framework with the future prices of crude oil and corn to determine the volatility response as well as the time-varying correlation over a period ranging from June 1, 1993 to March 19, 2015. While the conditional correlation of crude oil and corn was determined to be below 0.25 before 2007, it continued to rise to 0.50 during the period between 2007 and 2010. However, it was found to have dropped since 2010. Al-Maadid et al. (2017) employed a VAR-GARCH (1,1) model to examine the spillover of price volatility from energy to agriculture markets in the U.S. The study period comprising of daily returns ran from January of 2003 to June of 2015. Their results supported strong volatility transmission from oil to ethanol, soybeans, corn, and coffee markets. In another recent investigation, Mensi et al. (2017) employed a wavelet-based capula model on daily volatility indices ranging from July of 2012 to May of 2016 to explore the potential interdependence among crude oil, corn, and wheat. They found that there was varying volatility dependence across scales for both pairs (oil-corn and oil-wheat). A close scrutiny of the existing literature reveals that most of the research is concentrated on exploring volatility spillover from energy to agriculture markets with limited effort being invested in estimating hedge ratios and hedging effectiveness. Therefore, recognizing the increasing financialization of both energy and agricultural commodities and consequently estimating the conditional correlation along with calculating the hedge ratios and hedging effectiveness of crude oil and major U.S. energy and food crops is both timely and relevant.

Gt ¼ A t Y t A t

where At represents a diagonal matrix with standard deviations of a time-varying nature on the diagonal, and Yt denotes the conditional correlation matrix:

ut ¼ G1=2 t vt

(2)

(4)



  1=2 1=2 1=2 1=2 Yt ¼ diag p1;t ; :::pm;t Pt diag p1;t ; :::pm;t

(5)

gi;t ¼ ωi þ αi u2i;t1 þ βi gi;t1

(6)

Furthermore, Pt denotes a symmetric positive definite matrix as follows: Pt ¼ ð1  θ1  θ2 ÞP þ θ1 vt1 v't1 þ θ2 Pt1

(7)

where P denotes the m
m unconditional correlation matrix of vi;t . Both parameters θ1 and θ2 are non-negative and are used for computing dynamic conditional correlations through exponential smoothing. The DCC model is mean reverting until θ1 þ θ2 < 1. The correlation estimator is given by the following equation: p pi;i;t pj;j;t

i;j;t ρi;j;t ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi

(8)

Building on the asymmetric GARCH model suggested by Glosten et al. (1993) and the DCC model of Engle (2002), Cappiello et al. (2006) added an asymmetric term and proposed an asymmetric dynamic conditional correlation (ADCC) model as follows: gi;t ¼ ωi þ αi u2i;t1 þ βi gi;t1 þ γ i u2i;t1 Iðui;t1 Þ

(9)

where Iðui;t1 Þ represents an indicator function which is equal to 1 when ui;t1 < 0 or else 0. Following the given specifications, a positive γ denotes that the negative residuals would raise the variance so that it would be higher than the positive residuals. An asymmetric DCC is modeled to portray that an unanticipated fall in asset prices is likely to augment volatility higher than an unanticipated rise in asset prices of a similar magnitude. For the ADCC framework, Pt is expressed as follows:
  ' Pt ¼ P  E' PE  F ' PF  H ' P H þ E' vt1 v't1 E þ F ' Pt1 F þ H ' v t vt H

This paper employs the dynamic conditional correlation (DCC) model proposed by Engle (2002), the asymmetric dynamic conditional correlation (ADCC) model of Cappiello et al. (2006), and the generalized orthogonal GARCH (GO-GARCH) approach proposed by van der Weide (2002) for estimating volatility and conditional correlations along with the hedge ratios of oil with four major agricultural commodities (e.g., corn, soybeans, oats, and wheat). Assume yt is a m
1 vector for the returns of a set of assets. ARð1Þ represents yt , which is conditional on an information set Lt1 . Therefore, yt could be expressed as follows: (1)


1=2 At ¼ diag g1;t ; :::g1=2 m;t

The representations for g hold for univariate GARCH models, and GARCH (1,1) can be expressed as follows:

3. Empirical approach

yt ¼ μ þ ayt1 þ ut

(3)

(10) where E, F, and H are of the m
m matrices while v t denotes standardized errors with a zero-threshold equal to vt if less than 0 (and 0  otherwise). P and P represent the unconditional matrices of vt and v t , respectively. In the generalized orthogonal GARCH model, van der Weide (2002) stipulated the asset returns yt as follows: yt ¼ nt þ ut

(11)

where nt is the conditional mean, and ut represents the error term. The GO-GARCH model incorporates yt  nt on a set of unobserved exogenous factors as follows:

where Gt represents a m
m conditional covariance matrix of yt and vt denotes a m
1 i.i.d random vector of errors. Estimation of the DCC model proposed by Engle (2002) involves a

ut ¼ Bft

(12)

where B represents a mixing matrix that is disintegrated in an orthogonal 456

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matrix R and an unconditional covariance matrix Π: B ¼ Π1=2 R

well as (14) provides the following: yt ¼ nt þ BG1=2 t vt

(13)

(15)

While the rows of the mixing matrix B denote the assets, the columns include factors which are represented as follows:

The conditional covariance matrix of asset returns, yt  nt , is specified as follows:

ft ¼ G1=2 t vt

Π t ¼ BGt B'

(14)

(16)

The GO-GARCH model is based on two main assumptions: first, B is time invariant, and second, the Gt matrix is diagonal. In the study conducted by van der Weide (2002), a single-step maximum likelihood method was employed to simultaneously estimate the orthogonal matrix along with the dynamics. However, this method is difficult to follow for

where the random variable vt is characterized as Gðvit Þ ¼ 0 and Gðv2it Þ ¼ 1. The factor conditional variances can also be specified through a GARCH model. Consequently, the combination of Eqs. (11) and (12) as

Fig. 2. Price series of commodities. 457

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variability, and soybeans price return was the least variable. A JarqueBera test indicated that the series did not follow the normal distribution, and ARCH (12) LM tests revealed corroborative support for ARCH effects. Pearson correlations between the daily returns of the underlying variables are given in Table 2. Crude oil returns exhibited moderate correlations with the daily returns of corn and soybeans. Among the underlying commodities, the highest correlation was between corn and soybeans (i.e., 0.5458), indicating that corn and soybeans are substitute feed stocks for the biofuel industry. Fig. 3 plots the squared returns that capture the extent to which volatility has varied over different periods. Volatility clustering is visible for each series during 2008–09, the period of financial crisis. Furthermore, volatility clustering is more pronounced for crude oil along with corn.

several assets. In recent times, the orthogonal matrix R has been proposed for estimating through independent component analysis (Basher and Sadorsky, 2016; Broda and Paolella, 2009). A similar approach has been followed in this paper. 4. Data For the present analysis, we used daily spot closing prices of crude oil (West Texas Intermediate) and four major field crops cultivated in the U.S., namely, corn (No. 2 Yellow), soybeans (No. 1 Yellow), oats (No. 2 Milling Minneapolis) and wheat (No. 2 Hard Kansas). As spot prices are more significantly influenced by temporary random noise than futures prices, spot prices of commodities are believed to contain better risk information compared to the future prices. Consequently, the volatility of spot prices tends to be higher than that of the futures prices (Elyasiani et al., 2011; Yu et al., 2018). Hedgers and speculators who are interested in market premiums and have limitations in storage facilities would therefore be likely to choose to operate based on the futures market, but importers and consumers generally use spot prices for decision making (Silvapulle and Moosa, 1999; Arfaoui, 2018). Unlike spot prices, the price relationship between crude oil and agricultural commodities based on futures prices needs to be analyzed for both different maturities and times-to-expiration to capture all relevant information. Considering the above-mentioned reasons, we opted to use spot prices in this study. While the West Texas Intermediate (WTI) price series was obtained from the United States Energy Information Administration, price data on agricultural commodities was sourced from Data Stream International. Crude oil price is denoted in U.S.$ per barrel, and the prices of the agricultural commodities are measured in U.S.$ per bushel. As suggested by Andersen et al. (2003), price volatility must be counted on high frequency time series, so we have used daily spot closing prices spreading over the period from January 3, 2000 to January 4, 2018. Each price series contains 4,698 daily observations. Our choice to start our sample from 2000 was guided by the fact that from the early 2000s, exposure to commodities, specifically energy and agricultural commodities, has been vulnerable to a spiraling upswing to U.S.$250 billion in 2009 from only U.S.$15 billion in 2003 (Irwin and Sanders, 2011). Furthermore, the study period covers the energy crisis and financial turmoil between 2006 and 2009. The time series plots of spot prices are given in Fig. 2 that graphically demonstrates a co-movement between the price series of energy and that of the agricultural commodities since the financial crisis of 2008. Furthermore, for each price series, we have calculated continuously   t compounded daily returns based on the formula 100*ln PPt1 where Pt

5. Results and discussion We started our analysis by estimating with multiple versions of the DCC-GARCH model to determine the parsimonious one. The criteria of model selection included the DCC-GARCH having an AR(1) term in the mean equation following a multivariate t distribution for the best fit (Table 3). Subsequently, all three GARCH models, i.e., DCC-GARCH, ADCC-GARCH as well as GO-GARCH, were estimated as having an AR(1) term in the regression equation. 5.1. Regression results In Table 4, we present the parameter estimates of the DCC-GARCH and ADCC-GARCH models. The coefficient corresponding to a (i.e., the AR(1) term) in the mean equation was found to be significant at the conventional level with a negative value for both crude oil and soybeans. The results indicate the short-term persistence of crude oil as well as all four agricultural commodities (i.e., corn, soybeans, oats, and wheat); in case of all the underlying variables presenting with short-term persistence, ðαÞ was significant at the conventional level and lower than the long-term persistence value ðβÞ. Long-term persistence was also evident as the coefficient corresponding to long-term ðβÞ was also statistically significant. The statistical significance of both α and β also lends support to the presence of volatility clustering. With reference to Table 4, the estimated coefficient for the asymmetry ðγÞ of crude oil was significant with a positive value, indicating that for crude oil, negative shocks augment the conditional volatility (variance) such that its value is greater than the positive movement of a similar extent. In contrast, the corresponding asymmetric term was estimated to be negative and significant for soybeans, oats, and wheat. This implies that for these three agricultural commodities, negative shocks seemed to decrease the conditional volatility. Different coefficient of asymmetry across the underlying commodities seemed to have originated from heterogeneity in the asset class, different extent of information asymmetry as well as varying degree of market efficiency between energy and agricultural markets. With reference to the DCC-GARCH model, the corresponding coefficients of both θ1 and θ2 evolved to be positive and statistically significant at the level of 1 percent. The sum of θ1 and θ2 not exceeding 1

is the daily closing price. Table 1 presents the summary statistics of the underlying return series. The coefficient of variation denotes that, among the underlying commodities, corn price return had the highest degree of

Table 1 Summary statistics.

Number of Observations Minimum Maximum Range Median Mean Variance Std.dev Coef.var Jarque-Bera p-value ARCH(12) p-value

Crude oil

Corn

Soybeans

Oats

Wheat

4698 17.09 16.41 33.51 0.00 0.02 5.83 2.41 133.17 4200 0.00 540.00 0.00

4698 12.13 10.91 23.04 0.00 0.01 3.55 1.88 155.60 2300 0.00 290.00 0.00

4698 16.74 7.57 24.31 0.00 0.02 2.63 1.62 103.26 10000 0.00 240.00 0.00

4698 25.61 25.30 50.92 0.00 0.02 6.04 2.46 133.43 95000 0.00 580.00 0.00

4698 26.20 28.03 54.23 0.00 0.02 3.81 1.95 124.36 77000 0.00 820.00 0.00

Table 2 Pearson correlations.

Crude oil Corn Soybeans Oats Wheat

458

Crude oil

Corn

Soybeans

Oats

Wheat

1.0000 0.1907 0.2166 0.0720 0.0828

1.0000 0.5458 0.2921 0.2279

1.0000 0.2267 0.1670

1.0000 0.1112

1.0000

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Fig. 3. Squared daily return of price series.

indicates the mean reverting nature of DCC. The outcome of the ADCCGARCH was also found to be mean reverting. In addition, the shape parameter ðλÞ was estimated to be the maximum for crude oil (over 6), denoting that the distributions of the return series of the four underlying agricultural commodities carry heavier tails as compared to the distribution of crude oil returns. In Table 5, we present the parameter estimates of the GO-GARCH model. As the GO-GARCH factors were estimated, there were no standard errors. For each factor, the short-term parameters ðαÞ have lower values than the long-term parameters ðβÞ, thus indicating short-term persistence over the long-term. These results also confirm the findings of both the DCC and ADCC models.

Table 3 DCC-GARCH model with different specifications. Distribution

Multivariate t

Multivariate normal

AR(1)

No

Yes

No

Yes

Akaike Information Criteria Bayes Information Criteria Shibata Information Criteria Hannan-Quinn Information Criteria No of Observations Log-Likelihood

19.427 19.479 19.427 19.445 4698 45596

19.300 19.359 19.299 19.320 4698 45292

19.914 19.958 19.914 19.929 4698 46745

19.910 19.961 19.910 19.928 4698 46731

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Table 4 Parameter estimates of DCC and ADCC models. DCC

μoil aoil

ωoil αoil

βoil γ oil λoil

μcorn

acorn

ωcorn αcorn βcorn γ corn λcorn

μsoybeans

asoybeans

ωsoybeans αsoybeans βsoybeans γ soybeans λsoybeans

μoats aoats

ωoats αoats βoats γ oats λoats

μwheat

awheat

ωwheat αwheat βwheat γ wheat λwheat θ1 θ2 θ3 Λ Akaike Information Criteria Bayes Information Criteria Shibata Information Criteria Hannan-Quinn Information Criteria Log-Likelihood

ADCC

Coefficient

Std. Er.

t

p-value

Coefficient

Std. Er.

t

p-value

0.0683 0.0337 0.0235 0.0466 0.9503

0.0255 0.0147 0.0080 0.0048 0.0044

2.6803 2.3010 2.9280 9.7649 218.2427

0.0074 0.0214 0.0034 0.0000 0.0000

6.0928 0.0197 0.0116 0.0486 0.0640 0.9266

0.5348 0.0211 0.0144 0.0250 0.0178 0.0221

11.3929 0.9315 0.8070 1.9421 3.6034 41.9926

0.0000 0.3516 0.4197 0.0521 0.0003 0.0000

4.7478 0.0495 0.0422 0.0299 0.0496 0.9401

0.3390 0.0174 0.0138 0.0092 0.0086 0.0103

14.0062 2.8493 3.0626 3.2381 5.7748 90.8470

0.0000 0.0044 0.0022 0.0012 0.0000 0.0000

4.8161 0.0308 0.0125 1.3105 0.1861 0.6554

0.3498 0.0231 0.0132 0.4387 0.0488 0.0935

13.7679 1.3329 0.9466 2.9875 3.8131 7.0091

0.0000 0.1826 0.3438 0.0028 0.0001 0.0000

2.8692 0.0351 0.0136 0.1177 0.0817 0.9012

0.1319 0.0197 0.0134 0.0468 0.0214 0.0266

21.7604 1.7806 1.0156 2.5154 3.8253 33.9261

0.0000 0.0750 0.3098 0.0119 0.0001 0.0000

3.4412 0.0092 0.9839

0.2006 0.0034 0.0081

17.1568 2.6797 122.0598

0.0000 0.0074 0.0000

4.8211 19.3000 19.3590 19.2990 19.3200 45292

0.1396

34.5461

0.0000

0.0576 0.0343 0.0214 0.0226 0.9541 0.0389 6.2140 0.0210 0.0117 0.0456 0.0684 0.9289 0.0118 4.7392 0.0532 0.0444 0.0215 0.0621 0.9479 0.0315 4.8549 0.0352 0.0121 1.2153 0.2257 0.6763 0.0971 2.8760 0.0326 0.0136 0.1211 0.0981 0.8999 0.0341 3.4419 0.0088 0.9838 0.0012 4.8630 19.2920 19.3590 19.2920 19.3160 4698

0.0253 0.0147 0.0069 0.0051 0.0012 0.0093 0.5593 0.0211 0.0144 0.0262 0.0172 0.0237 0.0137 0.3407 0.0173 0.0138 0.0066 0.0076 0.0072 0.0102 0.3574 0.0231 0.0132 0.4064 0.0575 0.0881 0.0455 0.1312 0.0196 0.0134 0.0469 0.0265 0.0260 0.0204 0.2000 0.0032 0.0082 0.0012 0.1441

2.2751 2.3244 3.0889 4.4153 824.2441 4.1735 11.1096 0.9971 0.8118 1.7399 3.9809 39.1721 0.8617 13.9100 3.0829 3.2119 3.2511 8.1236 132.4343 3.0888 13.5837 1.5244 0.9185 2.9902 3.9245 7.6796 2.1337 21.9137 1.6626 1.0118 2.5827 3.7048 34.6296 1.6725 17.2128 2.7462 119.9604 0.9345 33.7559

0.0229 0.0201 0.0020 0.0000 0.0000 0.0000 0.0000 0.3187 0.4169 0.0819 0.0001 0.0000 0.3888 0.0000 0.0021 0.0013 0.0011 0.0000 0.0000 0.0020 0.0000 0.1274 0.3583 0.0028 0.0001 0.0000 0.0329 0.0000 0.0964 0.3116 0.0098 0.0002 0.0000 0.0944 0.0000 0.0060 0.0000 0.3500 0.0000

during the corresponding period. However, following the GO-GARCH model, dynamic conditional correlations of crude oil with oats and wheat were shown to have gradually weakened from 2016. Across the GARCH models, the dynamic conditional correlations between crude oil and corn were positive. The average correlation value was around 0.20. This finding is consistent with the increasing evidence supporting the interdependence of the oil and corn markets especially post-2008. As an example, Du et al. (2011) confirmed interdependence of crude oil and corn markets between October of 2006 and January of 2009. Along the same lines, Gardebroek and Hernandez (2013) suggested that the dynamic conditional correlation between crude oil and corn markets since 2007 has transformed from a weak correlation to a stronger positive correlation. In another study, de Nicola et al. (2016) found there to be a positive dynamic conditional correlation between the returns of crude oil and corn since 2006. Similarly, Silvennoinen and Thorp (2016) have suggested that during late 2007, with the rise in crude oil prices, the correlation between crude oil and corn increased from 0.1 to around 0.4. We found that the conditional correlation between crude oil and corn reached its peak in early 2016 followed by fair oscillation since the end of 2016. The plausible reason for such interdependence may be due to the significant fall in both crude oil and corn prices during 2016; the crude price was hovering around U.S.$30 per barrel and corn was priced at about U.S.$3.5 per bushel in contrast to U.S.$145 per barrel

Table 5 Parameter estimates of GO-GARCH.

ω α β skew shape Log Likelihood

f1

f2

f3

f4

f5

0.0187 0.0533 0.9275 0.0709 1.0390 45028.17

0.0042 0.0472 0.9493 0.0991 1.7414

0.0493 0.0850 0.8671 0.1101 0.7334

0.0181 0.0617 0.9221 0.0014 1.0907

0.1978 0.2080 0.5761 0.0034 0.4102

5.2. Dynamic conditional correlations In the next step, by applying a rolling window analysis, we established the dynamic conditional correlations (Fig. 4). The estimation window was set at 3698 observations, and this produced dynamic conditional correlations of 1,000 step-ahead. For every 20 observations, the GARCH models were refitted. The conditional correlations of crude oil and the underlying four agricultural commodities were found to be quite similar for both the DCC-GARCH and ADCC-GARCH models. While the dynamic conditional correlations of crude oil with corn and soybeans have experienced downward trends since June of 2016, the correlations of crude oil with both oats and wheat have exhibited upward trends 460

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Economic Modelling 82 (2019) 453–466

Fig. 4. One-step-ahead dynamic conditional correlations.

outcome has also been reported by Nazlioglu et al. (2013), indicating a strong volatility linkage across the oil and wheat markets after financial turmoil. In the same vein, Ott (2014) has also suggested that crude price volatility has carried a significant impact on the volatility of wheat prices after 2006. Overall, the empirical outcomes of our analysis strengthen the evidence in support of significant interrelations between the energy and agricultural markets. Interestingly, since 2007, the market has experienced the growing financialization of commodities and, more specifically, agricultural field crops, namely, corn, soybeans, oats, and wheat. A similar outcome has been described by Ji and Fan (2012) showing that volatility in the crude oil market was transmitted to the agricultural commodity market after the financial crisis. Such an increasingly strong link between energy and agriculture markers is apparently an outcome of following diversification as a risk mitigation strategy in a volatile market (Brooks and Prokopczuk, 2013). With reference to Table 6, for every pair of commodities, the correlation derived from the DCC-GARCH model was significantly correlated with the correlations yielded from the ADCC-GARCH specification. However, pair-wise correlations between those derived from DCC-

and U.S.$6.4 per bushel for crude oil and corn, respectively, during July of 2008. The dynamic conditional correlations between crude oil and soybeans were found to be positive for each of the GARCH models. The average correlation value was around 0.25. The conditional correlation between crude oil and soybeans experienced a considerable jump during early 2016, the period marked by a significant fall in both crude oil and soybeans prices. Similarly, Triantafyllou et al. (2015) confirmed tighter interdependence between the variances of crude oil and soybeans prices during the post-crisis period. In another study, Ahmadi et al. (2016) also provided evidence for a considerable correlation linkage between the oil and soybeans markets. The correlations between crude oil and oats oscillated between positive and negative values. The negative values reflect diversification benefits. The inverse relationship between oil and oats markets indicate that the oats market tends to lose money with rising volatility. However, the dynamic conditional correlations of crude oil with oats have mostly been shown to have a positive relationship, as illustrated in the work by Liu (2014). In contrast, in our study, the correlations between crude oil and wheat were largely positive across the GARCH models. A similar 461

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Φo;a;t

Table 6 Correlations between correlations.

DCC-GARCH/ADCCGARCH DCC-GARCH/GO-GARCH ADCC-GARCH/GO-GARCH

Oil/ Corn

Oil/ Soybeans

Oil/ Oats

Oil/ Wheat

0.9990

0.9993

0.998

0.9983

0.0523 0.0496

0.1197 0.1175

0.1928 0.196

0.1631 0.166

 ¼ hoa;t haa;t

(17)

where hoa;t denotes the conditional covariance between crude oil ðo Þ and one of the underlying agricultural commodities ðaÞ , and haa;t represents the conditional variance of the agricultural commodity at time t. It is possible for a U.S.$1 long position in crude oil to be hedged by a short position in the U.S.$ Φo;a;t agricultural commodity. A negative hedge ratio indicates that the market maker is in the short position; in other words, the investor is involved in the short sale. We computed optimal hedge ratios following the DCC-GARCH, ADCC-GARCH, and GO-GARCH specifications. The performance values of the optimal hedge ratios originating from the various GARCH estimations were then assessed by the hedging effectiveness (HE) index (Arouri et al., 2012; Basher and Sadorsky, 2016) as follows:

GARCH and GO-GARCH as well as ADCC-GARCH and GO-GARCH were very weak, and this is consistent with what is shown in Fig. 4. 5.3. Hedging effectiveness Following Kroner and Sultan (1993), the risk minimizing hedge ratio between asset o and asset a can be represented as:

HE ¼

varunhedged  varhedged varunhedged

Fig. 5. Optimal hedge ratios (rolling one-step-ahead) of crude oil with corn, soybeans, oats, and wheat. 462

(18)

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Economic Modelling 82 (2019) 453–466

whereas the values for ADCC-GARCH were found to be least effective. The mean values of the hedge ratio of crude oil with soybeans were 0.3181 under the DCC-GARCH model, 0.3488 under the ADCC-GARCH model, and 0.4792 under the GO-GARCH model. Consequently, the DCC-GARCH model has evolved to provide the highest hedging effectiveness, followed by the ADCC-GARCH model and the GO-GARCH model. The mean values of the hedge ratios between crude oil and oats were 0.0780, 0.0904, and 0.1154 under the DCC-, ADCC-, and GOGARCH models, respectively, with the DCC model again offering the highest hedging effectiveness. Finally, the mean values of the crude oil/ wheat hedge ratios were 0.0585, 0.0749, and 0.1661 under the DCC-, ADCC-, and GO-GARCH models, respectively, with the DCC model again proving to be most effective. A similar outcome has also been reported by Sadorsky (2014) who estimated the average value of the oil/wheat hedge at eight cents. Ultimately, the oil/soybeans relationship has offered the highest hedging effectiveness. In other words, soybeans are the preferred choice over other agricultural commodities when hedging against crude oil. Interestingly, oats have evolved to be the second best in terms of hedging effectiveness over corn and wheat.

Table 7 Correlations between hedge ratios.

DCC-GARCH/ADCCGARCH DCC-GARCH/GO-GARCH ADCC-GARCH/GO-GARCH

Oil/ Corn

Oil/ Soybeans

Oil/ Oats

Oil/ Wheat

0.2008

0.0082

0.5492

0.0007

0.2240 0.3656

0.0232 0.1158

0.6555 1.5855

0.0009 0.0143

where varhedged denotes the variance of the returns of the crude oil/ agricultural commodity portfolio, and varunhedged refers to the variance of the returns of the crude oil portfolio. A high HE index is consequently indicative of greater hedging effectiveness, i.e., the underlying hedging strategy is better than it would be for those with lower HE indices. With respect to previous research of this kind, Ghorbel et al. (2017) have employed GARCH-based specifications to estimate in-sample optimal hedge ratios between oil and agricultural commodities. However, their findings are not supported by hedging effectiveness. By using a rolling window analysis, out-of-sample hedge ratios were produced. At time t, conditional volatility (one period ahead) was forecasted to produce a one-period-ahead hedge ratio. Hedging portfolios were then built upon these forecasted hedge ratios. Here, we used a rolling window of 3,698 to produce hedge ratios of 1,000 days at one period ahead. In Fig. 5, we display the rolling one-step-ahead optimal hedge ratios of crude oil with corn, soybeans, oats, and wheat. The hedge ratios originated from the GO-GARCH model have exhibited maximum variability. Furthermore, the hedge ratios given by the DCC-GARCH models were largely similar to those computed from the ADCC-GARCH models. In Table 7, we display the correlations between hedge ratios. For the oil/corn and oil/oats hedges, the correlations between the hedge ratios were positive across all pair-wise GARCH models. Furthermore, the correlations between the hedge ratios originating from the ADCC-GARCH and GO-GARCH models were relatively higher except for oil/wheat. With reference to the middle panel of Table 8, the mean value of the hedge ratio of crude oil with corn under the DCC-GARCH model was 0.2008, denoting that the hedging of a U.S.$1 long position in crude oil is possible for a 20 cent short position in the corn market. The corresponding mean values under the ADCC-CARCH and GO-GARCH models were 0.2240 and 0.3656, respectively. Among the three GARCH models, DCC-GARCH demonstrated the maximum hedging effectiveness values,

5.4. Robustness test The hedging effectiveness discussed in sub-section 5.3 was based on a forecast length of 1,000 one-period-ahead with the model being refit for every 20 days. In this sub-section, we document the outcome of the robustness test. In Table 8, we also display the values of hedging effectiveness based on the model refits for 10 days as well as 60 days. Under every hedge and across the GARCH specifications, the values of hedging effectiveness were quite similar over various model refits. For instance, the hedging effectiveness values for the hedge between crude oil and soybeans under DCC-GARCH specification were 0.0215, 0.0216, and 0.0216 for model refits of 10 days, 20 days, and 60 days, respectively. Similarly, for the oil/oats hedge, the DCC-GARCH model offered the highest hedging effectiveness across model refits of 10 days, 20 days, and 60 days. This implies that the estimated hedge ratios and hedging effectiveness were fairly robust for each of the selected numbers of days and model refits. Table 9 highlights the extent to which the hedge ratios are robust with respect to the variations in forecast length. Results are displayed as capturing the mean hedge ratios and hedging effectiveness values from the models with forecast lengths of 500 days, 1,000 days, 1,500 days, and

Table 8 Hedging effectiveness and hedge ratio using DCC-GARCH, ADCC-GARCH and GO-GARCH models. Forecast length (days)

1000

1000

1000

Model refit (days)

10

20

60

Oil/Corn DCC-GARCH ADCC-GARCH GO-GARCH Oil/Soybeans DCC-GARCH ADCC-GARCH GO-GARCH Oil/Oats DCC-GARCH ADCC-GARCH GO-GARCH Oil/Wheat DCC-GARCH ADCC-GARCH GO-GARCH

Mean

Minimum

Maximum

HE

Mean

Minimum

Maximum

HE

Mean

Minimum

Maximum

HE

0.2013 0.2247 0.3663

0.0082 0.0232 0.1160

0.5543 0.6555 1.5908

0.0007 0.0009 0.0147

0.2008 0.2240 0.3656

0.0082 0.0232 0.1158

0.5492 0.6555 1.5855

0.0008 0.0010 0.0144

0.1997 0.2226 0.3633

0.0005 0.0320 0.1161

0.5400 0.6427 1.5492

0.0010 0.0007 0.0138

0.3186 0.3496 0.4805

0.0658 0.0773 0.1052

0.919 0.9816 1.8124

0.0215 0.0206 0.0123

0.3181 0.3488 0.4792

0.0658 0.0773 0.1062

0.9060 0.9658 1.8082

0.0216 0.0207 0.0128

0.3165 0.3465 0.4764

0.0658 0.0773 0.1093

0.9060 0.9658 1.7702

0.0216 0.0208 0.0131

0.0784 0.0909 0.1160

0.0400 0.0335 0.0228

0.3542 0.3533 0.6127

0.0066 0.0057 0.0009

0.0780 0.0904 0.1154

0.0400 0.0335 0.0229

0.3387 0.3533 0.6097

0.0068 0.0060 0.0012

0.0771 0.0893 0.1125

0.0400 0.0337 0.0249

0.3195 0.3304 0.5488

0.0065 0.0058 0.0022

0.0588 0.0753 0.1662

0.0820 0.0540 0.0127

0.3255 0.3234 0.9698

0.0077 0.0083 0.0219

0.0585 0.0749 0.1661

0.0808 0.0540 0.0126

0.3255 0.3234 0.9788

0.0075 0.0082 0.0217

0.0582 0.0744 0.1665

0.0809 0.0442 0.0115

0.3207 0.3192 0.9659

0.0075 0.0081 0.0215

Note: 1. Hedging ratios are constructed using a fixed width rolling window that would generate hedge ratios of 1000 days one-period-ahead. We refit the models for every 10, 20, and 60 observations. 2. HE denotes hedging effectiveness. 463

2,000 days. With respect to the oil/corn hedge, the DCC-GARCH model has evolved to be the best performer across forecast length, which is consistent with the findings shown in Table 8. For the oil/soybeans hedge, the DCC-GARCH model was again preferred since it consistently provided the highest hedging effectiveness for each forecast length except for 500 days, where it was only second best to the ADCC-GARCH model. This indicates the robustness of the results with respect to variations of forecast length.

Note: 1. Hedging ratios are computed using a fixed width rolling window that would generate 500 days, 1000 days, 1500 days, and 2000 days one-period-ahead hedge ratios. We refit the models for every 20 observations. 2. HE denotes hedging effectiveness.

0.0045 0.0044 0.0139 0.4405 0.4319 1.2132 0.2273 0.2281 0.8915 0.0737 0.0508 0.0066 0.0401 0.0514 0.1395

0.0054 0.0071 0.0244

0.0585 0.0749 0.1661

0.0808 0.0540 0.0126

0.3255 0.3234 0.9788

0.0075 0.0082 0.0217

0.0788 0.0962 0.1592

0.0976 0.0653 0.1439

0.3750 0.3728 1.1366

0.0070 0.0083 0.0249

0.1017 0.1194 0.1544

0.1012 0.0908 0.1630

0.0136 0.0122 0.0057 0.4077 0.3922 0.7130 0.3387 0.3533 0.6097 0.1483 0.1678 0.4101 0.0385 0.0473 0.0200 0.0931 0.1014 0.0959

0.0092 0.0097 0.0104

0.0780 0.0904 0.1154

0.0400 0.0335 0.0229

0.0068 0.0060 0.0012

0.0721 0.0850 0.1145

0.0296 0.0251 0.0581

0.4071 0.4019 0.7143

0.0053 0.0038 0.0064

0.0948 0.1080 0.1100

0.0280 0.0227 0.0636

0.0328 0.0313 0.0210 1.0910 1.1300 2.0390 0.0427 0.0404 0.0149 0.9060 0.9658 1.8082 0.7646 0.7849 1.6248 0.05671 0.07897 0.21496 0.2959 0.3143 0.4407

0.0315 0.0318 0.0265

0.3181 0.3488 0.4792

0.0658 0.0773 0.1062

0.0216 0.0207 0.0128

0.3097 0.3380 0.4515

0.0664 0.0777 0.0989

0.9830 1.0400 1.9290

0.0226 0.0210 0.0084

0.3379 0.3644 0.4487

0.6653 0.7670 1.7670 0.0086 0.0276 0.1367 0.0010 0.0012 0.0228 0.5966 0.6939 1.6854 0.0068 0.0310 0.1349 0.1971 0.2183 0.3526 0.0008 0.0010 0.0144 0.5492 0.6555 1.5855 0.0082 0.0232 0.1158 0.2008 0.2240 0.3656 0.0016 0.0027 0.0234 0.5075 0.5671 1.3354 0.02987 0.03291 0.13859 0.1835 0.1992 0.3347

Oil/Corn DCC-GARCH ADCC-GARCH GO-GARCH Oil/Soybeans DCC-GARCH ADCC-GARCH GO-GARCH Oil/Oats DCC-GARCH ADCC-GARCH GO-GARCH Oil/Wheat DCC-GARCH ADCC-GARCH GO-GARCH

HE Maximum Minimum

0.2168 0.2370 0.3393

Maximum Minimum Mean Mean Mean

Minimum

Maximum

HE

Mean

Minimum

Maximum

HE

20

2000 1500

20 Model refits (days)

1000

20

500

20

Forecast length (days)

Table 9 Hedging effectiveness and hedge ratio using DCC-GARCH, ADCC-GARCH and GO-GARCH models under different forecast length.

0.0138 0.0120 0.0046

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HE

D. Pal, S.K. Mitra

6. Conclusion In this paper, we compared the conditional correlations of crude oil and energy crops (e.g., corn and soybeans) with that of crude oil and food crops (e.g. oats and wheat). We employed the DCC-GARCH, ADCCGARCH, and GO-GARCH models to estimate the conditional correlations, and we used daily spot closing price spreading over the period from January 3, 2000 to January 4, 2018 as the data for this study. We also computed optimal hedge ratios between the underlying assets by using the DCC-GARCH, ADCC-GARCH, and GO-GARCH models. Finally, the models were evaluated in terms of their hedging effectiveness. The results indicate that the dynamic conditional correlations between crude oil and corn across the GARCH models were positive. The average correlation value was around 0.20. In a similar vein, the dynamic conditional correlations between crude oil and soybeans have also evolved to be positive for the DCC-GARCH, ADCC-GARCH, and GOGARCH models, with the average correlation value being around 0.25. However, the correlations between crude oil and oats oscillated between negative and positive values. The negative values indicate gains from diversification. Furthermore, the correlations between crude oil and wheat were mostly positive for each of the GARCH models. Overall, the results of our empirical analysis corroborate the available evidence regarding the reasonably high conditional correlation between the crude oil and energy crops. This finding is therefore consistent with the outcomes suggested by Ahmadi et al. (2016), Baek and Koo (2014), de Nicola et al. (2016), Du et al. (2011), Gardebroek and Hernandez (2013), Mensi et al. (2015) and Nazlioglu et al. (2013). We found that the average hedge ratio between crude oil and corn was 0.3656 under the GO-GARCH model, signifying that hedging of a U.S.$1 long position in crude oil is possible for 36 cents short position in the corn market. Similarly, a U.S.$1 long position in crude oil can be hedged for a 47 cents short position in soybeans. The corresponding hedge ratios of crude oil with oats and wheat are relatively low at 0.1154 and 0.1661, respectively. Finally, among the three GARCH models employed in this study, DCC-GARCH specification has evolved to be most effective for constructing hedge ratios. These findings have also been shown to be stable against robustness tests in terms of both the selection of numbers of days for model refits as well as forecast length. More interestingly, our results confirm the findings of Pindyck and Rotemberg (1990) who have attributed the excess price co-movement of crude oil with agricultural commodities to hedging. Our findings provide interesting insights for investors looking for higher returns from crude oil by hedging the tail risk to include agriculture commodities in their portfolios. Although hedging effectiveness is low with all underlying agricultural commodities, hedging is most effective between crude oil and soybeans, indicating that among the underlying agricultural commodities, soybeans are the preferred hedge over corn, oats, and wheat. Interestingly, oats have evolved to offer the second most effective hedge against crude oil, specifying the potential gain of including a non-biofuel agricultural commodity along with soybeans, a major ethanol feedstock, in a portfolio with crude oil. The findings should be relevant to investors interested in hedging opportunities between energy and agriculture markets. More specifically, institutional investors such as insurance companies, pension fund managers, and hedge fund managers aiming for risk minimization through diversification may benefit from considering our results. Our study would also add value to the agricultural producers as it 464

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shows a significant interdependence between crude oil and energy crop prices between 2008 and 2016, the period that witnessed spiraling rise of crude oil along with the implementation of the U.S. ethanol mandate since 2005. Increased derived demand of corn in response to the ethanol mandate along with rise in demand of soybeans for producing biodiesels triggered the price of major energy crops, such as corn and soybeans. For policy makers, our analysis offers a reliable clue that can be used to resolve the query regarding whether institutional investors in commodity markets can be held responsible for the spiraling rise of agricultural commodities. In contrast to traditional specialized commodity investors who earn risk premiums by hedging the price risks of the farmers and the processors, the objective of the new generation of institutional investors is to diversify their portfolios by investing in commodities. The high potential of major U.S. energy crops to offer hedges against crude oil, as shown by our study, justifies the large scale investment in the agricultural commodity market by institutional investors since the early 2000s. However, the increasing flow of commodity investment can accelerate the price of several field crops, making food costlier. It is therefore urgent for policy makers to probe the possible link between increased institutional investment and rising food prices (if any) and take remedial measures to offset any food crisis. In future work, the study may be extended to inquire into possible conditional correlations between crude oil and ethanol since after methyl tert-butyl ether is banned in the United States, ethanol would be the sole oxygenate for gasoline.

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