Can agricultural and precious metal commodities diversify and hedge extreme downside and upside oil market risk? An extreme quantile approach

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Can agricultural and precious metal commodities diversify and hedge extreme downside and upside oil market risk? An extreme quantile approach Jose Areola Hernandeza, Syed Jawad Hussain Shahzadb, Gazi Salah Uddinc, Sang Hoon Kangd,e,

⁎

a

Rennes School of Business, Rennes, Brittany, France Montpellier Business School, Montpellier, France c Department of Management and Engineering, Linköping University, 581 83 Linköping, Sweden d Department of Business Administration, Pusan National University, Busan 609-735, Republic of Korea e School of Commerce, University of South Australia, Australia b

ARTICLE INFO

ABSTRACT

JEL classification: C58 G10 G11 Q02

The cost-effectiveness measures for production, processing, and transportation adopted by wheat, rice, and corn farmers, as well as the price fluctuations of gold and silver, doubtlessly depend on the downside and upside price trends of global economic factors such as the oil market. This dependence between oil and agricultural commodities motivates an analysis of interdependence and spillover influence in extreme oil market scenarios. By means of an extreme quantile approach, this study models the return distribution of oil in relation to some of the most traded agricultural and precious metal commodities. We find that extreme lower quantiles of oil returns have a positive effect on the lower quantiles of gold, silver, and rice returns. These effects are more significant using daily-frequency data, while for weekly and monthly frequencies, the effect is less significant. The decrease in oil returns during a bearish oil market will cause a decrease in precious metal and rice returns; therefore, these cannot be used to hedge the downside risk of oil investments, especially in the short term. These commodities might only serve as a diversification strategy for oil investments. The lower quantiles of oil returns have either no effect, or a negative effect, on the lower quantiles of wheat and corn, making them suitable hedges for extreme downturns in oil prices.

Keywords: Energy market oil prices Agricultural commodities Precious metals Extreme quantile dependence Predictability

1. Introduction The oil market, as a global economic factor, is inevitably linked to the cost-effectiveness measures of producers of agricultural commodities such as wheat, rice, and corn, due to the oil dependency in the production, processing, and transportation stages of these commodities (Wang et al., 2014). Oil prices have a nonlinear and inverse relation to gold and silver prices in the downside and upside, making international oil price fluctuations a source of uncertainty. Spillovers affect both precious metals and agricultural commodities (Baffes, 2007; Bildirici and Turkmen, 2015; Du et al., 2011; Ji and Fan, 2012; Nazlioglu et al., 2013; Saghaian, 2010; Sari et al., 2010). Further, it is well understood that oil price changes exert a degree of upside influence on the price of precious metals (which serve as value stabilizers and wealth protectors) through the effect oil price changes have on inflation, and on corn prices through the substitution effect between corn-derived ethanol and oil. Nevertheless, the strength and bidirectional effect between these

commodities, primarily from oil towards precious metals and agricultural commodities, have not been investigated in extreme oil market scenarios, that is, when oil prices undergo sharp trends of decline or escalation (Andreasson et al., 2016; Chang et al., 2012; FernandezPerez et al., 2016; Chang et al., 2018). For instance, there is an indication that oil, wheat, and corn prices are mutually affected, with oil prices Granger causing those of wheat (not, however, under adverse and extreme oil market scenarios) (Nazlioglu, 2011; Saghaian, 2010). This association of oil price changes with those of precious metals and agricultural commodities suggests that precious metals or agricultural commodities could serve as tools for wealth protection and hedging against extreme downside or upside oil market innovations. On the other hand, the highlighted dependency of precious metals or agricultural commodities’ prices on those of the oil market, which acts as an underlying global economic factor, suggests that oil price fluctuations may influence the pricing of agricultural commodities and the determination of subsidy measures in the agro industry. Thus, a natural

Corresponding author at: Department of Business Administration, Pusan National University, Busan 609-735, Republic of Korea. E-mail addresses: [email protected] (J.A. Hernandez), [email protected] (S.J.H. Shahzad), [email protected] (G.S. Uddin), [email protected] (S.H. Kang). ⁎

https://doi.org/10.1016/j.resourpol.2018.11.007 Received 21 June 2018; Received in revised form 15 September 2018; Accepted 9 November 2018 0301-4207/ © 2018 Elsevier Ltd. All rights reserved.

Please cite this article as: Areola Hernandez, J., Resources Policy, https://doi.org/10.1016/j.resourpol.2018.11.007

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question arises, which also acts as the main motivation for our research study: can agricultural and precious metal commodities diversify and hedge investment portfolios under extreme downside and upside oil market scenarios? In order to address the above research question, this study implements an extreme quantile approach, namely, the cross-quantilogram (CQ) model of Han et al. (2016). The aim is to identify the sign (positive or negative) of the spillover influence oil has on the agricultural and precious metal commodities under consideration, when oil prices undergo sharp trends of decline and escalation, accounted for by extreme quantiles of the commodities’ return distribution. We also examine and compare the co-dynamics of linear and nonlinear dependence between pairs of energy, precious metals, and agricultural commodities to better justify the implemented modeling approach, which is suitable for nonlinear co-movements in the extreme of the tails. From a methodological perspective, our study is relevant in that it provides adequate measurements of nonlinear interdependence and asymmetries in the extreme quantiles (lower and upper, 0.05, 0.95) of the pairs of commodities’ joint distributions. The obtained measurements could be used to more accurately determine input costs and product pricing for precious metals and agricultural commodities (Balcilar et al., 2015; Bildirici and Turkmen, 2015; Nazlioglu, 2011; Serra et al., 2010). Our main contribution stems from the new and useful insights we derive about the direction and sign of the spillover influence between oil and precious metal and agricultural commodities. We specifically find that extreme low oil return quantiles positively affect the lowest quantiles of gold, silver, and rice (based on daily frequency observations). This effect is less significant for weekly and monthly frequency series. These findings suggest that a decrease in oil returns will cause a decrease in the commodities price series, thus making them inadequate for downside risk hedging in oil investments, especially in relation to daily data for lag = 1. In relation to wheat and corn, we observe that the lowest quantiles of oil either have no effect, or a negative effect, on their lower quantiles, thus making them suitable for hedging extreme oil downturns. Our analysis is relevant in the sense that it evaluates the influence of oil prices on precious metals and agricultural commodities when either of those commodity markets is affected by mild or large changes in the economic cycle. Economic booms and busts are known for affecting the demand and supply of commodities. Gold and silver prices, for instance, were at historic highs during the 2008 global financial crisis, justifying an in-depth study of comovements between the commodities under consideration. The positive spillover influence of oil price fluctuations on the lower quantiles of gold, silver, and rice suggest that none of these commodities serves for diversifying the oil price risk. Consequently, investors must look for alternative commodities such as corn and wheat, which in our study do serve as foils for oil risk and protectors of wealth under extreme negative tail-market scenarios. We can understand the negative effect that extreme oil price decreases have on corn prices from the perspectives of production costs (on the upside) and decreasing demand (on the downside) of corn. It can also partially be attributed, on the downside, to the substitute effect of corn-based ethanol production. Specifically, as oil prices undergo sharp trends of decline, corn-based ethanol demand and production also declines (lowpriced crude oil is more attractive), resulting in lower corn prices. The empirical results suggest that producers of agricultural commodities such as corn must pay careful attention to trends of decline in oil prices for the purpose of commodity pricing and cost risk management. In addition, given the specific dependence dynamics between oil, corn, and wheat prices, the latter two commodities are the only ones that can hedge or diversify a portfolio of assets under extreme oil market scenarios. Thus, gold, silver, and rice should not be considered for portfolio risk mitigation and management, as they appear to mimic more clearly in the short, mid, and long terms the price behavior of oil. For policy makers who are in a position to influence the determination of subsidy packages, and consequently commodity prices, a better

understanding of oil price dynamics and spillover effects could lead to an improved allocation of public resources and rebalancing of sector investments in the economy. The remainder of this research paper is structured as follows: Section 2 reviews the relevant literature. Section 3 explains the extreme quantile CQ methodology and justifies its use for spillover and predictability analyses. Section 4 explains the data and justifies the selected energy, precious metals, and agricultural commodities and the sample period. Section 5 discusses the empirical results and Section 6 concludes. 2. Related literature We identify two different strands of research in the literature on the interdependence among energy, precious metals, and agricultural commodity markets. One strand analyzes the correlation between volatility in various commodity markets without determining the causal direction of the volatility effects. Another strand analyzes the direction of the spillover effects among commodity markets. With respect to the first group of studies, Du et al. (2011) employ a stochastic volatility model with Merton jumps (SVMJ) to investigate the role of speculation on oil price volatility and the extent to which oil price volatility spillovers influence agricultural commodity (e.g., corn, wheat) prices. Their results show that oil price shocks cause sharp price changes in the agricultural market. Busse et al. (2011) use a multivariate dynamic conditional correlation (DCC) model to capture the time-varying volatility and co-movements between rapeseed, crude oil, and related agricultural commodity prices during and after the 2006–2008 food crisis. Their findings indicate significant increasing correlations between the returns of rapeseed and crude oil prices during the crisis, implying that rapeseed prices are relatively sensitive to market shocks. Liu (2014) investigates the non-linear cross-correlations between crude oil (West Texas Intermediate) and agricultural commodities (corn, soybean, oat, and wheat) during the recent food crisis period. The author concludes that the food crisis period reinforces the volatility crosscorrelations between crude oil and agricultural commodity markets, whereas high oil prices are indicated as making a partial contribution to the food crisis. Mensi et al. (2014) use the VAR-BEKK-GARCH and VARDCC-GARCH models to measure the dynamic volatility and spillovers of returns across international energy and cereal commodity markets, while accounting for the presence of three types of OPEC news announcements regarding oil production (cut, maintain, and hike). Sensoy et al. (2015) analyze the dynamic equicorrelations of different commodity markets (energy, precious metals, industrial metals, and agricultural). The results obtained from the implemented dynamic equicorrelation generalized autoregressive conditional heteroskedasticity model show strong evidence of co-movement for precious and industrial metals. These effects were particularly intensified during the recent financial crises, further implying that both volatility and correlation persistently move together over time. Using a copula approach, Koirala et al. (2015) provide strong evidence of dynamic correlations between energy and agricultural commodity prices. Their concluding remarks indicate that an increase in energy prices leads to increases in related agricultural commodity prices (i.e., corn and soybean). Mensi et al. (2015) investigate the time-varying linkages of a Saudi stock market with major commodity futures, including West Texas Intermediate (WTI) oil, gold, silver, wheat, corn, and rice. Their examination of the dynamics of dependence between these commodities is useful for designing optimal asset portfolios and hedging strategies, as well as for downside risk reduction and mitigation. Lucotte (2016) fitted a VAR model at different time horizons to two subsample periods—a pre-boom (1990M1–2006M12) and a post-boom (2007M1–2015M5)—to analyze the dynamics of co-movement between crude oil and food prices. Their results indicate strong positive co-movements between crude oil and food prices in the aftermath of the commodity boom, whereas no statistically significant co-movements are observed during the pre-boom 2

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Table 1 Descriptive statistics and unit root properties. Mean

Std. Dev.

Panel A: Daily data series Oil 0.020 2.340 Silver 0.022 1.911 Gold 0.029 1.107 Wheat 0.017 1.971 Corn 0.013 1.774 Rice 0.010 1.625 Panel B: Weekly data series Oil 0.102 5.094 Silver 0.113 4.306 Gold 0.150 2.517 Wheat 0.085 4.311 Corn 0.061 3.930 Rice 0.049 3.646 Panel C: Monthly data series Oil 0.381 10.27 Silver 0.472 8.450 Gold 0.636 4.908 Corn 0.229 8.332 Wheat 0.321 8.958 Rice 0.222 7.514

Q5%

Q95%

Skewness

Kurtosis

J-B

PP

KPSS

No. of Obs.

Correlation with oil

− 3.752 − 3.094 − 1.774 − 2.968 − 2.691 − 2.513

3.538 2.865 1.711 3.242 2.862 2.714

− 0.126 − 0.926 − 0.221 0.288 − 0.370 − 0.238

7.339 11.183 9.058 5.522 12.959 12.130

3820.1*** 14234.4*** 7459.5*** 1353.4*** 20165.8*** 16902.6***

− 72.53*** − 71.26*** − 70.50*** − 69.40*** − 67.97*** − 66.23***

0.106 0.163 0.267 0.075 0.103 0.102

4853 4853 4853 4853 4853 4853

0.258*** 0.217*** 0.173*** 0.202*** 0.089***

− 8.195 − 6.411 − 3.697 − 6.227 − 6.169 − 5.818

7.785 6.596 3.817 7.666 6.593 6.026

− 0.496 − 0.858 0.038 0.278 − 0.273 − 0.243

6.076 7.650 7.310 4.888 5.389 5.013

422.1*** 992.7*** 751.1*** 156.6*** 242.7*** 173.3***

− 33.11*** − 32.21*** − 32.61*** − 32.02*** − 31.34*** − 30.13***

0.109 0.189 0.380 0.093 0.105 0.106

970 970 970 970 970 970

0.248*** 0.189*** 0.142*** 0.190*** 0.074**

− 18.84 − 12.50 − 6.195 − 14.52 − 11.77 − 11.47

15.07 13.31 8.525 12.68 14.81 12.90

− 0.411 − 0.603 − 0.315 − 0.221 0.589 − 0.007

3.319 5.302 4.954 4.971 4.960 4.626

7.298* 62.8*** 39.2*** 37.9*** 48.6*** 24.6***

− 14.12*** − 14.96*** − 17.40*** − 14.15*** − 17.41*** − 14.90***

0.084 0.209 0.405 0.091 0.096 0.101

223 223 223 223 223 223

0.271*** 0.198*** 0.155** 0.078* 0.018*

Note: This table reports the descriptive statistics and unit root properties of the data. Std. Dev. stands for standard deviations. J-B refers to the Jarque-Bera test with the null hypothesis of normality. The PP and KPSS abbreviations stand for the empirical statistics of the Phillips and Perron (1988) unit root tests, and the Kwiatkowski et al. (1992) stationarity test, respectively. ***, **, and * stand for significance at the 1%, 5%, and 10% levels, respectively.

oil price shocks (Brent) on the price of agricultural products before and after the food crisis of 2006–2008. Their concluding remarks indicate that oil price shocks have a much stronger influence on agricultural commodity markets in the post-crisis period, relative to the pre-crisis period. Through the fit of a structural VAR heteroskedasticity method, Fernandez-Perez et al. (2016) examine the contemporaneous interaction between energy (oil and ethanol) and agricultural (corn, soybean, and wheat) commodities for the June 1, 2006 - January 22, 2016 period. They find evidence of crude oil prices having a unidirectional contemporaneous impact on the price of agricultural commodities. Ahmadi et al. (2016) show that the response of commodities’ volatility to an oil price shock differs significantly depending on the underlying cause of the shock, whereas the explanatory power of oil shocks becomes stronger after the crisis. Batten et al. (2015) apply the Diebold and Yilmaz (2009) spillover index method to examine the spillovers and their time-varying direction in four precious metals, namely, gold, silver, platinum, and palladium. Their findings indicate that geopolitical and economic situations alter the direction of the commodities’ spillover effects. Kang et al. (2017) fit a multivariate dynamic equicorrelation (DECO) and a spillover index model to understand the volatility spillovers among energy, precious metals, and agricultural commodities (gold, silver, WTI crude oil, corn, wheat, and rice). They show that gold and silver are volatility transmitters to other commodity markets, whereas crude oil, corn, wheat, and rice are receivers of spillovers during stressed market scenarios. Algieri and Leccadito (2017) employ the quantile-based conditional Value-at-Risk method to investigate risk transmission between energy, food, and metal commodity markets for the May 2005 - June 2013 period. Their results show that energy markets are the main contagion risk triggers rather than metal and food markets. They also observe spillovers from energy to food markets. Despite several attempts to explain the interdependence and predictability between the prices of energy, precious metals, and agricultural commodities, no clear consensus has been reached, partly because of differences in methodological approaches such as model specifications, number of variables considered, and data usage. Further, the literature understands relatively little about the sign (positive or negative) of the spillover influence oil prices have on those of agricultural and precious metal commodities under investigation, particularly under extreme downside and upside oil market scenarios. This

period. The dynamic conditional correlation (DCC) model fitted by De Nicola et al. (2016) to analyze the degree of time-varying dependence among the nominal price returns of 11 major energy, agricultural, and food commodities shows that the price returns of energy and agricultural commodities are highly correlated. Using a two-stage procedure that relies on mean specification by means of vector error correction, and on the modeling of volatilities and volatility transmission through a multivariate GARCH (MGARCH) model, Cabrera-Lopez and Schulz (2016) examine the dependence relationship between energy and agricultural commodity prices in Germany. Their analysis, which is based on weekly data of biodiesel, crude oil, and rapeseed oil, identifies long-term co-movements between these commodities’ prices. Moreover, they acknowledge the strong volatility effects of biodiesel on the prices of agricultural commodities. Sadorsky (2014) implements a VARMAAGARCH and DCC-AGARCH to understand the dynamic volatilities and conditional correlations between the prices of stocks from emerging markets, and those of mineral (copper), energy (oil), and agricultural (wheat) commodities. His results indicate noticeable increases in the correlation between these commodities after 2008. The correlations are also observed to gradually return to pre-2008 levels, as the mid- and long-term effects of the 2008–2009 global financial crisis became milder. In relation to the second group of studies that examines the direction of the spillover effects between energy and other commodity markets, Saghaian (2010) uses Granger causality to test for the correlation and causality among oil, ethanol, and agricultural commodities (e.g., corn, soybean, and wheat) and identifies a strong correlation between some of the commodities modeled. However, we find mixed evidence of causality from oil to agricultural products. Sari et al. (2010) investigate the interdependence and spillover transmission between precious metals, exchange rates, and oil prices. Their findings indicate evidence of a strong short-run feedback relationship between the prices of precious metals and those of energy commodities. Nazlioglu et al. (2013) use a variance impulse response function (VIRF) and identify critical points in time at which the spillover effects between oil and agricultural commodities (i.e., corn, soybeans, wheat, and sugar) are significantly different both, before and after the 2006–2008 food crisis. In addition, they observe that, the volatility of oil markets spillover on the prices of agricultural commodities in the post-crisis period. Wang et al. (2014) apply a structural VAR analysis to investigate the impact of 3

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Fig. 1. Time series plots of oil (blue) and commodity (red) prices. Note: Plots of oil price series (left axis) relative to those of precious metals and agricultural commodities prices (right axis). The sample data span January 3, 2000 to August 9, 2018.

paper fills a gap in the relevant literature by adequately tackling that extreme oil market-based interdependence and spillover problem, through the fit of the CQ modeling technique of Han et al. (2016).

account for extreme comovements of the variables under consideration. Another advantage of the CQ methodology is that it makes the measurement of cross-correlation for large lags possible. The methodology is a recent proposition and as such, it is an innovative measure of dynamic interdependence under varying market conditions. In estimating the interdependence and directional predictability between time series, the CQ considers the time series’ time lead-lag codependence. Analytically, let us define {x i, t ,t Z } , for i = 1, 2, as two strictly stationary time series and x1, t and x2, t represent the returns of oil and that of a precious metal (gold and silver) or an agricultural commodity (corn, wheat, rice), respectively. Now, let Fi ( ) and fi ( ) stand for the probability cumulative distribution and density functions of time series x1, t and x2, t , respectively. The quantile of a certain time series x i, t , which captures and models observations at various locations (negative tail, center, and positive tail) of a marginal distribution, can be represented by qi ( i ) = inf {v:Fi (v ) i} , for i [0,1]. In contrast, the quantiles of the two-dimensional series, where α ≡ ( 1, 2) , can be expressed by (q1 ( 1) q2 ( 2)) . The CQ for -quantile with k lags is

3. Cross-quantilogram methodology Han et al. (2016) introduced the Cross-Quantilogram (CQ) methodology for the modeling of interdependence and spillover influence between time series at stationary levels for different quantiles of the return distribution. The CQ is an extension of the Quantilogram method proposed by Linton and Whang (2007). Han et al. (2016) specifically extended the applicability of the CQ by broadening it to accommodate bivariate joint distributions. The CQ is advantageous in that it captures the lead-lag causal relationship and correlation between pairs of variables and is not dependent on the second moment (conditional variances) of the distribution to draw the interdependence between variables at different quantiles. The CQ also relies on cross-quantiles of variables and by employing lower, medium, and upper quantiles, it can 4

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Table 2 Linear Granger causality tests.

Table 4 Parameter (in)stability tests.

H0: WTI does not Granger cause commodities returns Panel A: Daily data series Silver 5.3718*** Gold 0.9968 Wheat 7.4824*** Corn 3.3792* Rice 1.9562 Panel B: Weekly data series Silver 0.6910 Gold 0.6139 Wheat 0.0853 Corn 0.6925 Rice 0.9642 Panel C: Monthly data series Silver 0.6969 Gold 1.2853 Wheat 0.4262 Corn 0.1584 Rice 3.9109**

Order of the VAR(p)

Silver Panel A: Daily data series Sup LR 7.053*** Exp LR 5.527*** Mean LR 6.014*** Panel B: Weekly data series Sup LR 9.718*** Exp LR 4.555*** Mean LR 4.987*** Panel C: Monthly data series Sup LR 7.007*** Exp LR 3.697*** Mean LR 5.032***

2 6 1 1 1 1 5 1 1 1

Commodities equation Panel A: Daily data series Silver 10.829*** 13.394*** Gold 5.495*** 7.394*** Wheat 6.891*** 8.697*** Corn 11.270*** 14.429*** Rice 11.357*** 12.801*** Panel B: Weekly data series 4.822*** Silver 3.947*** Gold 5.692*** 6.688*** Wheat 4.287*** 6.076*** Corn 3.550*** 4.847*** Rice 2.098** 3.128*** Panel C: Monthly data series Silver 0.385 1.625 Gold 0.568 1.447 ** Wheat 2.123 2.405** Corn 1.830 1.465 Rice 3.008*** 3.659*** Oil equation Panel A: Daily data series Silver 10.970*** 13.784*** Gold 10.980*** 13.787*** Wheat 10.959*** 13.771*** Corn 10.978*** 13.785*** Rice 10.983*** 13.789*** Panel B: Weekly data series Silver 5.632*** 6.970*** Gold 5.562*** 6.909*** Wheat 5.529*** 6.846*** Corn 5.545*** 6.846*** Rice 5.590*** 6.880*** Panel C: Monthly data series 4.697*** Silver 3.958*** Gold 4.200*** 4.758*** Wheat 4.409*** 5.174*** Corn 4.632*** 5.304*** Rice 4.671*** 5.343***

Corn

Rice

6.117*** 4.719*** 5.265***

4.792*** 2.609*** 3.166***

4.471*** 3.676*** 3.300***

2.770** 1.829** 1.957**

8.404*** 3.484*** 5.866***

3.592** 2.217** 2.411**

7.364*** 3.180*** 3.344***

6.283*** 3.359*** 3.609***

5.031*** 3.852*** 4.307***

6.703*** 4.891*** 5.565***

4.973** 3.000*** 2.739***

5.467*** 1.886*** 2.220***

defined as:

(k ) =

m= 4

m= 5

m= 6

15.385*** 9.180*** 9.910*** 16.386*** 13.734***

17.224*** 10.469*** 11.297*** 18.480*** 14.389***

19.087*** 11.646*** 12.686*** 20.597*** 15.276***

6.020*** 7.395*** 6.868*** 5.840*** 4.034***

7.243*** 8.574*** 7.790*** 6.717*** 5.009***

8.392*** 9.304*** 8.456*** 7.176*** 5.657***

2.329** 2.061** 2.115** 2.352** 3.702***

3.193*** 2.487** 2.069** 2.853** 4.257***

4.244*** 2.882** 1.912 2.937** 4.404***

16.437*** 16.433*** 16.431*** 16.457*** 16.448***

18.247*** 18.246*** 18.241*** 18.294*** 18.256***

20.293*** 20.293*** 20.288*** 20.354*** 20.300***

8.014*** 7.995*** 7.845*** 7.868*** 7.916***

8.660*** 8.670*** 8.476*** 8.510*** 8.579***

9.345*** 9.378*** 9.113*** 9.163*** 9.262***

5.001*** 4.928*** 5.517*** 5.607*** 5.644***

5.080*** 4.980*** 5.699*** 5.734*** 5.807***

5.370*** 5.317*** 6.043*** 6.159*** 6.265***

E[ E[

1 (x1, t 2

q1 ( 1))

1 (x1, t

2 (x2, t k

q1 ( 1))] E [

2

q2 ( 2))]

2 (x2, t

(1)

q2 ( 2))]

For the time lags k = 0, ± 1, ± 2, …, and where the function a (µ) ≡ 1 [µ < 0] , the term I ( ) is an indicator function. The upper boundary process 1 [x i, t qi ( i )] refers to a quantile exceedance (or quantile hit). The parameter (1) is a quantile-based estimator of crosscorrelation between pairs of variables, i.e., energy, precious metals, or agricultural commodities. Unlike standard estimators of correlation (e.g., Pearson, Spearman, and Kendall tau), the cross-correlation (1) accounts for time lag effects between series. Accordingly, the CQ measures the cross-correlation of a time series below or above a quantile qret ( ret ) or qvol ( vol ) at time t with respect to another time series that is above or below the quantile qbs ( bs ) at time t–1. When (1) = 0 , no time lead-lag effect or predictability is identified between two time series of returns. Therefore, the distribution of x2, t (when estimating the time lead-lag effect from x1, t to x2, t ) is below or above a quantile qbs ( bs ) at time t. On the contrary, the case (1) 0 suggests that the cross-correlation and predictability effect is identified from one series to another at = ret ( bs ) or vol ( bs ). The CQ sample counterpart cross-correlation in the inverse direction is estimated as follows:

Table 3 BDS test of Brock et al. (1996). m= 3

Wheat

Note: * ** , * * and * denote significance at 1%, 5%, and 10%, respectively. Significance level is determined by the p-value calculated using 2000 bootstrap repetitions.

5 2 1 1 1

Note: The table reports the F-statistics for the “no Granger causality” restrictions imposed on a linear vector autoregressive (VAR) model under the null hypotheses H0. The order (p) of the VAR is determined by the Akaike Information Criterion (AIC). *** indicates rejection of the null hypothesis of no Granger causality at the 1% level of significance.

m= 2

Gold

T t = k +1

ˆ (k ) =

T t = k +1

2

1 (x1,

1 (x1, t t

q1 ( 1)) qˆ1 ( 1))

2 (x2, T t = k +1

t k 2

2 (x2,

qˆ2 ( 2)) t k

qˆ2 ( 2 )) (2)

The qˆi ( i ) parameter in Eq. (2) stands for the unconditional sample quantile of x i, t . In addition, when verifying and testing for the estimated cross-correlations, we fit a quantile version of the Ljung-Box-Pierce statistic as H0 : (k ) 0 for all k ϵ 1, …, p, against the alternative hypothesis of H1 : (k ) = 0fork 1, …, p , under the following statistic: (p) Qˆ =

T (T + 2) T (p)

p k=1

k

ˆ 2 (k )

(3)

where Qˆ represents a portmanteau test of directional predictability from one time series to another according to p lags and the quantile pair = ( 1, 2 ). Considering that the asymptotic distribution of the estimated CQ may be subject to noise, Han et al. (2016) recommend the stationary bootstrap test of Politis and Romano (1994) to reduce this noise. By accommodating random block lengths of the distribution, this test more accurately approximates the asymptotic distribution of serial dependence. Specifically, let Bki, Li = {(x1, t x2, t k )}tL=i ki1 be the ith block with length Li starting from ki , whereas Li stands for an independent ) s 1, and identically distributed (i.i.d.) variable with Pr (Li = s ) = (1 s = 1, 2, …, for (0,1) . The sequence parameter ki is distributed

Note: The entries indicate the BDS test based on the residuals of the WTI return series and the commodity return series in a VAR for various countries. m denotes the embedded dimension of the BDS test. *** indicates the rejection of the null of residuals being i.i.d. at the 1% level of significance. 5

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Fig. 2. Heat maps of cross-correlation between daily WTI oil returns and commodity returns. Note: These figures show the CQ in the form of heat maps. The quantile levels with no significant directional predictability are set to zero. The colored rectangles are the predictable regions where the Box–Ljung test statistic is statistically significant. In each heatmap, the horizontal axis represents oil return quantiles, while the vertical axis represents precious metals/commodities return quantiles.

according to {i = 1,2, …T } and is also an i.i.d. sequence. Moreover, given that the upper limit Bki, Li may exceed the sample size T , when t > T we substitute the pair (x1, t x2, t k ) by (x1, j x2, j k ) with j = k + (t mod(T k )) . In obtaining the confidence intervals through bootstrapping, we pseudo-resample according to the sequence of blocks, implement the CQ methodology, and fit the portmanteau test defined in Eq. (3). The CQ analysis is visually presented as heat maps, which provides the cross-quantile unconditional bivariate correlation between two distributions. The quantile hits represent the quantile distributions [q = (0.05, 0.1,0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95)] of the two variables in the x- and y-axes. Note that the heatmap shows the 121 cells of the quantile combinations of variables and the color scale indicates the

correlation between -1.0 and 1.0. 4. Data and preliminary analysis The data set consists of daily, weekly, and monthly future continuous settlement prices for oil, precious metals, and agricultural commodities, namely, WTI oil, silver, gold, wheat, corn, and rice. Our motivation for selecting oil in our analysis, in relation to precious metals and agricultural commodities, is that oil in its role as a global economic factor is likely to influence gold and silver prices, which have historically been stable (more noticeably for silver) or have appreciated (more noticeably for gold) as inflation, being positively correlated with 6

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Fig. 3. Heatmaps of cross-correlation between weekly WTI oil returns and commodity returns. Note: These figures show the CQ in the form of heat maps. The quantile levels with no significant directional predictability are set to zero. The colored rectangles are the predictable regions where the Box–Ljung test statistic is statistically significant. In each heatmap, the horizontal axis represents oil return quantiles, while the vertical axis represents precious metals/commodities return quantiles.

oil prices, increases.1 Our motivation to select and model corn prices in relation to oil prices is that corn, which is used to produce ethanol fuel, can affect oil demand through the substitution effect. Accordingly, since ethanol fuel prices partially depend on those of oil prices, an indirect

relationship of spillover influence must exist between oil prices and corn prices. Thus, increases in oil prices would lead to higher demand for corn, which in turn would lead to higher ethanol fuel prices. The inclusion of wheat markets is justified by the impact corn has on the price of wheat. Both corn and wheat prices have been observed to display a bidirectional influence. Moreover, wheat prices are said to be Granger caused by oil prices (Saghaian, 2010). We include rice in our analysis because oil-derived products are used in rice production. In modern agriculture in particular, rice processing depends on oil products to deliver rice to end consumers and to produce it using farming

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Due to the positive correlation of oil prices with inflation, investors tend to seek hedging and diversification, when interest rates and inflation increase, through divestment in assets liable to inflation increases, and by investing in value stabilizers or wealth protectors such as gold and silver that negatively correlate with inflation. 7

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Fig. 4. Heatmaps of cross-correlation between monthly WTI oil returns and commodity returns. Note: These figures show the CQ in the form of heat maps. The quantile levels with no significant directional predictability are set to zero. The colored rectangles are the predictable regions where the Box–Ljung test statistic is statistically significant. In each heatmap, the horizontal axis represents oil return quantiles, while the vertical axis represents precious metals/commodities return quantiles.

equipment. Further, some chemicals and fertilizers used in rice production are partly extracted from petroleum. Consequently, we could expect some type of spill over influence from changes in oil prices to rice prices. The time series sampled span from January 3, 2000 to August 9, 2018. We choose this period because it accounts for two escalating trends in oil prices (e.g., from around 2002 to the middle of 2008, and from early 2009 to early 2011) and two declining trends in oil prices (e.g., from the middle of 2008 to the beginning of 2009, and from August 2014 to the end of 2015). We calculate continuously

compounded daily returns by taking the difference in the logarithms of two consecutive prices. The data was extracted from Thompson Reuters Datastream international.2 Table 1 displays the descriptive statistics of WTI oil, the precious metals (gold and silver), and the agricultural commodities (wheat, corn, and rice). Precious metal commodities appear to have the largest historical mean returns, with gold taking the lead. A risk return analysis

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Data codes are provided in Table A.1 in the Appendix A.

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Fig. 5. Recursive CQ between daily WTI oil and commodity returns. Note: The vertical (horizontal) axis represents the quantile hits for the precious metal and agricultural commodity markets (time). The starting year of the rolling window is marked on the horizontal axis. The left, middle, and right columns, respectively, show the 5%, 50%, and 95% quantiles for the oil returns while, the red, blue, and green lines represent the 5%, 50%, and 95% quantiles for the precious metals/ commodities returns. Lag p = 1.

indicates that the best risk-return trade-off is offered by gold for daily, weekly, and monthly observations, followed by silver, while the worst return relative to risk is offered by oil, followed by rice. Interestingly, the two precious metals that offer the highest returns are also those with the largest negative skewness, thus displaying a higher propensity to undergo negative short- and long-term price trends once a downward trend sets in. The kurtosis values for all return series are greater than three (> 3), with corn daily returns having the largest kurtosis. These values indicate the presence of fat tails and of abnormally distributed observations. The Jarque-Bera (J-B) test for each of the commodity return time series is statistically significant at the 1% significance level, indicating the absence of a Gaussian or normal

distribution in the returns. In examining the stationarity process, we use the Phillips and Perron (1988) unit root test and the Kwiatkowski et al. (1992) stationary test. The results indicate that all index return series are stationary at conventional levels. Fig. 1 displays the times series plots for all energy, precious metal, and agricultural commodities modeled. It demonstrates that each of them is strongly affected in the downside by the 2008 financial crisis that stemmed from the US subprime mortgage-backed security market. There is, moreover, a positive correlation between the oil price series (in blue) and the commodities series during that period (in red). There is also an overall parallel positive trend between all commodity price series and those of oil in the medium term from the start of the sample 9

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Fig. 6. Recursive CQ between weekly WTI oil and commodity returns. Note: The vertical (horizontal) axis represents the quantile hits for the precious metal and agricultural commodity markets (time). The starting year of the rolling window is marked on the horizontal axis. The left, middle, and right columns, respectively, show the 5%, 50%, and 95% quantiles for the oil returns while, the red, blue, and green lines represent the 5%, 50%, and 95% quantiles for the precious metals/ commodities returns. Lag p = 1.

period until the 2008 crisis, and for some commodities even afterwards (except for gold and rice). Looking at the long-term behavior of the pairs of oil-commodity series, the commodities that could act less as diversifiers of oil risk are gold, silver, and rice (they display a stronger positive correlation or greater trend resemblance at different scales), while those for corn and wheat may serve for diversifying oil price risk mainly in the short and medium terms. A large spike can be observed in all commodities prior to the 2008 crisis, reflecting the effects of the peak in the global economic boom (from 2007 to the first quarter of 2008). It is also worth noting that during the last years of the data sample, with the exception of gold and rice, all other commodities would not diversify oil price risk, given that they are influenced on the downside by the 2014 sharp oil price decline.

5. Empirical results and discussion In this section, we first present the results obtained from the linear Granger causality tests; Brock, Dechert and Scheinkman (BDS) tests of nonlinearity; and the parameter (in)stability tests for daily, weekly, and monthly observations (returns). These tests are included to justify the use of the CQ approach and to highlight its adequacy in accounting for nonlinear dependence behavior in extreme data quantiles. The results of the linear Granger causality tests displayed in Table 2 indicate that oil markets better explain and predict daily future silver and wheat prices, based on a 99% confidence level. Table 3 displays the outcome of the BDS test. This test accounts for nonlinear serial dependence between the modeled commodity time series. All commodity 10

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Fig. 7. Recursive CQ between monthly WTI oil and commodity returns. Note: The vertical (horizontal) axis represents the quantile hits for the developed markets (time). The starting year of the rolling window is marked on the horizontal axis. The left, middle, and right columns, respectively, show the 5%, 50%, and 95% quantiles for the oil returns while, the red, blue, and green lines represent the 5%, 50%, and 95% quantiles for the precious metals/commodities returns. Lag p = 1.

pairs are observed to display some degree of nonlinear dependence at the 99% confidence level, indicating that linear Granger causality does not adequately capture interdependence and predictability effects when the joint distribution of pairs of variables is asymmetric and nonlinear. Table 4 displays the values of short-run parameter (in)stability tests, the Sup-LR, Mean-LR and Exp-LR tests, proposed by Andrews (1993) and Andrews and Ploberger (1994).3 These tests are applied to examine the stability of short-run parameters. Based on the sequence of Lagrange multiplier statistics, they test the null hypothesis of parameter stability

against the alternative of a one-time structural change. They require trimming of the sample (15% from both ends) and the critical values (and p-values) are obtained using a parametric bootstrapping (Monte Carlo simulation using 2000 samples) to circumvent the use of asymptotic distributions (See Balcilar et al., 2010 for a detailed explanation of these tests). The test results (reported in Table 4) indicate significant evidence of short-run parameter instability and hence the usual Granger causality tests, based on the short-run parameters, will not be reliable. To show the directional predictability from oil to commodities for an entire range of quantiles, we present our results in the form of heat maps, where the x-axis always corresponds to a quantile of WTI oil returns and the y-axis always corresponds to a quantile of precious

3 The acronyms Sup-LR, Mean-LR and Exp-LR stand for supremum likelihood ratio, mean likelihood ration, exponential likelihood ratio.

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estimation in each step.6 To have reliable results, our initial sample includes 500 observations (approx. 2 years). The initial sample includes 100 and 30 observations for weekly and monthly data, respectively. This recursive estimation process continues until the last observation of the sample is reached. Figs. 5–7 display the dynamic interdependence and spillovers, based on recursive sampling design, from oil returns to precious metals and agricultural commodities returns using daily, weekly, and monthly frequency data and for lower (0.05), middle (0.50) and upper (0.95) quantiles. The vertical (horizontal) axis represents the quantile hits for the commodity markets (time). The left, middle, and right columns, respectively, show the 5%, 50%, and 95% quantiles for the oil returns while, the red, blue, and green lines represent the 5%, 50%, and 95% quantiles for the precious metals/ commodities returns. A broad look at the plots for all three quantile levels shows that the largest co-dependence from oil to most of the commodities occurred in the lower quantiles (most noticeably), and in the upper quantiles. This implies that oil price spillovers are stronger and most significant on all precious metal and agricultural commodities when oil prices undergo sharp trends of decline. The daily frequency quantile spillover dependence displays a more or less similar pattern to those based on weekly and monthly frequency quantiles.

metals and agricultural commodity returns. Figs. 2–4 show only significant dependencies for daily, weekly, and monthly frequency data, respectively. These figures show 121 (11 ×11) measures of dependence across the entire range of quantiles of the bivariate distribution of returns and the magnitude of the dependency measures (using the color scale). Note that heat maps are provided for different values of the lag order, for a robustness check. We mainly focus on the results of the baseline model with a lag order equal to 1.4 According to Fig. 2, the daily spillover and directional predictability from oil markets to commodities occur at varying degrees for the lower quantiles (0.05) or in extreme downside of the oil market when oil prices undergo sharp decline. This indicates that spillovers more clearly and strongly occur during oil market downturns, compared with oil market upturns. The positive (negative) effects of lower oil returns quantiles are significant on gold, silver, and rice (wheat) returns whereas this effect is less significant on corn returns. This effect of oil on wheat and corn prices could have to do with the use of oil-derived fuels for the production, processing, and transportation of wheat and corn. Indirectly, oil price changes could also be expected to influence wheat prices through their impact on corn prices, which have been identified to bi-directionally correlate with wheat prices (Saghaian, 2010). The negative impact of oil prices on those of corn may occur indirectly through decreasing demand in ethanol fuel, which is a substitute, extracted from corn processing. In the upper quantiles (0.95) or in extreme upside oil market circumstances, when oil prices undergo sharp trends of escalation, we observe that spillover and directional predictability are significant for gold, silver, and corn only. This negative effect is coherent with the response of corn prices as oil prices increase because higher oil prices create higher demand for alternative fuels, such as ethanol fuel that is extracted from corn. It is also congruent with the positive response of gold and silver prices to oil price increases, given the aforementioned positive correlation between oil prices and inflation rates. In other words, as the oil price increases inflation rates also increase, investors in turn invest in gold and silver to hedge against the rise in inflation. In the middle quantiles (0.50) or in normal oil market circumstances, when oil prices neither undergo sharp trends of escalation nor sharp trends of decline, no spillover effect and predictability from oil to each of the precious metals and agricultural commodities under investigation are observed. No sufficient financial incentive is triggered in these precious metal and agricultural commodity markets by relatively small changes in oil prices.5 The above identification of spillover and predictability effects in the lower and upper quantile distributional segments, where nonlinear behavior tends to occur, justifies the adequacy and implementation of the CQ methodology. On the other hand, it highlights the inability of the Granger causality modeling approach to capture anomalous behavior in the distribution of the commodities’ price observations. From the perspective of hedging and diversification, silver and gold, which have traditionally been used to stabilize value and protect wealth when oil prices undergo mid- and long-term sharp trends of escalation, do not offer the expected diversification benefits. From the agricultural commodities considered, only corn and wheat investments could be used to hedge against sharp trends of oil price decline. Finally, we use a recursive sampling approach and the length of the sample window increases by 22 days (approx. 22 days) for the

6. Conclusion and policy implications As the demand for agricultural commodities and their consumption increases worldwide in response to population growth and increasing income levels in emerging and developing countries, the funding and subsidizing involved in producing and delivering these commodities to end consumers are rising significantly. This increases their risk exposure to changes in global factors, such as oil, which plays an important role in driving and determining their prices through its influence on countries’ macroeconomic variables and in substitute oils from the agro industry. Sharp and extreme negative or positive fluctuations in oil prices may indeed lead to significant losses for agricultural producers (particularly corn producers in our study), thus making it less affordable in many countries to continue in the agro industry, particularly in those countries where agricultural subsidy packages are not significant (i.e., where agricultural sectors are more vulnerable to extreme trends of oil price escalation). By contrast, considering the positive correlation that oil prices have with inflation and with the increase of foreign direct and capital investments, which tend to increase inflation, the demand for precious metals such as gold and silver, and consequently, their prices as well, could be expected to rise. Given the aforementioned structure of interdependence and spillover effect between oil prices and those of agricultural and precious metal commodities, this research attempts to find out whether these commodities can be used to diversify and hedge investment portfolios under extreme downside and upside oil market scenarios. This is accomplished through implementing the extreme quantile cross-quantilogram methodology of Han et al. (2016). We find evidence of extreme low oil return quantiles having a positive effect on the lowest quantiles of gold, silver, and rice, based on the analysis of daily frequency data. The implication of these results is that these precious metal and agricultural commodities cannot act as diversifiers of oil price risk in downside extreme market circumstances. The results are similar for weekly and monthly frequency data, however less strong. The lowest quantiles of oil either have a negative affect or do not have any effect on the lower quantiles of wheat and corn, making them suitable for extreme oil downturn hedging. The implications of the results suggest that producers of agricultural commodities such as corn and wheat must pay careful attention to trends of decline in oil prices to adequately design pre-emptive

4 It should be noticed that the daily, weekly, and monthly spillovers are found in general to be effective in the short-term (lag p = 1), implying that the effect of oil prices on those of agricultural and precious metal commodities is most significant in the short-term periods. 5 It should be noted that for all daily, weekly, and monthly observations, the interdependence between variables is significant mainly for lag p = 1. We also observe no change in the results when 2000 bootstrapped replications are considered. These results can be provided by the corresponding author on request.

6 The window increases by 4 weeks and one month for weekly and monthly frequency data, respectively.

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measures for commodity pricing and for the risk management of increasing production, processing, and delivery costs. For these stakeholders the determination of optimal time and amount of price increases in the commodities they deal with could affect their financial statements positively or negatively. Mistiming may decrease gains and increase costs. Delays in increasing or decreasing production, taking into account that crop production, processing, and delivery have their own timing (lapses), according to forecasted changes in oil prices may also increase or decrease opportunity costs and gains. Producers aware of the short-term spillover characteristics of oil under extreme market scenarios are in a better position to adjust prices (i.e., for corn, gold, and silver) when oil prices increase, taking into account the corn-based ethanol substitution effect and the positive correlation inflation has with oil price changes. For producers of these commodities specifically, an initial trend of price escalation in oil prices signals and suggests to them the consideration of price increases scaled by the coefficients of the strength of association between variables and the forecasted consumer price index levels of the commodity and sector. Further, the identified dynamics of dependence between oil prices and those of the commodities most strongly affected by oil price changes could serve for better determining the allocation of subsidy packages in the energy and

agricultural sectors (two sectors largely subsidized in developed and developing countries), and for more adequate rebalancing of public sector resource allocation and investments. If oil prices are expected to affect the prices of agricultural commodities negatively, subsidy determination should be adjusted to support producers and maintain product prices within a reasonable range to allow for their affordability to the lowest income earners. From the perspective of hedging and diversification, silver and gold may serve to stabilize value and protect wealth when oil prices undergo mid- and long-term sharp trends of escalation, due to the positive correlation between oil prices and inflation. Moreover, only corn investments could be used to hedge against sharp trends of decline in oil prices, as sharp decreases in oil prices only mildly influence those of wheat and rice. Acknowledgments The last author acknowledges receiving financial support from the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF- 2017S1A5A8019204). The third author is thankful for the financial support provided by the Jan Wallander and Tom Hedelius Foundation.

Appendix A See Table A.1 Table A.1 Data and code. Source: Thompson Reuters Datastream International Name

Code

NYM-Light crude oil continuous settlement price CMX-Silver 5000 OZ continuous settlement price CMX-Gold 100 OZ continuous settlement price CBT-Corn composite continuous settlement price CBT-Wheat composite continuous settlement price ECBOT-Rough rice continuous settlement price

nclcs00 nslcs00 ngccs00 ccfcs00 cwfcs00 czrcs00

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Further reading Quantile dependence between foreign exchange market and stock market: the case of Korea. East Asian Economic Review 20(4), pp. 519–544.

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