Commodity Dynamics: A Sparse Multi-class Approach
CCommodity Dynamics: A Sparse Multi-class Approach
Luca Barbaglia ∗ , Ines Wilms, and Christophe Croux KU Leuven, Faculty of Economics and Business
Abstract.
The correct understanding of commodity price dynamics can bring relevant improvementsin terms of policy formulation both for developing and developed countries. Agricultural, metal and energycommodity prices might depend on each other: although we expect few important effects among the totalnumber of possible ones, some price effects among different commodities might still be substantial. Moreover,the increasing integration of the world economy suggests that these effects should be comparable for differentmarkets. This paper introduces a sparse estimator of the Multi-class Vector AutoRegressive model to detectcommon price effects between a large number of commodities, for different markets or investment portfolios.In a first application, we consider agricultural, metal and energy commodities for three different markets.We show a large prevalence of effects involving metal commodities in the Chinese and Indian markets, andthe existence of asymmetric price effects. In a second application, we analyze commodity prices for fivedifferent investment portfolios, and highlight the existence of important effects from energy to agriculturalcommodities. The relevance of biofuels is hereby confirmed. Overall, we find stronger similarities in com-modity price effects among portfolios than among markets.
Keywords:
Commodity prices; Multi-class estimation; Vector AutoRegressive model
JEL classification:
Q02; O13; C32 ∗ Corresponding author: KU Leuven, Faculty of Economics and Business, Naamsestraat 69, B-3000 Leuven, Belgium.
Email address : [email protected],
Phone : +32 16 37 37 84. a r X i v : . [ q -f i n . E C ] O c t Introduction
Commodity price dynamics are crucial for the worldwide economic activity (Labys, 2006). Up to 20% ofthe world merchandise trade involves commodities (Nazlioglu et al., 2013). Commodities are central forboth producing and consuming countries. For producing countries, export earnings from commodities areoften the main source of revenues. Therefore, commodity price dynamics have an important impact on themacro-economic performance and living standards of these countries, often developing countries (Cashin andMcDermott, 2002; Deaton, 1999; Rossen, 2015). For consuming countries, commodities are important inputsfor many industries. As such, understanding commodity price dynamics is essential for economic planningand forecasting (Arezki et al., 2014; Rossen, 2015). Hence, studying commodity price dynamics has socialand political relevance.We study the effects between a large number of commodity prices. The Vector AutoRegressive (VAR)model is a standard tool to model these commodity price dynamics (Akram, 2009; Rezitis, 2015; Smiechet al., 2015). Most studies (e.g. Akram, 2009; Rezitis, 2015; Smiech et al., 2015) focus on one type ofcommodities, such as agriculture, energy, or metal, and model the price effects between a relatively limitednumber of commodities. They do this to tackle the over-parametrization problem of the VAR model sincethe number of parameters that need to be estimated increases quadratically with the number of includedtime series. An exception is Rossen (2015) who models up to 20 commodities, but requires more than 100years of monthly data to estimate the model using the standard least-squares estimator.We contribute to the extant literature on commodities by modeling a large set of prices belonging todifferent commodity types - namely agriculture , energy and metal - in a VAR framework. From an economicpoint of view, commodity prices can be interlinked. Commodities are exposed to spillover effects, that isprice effects from one commodity type (e.g. energy) to another (e.g. agriculture), as their production andconsumption might be dependent on each other (Akram, 2009; Nazlioglu et al., 2013; Smiech et al., 2015).Still, most studies consider only the effects between either energy and/or agricultural goods (Balcombe andRapsomanikis, 2008; Chen et al., 2010; Hassouneh et al., 2012; Nazlioglu and Soyatas, 2012; Serra et al.,2011). On the contrary, only few studies, such as Chen (2015), jointly study the effects between energy,metal and agricultural commodities. We extend this branch of the literature and jointly model the priceeffects between agriculture, energy and metal commodities. Although price effects among these commoditiesmight be substantial, we do not expect that each commodity influences each and every other commodity.To detect the most important commodity price effects, we use sparse estimation. The estimation is sparsein the sense that some of the commodity price effects are estimated as exactly zero. As such, only a smallnumber of effects are estimated as non-zero, which eases the interpretation.Another relevant contribution to the literature on commodities is that we jointly model commodity price2ffects for different markets . We would expect commodity price effects to be similar for the different marketssince commodity prices are assumed to follow global macro-economic trends (Rossen, 2015; Smiech et al.,2015 and references therein). In the economic literature, the standard methodology requires to first studyeach market independently, and only in a second step to verify the existence of comparable price effects forthe different markets. For instance, Rapsomanikis (2011) analyzes the price transmission structure betweena set of six food commodity markets in developing countries and the world index: he models each marketseparately and then compares the results in order to identify similar patterns. We extend this approach andpropose, instead of a standard VAR model, a Multi-class VAR , where the different classes are the differentmarkets. By jointly studying several markets in one large model we expect to obtain a more accurateestimation of the commodity effects and a more reliable comparison of these effects for different markets.We also propose a network analysis tool for the interpretation of the estimated effects that yields insightfulresults for commodity analysts. Yang et al. (2000) were the first to provide a network representation ofcommodity effects, but no further attempts followed. Nevertheless, network analysis has experienced greatpopularity in recent years in the field of financial econometrics (Diebold and Yilmaz, 2015) and big-dataanalysis (Kolaczyk, 2009). Our approach consists in drawing a network, one for each market, where only themost important commodity price effects are visualized. Similarities and/or differences in price effects can beimmediately detected by comparing the different market networks.We employ the sparse estimator of the Multi-class VAR to verify the interactions in two data sets ofcommodity spot prices: a market and a portfolio data set. The first data set considers prices of J = 14energy, metal and agricultural commodities for each of the K = 3 different markets, namely World, Indiaand China. Our results highlight the existence of effects from energy towards agriculture in all markets, andfrom energy and agriculture towards metal in the Indian and Chinese market. The second data set considersprices of J = 17 global, energy, metal and agricultural commodities for each of the K = 5 investmentportfolios. As for the markets, we expect to find comparable price effects for the portfolios (Anson, 2006).We detect important effects from energy towards agricultural commodities, in line with Chen et al. (2010);Nazlioglu and Soyatas (2012); Rezitis (2015), and towards precious metals, in line with Sari et al. (2010).The remainder of this article is organized as follows. The next section reviews the recent literatureon commodity price dynamics. Section 3 introduces the Multi-class VAR model, the corresponding sparseestimator and the network tools used to interpret the results. Section 4 considers the two data sets andverifies the effects among commodity prices using network analysis. Conclusions and directions for futureresearch are given in Section 5. 3 Background on Commodity Price Dynamics
Over the last decades commodity prices have tended to move together. A common explanation of this ten-dency is that commodity prices jointly respond to macro-economic trends (Pindyck and Rotemberg, 1990).Subsequent studies confirm these findings and suggest some possible economic explanations. Franckel andRose (2010), for instance, underline that rapid global growth, permissive monetary policy resulting in lowinterest rates, and increasing financial speculation might explain why commodity prices move closely to-gether. Nevertheless, commodity dynamics cannot only be explained by macro-economic factors. Additionalcomplexities might be encountered when considering, for instance, (i) different price types (e.g. spot pricesor derivatives), (ii) different commodity types (e.g. energy goods or precious metals) or (iii) inventory data.Furthermore, the recent “financialization” of commodity markets, i.e. commodities treated as a distinct assetclass by financial agents, has introduced a further level of complexity (Arezki et al., 2014; Belke et al., 2013).In recent years, a large flow of investment has been directed towards commodities, which are considered asmere alternative investment assets by financial agents.An important branch of the commodity literature looks at price convergence between national and inter-national markets (Bukenya and Labys, 2005). Two theoretical frameworks emerge from the literature: the“law of one price” and the concept of “market integration”. On the one hand, the “law of one price” statesthat for a given good, should all prices be expressed in the same currency, then a single price would be presentthroughout the world (Isard, 1977). On the other hand, “market integration” is observed when related goodsfollow comparable patterns over markets that are differently located (Ravaillon, 1986). Both theories havebeen tested empirically and contradictory results have been found for commodity markets. For instance,Yang et al. (2000) finds evidence of price convergence in the markets of soybean meal, whereas Bukenya andLabys (2005) do not verify price convergence when considering a lager set of metal and agricultural goods.The rising importance of numerous developing countries requires special attention when studying priceconvergence. Indeed, the rapid growth of the BRIC has played a central role in reshaping commoditydynamics (Franckel and Rose, 2010). The demand of energy and raw material is rising steadily drivenby the growing consumption in developing countries (Arezki et al., 2014). At the same time, the offerside is characterized by continuous changes and countries like India and China are now key players in thecommodity market. Consider, for instance, metal commodities: China not only represents the world’s largestconsumer of minerals and metals, but also the world’s largest producer (Klotz et al., 2014). These overallchanges in demand and offer sides should increase the interconnectedness among markets and might resultin stronger similarities among commodity markets (Chen, 2015). To address the topic of market integrationin developing countries, we compare commodity price effects for the Chinese, Indian and World markets.Another critical factor that has to be taken into account when studying commodity dynamics is tech-4ological change. A technological breakthrough might drastically change commodity price dynamics. Forexample, the “shale gas revolution” (Arezki et al., 2014), with the development of two key drilling tech-nologies (i.e. horizontal drilling and hydraulic fracturing), has made the extraction of unconventional gaspossible. As a result, the availability of natural gas steadily expanded and the overall energy price dynamicsadapted to the change. Biofuels (like ethanol or biodiesel) might be analyzed in a similar perspective sincetheir rapid development has drastically changed the dynamics between energy and agricultural commodities.The crops employed in biofuel distillation were no longer harvested only for food or feedstock purposes,but also for energy production. While prior to 2005 there were few effects between energy and agriculturalcommodities, Tyner (2010) shows that since 2006 stronger effects have been established among energy andagricultural goods.Numerous recent works have investigated the impact of biofuels on commodity dynamics, providingevidence of important effects from energy towards agricultural prices (Balcombe and Rapsomanikis, 2008;Chen et al., 2010; Hassouneh et al., 2012; Nazlioglu and Soyatas, 2012; Serra et al., 2011). Among them,Serra et al. (2011) prove the existence of strong effects between energy prices and corn in the US. Moreover,their findings confirm that the effects from energy towards corn occur through ethanol. Nazlioglu andSoyatas (2012) are the first ones to study a large set of commodities at world level. They model up to twentyagricultural prices and verify the existence of strong effects from the world oil prices to agricultural goods.This paper is in line with the analysis of Nazlioglu and Soyatas (2012) and investigates the effects fromenergy towards agricultural commodities and vice versa, for different markets and investment portfolios.
To study the commodity dynamics between J commodities for K markets (or K portfolios), we use theMulti-class VAR model of order P with K classes and J time series given by y ( k ) t = B ( k )1 y ( k ) t − + . . . + B ( k ) P y ( k ) t − P + e ( k ) t . (1)Here, y ( k ) t = [ y ( k ) t, , . . . , y ( k ) t,J ] (cid:48) contains the values of the J commodity prices for each class k ∈ { , . . . , K } at a given point in time t ∈ { , . . . , T } , where T is the length of the time series. The parameters B ( k ) p , for p ∈ { , . . . , P } and k ∈ { , . . . , K } , are J × J matrices capturing commodity price effects at lag p for class k . We denote each ij th entry of B ( k ) p as B ( k ) p,ij with i, j ∈ { , . . . , J } . These elements measure the direct,lagged effect of one commodity on another commodity (including itself). The error term e ( k ) t is assumed tofollow a multivariate normal distribution N ( , Σ ( k ) ), with the inverse error covariance matrix of each class5 denoted as Ω ( k ) = ( Σ ( k ) ) − . Without loss of generality, we assume that all series are mean centered suchthat no intercept is included.In our market application with K = 3 markets and J = 14 commodities, 3 × ×
14 = 588 autoregressiveparameters need to be estimated in the VAR of order P = 1. To make estimation possible and to easeinterpretation, we use sparse estimation such that many elements of the matrices B ( k ) p , for p ∈ { , . . . , P } and k ∈ { , . . . , K } , are estimated as zero. Moreover, we expect the parameter vector to be sparse ina structured manner, not in an irregular way (Wainwright, 2014). In particular, we expect the effect ofcommodity A on commodity B to be similar for the different markets (or portfolios). Structured sparsitymethods take this into account in the estimation procedure (e.g. Jenatton et al., 2011). We use the fusedlasso (Tibshirani et al., 2005) to encourage such shared patterns of sparsity among classes (cfr. Subsection3.2).Furthermore, 3 × (14 × / Ω ( k ) ,for k ∈ { , . . . , } of our market application need to be estimated. The elements of Ω ( k ) are the partialcorrelations between the error terms of the J equations of class k . Should the ij th element of Ω ( k ) bezero, then there would be no partial correlation between the error terms of equation i and j of class k . Weencourage a similar sparsity pattern of the partial error correlations among classes by using the fused lasso. We define the penalized least-squares estimator for the Multi-class VAR. Let N = T − P be the number oftime observations actually available given the VAR of order P . We seek (cid:98) B = [ (cid:98) B (1) (cid:48) , . . . , (cid:98) B ( K ) (cid:48) ] (cid:48) such that (cid:98) B =argmin B K (cid:88) k =1 N (cid:88) t =1 ( y ( k ) t − B ( k ) Y ( k ) ) (cid:48) ( y ( k ) t − B ( k ) Y ( k ) )+ λ K (cid:88) k =1 J (cid:88) i,j =1 P (cid:88) p =1 | B ( k ) p,ij | + λ K (cid:88) k (cid:54) = k (cid:48) J (cid:88) i,j =1 P (cid:88) p =1 | B ( k ) p,ij − B ( k (cid:48) ) p,ij | , (2)where B ( k ) = [ B ( k ) (cid:48) , . . . , B ( k ) (cid:48) P ] is the J × JP matrix of autoregressive coefficients, and Y ( k ) = [ y ( k ) (cid:48) t − , . . . , y ( k ) (cid:48) t − P ] (cid:48) is the JP × λ , λ > lasso and fusion penalties of the autoregressive coefficients. In the context ofunivariate regression a similar estimator was proposed by Kim and Xing (2009).The first penalty corresponds to the lasso penalty (Tibshirani, 1996): the L -norm of the autoregressivecoefficients shrinks the elements of B and sets some of them exactly to zero. The larger the parameter λ , the sparser the estimate of B . The second penalty term corresponds to the fusion penalty (Tibshiraniet al., 2005): the L -norm of the difference between B ( k ) p,ij and B ( k (cid:48) ) p,ij encourages corresponding autoregressivecoefficients in class k and k (cid:48) to take the same value by shrinking their difference towards zero. The largerthe value of λ , the more elements of B will be identical for the different classes.6he error terms of class k are not likely to be independently drawn and gains in estimation accuracymight be achieved by accounting for their correlation structure (e.g. Rothman et al., 2010). Therefore, weuse a generalized version of the penalized least-squares criterion in (2). We replace the first term in formula(2) by K (cid:88) k =1 N (cid:88) t =1 (( y ( k ) t − B ( k ) Y ( k ) ) (cid:48) Ω ( k ) ( y ( k ) t − B ( k ) Y ( k ) ) − log | Ω ( k ) | ) , and also estimate the inverse error covariance matrix Ω ( k ) for each class k . Moreover, we include tworegularization parameters for the sparse multi-class estimation of the elements of the inverse error covariancematrix as in Danaher et al. (2014). As done for the autoregressive coefficients, we guarantee sparsityof the inverse error covariance matrix with a lasso penalty on the elements of Ω ( k ) . Furthermore, weencourage similar sparsity patterns among classes with a fusion penalty, which considers the differencebetween corresponding elements of the inverse error covariance matrix among classes. Throughout theremainder of the paper we use the generalized version of the penalized least-squares criterion in (2).We use an iterative algorithm to obtain the estimates of the autoregressive parameters (cid:98) B ( k ) and theestimates of the inverse error covariance matrices (cid:98) Ω ( k ) of each class k ∈ { , . . . , K } . First, we solve for theautoregressive parameters conditional on the inverse error covariance matrices using the Smoothing ProximalGradient (SPG) algorithm (see Chen et al., 2012). The SPG algorithm provides a flexible way to approximatethe minimizer of an objective function that incorporates both fusion and lasso penalties. Second, we solvefor the inverse error covariance matrices conditional on the autoregressive parameters, which correspondsto the Joint Graphical Lasso on the residuals of the Multi-class VAR model. This Joint Graphical Lassois computed using the Alternating Directions Method of Multipliers algorithm (Danaher et al., 2014). Thecode of the algorithm is available from the authors upon request. The interpretation of the estimated coefficients (cid:98) B (1) , . . . , (cid:98) B ( K ) is done via network analysis. We focus on thecross-commodity effects , i.e. the off-diagonal elements of (cid:98) B (1) , . . . , (cid:98) B ( K ) . We build a directed network ofcommodities for each class, where the nodes are the different commodities and an edge from commodity i tocommodity j is drawn when the corresponding price effect is estimated non-zero by the proposed estimator.This network analysis helps commodity analysts to interpret the results. The effects are visualized foreach class, thereby immediately highlighting the differences between classes (i.e. markets or portfolios). Onlythe important effects (i.e. estimated non-zero effects) are drawn such that they are immediately distinguishedfrom the unimportant effects (i.e. estimated zero effects). Measures of connectedness among commoditiescan be calculated from the networks. Define the following indicator of connectedness from commodity i to We refer to them as commodity price effects or, more simply, just effects in the remainder of the paper. , which takes value one if the sum of the associated autoregressive coefficients is non-zero:( i → j ) = if (cid:80) Pp =1 (cid:98) B ( k ) p,ji (cid:54) = 00 otherwise with k = 1 , . . . , K. Following Billio et al. (2012), we assess the connectedness of commodity i by accounting for the proportionof edges (i) directed towards it ( in-going connectedness), (ii) originating from it ( out-going connectedness)and (iii) in both directions ( total connectedness). Each measure is standardized by the maximum valueregistered for class k to ease the comparison. Let S ( k ) be the set of all commodities in class k , we proposethree measures of connectedness for commodity i :(i) in-going connectedness: ( S ( k ) → i ) = ν ( k ) i ν ( k )max , where ν ( k ) i = (cid:80) Jj (cid:54) = i ( j → i ) and ν ( k )max = max i [ ν ( k ) i ];(ii) out-going connectedness: ( i → S ( k ) ) = η ( k ) i η ( k )max , where η ( k ) i = (cid:80) Jj (cid:54) = i ( i → j ) and η ( k )max = max i [ η ( k ) i ];(iii) total connectedness: ( i ↔ S ( k ) ) = µ ( k ) i µ ( k )max , where µ ( k ) i = (cid:80) Jj (cid:54) = i (( i → j ) + ( j → i )) and µ ( k )max = max i [ µ ( k ) i ].In Section 4 we present these networks for the market and portfolio data sets using a Multi-class VAR(1)model. Then we can consider a weighted network where the edge width represents the magnitude of theeffect. Moreover, positive effects (in blue) are distinguished from negative ones (in red) . We complete thenetwork analysis by verifying the prevalence of within and spillover effects among different commodity types.Within effects are effects among commodities of the same type, for instance agriculture. Spillover effects areeffects among commodities of different types, for instance energy and agriculture. We use the sparse estimator of the Multi-class VAR to study commodity price effects. We consider two datasets: a market and a portfolio data set. In the first one, we study spot prices of J = 14 energy, metal and On a gray scale: positive effects are shown in dark gray and negative ones in light gray. K = 3 markets. The second data set considers indexes of spotprices of J = 17 global, energy, metal and agricultural commodities for each of the K = 5 portfolios. Thechoice of considering spot prices is coherent with the analysis of Pindyck (2001), who underlines the existenceof two parallel trade levels: a cash trading for commodity spot purchases and sales, and a storage tradingfor inventories held by traders and producers. These two trade levels are highly connected since a spotpurchase of a commodity involves the physical delivery of the good and therefore its stocking as inventory .Spot price dynamics depend on the storage levels, consequently they are less volatile than the associatedderivative products, as futures or swaps (Pindyck, 2001): this justifies our choice of using spot prices.The details of the two data sets are respectively reported in Table 1 and 2. Data are obtained fromDatastream. The commodity spot price time series are non-stationary, we therefore follow standard practicein taking each time series in log-differences, which corresponds to the spot daily return. Next, we standardizethese spot daily returns by subtracting the mean and dividing by the standard deviation . We check forstationarity using the Augmented Dickey-Fuller test and the pooled unit root test of Levin et al. (2002): inboth cases we find strong evidence in favor of stationarity ( p -values < . P of the Multi-classVAR is selected using the Bayesian Information Criterion (BIC) and equals one for both data sets. We use daily spot returns ranging from November 1st, 2013 to November 2nd, 2015, hence, T = 522 timeobservations of three commodity types (energy, metal and agricultural), see Table 1. The price effect networksfor the three markets are presented in Figure 1. For instance in the World network , an edge is drawn fromgold to silver since the effect of the first on the second is estimated as non-zero.
Market comparison
Table 3 reports the proportions of shared non-zero effects among the three markets.The networks show limited evidence of shared commodity effects in the three markets. India shares only33% of its effects both with World and China. Besides, only 17% of the effects observed in China are alsopresent in the World network. This little evidence of shared effects between markets is in line with theexisting literature. Bukenya and Labys (2005) underlines the existence of few similarities between local andworld markets for agricultural and metal commodity spot price effects. Achvarina and Burda (2006) derivesimilar conclusions for the Chinese and World aluminum markets. The corresponding indexes from the different portfolios are all based on the same commodity spot price, but they differfrom one portfolio to another since each portfolio uses a different weighting scheme. An introduction to commodity indexes isprovided in Anson (2006). Electricity represents an exception since it can be hardly stocked. For this reason we do not include electricity. Standardization guarantees that all time series are on the same scale, such that the penalty terms have the same impacton each time series independently of its scale (Tibshirani et al., 2012). able 1: Market data set. Spot prices of J = 14 commodities are collected for each of the K = 3 markets. Commodity (type) Label Source in Datastream
World India China
Crude Oil a (Energy) CRUO Crude Oil Dated FOB Crude Oil Dated FOB Crude Oil Dated FOBNatural Gas a (Energy) NATG Henry Hub Henry Hub Henry HubAluminum (Metal) ALLU LME 99.7% Cash MCI Mumbai Bonded Whse Premium SptCopper (Metal) COPP LME Grade A Cash MCI Mumbai Bonded Whse Premium SptLead (Metal) LEAD LME Cash MCI Mumbai Bonded Whse Premium SptNickel (Metal) NICK LME Cash MCI Mumbai Bonded Whse Premium SptZinc (Metal) ZINC LME 99.995% MCI Mumbai Bonded Whse Premium SptGold (Metal) GOLD Handy&Hardman Base MCI 99.5% 99.95% ShanghaiSilver (Metal) SILV Handy&Hardman (NY) MCI Ahmedabad 1 a For CRUO and NATG the world price is used, and this for all three markets (due to data availability).
Table 2: Portfolio data set. Spot prices of J = 17 commodities are collected for each of the K = 5 portfolios. Index (type) Label Source in Datastream
Credit Suisse Dow Jones Merrill Lynch Standard & Poor’s Thomson Reuters
Agriculture (Global) AGRI CSCB Spt Ret DJ Capd. Comp. MLCX Spt Indx S&P GSCI Spt TR Equal Weight CCIEnergy (Global) ENER CSCB Spt Ret DJ Comm. Indx MLCX Spt Indx S&P GSCI Spt TR Equal Weight CCIGrain (Global) GRAI CSCB Spt Ret DJ Comm. Indx MLCX Spt Indx S&P GSCI Indx Spt TR Equal Weight CCIInd. Metals (Global) INDM CSCB Spt Ret DJ Comm. MLCX Spt Indx S&P GSCI Spt TR Equal Weight CCICrude Oil (Energy) CRUO CSCB Spt Ret DJ Comm. MLCX Spt Indx S&P GSCI Spt TR/CC CRB IndexHeating Oil (Energy) HETO CSCB Spt Ret DJ Comm. MLCX Spt Indx S&P GSCI Spt TR/CC CRBNatural gas (Energy) NATG CSCB Spt Ret DJ Comm. MLCX Spt Indx S&P GSCI Spt TR/CC CRBAluminum (Metal) ALLU CSCB Spt Ret DJ Comm. Indx MLCX Spt Indx S&P GSCI Spt TR/CC CRB IndexNickel (Metal) NICK CSCB Spt Ret DJ Comm. Indx MLCX Spt Indx S&P GSCI Spt TR/CC CRB IndexGold (Metal) GOLD CSCB Spt Ret DJ Comm. Indx MLCX Spt Indx S&P GSCI Spt TR/CC CRB IndexSilver (Metal) SILV CSCB Spt Ret DJ Comm. Indx MLCX Spt Indx S&P GSCI Spt TR/CC CRB IndexCorn (Agriculture) CORN CSCB Spt Ret DJ Comm. Indx MLCX Spt Indx S&P GSCI Spt TR/CC CRB IndexWheat (Agriculture) WHEA CSCB Spt Ret DJ Comm. Indx MLCX Spt Indx S&P GSCI Kansas TR/CC CRB IndexSoybeans (Agriculture) SOYB CSCB Spt Ret DJ Comm. MLCX Spt Indx S&P GSCI Spt TR/CC CRB IndexSugar (Agriculture) SUGA CSCB RUONATGALLUCOPPLEADNICKZINCGOLDSILV CORN SOYB SUGA WHEACOTT
World
CRUONATGALLUCOPPLEADNICKZINCGOLDSILV CORN SOYB SUGA WHEACOTT
India
CRUONATGALLUCOPPLEADNICKZINCGOLDSILV CORN SOYB SUGA WHEACOTT
China
Figure 1: Market data set. Commodity effect networks: a directed edge is drawn from one commodityto another if the associated commodity price effect is estimated non-zero. The edge width represents themagnitude of the effect. Positive effects are shown in blue (dark gray) and negative effects in red (light gray).11able 3: Market data set. Proportions of shared non-zero effects among markets: each cell indicates theproportion of effects for market i (row) that are also present for market j (column).World India ChinaWorld 1.00 0.26 0.17India 0.33 1.00 0.33China 0.17 0.25 1.00 Commodity connectedness
Figure 2 pictures the measures of connectedness (cfr. Subsection 3.3) foreach market. The most connected commodities are mainly found among metals for all three markets, eitherby looking at out-going, in-going or total connectedness. This finding is coherent with our expectations onthe Indian and Chinese markets, since both Asian economies heavily depend on their metallurgic sectors.The Shanghai Metal Exchange is one of the largest commodity exchanges in the world for metals (Klotzet al., 2014): China represents the biggest producer and consumer of different metals and minerals worldwide(Pitfield et al., 2010). Similar considerations are found for India (Jain and Ghosh, 2013; Pitfield et al., 2010).Besides, crude oil presents high out-going connectedness in the Indian and Chinese markets, signaling thatthe crude oil price is a leading factor of commodity price dynamics in the two Asian economies.With respect to agricultural commodities, cotton (COTT) is the most connected commodity in terms oftotal connectedness. In China (and to a lesser extent India) this is due to the presence of high out-goingconnectedness (there is no in-going connectedness in both markets), whereas in World there is a higherprevalence of in-going connectedness. The different behavior of cotton markets could be due to differentexport strategies. Indeed, Indian and Chinese cotton mostly satisfy the local demand (respectively, only14% and 0.2% of the total cotton production in 2014 was exported). On the contrary, US cotton, whichwe take as the world benchmark, is largely exported to international markets (69% of the US total cottonproduction in 2014 was exported). Therefore, it largely depends on the world demand conditions and ismore responsive to other commodity behavior.
Effects across commodity types
Table 4 reports on the main diagonal the proportions of non-zeroeffects within each commodity type for each market. For instance, out of the 20 possible effects from oneagricultural commodity towards another agricultural commodity, only four of them are estimated as non-zero in the World network, hence there are 20% of non-zero within agriculture effects. In the World networknon-zero within effects involve both metal (21%) and agricultural commodities (20%), whereas in India andChina there is a higher prevalence of non-zero effects within metal commodities (19% and 12% respectively)than within agricultural commodities (both 5%). Hereby, it is confirmed the relevance of the metal sector12 W o r l d I nd i a C h i na CRUONATGALLUCOPPLEADNICKZINCGOLDSILVCORNSOYBSUGAWHEACOTT (a) Out-going connectedness W o r l d I nd i a C h i na CRUONATGALLUCOPPLEADNICKZINCGOLDSILVCORNSOYBSUGAWHEACOTT (b) In-going connectedness W o r l d I nd i a C h i na CRUONATGALLUCOPPLEADNICKZINCGOLDSILVCORNSOYBSUGAWHEACOTT (c) Total connectedness
Figure 2: Market data set. Measures of (a) out-going, (b) in-going and (c) total connectedness for eachcommodity (rows) in each market (columns). The size (and the color) of the circle reflects the magnitude ofthe connectedness: the larger (and darker), the more connected the commodity.in the two Asian economies. In all three markets, there are no effects within energy commodities.Table 4 reports on the off-diagonal entries the proportions of spillover effects among commodity types foreach market. For instance, out of the 10 possible effects from an energy commodity towards an agriculturalcommodity, only one of them is estimated as non-zero in the World network, hence 10% of the spilloverseffects are estimated as non-zero. In all three networks we observe strong spillover effects in commodityreturns from energy towards agriculture (10% in each market), confirming the studies of Tyner (2010); Serraand Zilberman (2013) and references therein. Furthermore, in the Indian and Chinese network there arerelevant spillover effects from energy towards metal (14% and 29% respectively). This finding is in line withprevious studies where energy prices are found to be highly influential towards industrial metal commodities(Akram, 2009; Klotz et al., 2014) and precious metals (Sari et al., 2010). Besides, the Indian and Chinesemarkets present unidirectional spillover effects from agriculture towards metal (6% and 11% respectively):this asymmetric structure of the spillover effects is outspoken and might reflect an additional effect fromenergy towards metal via agricultural commodities.This asymmetric spillover structure is not present in the World network. The high proportion of spillover13able 4: Market data set. For each market, the proportion of non-zero effects within each commodity type(diagonal elements) and spillover effects across commodity types (off-diagonal elements) are given.
World To F r o m Energy Metal AgricultureEnergy 0.00 0.00 0.10Metal 0.07 0.21 0.11Agriculture 0.00 0.00 0.20
India To F r o m Energy Metal AgricultureEnergy 0.00 0.14 0.10Metal 0.00 0.19 0.00Agriculture 0.00 0.06 0.05
China To F r o m Energy Metal AgricultureEnergy 0.00 0.29 0.10Metal 0.14 0.12 0.00Agriculture 0.00 0.11 0.05 effects from metal to agriculture (11%) is mainly driven by the high in-going connectedness of cotton (cfr.Table 2). However, cotton represents a special case. Indeed, when cotton is traded no actual delivery happensand the cotton price is the result of an average of offer quotations (Bukenya and Labys, 2005). This mightresult in distorted dynamics involving cotton.
We use daily spot return indexes ranging from November 1st, 2013 to November 2nd, 2015, hence, T = 522time observations of four different commodity types (global index, energy, metal, agriculture), see Table 2.The price effect networks for the five portfolios are presented in Figure 3. Portfolio comparison
Table 5 reports the proportions of shared non-zero effects among the five portfolios.The networks show much more evidence of shared effects in the portfolios (on average 56%) compared to themarket data set (on average 25%). For instance, 89% of the effects observed in Standard & Poor’s are alsopresent in Merrill Lynch. Moreover, the direction, the sign and the magnitude of the effects are comparablein the different portfolios. Although each commodity index is differently built, they present similar featuresand guarantee comparable performances (Anson, 2006). The only exception is represented by ThomsonReuters, with smaller proportions of shared effects with the other portfolios . Moreover, Thomson Reuters For instance, only 24% of the effects observed in Thomson Reuters are also observed in Credit Suisse. GRIENERGRAIINDMCRUOHETONATGALLUNICKGOLDSILVCORN WHEA SOYB SUGACOFFCOTT
Credit Suisse
AGRIENERGRAIINDMCRUOHETONATGALLUNICKGOLDSILVCORN WHEA SOYB SUGACOFFCOTT
Dow Jones
AGRIENERGRAIINDMCRUOHETONATGALLUNICKGOLDSILVCORN WHEA SOYB SUGACOFFCOTT
Merrill Lynch
AGRIENERGRAIINDMCRUOHETONATGALLUNICKGOLDSILVCORN WHEA SOYB SUGACOFFCOTT
Standard & Poor's
AGRIENERGRAIINDMCRUOHETONATGALLUNICKGOLDSILVCORN WHEA SOYB SUGACOFFCOTT
Thomson Reuters
Figure 3: Portfolio data set. Commodity effect networks: a directed edge is drawn from one commodity toanother if the associated price effect is estimated non-zero. The edge width represents the magnitude of theeffect. Positive effects are shown in blue (dark gray) and negative effects in red (light gray).15able 5: Portfolio data set. Proportions of shared non-zero effects among portfolios: each cell indicates theproportion of effects for portfolio i (row) that are also present for portfolio j (column). Credit Suisse Dow Jones Merrill Lynch Standard & Poor’s Thomson ReutersCredit Suisse 1.00 0.56 0.47 0.50 0.23Dow Jones 0.66 1.00 0.76 0.83 0.38Merrill Lynch 0.61 0.85 1.00 0.96 0.42Standard & Poor’s 0.61 0.86 0.89 1.00 0.39Thomson Reuters 0.24 0.33 0.33 0.33 1.00 has non-zero commodity effects that differ in terms of sign, direction and magnitude. Since the indexweighting scheme of Thomson Reuters is not publicly available, we cannot examine this anomaly. If weexclude Thomson Reuters from the analysis, then the four remaining portfolios have on average 71% ofshared effects.
Commodity connectedness
Figure 4 pictures the three measures of connectedness for each commodityindex in each portfolio. In the majority of the cases, the most connected commodities, in terms of totalconnectedness, are either found among global or energy indexes. Global indexes have in general higher out-going than in-going connectedness: the most connected indexes are the energetic (ENER) and agriculturalones (AGRI and GRAI). Overall, these agricultural and the energy global indexes play a relevant role in ournetwork analysis. Moreover, the high out-going connectedness of global indexes suggests that they are drivingforces among the set of commodities in our analysis. Energy indexes show high total connectedness, whichis either due to high out-going connectedness, as for natural gas (NATG), or to high in-going connectedness,as for crude oil (CRUO). Agriculture commodities show a moderate out-going connectedness, in particularsoybeans (SOYB), sugar (SUGA) and coffee (COFF), and moderate in-going connectedness, in particularwheat (WHEA) and corn (CORN). Metal commodities show overall little total connectedness, with the onlyexception of silver (SILV).
Effects across commodity types
Table 6 reports on the main diagonal the proportions of non-zero effectswithin each commodity type for each portfolio. The largest proportion of non-zero effects is estimated withinenergy commodities in each portfolio, thus indicating that a large part of the total connectedness of energycommodities is explained by effects among crude oil, natural gas and heating oil. Apart from Credit Suisse,all portfolios show non-zero effects within agricultural commodities. In particular, there is an outspoken This finding might seem contradictory to the market data application where no within energy effects were found. Here,however, all within energy effects involve heating oil which was - due to data availability - not included in the market data set.In line with the market application, we found no effects between natural gas and crude oil. C S D J M L S P T R AGRIENERGRAIINDMCRUOHETONATGALLUNICKGOLDSILVCORNWHEASOYBSUGACOFFCOTT (a) Out-going connectedness C S D J M L S P T R AGRIENERGRAIINDMCRUOHETONATGALLUNICKGOLDSILVCORNWHEASOYBSUGACOFFCOTT (b) In-going connectedness C S D J M L S P T R AGRIENERGRAIINDMCRUOHETONATGALLUNICKGOLDSILVCORNWHEASOYBSUGACOFFCOTT (c) Total connectedness
Figure 4: Portfolio data set. Measures of (a) out-going, (b) in-going and (c) total connectedness for eachcommodity (rows) in each portfolio (columns). The size (and the color) of the circle reflects the measure ofconnectedness: the larger (and darker), the more connected the commodity.positive effect from sugar towards corn: a sugar price increase is reflected in a corn price increase. Thisrelation is not surprising since both sugar and corn are used in ethanol production: they are not substitutegoods (since the production process of ethanol is different when using sugar or corn), but they both respondto the same price dynamics, thereby explaining the positive sign of the effect.Table 6 reports on the off-diagonal entries the proportions of spillover effects among commodity types foreach portfolio. In all portfolios spillover effects are estimated from global towards agriculture: for instance,12% of the spillover effects in this direction are estimated non-zero in Standard & Poor’s. The majority ofthese spillover effects derive from the global index for energy (cfr. Figure 3). Moreover, spillover effects arealso present from energy towards agriculture in all portfolios: 28% of the spillover effects in this direction areestimated non-zero in Credit Suisse, Merrill Lynch and Standard & Poor’s. Our analysis not only confirmsthe existence of spillovers from energy towards agricultural, as in Chen et al. (2010); Nazlioglu and Soyatas(2012), but also finds evidence of spillover effects in the opposite direction, as in Rezitis (2015). Indeed, 11%of the spillover effects from agriculture towards energy are estimated non-zero in all portfolios apart fromThomson Reuters. 17able 6: Portfolio data set. For each portfolio, the proportion of non-zero effects within each commoditytype (diagonal elements) and spillover effects across commodity types (off-diagonal elements) are given.
Credit Suisse To F r o m Global Energy Metal AgricultureGlobal 0.08 0.25 0.06 0.08Energy 0.08 0.17 0.00 0.28Metal 0.25 0.17 0.00 0.00Agriculture 0.33 0.11 0.04 0.00
Dow Jones To F r o m Global Energy Metal AgricultureGlobal 0.00 0.25 0.12 0.08Energy 0.00 0.33 0.08 0.22Metal 0.19 0.17 0.00 0.00Agriculture 0.04 0.11 0.04 0.07
Merrill Lynch To F r o m Global Energy Metal AgricultureGlobal 0.00 0.04 0.00 0.12Energy 0.00 0.33 0.08 0.28Metal 0.19 0.17 0.00 0.00Agriculture 0.04 0.11 0.04 0.03
Standard & Poor’s To F r o m Global Energy Metal AgricultureGlobal 0.00 0.17 0.06 0.12Energy 0.00 0.33 0.00 0.28Metal 0.19 0.25 0.00 0.00Agriculture 0.04 0.11 0.04 0.03
Thomson Reuters To F r o m Global Energy Metal AgricultureGlobal 0.25 0.17 0.06 0.08Energy 0.33 0.33 0.08 0.06Metal 0.19 0.17 0.00 0.00Agriculture 0.25 0.00 0.08 0.03
These spillover effects might be explained by the rising importance of the ethanol and biofuel industry.In Figure 3, we notice that the majority of the effects among agricultural commodities involve crops thatcan be used for the biofuel production (like corn, wheat, soybeans), whereas it is not the case for otheragriculture goods (for instance cotton). Moreover, recall that the global index for energy (ENER) presents ahigh out-going connectedness. Hence, we find important spillover effects from energy towards biofuel crops,in line with Chen et al. (2010); Nazlioglu and Soyatas (2012).Bidirectional spillovers are also observed between energy and metal in three portfolios, namely Dow Jones,Merrill Lynch and Thomson Reuters. The majority of these spillover effects involve gold and silver, whichare the most connected metal commodities (cfr. Table 4), confirming the existence of strong dependencebetween energy and precious metals (Sari et al., 2010).18 ther data period
We redo the portfolio analysis considering the period from November 2nd, 2011 toNovember, 1st 2013. During 2013, commodity prices experienced a sharp drop mainly due to the slowdownof some emerging economies, among which China. For instance, the world corn price dropped by almost40% in 2013. As a result, we should not assume constant parameter values for both periods.The commodity effect networks show major differences with the ones in Figure 3. The average proportionof non-zero estimated effects has almost doubled: from 6% for the 2011-13 period to 10% for the 2013-15period. The lower connectedness in the period 2011-13 can be linked to the crude oil price drop thatoccurred in 2014, when crude oil price decreased by almost 50%. As in Baffes (2013), a low crude oil pricecould result in weaker policies sustaining the use of biofuels, hence making alternative fuel less attractive.As a consequence, agricultural prices drop consistently and the overall connectedness among energy andagricultural commodities increases, thus explaining the higher connectedness in the period 2013-15.The proportion of shared non-zero effects among portfolios has also increased: from 40% for 2011-13to 56% for 2013-15. Similar to the 2013-15 period, Thomson Reuters shows the least similarity with theother portfolios (sharing on average only 10% of its non-zero effects with the other portfolios). But in2011-13 Credit Suise has a considerable amount of non-zero commodity effects that differ in terms of sign,direction and magnitude from the other portfolios. The importance of the agricultural index in the CreditSuisse network is more evident in 2011-13, it has in-going positive effects not only coming from agriculturalcommodities, but also from the metal and energy commodities.Overall, we obtain different results in the two periods of analysis suggesting the presence of a structuralbreak in commodity price dynamics. Detailed results are available from the authors upon request.
This paper proposes the
Multi-class VAR model to analyze commodity price dynamics. Our method extendsthe literature on commodity analysis in three main directions. First, we study a large set of prices of differentcommodity types (e.g. agriculture, metal and energy). Second, we compare the resulting effects betweenmarkets (or investment portfolios). We accomplish both tasks by using sparse estimation of the Multi-classVAR model, which addresses the problem of over-parameterization and allows a joint comparison betweenmarkets (or investment portfolios). Third, we interpret the results using networks.We exploit the Multi-class VAR model to estimate the price effects among commodities in two datasets. The first one considers agricultural, metal and energy commodity prices in three different markets,namely World, India and China. The second data set analyzes commodity prices of global, energy, metaland agriculture indexes in five different investment portfolios. Overall, we find few common effects betweenthe World, Indian and Chinese markets, whereas we find evidence of more common effects among portfolios.19ith respect to the first data set, our results highlight the prevalence of effects involving metal goods in Indiaand China. Moreover, we underline the existence of more spillover effects from agriculture to metal thanvice versa. In the second data set, we observe outspoken spillover effects from energy towards agriculture(Tyner, 2010) and we highlight the relevance of biofuel commodities. While our modeling approach has anexploratory flavor, the majority of our results are in line with the literature on commodity price dynamics.The network representation of the results brings relevant information to commodity analyst and eases theinterpretation. In our application, we consider a VAR of order one, but the analysis also applies for higherorder models. The choice of the VAR is in line with a large trend of the extant literature on commoditymarkets. We do acknowledge, however, that we did not include possible co-integration relations in the model.Further research might extend our analysis by including exogenous factors. For instance, the inclusionof interest rates might bring important insights and explain part of the overall commodity prices dynamics(Akram, 2009; Smiech et al., 2015). Another factor that might be relevant to study is the impact of excessliquidity on commodity prices. A result of the “financialization” is the rapid increase in financial investmentin commodity markets and the detachment of their trends from simple demand-offer dynamics: for instance,Belke et al. (2013) provide evidence that global liquidity is one of the main drivers of commodity price.The Multi-class VAR might also be employed to study volatility spillover effects among a set of com-modity prices. Various studies in the related literature underline the importance of the volatility analysisin commodity markets for both spot prices and derivatives (Pindyck, 2004), with important implications interms of risk and storage management (Pindyck, 2001). Following Diebold and Yilmaz (2015), it is possibleto incorporate the volatility spillover effects in a VAR framework. An extension of their approach to theMulti-class VAR model would take the shared volatility dynamics between markets into account.
Acknowledgments.
We gratefully acknowledge support from the FWO (Research Foundation Flanders,contract number 11N9913N) and from the GOA/12/014 project of the Research Fund KU Leuven.20 eferenceseferences