ISSN: 2279-7807 Quaderni di Diparimeno Reurns in commodiies fuures markes and financial speculaion: a mulivariae GARCH approach Maeo Manera (Universià di Milano-Bicocca e Fondazione Eni Enrico Maei) Marcella Nicolini (Universià di Pavia) Ilaria Vignai (Fondazione Eni Enrico Maei) # 170 (04-12) Diparimeno di economia poliica e meodi quaniaivi Universià degli sudi di Pavia Via San Felice, 5 I-27100 Pavia Aprile 2012
Maeo Manera, a* Marcella Nicolini, b and Ilaria Vignai c Reurns in commodiies fuures markes and financial speculaion: a mulivariae GARCH approach Absrac: This paper analyses fuures prices for four energy commodiies (ligh swee crude oil, heaing oil, gasoline and naural gas) and five agriculural commodiies (corn, oas, soybean oil, soybeans and whea), over he period 1986-2010. Using CCC and DCC mulivariae GARCH models, we find ha financial speculaion is poorly significan in modelling reurns in commodiies fuures while macroeconomic facors help explaining reurns in commodiies fuures. Moreover, spillovers beween commodiies are presen and he condiional correlaions among commodiies are high and ime-varying. JEL Codes: C32; G13; Q11; Q43. Keywords: Energy; Commodiies; Fuures markes; Financial speculaion; Mulivariae GARCH. a Universiy of Milan-Bicocca, Milan and Fondazione Eni Enrico Maei, Milan. email: maeo.manera@unimib.i b Universiy of Pavia, Pavia and Fondazione Eni Enrico Maei, Milan. email: marcella.nicolini@unipv.i c Fondazione Eni Enrico Maei, Milan. email: ilaria.vignai@feem.i * Corresponding auhor. A previous version of his paper has been presened a he FEEM Inernaional Conference on Financial Speculaion in he Oil Marke and he Deerminans of he Oil Price, held in Milan, 12-13 january 2012. We would like o hank Bahain Büyükşahin, Leo Drollas, Marzio Galeoi, Alessandro Lanza and seminar paricipans a FEEM, Deparmen of Saisics, Universiy of Milan-Bicocca, and Universiy of Pavia for providing helpful commens. All remaining errors are our own responsibiliy. 1
1. Inroducion The las decades have winessed a number of changes in commodiies fuures markes. The oil marke has coninuously grown, becoming he world's bigges commodiy marke and urning from a primarily physical produc aciviy ino a sophisicaed financial marke (Chang e al. 2011). Secondly, he increasing presence of hedgers, as well as speculaors, has led o allegaions ha speculaion drives crude oil prices, and speculaors, index funds and hedge funds have been responsible for he increase in energy and food prices from 2004 onwards (Masers 2008). The lieraure however has provided, so far, lile empirical evidence in suppor of his claim. Speculaors have hisorically been presen in non-energy commodiies fuures markes as well: i is herefore reasonable, while esing he role of speculaors and any possible impac on commodiies reurns, o exend he analysis o boh energy and non-energy commodiies. Moreover, he common behaviour displayed by energy and non-energy commodiies prices in recen imes, characerized by a seep rise around year 2008 which has been followed by a sharp decrease during he grea recession, has posed he quesion of he linkage beween hese markes, and he spillovers ha may be presen. The aim of his paper is o shed some ligh on hese compelling quesions. More precisely, we focus on four research quesions. Firs, are macroeconomic facors relevan in explaining reurns of energy and non-energy commodiies? Second, is financial speculaion significanly relaed o reurns in fuures markes? Third, are here significan relaionships among reurns, eiher in heir mean or variance, across differen markes? Finally, is speculaion in one marke affecing reurns in oher markes? Or, in oher words, are here spillovers across markes in speculaion? Our empirical exercise considers weekly daa over he ime period 1986:3 o 2010:52. We collec daa on reurns of four energy commodiies (gasoline, heaing oil, naural gas and crude oil) and four non-energy commodiies (corn, oas, soybeans and whea). Addiionally, we include in our analysis a biofuel, soybean oil, o invesigae if he relaionship among he laer and energy commodiies is sronger han wha can be found in he case of food commodiies. We consider a generalized auoregressive condiional heeroskedasiciy (GARCH) model o esimae commodiies reurns: we firs discuss an univariae analysis, where reurns are explained by macroeconomic variables an a measure of speculaion. Then, we presen mulivariae GARCH models o invesigae he presence of spillovers across commodiies. Our resuls sugges ha macroeconomic variables are relevan o explain commodiies reurns, more precisely he Sandard & Poor s (S&P) 500 index has a posiive and significan coefficien, while he mulilaeral exchange rae has a negaive effec, as expeced. As concerns he second 2
research quesion, we observe ha speculaion, measured by he Working s T index, does no seem o significanly affec reurns. Finally, we observe ha he dynamic condiional correlaions among commodiies are higher in recen years. As speculaion is generally poorly significan, we do no deec a relevan impac on own marke and oher markes reurns. However, we find an ineresing resul concerning he speculaion index in crude oil marke: i assumes a posiive and significan coefficien on soybean oil reurns afer 2004, indicaing a linkage beween energy markes and a biofuel one in recen imes. The remainder of his paper is srucured as follows. Secion 2 discusses he debae on he impac of speculaion in fuures markes and he presence of spillovers across commodiies. Secion 3 presens he daa and some descripive saisics. Secion 4 describes he economeric model while Secion 5 presens he resuls. Finally, Secion 6 concludes. 2. Lieraure review The asse pricing lieraure provides empirical evidence of he abiliy of few macroeconomic variables o forecas reurns on commodiies fuures. The firs is he reurn on he 90-day Treasury bill, which represens he shor-erm discoun rae free of a risk premium. The T-bill ends o be lower during economic recessions and higher during periods of growh. Thus, i is expeced o be negaively correlaed wih real economic oupu growh. A negaive relaionship beween real commodiy prices and real ineres raes has been confirmed empirically (Frankel 2008a). The second variable is he equiy dividend yield: fuures commodiy prices are expeced o reflec he sysemic risk embedded wihin he evoluion of sock marke condiions (Chevallier 2009). A hird variable is he junk bond premium, which is he premium on long-erm corporae bonds raed BAA by Moody s over he AAA raed ones. This difference represens he moneary compensaion for risk. Recen works on peroleum fuures reurns and carbon fuures reurns (Sadorsky 2002, Chevallier 2009) find however ha hese macroeconomic risk variables are poorly significan. Finally, exchange raes are hough o be closely relaed o commodiies fuures prices, alhough he direcion of he causaliy among hese variables is sill debaed. Indeed, Chen e al. (2010) show ha exchange raes have robus forecasing power over global commodiy prices and ha commodiy prices Granger-cause exchange raes in-sample. Some commenaors (Frankel 2008b, Michell 2008, Verleger 2009) sugges ha he causes of price increases have o be idenified in economic fundamenals as low ineres raes in he USA, which forced o look for oher invesmen opporuniies. Anoher facor is he rapid economic growh worldwide, especially in China and India, which has been accompanied by growing demand for 3
food commodiies. Insabiliy among oil producers, especially in he Middle Eas, and herefore uncerainy in he supply of oil has o be accouned for as well. Finally, misguided ehanol subsidies have increased biofuel producion and migh have affeced prices. Baffes and Haniois (2010) add o he laer argumen claiming ha he fuure pah of commodiies prices is uncerain due o he sric relaionship beween energy and non-energy prices. In paricular, his relaionship has increased considerably in he recen boom, indicaing ha evens and policy changes happening in one marke affec oher markes. Gilber (2010) collecs daa on hree food price indexes over he period 1971-2008 and shows ha demand-side variables (i.e. GDP growh) and moneary expansion, measured by world real money supply, are he main cause of price increase by means a Granger-causaliy es. Moreover, he finds ha, in he las years, oil prices have had more influence on food ones hus supporing he idea of an increasing link among markes. He claims however ha his is he resul of common causaion raher han of a direc causal link. More recenly, several researchers and analyss suggesed ha he increasing presence of speculaors in commodiy fuure markes could explain he spike in prices in he 2007-2008 period (see, among many, Eckaus 2008, Masers 2008, Soros 2008). Indeed, Medlock III and Jaffe (2009) show ha non-commercial agens in 2009 represened abou 50% of oal open ineres in he oil marke, compared o abou 20% prior o 2002. Moreover, he open ineres held by speculaors moved from a lagging indicaor of price o a leading indicaor around January 2006, suggesing a possible cause in oil prices increase. Khan (2009) argues ha speculaion played a role comparing movemens in he price of crude oil and he price of gold, which used o move ogeher unil 2000, while hey display a gap from 2002 onwards. Robles e al. (2009) find some evidence ha speculaive aciviy, measured in urn as scalping, which is he raio of volume o open ineres, or he share of non commercial posiions over oal posiions or he index raders ne posiion, Granger-causes curren commodiy prices of whea, maize, soybeans and rice. Du e al. (2011) show ha scalping and speculaion affec posiively crude oil price volailiy. Moreover, afer 2006, hey find ha he oil price shock has riggered price changes in corn and whea markes, poenially because of an increase in ehanol producion. Oher auhors insead do no find a saisically significan relaionship beween commodiy prices and index funds, which are held responsible for speculaion. Index Invesmen Daa (IID) have been made available by CFTC from December 2007. Using hese daa Irwin and Sanders (2012) find lile evidence ha IID posiions influence reurns or volailiy in 19 commodiy fuures markes. Auhors ineresed in analysing he previous period proxied index funds aciviy using daa on swap dealers. Empirical ess provide no evidence ha posiion changes by any rader group Granger- 4
cause price changes in boh energy and non-energy commodiies fuures markes (Brunei and Büyükşahin 2009, Soll and Whaley 2010, Büyükşahin and Harris 2011). Sanders e al. (2010) sudy agriculural fuures markes over he period 1995-2008 and show ha he Working (1960) s T index, radiionally adoped o measure excess speculaion (see Secion 3 for a formal definiion), has remained sable or below hisorical levels in recen years. However, hey sugges ha his resul migh be due o he naure of he index iself: he recen rise in long speculaive posiions has been paralleled by an increase in shor hedging, hus implying an overall decrease in he Working s T index. Oher auhors sugges ha he crude oil price spike and collapse in 2007-08, while being mainly driven by increasing world demand, can no be explained by macroeconomic facors only and sugges ha speculaion played a role (Kaufmann and Ulman 2009, Kaufmann 2011). We follow his approach, and in he subsequen economeric analysis we invesigae he role of macroeconomic variables and speculaion on fuures reurns. Anoher issue we ackle wih he presen economeric exercise is he relaionship among commodiies prices and price changes. The lieraure has largely debaed on his. Granger (1986) affirms ha wo series of prices can no be coinegraed as, if hey were, one could be used o forecas he oher, and his would go agains he hypohesis of efficien markes. However, Malliaris and Urruia (1996) es for coinegraion beween fuures prices of six agriculural commodiies (corn, whea, oas, soybeans, soybean meal and soybean oil) over daa for he period from January 1981 o Ocober 1991 a daily frequency, finding a srong and saisically significan long-erm relaionships among all he six commodiies, hus rejecing he hypohesis ha prices of hese agriculural producs move independenly. The auhors sugges ha i could be explained by subsiuabiliy and complemenariy beween agriculural commodiies, common geographical and climaic facors, global demand shocks and he excess co-movemen hypohesis, firs proposed by Pindyck and Roemberg (1990) (see more infra). Also Chaudhuri (2001) finds coinegraion beween real oil prices and oher real commodiy prices in he period 1973-1996. Pindyck and Roemberg (1990) analyze monhly reurns of 7 commodiies (whea, coon, copper, gold, crude oil, lumber and cocoa) from 1960 o 1985. The commodiies are chosen o be no subsiues nor complemens, neiher co-produced and neiher inpus for ohers producion: hey are hus expeced o be uncorrelaed. However, he auhors find ha he residuals of a regression of hese commodiies prices on macroeconomic variables are highly correlaed, meaning ha prices move ogeher even afer accouning for a se of macroeconomic variables. This excess comovemen is possibly explained by he so called herd behaviour of financial raders: raders 5
are alernaively bullish or bearish on all commodiies for no plausible economic reason (Pindyck and Roemberg 1990, 1173). Subsequenly, several papers have challenged he excess co-movemen hypohesis. Palaskas and Varangis (1991) show he exisence of co-movemens bu no excess co-movemens beween nine commodiy prices. LeyBourne e al. (1994) find ha only 4 ou of 15 commodiy prices pairs exhibi excess co-movemen and ha only 2 of 10 commodiy prices exhibi co-movemen, confirming a weak evidence of his phenomenon. Deb e al. (1996) find weak evidence of excess co-movemen, Cashin e al. (1999), using a measure of concordance, 1 find no evidence of comovemen in he prices of unrelaed commodiies, bu find srong evidence of co-movemens in groups of relaed ones. Ai e al. (2006) show ha, afer considering commodiy-specific demand and supply facors, here does no seem o be any excess co-movemen. Finally, Vanseenkise (2009) esimaes a dynamic facor model using Kalman Filering echniques on 32 non-fuel commodiy prices from 1957 o 2008, separaing beween common and idiosyncraic (i.e. specific for a group of commodiies) shocks in affecing prices. The main finding is ha a common facor does exis and i is linked o macroeconomic fundamenals, raher hen speculaion in fuures markes. However, from 2000 onwards, idiosyncraic effecs became more relevan. More recenly he lieraure has concenraed on possible linkages beween energy and non-energy commodiies. Indeed, crude oil is an imporan inpu in agriculural producion, eiher in he form of diesel, ferilizers or pesicides. Baffes (2007) measures he effec of crude oil prices on he prices of 35 inernaionally raded primary commodiies for he 1960 2005 period, finding ha he passhrough of crude oil price changes o he overall non-energy commodiy index is 0.16, suggesing ha a 10% increase in he price of crude oil brings a 1.6% increase in he non-energy commodiy prices. Baffes (2009) expands his analysis considering an index which includes also naural gas and coal and exending he sample up o 2008. This analysis finds ha a 10% increase in energy prices brings a 2.8% increase in non-energy prices, suggesing ha he 2008 financial crisis has srenghened he relaionship beween energy and non-energy prices. The research has focussed recenly also on a specific class of commodiies, biofules, and on he possible linkages beween biofuels and oher food commodiies. The corn designed o ehanol producion in he U.S. was 10% of oal crop in 2002/03 and ran up o 24% in 2007/08 (Trosle 2008). Acually, Naanelov e al. (2011) show a lack of coinegraion beween corn and crude oil price beween mid 2004 and July 2006, which is due o policy inervenions on biofules. However, afer surpassing a cerain hreshold in crude oil price he wo series are coinegraed. Ciaian and Kanks (2011) show ha he inerdependencies among crude oil and agriculural commodiies 1 Concordance measures he exen o which he cycles of wo series are synchronized. I is a useful concep of comovemen because i represens a way o summarize informaion on he economic phases of commodiy prices. 6
(included corn and soybean) are increasing over ime: significan coinegraing relaionships are deeced only afer 1994. FAO (2009) as well suggess ha he main drivers of he agriculural prices boom are demand facors (mainly biofuel demand) and high oil prices, which have a direc impac on he coss of agriculural producion. 3. Daa descripion We collec daa on fuures prices for four energy commodiies (ligh swee crude oil, heaing oil, gasoline and naural gas) and five agriculural commodiies (corn, oas, soybean oil, soybeans and whea). All he energy commodiies are raded on he New York Mercanile Exchange (NYMEX), while he agriculural ones are raded on Chicago Board of Trade (corn, oas, soybean oil and soybeans) and Kansas Ciy Board of Trade (whea). Daily daa are rerieved from Daasream and hen urned ino weekly averages of fuures prices 2 for each commodiy. Indeed, daa necessary o build he speculaion index are provided by he Commimens of Traders (COT) repors of U.S. Commodiy Fuures Trading Commission (CFTC) on a weekly basis, hus we have o adop his daa frequency. CFTC collecs every week he open ineres for specific caegories of raders: commercial (hedgers) 3 and non-commercial (speculaors and arbirageurs), 4 disinguishing beween shor and long posiions. The period considered spans from 1986:3 o 2010:52. 5 Table 1 provides some reference on he series employed in he analysis. The daa colleced allow o calculae he Working s T (1960) index, which is a measure of speculaive aciviy ha proxies he excess of speculaion relaive o hedging aciviy. This index is calculaed as he raio of non-commercial posiions o oal commercial posiions: SS 1 + HS + HL SL 1+ HS + HL if if HS HL HS < HL 2 We use he coninuous fuures price series, calculaed by Thomson Financial. They sar a he neares conrac monh which forms he firs values for he coninuous series and swich over on 1 s day of new rading monh. 3 Commercial agens are also acive in he spo marke. In his caegory CFTC includes producers, merchans, processors and users, i.e. who use fuures markes o manage or hedge risks associaed wih he physical aciviy of commodiies, and swap dealers, i.e. all he agens who use hese markes o manage or hedge he risk associaed wih swap ransacions. 4 Non-commercial agens are in fuures markes o make profis from selling and buying fuures conracs. In his caegory CFTC includes money managers, i.e. a caegory which includes a regisered commodiy rading advisor (CTA), a regisered commodiy pool operaor (CPO) or an unregisered fund idenified by CFTC, and oher reporables, i.e. any rader ha is no idenified in he previous caegories. 5 From January 1986 o Sepember 1992 CFTC repors daa wih bi-monhly frequency. Missing daa are replaced by he average beween he previous and he following observaion. 7
where SS is speculaion shor (open ineres held by speculaors who sell fuures conracs), SL is speculaion long (open ineres held by speculaors who have long posiions), HS is hedging shor and HL is hedging long. I should be noed ha he calculaion of he Working s T index crucially depends on he classificaion of he marke operaors beween hedgers and speculaors. CFTC also provides daa for Non Reporable operaors, 6 which are no classified ino any of he wo caegories. However, open ineres held by hese subjecs should be included in he compuaion of he index. Several rules o rea hem are a hand. One could consider hem as being all hedgers or, more likely, all speculaors. Indeed, hedgers are generally known by CFTC and are less likely o be unknown. We follow an inermediae approach, assuming ha 70% of hem are speculaors and 30% are hedgers. 7 However, we calculae he speculaion index also in he wo exreme hypoheses and perform he economeric exercise wih hese variables. 8 To conrol for macroeconomic facors we collec daily (5 days) daa, which we urn ino weekly averages, on Moody s AAA and BAA corporae bond yield, 3-monh Treasury bill, S&P 500 index and a weighed exchange rae index of he U.S. dollar agains a subse of broad index currencies ouside U.S. for he period 01/02/1986-12/31/2010 from he Federal Reserve Economic Daa (FRED) provided by he Federal Reserve of S. Louis. 9 Descripive saisics of he variables are repored in Table 2. The able is divided in four panels, one for each se of variables. Fuures prices and macroeconomic variables conain a uni roo, as he Augmened Dickey-Fuller (ADF) es saisics does no rejec he null hypohesis for almos all series in he daase. Therefore, for each commodiy we consider he reurn r i, which is defined as log( P i / P i 1), where P i and P i 1 are he prices of commodiy i a weeks and -1, respecively. This ransformaion allows o obain saionariy, as shown in he second panel of Table 2. 6 CFTC defines his caegory as follows: The long and shor open ineres shown as "Non Reporable Posiions" is derived by subracing oal long and shor "Reporable Posiions" from he oal open ineres. Accordingly, for "Non Reporable Posiions," he number of raders involved and he commercial/non-commercial classificaion of each rader are unknown. (see hp://www.cfc.gov/markerepors/commimensoftraders/explanaorynoes/index.hm) 7 So, in (1), SS comprises Money Manager shor, Oher Reporables shor and 70% of Non Reporable shor; SL comprises Money Manager long, Oher Reporables long and 70% of Non Reporables long; HS comprises Producer/Merchan/Processor/User shor, Swap Dealer shor, Swap Dealer Spread (in he Spread caegory are included raders ha go boh long and shor on fuures markes) and 30% of Non Reporable shor; HL comprises Producer/Merchan/Processor/User long, Swap Dealer long, Swap Dealer Spread and 30% of Non Reporable long. 8 Resuls are similar using alernaive definiions of he Working s T index. They can be found in he echnical appendix available from he auhors upon reques. 9 The rade weighed exchange index is defined as a weighed average of he foreign exchange value of he U.S. dollar agains a subse of he broad index currencies ha circulae widely ouside he counry of issue. Major currency index includes he Euro Area, Canada, Japan, Unied Kingdom, Swizerland, Ausralia, and Sweden. According o his definiion, a decrease of he index corresponds o a depreciaion of he U.S. dollar. 8
Figure 1 repors he behaviour of fuures prices over he ime period considered. The plos confirm ha fuures prices are no saionary. Moreover, we observe ha boh energy and agriculure commodiies display a spike in prices in 2008. 10 As said before, Working s T index measures he excess of speculaion relaive o hedging aciviy: if i is equal, for example, o 1.2, i indicaes 20% of speculaion in excess of wha is necessary o mee hedging needs. By consrucion, he minimum value is 1, when here is no any excess speculaion in he marke. The hird panel of Table 2 shows ha Working s T index ranges from mean values of 10.5% (in gasoline) o 26.8% (in soybeans) and, in he enire sample, i reaches maximum values of around more han 50% (in naural gas and oas). The index is saionary in levels and herefore i is no ransformed. However, he long ime span considered in our sample may, on average, conceal he role of speculaion in recen imes. We hen repor summary saisics for wo differen periods: 1986-2003 and 2004-2010 o inspec if any change of his index occurred across differen commodiies over ime. We choose 2004 as in his year he oil demand excepionally reaches a record level of almos 3 millions barrels a day 11 and he S&P GSCI (Goldman Sachs Commodiy Index) sharply acceleraes. Resuls are repored in Table 3. Firs, we observe ha in he 1986-2003 period energy commodiies display lower mean values han non-energy ones. Second, mean values are generally lower in he 2004-2010, wih he noable excepion of naural gas, crude oil and whea: as hese commodiies show higher values in he second period, his suggess ha speculaion has increased in recen imes. The conemporaneous rise in agriculural and energy prices, repored in Figure 1, poses he quesion of he linkages beween hese markes and he spillovers ha may ake place: preliminary evidence is provided by he correlaion marix beween he variables employed in he esimaion, presened in Table 4. The highes correlaions are hose beween reurns of energy commodiies (generally higher ha 0.7), while soybean oil, nowihsanding is widespread use as fuel, is poorly correlaed wih hem. Correlaions beween reurns and Working s T indexes are in almos all cases no significan, suggesing ha he relaionship linking hese variables is weak and anicipaing he resul found in he economeric analysis ha speculaion is no relevan in explaining fuures reurns. Correlaions beween speculaion indexes are generally no large and mixed in sign bu always significan. 10 For gasoline, heaing oil, crude oil, soybean oil, corn, oas and soybeans he spike corresponds o he 27 h week (July) of 2008; for whea i is he 11 h week (March) of 2008; for naural gas we find wo peaks: in he 50 h week (December) of 2005 and in he 27 h week (July) of 2008. 11 See U.S. Energy Informaion Adminisraion (2008). 9
4. The economeric specificaion We aim a modelling he reurns of commodiies fuures prices. As a preliminary sep, we es for saionariy of all he series, and ake he difference in logs if necessary (see Table 2). Then, we esimae he following equaion: r = α + α in _ rae + α junk _ bond _ yield + α S & P + α exc _ rae + α WT + ε (1) i 0 1 2 3 4 5 i i where he dependen variable is he reurn in commodiy marke i a ime. The macroeconomic conex is summarized by he reurns of 3-monh reasury bills (in_rae ), he junk bond yield, which is defined as he difference beween BAA and AAA corporae bond yield, he reurns of he S&P 500 index (S&P ) and he exchange rae beween U.S. dollar and oher currencies, and he speculaion presen in markes, represened by he Working s T (WT i ) for he marke i a ime. We consider nine markes and he ime period spans from 1986:3 o 2010:52. 12 We firs esimae he model wih ordinary leas squares (OLS) and es for auoregressive condiional heeroskedasiciy (ARCH) effecs in he residuals. If such effecs are presen, we rever o a generalized condiional heeroskedasiciy (GARCH) model. If he GARCH erm is saisically significan, we op for a GARCH(1,1) model, conrolling ha he second momen and log momen condiions are respeced. We also es for auocorrelaion in he residuals and include an auo regressive erm if necessary. As will be discussed in he nex secion, he GARCH (1,1) model wih an AR(1) erm is he preferred specificaion o model he reurns. Therefore, we end up esimaing a model where he condiional mean equaion is: r = γ + γ in _ rae + γ junk _ bond _ yield + γ S & P + γ exc _ rae + γ WT + γ r + ε (2.a) i 0 1 2 3 4 5 i 6 i 1 i and he condiional variance is defined as: 2 i i + + pi 2 qi α j 1 jε = i j j= 1 σ = s β σ (2.b) j 2 i j 12 For naural gas daa are available from 1990:14. 10
2 where he variance σ i of he regression model s disurbances is a linear funcion of lagged values of he squared regression disurbances and of is pas value: p defines he order of he ARCH erm, and q of he GARCH erm. In he economeric exercise, we esimae a model where p=q=1. The univariae analysis is however limied in is scope: he common rend in fuures prices, shown in Figure 1, suggess ha a mulivariae approach should be implemened o invesigae he presence of spillovers, boh in he mean and in he variance equaion. Indeed, a mulivariae-garch model capures he effecs on curren volailiy of own innovaion and lagged volailiy shock originaed in a given marke, as well as cross innovaion and volailiy spillovers from oher fuures markes. This allows o beer undersand volailiy, as well as volailiy persisence, in inerconneced markes. A general mulivariae GARCH model is defined as: r = + ε (3.a) Cx 1/ 2 ε = H υ (3.b) where r is an m 1 vecor of dependen variables, C is an m k marix of parameers, x is a k 1 vecor of independen variables, which conains, following he resuls obained in he univariae analysis, firs lags of he reurns r 1, 1/ H 2 is he Cholesky facor of he ime varying condiional covariance marix of he disurbances H and υ is a m 1 vecor of i.i.d. innovaions wih zero mean and uni variance. As i =1,,9 we would ideally consider a mulivariae GARCH model where m = 9. In he condiional correlaion family of mulivariae GARCH models, he diagonal elemens of H are modelled as univariae GARCH models, whereas he off-diagonal elemens are modelled as nonlinear funcions of he diagonal erms: h ij = ρ h h (4) ij ii jj The consan condiional correlaion (CCC) model assumes ha he diagonal elemens h ii and h jj follow a univariae GARCH processes and ρ ij is a ime-invarian weigh inerpreed as a condiional correlaion. In oher words, condiional correlaions among reurns are consan over ime. Formally, his implies ha marix H is modelled as: 11
H = D RD (3.c) 1/ 2 1/ 2 where D is a diagonal marix of condiional variances in which each 2 σ i evolves according o a univariae GARCH process defined as in he univariae analysis as 2 i i + + pi 2 qi α j 1 jε = i j j= 1 σ = s β σ (again we will presen he resuls specifying p=q=1) and R is a j 2 i j marix of ime-invarian uncondiional correlaions of he sandardized residuals D 1/ 2 ε. While he consan condiional correlaion assumpion allows o esimae large sysems as i reduces he number of parameers o be esimaed, several sudies on crude oil reurns have shown ha his hypohesis is unrealisic as condiional correlaions are generally found o be ime varying (Lanza e al. 2006, Manera e al. 2006, Chang e al. 2009, 2010). Indeed, as will be shown in he nex secion, his hypohesis does no fi our daa, boh in energy and agriculural markes. Therefore, we presen he resuls obained wih he dynamic condiional correlaion (DCC) model, which drops he laer assumpion. More precisely, he diagonal elemens h ii and h jj in (4) sill follow a univariae GARCH processes while ρ ij now follows a dynamic process (Engle 2002). Formally, he D marix in (3.c) is defined as before, while he R marix is now defined as: R Q 1/ 2 = diag( Q ) Qdiag( Q ) = (1 λ λ ) R + λ ~ ε ~ ε 1 2 1/ 2 ' 1 1 1 + λ Q 2 1 (5) where R is a marix of ime-varying condiional quasicorrelaions, ~ ε is an m 1 vecor of sandardized residuals ( D 1/ 2 ε ) and λ 1 and λ 2 are he wo parameers ha deermine he dynamics of condiional quasicorrelaions. They are boh non-negaive, and hey mus saisfy he condiion λ + λ 1. When Q is saionary, he R marix is a weighed average of he uncondiional 0 1 2 < covariance marix of he sandardized residuals ~ ε and he uncondiional mean of Q. As he wo marices are differen, he R marix is neiher he uncondiional correlaion marix, nor he uncondiional mean of (Engle 2009). Q. As a consequence, he parameers in R are known as quasicorrelaions A minor shorcoming of his model is ha he complexiy involved, in erms of number of coefficiens o be esimaed, migh imply some problems in he maximizaion of he likelihood funcion. 12
As a consequence, we presen our resuls dividing he commodiies ino wo subgroups. In he firs one, which we label fuels, we include he four energy commodiies and he soybean oil: in his way, we are able o invesigae possible spillovers beween energy markes and a biofuel. The second one includes he five agriculural commodiies: his allows o es he presence of spillovers beween food commodiies and a biofuel, which has been proposed in he lieraure (Michell 2008, FAO 2009). Indeed, several auhors suggess ha spillovers migh be presen beween energy and agriculural markes as well (Michell 2008, Baffes 2007, 2009, Du e al. 2011, Baffes and Haniois 2010). To es his hypohesis, we exend he second sysem of equaions (i.e. agriculural commodiies) by including a sixh endogenous variable. We could include reurns in crude oil marke o invesigae if and how energy markes influence agriculural commodiies. I has been highlighed however ha oher energy commodiies are relevan in he formaion of agriculural prices. For example, naural gas is he basis for nirogen ferilizer producion. As a consequence, we prefer o summarize dynamics in energy fuures markes by means of a principal facor analysis. Noice ha he facor is consruced using informaion conained in he four purely energy commodiies, i.e. no including soybean oil. As a consequence, he laer sysem allows o separaely consider he spillover beween energy markes, a biofuel and food commodiies. 5. Resuls Esimaion resuls for he univariae specificaion are shown in Table 5. For all he commodiies, he Lagrange muliplier es for ARCH effecs indicaes he presence of ARCH effecs in he residuals of he OLS esimae of he model. Thus, we move o a GARCH(1,1) specificaion. Addiionally, he Ljung-Box es (no repored) on he GARCH(1,1) model shows ha he residuals conain auocorrelaion up o order 1. However, inroducing an AR(1) erm in he models eliminaes auocorrelaion of he residuals, as shown by he Ljung-Box es repored. The speculaion index is negaive or no significan. This resul conrass wih claims ha speculaion has affeced reurns in a posiive way. A negaive sign implies ha an increase in excess speculaions corresponds o a decrease in reurns. As for he macroeconomic conrols in he models, we observe ha he S&P 500 index is posiive and generally significan, and ha he exchange rae is negaive and generally significan, suggesing ha a depreciaion of U.S. dollar compared o oher currencies increases fuures prices 13
and is hus correlaed wih posiive reurns. 13 As expeced, he ARCH (α ) and GARCH ( β ) erms are always saisically significan: he ARCH esimaes are generally small (beween 0.072 for soybean oil and 0.173 for soybeans) and he GARCH esimaes are generally high and close o one (beween 0.741 for heaing oil and 0.892 for whea). This indicaes a near long memory process: a shock in he volailiy series impacs on fuures volailiy over a long horizon. Noice however ha as α + β < 1 for all commodiies, he second momen and log-momen condiions are saisfied in all markes, and his is a sufficien condiion for consisency and asympoic normaliy of he QMLE esimaor (McAleer a al. 2007). To analyze he spillovers beween differen commodiies and he linkages beween differen fuures markes we move o a sysem where he reurns are joinly esimaed, allowing for condiional variances. In his way i is possible o invesigae, for example, if gasoline or naural gas reurns are affeced or affec oil reurns, or if reurns of agriculural commodiies are affeced by energy reurns. Addiionally, we may check if he speculaion index of one commodiy influences reurns of oher ones. Saring from a GARCH(1,1)-AR(1) specificaion ha is suppored for all commodiies in he univariae case, we consider a CCC mulivariae GARCH and we compare i wih a DCC model. The laer model is he preferred specificaion, as he condiional correlaions obained are clearly no consan over ime (more infra). In each equaion he reurns of each commodiy are regressed on he macroeconomics conrols, on he lagged dependen variable 14 and on he lagged reurns of he oher commodiies. Finally, we include among he regressors he own speculaive index as well as he Working s T of all he oher commodiies, o invesigae if speculaion in one marke is significan in oher markes. The resuls for he group of fuels commodiies are presened in Tables from 6.a o 7.b. Table 6.a repors he resuls for he CCC model. Among macroeconomic variables, he S&P index is always posiive and significan and he exchange rae is generally negaive and significan. We mainly observe, wih he excepion of heaing oil, ha lagged values of he dependen variable are posiive and significan, suggesing persisence in reurns. Moreover, lagged reurns in crude oil and naural gas posiively affec reurns of he oher commodiies. The esimaes sugges ha speculaion is widely no significan: he Working s T index in own markes is generally negaive, confirming he resuls obained in he univariae analysis. The ARCH (α ) and GARCH ( β ) erms are always posiive and saisically significan and heir sum is smaller han one. Again, he ARCH esimaes 13 As noed before some auhors sugges ha causaliy beween exchange rae and reurns could run in boh direcions. We replicae he whole se of resuls omiing exchange rae among he regressors. The resuls concerning he oher regressors are unaffeced. 14 We include only one lag as he univariae case suppors an AR(1) model. 14
are ypically small and he GARCH esimaes are generally high, confirming he presence of a near long memory process. We esimae he models assuming a mulivariae Suden s T disribuion for he error erms. The degrees of freedom of he disribuion are esimaed and repored a he boom of Table 6.a. Table 6.b presens he consan condiional correlaions among commodiies: hey are all posiive and saisically significan a 1% level. The highes is he one beween crude oil and heaing oil (0.815). Noice however ha, albei smaller in size, posiive and saisically significan a 1% correlaions exis beween soybean oil and he oher energy commodiies. Table 7.a repors he resuls obained wih he DCC specificaion. Noice ha he DCC model reduces o he CCC if he λ parameers are boh equal o zero. We es he null hypohesis ha λ = λ 1 2 = 0 : he es srongly rejecs he null, hus supporing he dynamic specificaion. Resuls of DCC model confirm hose of CCC. Among macroeconomic facors, S&P and exchange rae are significan. Own lagged reurns are generally significan and he same holds for lagged reurns of crude oil and naural gas. Again speculaion is poorly significan. Moreover, he DCC model allows o rerieve he ime-varying condiional correlaions, which are ploed in Figure 2.a: he graphs clearly show ha he correlaions are ime-varying. Ineresingly, he correlaions beween soybean oil and he oher energy commodiies presen high values around he year 2008, i.e. in he peak period of prices (see Figure 1). Descripive saisics on he condiional correlaions are repored in Table 7.b. Albei on average slighly smaller han he correlaions obained in he CCC model, he dynamic condiional correlaions confirm he resuls repored in Table 6.b: he highes mean values observed is beween heaing oil and crude oil (0.773) followed by he one beween gasoline and crude oil (0.723) and beween gasoline and heaing oil (0.706). The lowes mean values are hose relaed o soybean oil. Besides, all he correlaions vary dramaically displaying also negaive values and having a large range of variaion. For example, if we consider he correlaion beween heaing oil and crude oil, a maximum value of 0.875 means ha, on he corresponding week (13 h week of 1998), heaing oil and crude oil reurns would have brough almos he same risk, so ha invesing in he fuures marke and choosing beween one of hem, brings he same risk. On he conrary, a minimum value of -0.206 (50 h week of 2000) beween naural gas and crude oil means ha shocks o hese wo commodiies are no perfec subsiues in erms of risk. Finally, skewness and kurosis values indicae negaively skewed disribuions in he majoriy of correlaions. Resuls for he agriculure group of commodiies are repored in Tables 8.a-9.b. Again, he CCC and DCC provide similar resuls. Among macroeconomic conrols, only he S&P reurn and he exchange rae display significan coefficiens, wih he expeced signs. We do no observe spillovers 15
in he mean equaion: only he own lagged reurn shows posiive and significan coefficiens. Measures of speculaion are poorly significan: he Working s T index of corn and soybean oil are generally negaive and significan. The condiional correlaions implied by he CCC model repored in Table 8.b are generally high and saisically significan. Similar resuls are found in he dynamic condiional correlaions, ploed in Figure 2.b. Noice ha, conrary o he fuels DCC, we do no observe marked peaks in recen imes. The minimum values of he correlaions repored in Table 9.b are, wihin his group, always posiive, meaning ha he subsiuion effec in risk is absen in hese fuures markes. Finally, we discuss he resuls for he exended group, which includes agriculural commodiies and a facor summarizing he four energy variables, which has been obained using he principal facor mehod o analyze he correlaion marix among he reurns of he four energy commodiies. Resuls repored in Tables 10.a-11.b confirm previous evidence concerning he five agriculural commodiies. However, we observe no eviden spillover in he mean equaion among food commodiies, a biofuel and he energy facor. The consan condiional correlaions, repored in Table 10.b, are generally posiive and significan. Ineresingly, he correlaions beween he energy facor and he oher commodiies are generally low, wih he highes value being he correlaion wih soybean oil (0.134). Figure 2.c repors he dynamic condiional correlaions, and shows ha, while being on average small, he condiional correlaions wih he energy facor display a peak around year 2008. The descripive saisics repored in Table 11.b for he DCC show ha negaive and significan values exis, only when considering correlaions wih he energy facor. This las resul confirms ha spillovers beween energy and agriculure commodiies exis: negaive correlaions indicae ha high volailiy values in he energy markes correspond o low volailiy levels in he markes for agriculural commodiies. 5.1 Sensiiviy over ime Our sample has a long ime span, so i is ineresing o see if spillover effecs in he volailiy of commodiy reurns become more marked in recen years. This is shown in Table 12.a, where are repored mean ess on dynamic condiional correlaions of fuels group. All he -saisics are significan a 1% level, meaning ha mean values are saisically differen in he wo samples. In paricular, values afer 2004 are higher han hose in he 1990-2003 period and mean values beween energy commodiies and soybean oil are almos doubled in he second period. This resul confirms he increasing ineracion beween markes, especially when biofuels are considered. Table 12.b shows ha, also for he agriculure group, mean values are increased afer 2004, bu, his 16
ime, he increase is less eviden and he relaionship wih biofuels is less marked. Finally, Table 12.c confirms ha, also in his las group, mean values of dynamic condiional correlaions beween agriculural commodiies and he energy facor are doubled or more han doubled afer 2004. I is also ineresing o see if here are changes in mean equaions before and afer 2004 and, in general, in he resuls of CCC and DCC esimaions. 15 As regards he fuels group i is relevan o noice ha he influence of crude oil (wih reference o is pas reurns and is Working s T index) on oher commodiies and, in paricular, on soybean oil, appears o be significan only afer 2004, suggesing ha spillovers in he mean equaion happen mosly in he las period. Ineresingly, we find ha he condiional correlaions increase in size afer 2004 and ha he correlaions beween fuels and soybean oil become significan and posiive, confirming again spillover effecs in recen imes. Resuls for he agriculure group, boh in CCC and DCC models, do no show marked differences before and afer 2004. Finally, looking a he agriculure sysem enriched wih he energy facor, we observe ha he correlaions beween he energy facor and he agriculural commodiies and biofuel become significan only afer 2004. These las resuls suppor once again he increasing ineracion beween differen markes and are in line wih similar resuls obained adoping alernaive economeric approaches (Naanelov e al. 2011, Ciaian and Kancs 2011). 6. Conclusions The recen spike in commodiies prices in 2008 has lead o claims ha prices are driven by speculaors. Moreover, as he rise has affeced boh energy and food commodiies a generalized financializaion of commodiies fuures markes has been held responsible. Anoher channel for he ransmission of price shocks has been alleged o be he increasing relevance of biofules, which inerconnec energy and food markes. However, mos of he evidence in suppor of hese hypoheses is based on descripive saisics. We collec daa on fuures prices for four energy commodiies (ligh swee crude oil, heaing oil, gasoline and naural gas) and five agriculural commodiies (corn, oas, soybean oil, soybeans and whea) over he period 1986-2010 a weekly frequency and measure financial speculaion by means of he Working s T (1960) index. Wih his sample we aim a answering o four research quesions. Firs, we look a he role of macroeconomic facors as possible drivers of reurns of energy and nonenergy commodiies. Secondly, we consider wheher financial speculaion is significanly relaed o reurns in fuures markes. Finally, we focus on he relaionship among reurns across differen 15 These resuls are repored in he Saisical Appendix, which is available from he auhors upon reques. 17
markes boh wih respec o he mean and he variance. Moreover, we invesigae if and how speculaion in one marke affecs reurns in oher markes. Descripive evidence shows ha he Working s T index has significanly increased afer 2004 only in crude oil, naural gas and whea fuures markes. Addiionally, if we look a he correlaions wih commodiies reurns, Working s T indexes are in almos all cases no significan, suggesing a weak relaionship beween speculaion in differen markes. The economeric exercise presens an univariae analysis where commodiy reurns are modelled according o a GARCH(1,1) wih an AR(1) erm. Working s T index is always negaive or no significan: a negaive sign implies ha an increase in excess speculaion corresponds o a decrease in reurns. This resul conrass wih he claims in he lieraure ha speculaion has affeced reurns in a posiive way (Eckaus 2008, Masers 2008, Soros 2008). Among macroeconomic facors, S&P500 index is posiive and significan and he exchange rae is negaive and generally significan, suggesing ha a depreciaion of U.S. dollar increases fuures prices. To analyze spillovers beween commodiies and differen fuures markes we presen resuls from mulivariae GARCH models. We group he commodiies ino wo subgroups, fuels (gasoline, heaing oil, naural gas, crude oil and soybean oil) and agriculure (corn, oas, soybeans, whea and soybean oil) and we esimae a sysem where reurns are joinly esimaed, allowing for condiional correlaions. The mulivariae-garch DCC model is always preferred o he CCC, as he condiional correlaions obained are no consan over ime. As in he univariae case, S&P500 index is always posiive and significan and he exchange rae is generally negaive and significan. Thus, as concerns our firs research quesion, few macroeconomic variables seems o significanly affec he reurns in commodiies fuures: he S&P index and he mulilaeral exchange rae. As regard our second research quesion, esimaes sugges ha speculaion is generally no relevan. However, when including an energy facor in he agriculure group, we find an ineresing resul: Working s T index in crude oil marke assumes a posiive and significan effec on soybean oil reurns afer 2004, indicaing a linkage beween energy markes and a biofuel one in recen imes. As for he hird issue, i.e. possible spillovers across commodiies, boh in he mean and variance equaion, we observe ha lagged reurns of crude oil and naural gas posiively affec reurns of he oher energy commodiies. Looking a volailiies, i is ineresing o noe ha correlaions beween soybean oil and he oher energy commodiies and hose beween agriculural and energy facor presen high values around 2008, i.e. in he peak period of prices. Moreover, when we disinguish beween ime periods, we noice ha: (i) mean values of dynamic condiional correlaions always increase afer 2004 and, in fuels markes, hey even double; (ii) condiional correlaions and quasicorrelaions beween commodiies in hese wo groups become significan and posiive only in 18
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