CRUDE OIL HEDGING WITH PRECIOUS METALS: A DCC-GARCH APPROACH

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1 Academy of Accouning and Financial Sudies Journal Volume 22, Number 1, 2018 CRUDE OIL HEDGING WIH PRECIOUS MEALS: A DCC-GARCH APPROACH Vanee Bhaia, Indian Insiue of Managemen Raipur Sayasiba Das, Indian Insiue of Managemen Raipur Subraa Kumar Mira, Indian Insiue of Managemen Raipur ABSRAC he objecive of his sudy is o invesigae he dynamic relaionship beween crude oil and precious meals by employing DCC-GARCH model. he correlaion srucure obained from he DCC-GARCH model is used o consruc hedging raios and porfolio weighs. he analysis is repeaed wih ADCC-GARCH o check he robusness of he findings. he resuls of his sudy can be summarized as follows: Firs, here exiss a dynamic condiional correlaion beween crude oil and precious meals. Second, on an average, he dynamic correlaion beween crude oil and precious meals increased wih he adven of recen financial crisis ill he effec of he crises subsided. hird, DCC resuls beween crude oil and precious meals sugges ha, precious meals seem o behave as a single asse class during he periods of uncerain oucomes. Fourh, silver and palladium exhibi beer hedging capabiliy han gold. Keywords: Crude Oil, DCC, GARCH, Hedging, Precious Meals. INRODUCION he increased associaion beween commodiy markes has always araced he ineres of researchers, invesors and policymakers. In one of he earlier sudies on commodiy price movemens, Pindyck and Roemberg (1990) observed a paern in price movemens beween unrelaed commodiies. his finding led o several sudies analysing his phenomenon and he debae was furher inensified wih he financializaion of commodiy markes during early 2000s. For example, Soyas, Sari, Hammoudeh and Hacihasanoglu (2009) argued ha he excess comovemen among commodiies could be aribued o he similar influence of macroeconomic variables on all commodiy markes. Neverheless, among all commodiies, crude oil has acquired unprecedened imporance because of is share in he energy secor across naions. Mos economies are exceedingly relian on crude oil for heir energy needs and as a resul i could resul in huge impor bills for crude oil imporing naions. Besides, such economies could find i difficul o susain heir rade balances because of price flucuaions in inernaional crude oil markes. herefore, he imporance of he commodiy markes like crude oil, underlines he need o invesigae he crude oil price flucuaions o safeguard he ineres of numerous sakeholders. he uncerainy in crude oil markes may rigger invesmens in oher asses or in hedging insrumens like precious meals. For example, Melvin and Sulan (1990) repored ha he increase in crude oil prices is usually associaed wih increased invesmen in gold. he linkages beween crude oil and precious meals like gold may be because reserve porfolios of oil exporing counries generally comprises gold. iwari and Sahadudheen (2015) argue ha some of he oil imporing counries pay hrough gold and herefore, here exiss a relaionship beween crude oil and gold hrough impor channels. Kanjilal and Ghosh (2017) sugges a lead-lag relaionship beween crude oil and gold. here is also an evidence of increased invesmen in gold during he periods of marke uncerainy (Jain & Biswal, 2016). Moreover, during financial

2 Academy of Accouning and Financial Sudies Journal Volume 22, Number 1, 2018 crisis or periods of high volailiy, gold was found o be uncorrelaed wih oher financial asses (Baur & Lucey, 2010; Baur & McDermo, 2010). hese properies of gold have also moivaed researchers o consider he relaionship beween crude oil wih oher precious meals. For example, Sari, Hammoudeh and Soyas (2010) suggesed ha silver prices are beer predicor of oil price movemens in comparison o oher precious meals. Jain and Ghosh (2013) indicaed some dependence beween oil prices and precious meals. Bildirici and urkmen (2015) argue ha recen periods of uncerainy have resuled in he renewed relaionship beween crude oil and precious meal prices. Moivaed by he earlier lieraure, he primary objecive of his sudy is o invesigae he dynamic correlaion beween crude oil and precious meals (gold, silver, plainum and palladium) using Dynamic Condiional Correlaion-Generalized auoregressive condiional heeroscedasiciy (DCC-GARCH) approach proposed by Engle (2002). Second, he covariance and variance srucure obained from DCC-GARCH framework were used o generae he hedging raios and porfolio weighs beween crude oil and precious meals. Kroner and Sulan (1993) approach was used o consruc he hedging raios and Kroner and Ng (1998) approach was used o consruc he porfolio weighs. Several auhors have used he hedging raios and porfolio weighs o invesigae he dynamics beween differen markes, for example, Baser & Sardorsky (2016), Ku e al. (2007) and Maghyereh e al. (2017). hird, o check he robusness and asymmeric characerisic of he relaionship, he invesigaion was also carried ou using Asymmeric DCC. Res of he paper is srucured as follows: Nex secion explains he mehodology. Secion 3 repors he daa and preliminary analysis. Secion 4 explains he empirical findings followed by conclusion in secion 5. DCC-GARCH MEHODOLOGY DCC-GARCH is based on he decomposiion of he condiional covariance marix ino wo ime-varying pars: Firs, condiional sandard deviaions marix and second ino correlaions marix (Engle & Sheppard, 2001; Engle, 2002). he DCC-GARCH process can be explained as follows: H D R D (1) H is n n marix of condiional variances of mean-correced n-commodiy (c) a ime. Cov C H D is a n n, diagonal marix of ime-varying sandard EC 0and herefore,. deviaions from n univariae GARCH model a ime. R is he ime-varying condiional, D C ~ N 0,R. A leas wo crieria correlaion marix of sandardized disurbances needed o be saisfied while defining he DCC-GARCH process. Firs, H is o be posiive definie. Second, elemens in R should be less han or equal o one. R U U U * * (2) U U U (3)

3 Academy of Accouning and Financial Sudies Journal Volume 22, Number 1, 2018 U * is a diagonal marix wih he elemens consising of square roo of he diagonal elemens of U.U * rescales he elemens in U such ha qij, p ij q q ii, jj, U has o be posiive definie so ha R is posiive definie. Where U Cov E represens he uncondiional covariance marix of 1 (sandardised errors) and U can be esimaed as U Maximum likelihood esimaion is used o esimae he model. he scalar parameers α and β have o mee cerain condiions o ensure H o be posiive definie: firs, α 0, β 0 and second α + β <1. he resulan correlaion beween wo series depends on he sandardized residuals. When he residuals move in he same direcion, hey push he correlaion up and hen wih he passage of ime and wih complee informaion absorpion gradually fall back o he average level. On he oher hand when residuals move in opposie direcions, i will resul in low correlaion and again he correlaion will move owards he average wih he passage of ime. he ime aken o move o differen posiions is governed by he parameers α (shor run persisence) and β (long-run persisence). ADCC-GARCH Capeeiello e al. (2006) suggesed he modificaion of DCC model by adding an asymmeric erm o he model, which was ermed as ADCC-GARCH (Asymmeric DCC). A posiive asymmeric erm indicaes ha negaive residuals have more impac on he variance han posiive residuals. I is designed o capure he asymmeric effec, i.e., he volailiy of any financial asse ends o ge affeced more during he unexpeced fall in asse prices (bad news) han an unexpeced increase in asse price (good news). Wih regard o ADCC he dynamics of U can be shown as: U U A UA B U B A B U B G G (4) Hedging Raio and Porfolio Weighs Kroner and Sulan (1993) argue ha hedge raios may be consruced by using he condiional volailiy esimaes. An asse (x) on which a long-posiion is aken may be hedged wih a second asse (y) by aking a shor posiion. hus, he hedge raio beween he wo asses may be represened as: hxy, xy, (5) h yy, βxy, is he hedge raio beween asse x and y a ime, hxy, is he condiional covariance beween asse x and y a ime, hxy, is he condiional variance of asse y. Kroner and Ng (1998) sugges ha mulivariae GARCH esimaes can be used o consruc opimal porfolio weighs. hyy, hxy, Wxy, (6) h 2h h xx, xy, yy,

4 Academy of Accouning and Financial Sudies Journal Volume 22, Number 1, if wxy, 0 Wxy, Wxy,, if 0 wxy, 1, If wxy, wxy, is he weigh of asse x in a one dollar porfolio of x and y, a ime. hxy, is he condiional covariance beween asse x and y a ime, hyy, is he condiional variance of asse y. he weigh of asse y a ime is 1 wxy,. DAA AND PRELIMINARY ANALYSIS Weekly daa has been colleced from January 2000 o March Crude oil spo prices have been colleced from US Energy Informaion Adminisraion and are repored in US dollar per barrel. On he oher hand, world precious meal prices for gold, silver, plainum, palladium have been colleced from Bloomberg daa services and are repored in US dollar per roy ounce. Log reurn series were calculaed o ake care of he uni roo and same were used for he res of he analysis. Descripive saisics are shown in able 1. I can be noed ha gold provides highes mean reurns followed by silver and palladium provides he leas reurn among he seleced series. he iniial volailiy esimaes (sandard deviaion) suggess palladium reurns o be highly volaile followed by crude oil reurns. Skewness values are negaive for all he reurn series indicaing ha mos values are disribued o he righ and suggess longer ail on he lef. Excep for silver reurns, all oher reurns are playkuric indicaing shorer and hinner ails. he las four columns of able 1 show he resul for Ljung-Box es and Jarque-Berra es respecively. Ljung Box es indicaes he presence of serial correlaion of second momens in he case of crude oil, plainum and palladium. Jarque Berra es suggess he non-normal disribuion of all he reurn series. hese ess sugges he possibiliy of using GARCH like models o examine he dynamics beween crude oil and precious meals. EMPIRICAL RESULS able 2 repors DCC and ADCC-GARCH parameer esimaes and are significan a 1% level of significance. he low value of α and high value of β indicaes he imporance of long-run persisence in comparison o shor-run persisence. he ADCC parameer esimae () for asymmeric relaionship is no saisically significan and suggess ha volailiy esimaes beween crude oil and precious meals are no influenced by negaive shocks or sharp increase in reurns. herefore, i may be he reason ha our resuls are almos similar in boh DCC and ADCC framework. Figures 1 and 2 show he DCC and ADCC beween crude oil and precious meals over he sample period respecively. he dynamic correlaion beween crude oil and precious meals exhibi similar paerns during several ime periods. For example, DCC beween crude oil and precious meals show similar paerns during and before he recen financial crisis and hen from 2011 o firs half of he period from 2011 depics he impac of he Arab uprising, Libyan unres and he excess capaciy (supply) during On an average, he dynamic correlaion beween crude oil and precious meals increased on he eve of he financial crisis and sared o decrease afer he effec of crisis subsided in I suggess ha during such urmoil s invesors can expec high correlaion in volailiies and need o adjus heir invesmens in hese markes

5 Academy of Accouning and Financial Sudies Journal Volume 22, Number 1, 2018 Mean Reurn able 1 DESCRIPIVE SAISICS SD Skewness Kurosis Ljung-Box es Jarque-Berra Chi-squared p-value Chisquared p-value Crude oil Gold Silver Plainum Palladium Noe: SD: Sandard Deviaion; Ljung-Box es: H0: Zero serial correlaion of residuals; Jarque- Berra: H0: Series is normally disribued. able 2 MULIVARIAE DCC-GARCH PARAMEER ESIMAES DCC ADCC Parameer Esimae Sd. Error -value p-value Esimae Sd. Error -value p-value α β Akaike Bayes Shibaa Hannan- Quinn Noe: DCC: Dynamic Condiional Correlaion, ADCC: Asymmeric DCC able 3 HEDGING RAIO BEWEEN CRUDE OIL AND PRECIOUS MEALS DCC ADCC Mean SD Mean SD CO wih Gold CO wih Silver CO wih Plainum CO wih palladium Gold wih CO Silver wih CO Plainum wih CO Palladium wih CO Noe: CO represens crude oil. For example, CO wih gold shows ha on an average $1 long posiion in crude oil can be hedged wih 24 cens shor posiion in gold. DCC: Dynamic Condiional correlaion, ADCC: Asymmeric DCC, SD: Sandard Deviaion

6 Academy of Accouning and Financial Sudies Journal Volume 22, Number 1, 2018 FIGURE 1 DYNAMIC CONDIIONAL CORRELAION BEWEEN CRUDE OIL (CO) AND PRECIOUS MEALS. FIGURE 2 ASYMMERIC DYNAMIC CONDIIONAL CORRELAION BEWEEN CRUDE OIL (CO) AND PRECIOUS MEALS able 3 repors he hedging raios calculaed from he variance and covariance srucure obained from DCC and ADCC-GARCH processes. For example, he average value of hedge raio beween crude oil and gold is 0.24 and for gold and crude oil is I indicaes ha $1 long posiion in crude oil can be hedged for 24 cens wih a shor posiion in gold. Similarly, a $1 long posiion in gold can be hedged wih a shor posiion for 12 cens in crude oil. From able 3, i can be noiced ha cheapes hedge for a $1 long posiion in crude oil is a shor posiion in palladium (18 cens). herefore, mos economical way o hedge $1 posiion in crude oil is wih

7 Academy of Accouning and Financial Sudies Journal Volume 22, Number 1, 2018 palladium followed by silver, gold and plainum. able 4 shows he opimal porfolio weighs of wo asse porfolios of crude oil wih precious meals. For example, he average weigh for he crude oil/gold porfolio is I indicaes ha for a $1 porfolio, 27 cens should be invesed in crude oil and 73 cens in gold. Porfolio weighs sugges ha for an opional porfolio beween crude oil and precious meals, gold is required in highes proporions followed by plainum, silver and palladium. able 4 PORFOLIO WEIGHS DCC ADCC Mean SD Mean SD CO, Gold CO, Silver CO, Plainum CO, Palladium Noe: CO: Crude Oil, DCC: Dynamic Condiional Correlaion, ADCC: Asymmeric DCC, SD: Sandard Deviaion he resuls of his sudy show ha a porfolio of crude oil spo and precious meal spo can be buil and precious meals can be used o hedge he invesmen in crude oil and vice versa. he high correlaion beween crude oil and precious meals during normal ime periods, however, may creae confusion o he average invesor, bu if examined appropriaely, could be exremely useful during sressful evens. Resuls also show ha invesors and oil imporing counries can arge precious meal oher han gold, o hedge he invesmens in he crude oil marke. Similarly, oil imporing counries while designing reserve porfolio could also include silver, plainum and palladium raher han relying only on gold. CONCLUSION he objecive of his paper was o invesigae he dynamic relaionship beween crude oil and precious meals (gold, silver, plainum and palladium) from January 2000 o March Linear models usually fail o capure he dynamics beween such commodiies due o serial correlaion and non-normal disribuion properies. herefore, his paper invesigaes he imevarying relaionship beween crude oil and precious meals using GARCH framework. his paper relies on DCC-GARCH model o invesigae he relaionship beween crude oil and precious meals and furher checks he robusness of he resuls wih ADCC model. he condiional volailiies obained from boh he models (DCC and ADCC) are hen used o invesigae he hedging raios and porfolio weighs. he empirical resuls of DCC and ADCC esimaion reveal several ineresing findings. Firs, here is a ime varying relaionship beween crude oil and precious meals. Second, here was a significan increase in correlaion beween crude oil and precious meals afer he crude oil shock and financial crisis ( ). I suggess ha volailiies of crude oil and precious meals end o be highly correlaed during he periods of uncerainy. hird, he DCC beween crude oil and precious meals indicae ha, precious meals end o behave as a single asse class during he periods of uncerain oucome. Fourh, he asymmeric effec (ADCC) does no seem o work in he case of crude oil and precious meals. I suggess ha saisically here is no heerogeneiy in he influence of sharp rise and fall in prices of crude oil and precious meals on condiional volailiies. Fourh, he hedging raios indicae ha in conras o general belief, silver and palladium offer economical hedging opion in comparison o gold

8 Academy of Accouning and Financial Sudies Journal Volume 22, Number 1, 2018 Resuls have imporan implicaions for invesors, porfolio managers and policymakers. Firs, he rising dynamic correlaion for exended periods may indicae a recessionary phase. Second, he dynamic correlaion of crude oil and any precious meal may also indicae he dynamic correlaion of crude oil and oher precious meals. hird, including non-linear characerisics while modelling he relaionship beween commodiies may resul in superior hedging and porfolio sraegies. ACKNOWLEDGMEN his research is suppored by using a research gran from Indian Insiuion of Managemen. REFERENCES Basher, S.A. & Sadorsky, P. (2016). Hedging emerging marke sock prices wih oil, gold, VIX and bonds: A comparison beween DCC, ADCC and GO-GARCH. Energy Economics, 54, Baur, D.G. & Lucey, B.M. (2010). Is gold a hedge or a safe haven? An analysis of socks, bonds and gold. Financial Review, 45(2), Baur, D.G. & McDermo,.K. (2010). Is gold a safe haven? Inernaional evidence. Journal of Banking & Finance, 34(8), Bildirici, M.E. & urkmen, C. (2015). Nonlinear causaliy beween oil and precious meals. Resources Policy, 46, Cappiello, L., Engle, R.F. & Sheppard, K. (2006). Asymmeric dynamics in he correlaions of global equiy and bond reurns. Journal of Financial Economerics, 4(4), Engle, R. (2002). Dynamic condiional correlaion: A simple class of mulivariae generalized auoregressive condiional heeroskedasiciy models. Journal of Business & Economic Saisics, 20(3), Engle, R.F. & Sheppard, K. (2001). heoreical and empirical properies of dynamic condiional correlaion mulivariae GARCH (No. w8554). Naional Bureau of Economic Research. Ghalanos, A. (2015). he rmgarch models: Background and properies. (Version 1.3-0). Jain, A. & Biswal, P. (2016). Dynamic linkages among oil price, gold price, exchange rae and sock marke in India. Resources Policy, 49, Jain, A. & Ghosh, S. (2013). Dynamics of global oil prices, exchange rae and precious meal prices in India. Resources Policy, 38(1), Kanjilal, K. & Ghosh, S. (2017). Dynamics of crude oil and gold price pos 2008 global financial crisis New evidence from hreshold vecor error-correcion model. Resources Policy, 52, Kroner, K.F. & Ng, V.K. (1998). Modelling asymmeric comovemens of asse reurns. he Review of Financial Sudies, 11(4), Kroner, K.F. & Sulan, J. (1993). ime-varying disribuions and dynamic hedging wih foreign currency fuures. Journal of Financial and Quaniaive Analysis, 28(4), Ku, Y.H.H., Chen, H.C. & Chen, K.H. (2007). On he applicaion of he dynamic condiional correlaion model in esimaing opimal ime-varying hedge raios. Applied Economics Leers, 14(7), Maghyereh, A.I., Awarani, B. & ziogkidis, P. (2017). Volailiy spillovers and cross-hedging beween gold, oil and equiies: Evidence from he Gulf Cooperaion Council counries. Energy Economics, 68, Melvin, M. & Sulan, J. (1990). Souh African poliical unres, oil prices and he ime varying risk premium in he gold fuures marke. Journal of Fuures Markes, 10(2), Pindyck, R.S. & Roemberg, J.J. (1990). he Excess Co-Movemen of Commodiy Prices. he Economic Journal, 100(403), Sari, R., Hammoudeh, S. & Soyas, U. (2010). Dynamics of oil price, precious meal prices and exchange rae. Energy Economics, 32(2), Soyas, U., Sari, R., Hammoudeh, S. & Hacihasanoglu, E. (2009). World oil prices, precious meal prices and macroeconomy in urkey. Energy Policy, 37(12), iwari, A.K. & Sahadudheen, I. (2015). Undersanding he nexus beween oil and gold. Resources Policy, 46,