Volatility spillovers between crude oil futures returns and oil company stock returns

Transcription

1 8 h Word IMACS / MODSIM Congress, Cairns, Ausraia 3-7 Juy 2009 hp://mssanz.org.au/modsim09 Voaiiy spiovers beween crude oi fuures reurns and oi company sock reurns Tansucha, R.,2, M. McAeer 3, 4 and C. Chang 4 Facuy of Economics, Maejo Universiy, Chiang Mai, Thaiand 2 Facuy of Economics, Chiang Mai Universiy, Chiang Mai, Thaiand 3 Economeric Insiue, Erasmus Universiy Roerdam, The Neherands 4 Deparmen of Appied Economics, Naiona Chung Hsing Universiy, Taichung, Taiwan Emai: roengchaian@gmai.com Absrac: The purpose of his paper is o invesigae voaiiy spiovers beween crude oi fuures reurns and oi company sock reurns by using he recen muivariae GARCH mode, namey he CCC of Boersev (990), VARMA-GARCH mode of Ling and McAeer (2003) and VARMA-AGARCH mode of McAeer, e a. (2008). This paper invesigaes he WTI crude oi fuures reurns and sock reurns of en oi companies; which are composed of he supermajor group of oi companies, namey Exxon Mobi (XOM), Roya Duch She (RDS), Chevron Corporaion (CVX), ConocoPhiips (COP), BP (BP) and Toa S.A. (TOT), and oher arge oi and gas companies in he word, namey Perobras (PBRA), Lukoi (LKOH), Surgunefegas (SNGS), and Eni S.p.A. (ENI). The empirica resus presen condiiona correaion beween WTI crude oi fuures reurns and very ow reurns in sock of he CCC mode oi company. Surprisingy, for he VARMA-GARCH and VARMA-AGARCH modes, no voaiiy spiover effecs are observed in every pairs of reurn series. The paper aso presens he evidence of asymmeric effec of negaive and posiive shock on condiiona variance in every pairs of reurn series. Keywords: Muivariae GARCH, Asymmeries, Voaiiy spiovers, Crude oi fuures reurns, Oi company sock reurns 356

2 Tansucha e a., Voaiiy spiover beween crude oi fuures reurns and oi company sock reurns. Inroducion Crude oi is arguaby he mos infuenia physica commodiy in he word and pays a prominen roe in an economy. Therefore, oi prices fucuaion ceary affecs he word economy in many differen ways. Rising crude oi prices raises he cos of producion of goods and services, ransporaion and heaing cos. As a resu, i provokes concerns abou infaion and resriced discreionary spending of consumer and produces a negaive effec o financia markes, consumer confidence, and he macroeconomy (see for exampe, Mork (994), Sadorsky (999), Lee e a. (200), Hooker (2002), Hamion and Herrera (2004), Cunado and Perez de Garcia (2005), Jimenez-Rodriguez and Senchez (2005), Kiian (2008), Coogni and Manera (2008) and Park and Rai (2008)). The vaue of sock prices in an equiy pricing mode heoreicay equas he discouned earning expecaion of companies or fuure cash fows. Therefore, oi price shocks infuence sock prices hrough expeced cash fow and discoun rae. Since oi is one of he crucia inpus for goods and services producion, a rise in oi prices wihou subsiue inpus increases producion coss; which in urns decrease cash fows and sock prices. In addiion, rising oi prices affecs he discoun rae by infuencing he infaion pressures which aso eads o he decision making by he cenra bank o raise ineres rae. Therefore, he corporae invesmen decision can be affeced direcy by change in he discoun rae and change in sock price reaive o book vaue. However he direcion of sock price change depends on wheher a sock is a producer or consumer of oi and oi reaed producs. Since mos companies in he word marke are oi consumer, i is ogica o see ha he performance of oi prices and sock marke migh be negaivey correaed. A number of previous papers have observed and provided expanaion of he oi price and sock marke reaionship and he negaive impac of oi price on sock markes (see for exampe, Jones and Kau (996), Faff and Braisford (999), Hammoudeh and Aeisa (2002) and (2004), Nandha and Faff (2008), Sadorsky (2008)). However, Maghyereh (2004) does no find he significan impac on sock index reurns in 22 emerging economy empoying VAR mode. This impies ha he sock marke reurns in hese economies do no raionay signa shocks in he crude oi marke. Surprisingy up o his period, here is a very imied amoun of ieraure work based on he reaionship beween oi price and oi company sock price. There is a posiive reaionship beween he oi price and sock price of he oi company (see for exampe, Faff and Braisford (999), Sadorsky (200), Boyer and Fiion (2004), E-Sharif e a. (2005), Basher and Sadorsky (2006), Nandha and Faff (2008) and Henriques and Sadorsky (2008)). As voaiiy (or risk) is unobservabe bu a he same ime imporan in finance, here appears o be voaiiy spiover paerns ha is widespread in he financia markes (Miunovich and Thorp (2006)), energy markes, and sock marke (Sadorsky (2004)). Consequeny, a voaiiy spiover occurs when changes in price or reurn voaiiy in one marke produce a agged impac on voaiiy in oher markes or each oher. However, here seems o be a sma amoun of research sudy in voaiiy spiovers beween he oi marke and sock marke. Ågren (2006) invesigaes voaiiy spiovers from oi prices o sock markes using asymmeric BEKK mode, and presens srong evidence of voaiiy spiovers in Japan, Norway, U.K. and he U.S. sock markes; bu quie weak in Swedish. The assessmen of he voaiiy of oi company sock price reurns and he inkage beween oi price voaiiy and oi company sock price voaiiy are cruciay imporan for invesmen decisions and poicy makers o impemen appropriae poicies for managing sock markes and aso financia hedgers, porfoio managemen, asse aocaor, or oher financia anaysis. Wih he Oi & Gas indusry secor being one of he arges indusries in he word, hey have differen companies and business invoved in he differen chains of producion, disiaion and disribuion. Surprisingy, none of hese papers have ooked a he reaionship beween crude oi fuures reurns voaiiy and oi company sock price voaiiy. To mode voaiiy spiovers, here are severa condiiona voaiiy modes which specify he risk on one asse as depending dynamicay on is own pas risk and on he pas risk of he oher asses, see McAeer (2005). de Veiga and McAeer (2004) presened ha he muivariae VARMA-GARCH mode of Ling and McAeer (2003) and VARMA-AGARCH mode of McAeer e a. (2008) provided beer voaiiy han he nesed univariae mode, namey GARCH of Boersev (986) and GJR of Gosen, Jagannahan and Runke (992), respecivey. Even hough hese modes assume consan condiiona correaion, hey do no suffer form he curse of dimensionaiy when hey are compared o VECH and BEKK modes. On he oher hand, in order o capure he dynamics of ime-varying condiiona correaion, receny deveopmen mode is generaized auoregressive condiiona correaion (GARCC) of McAeer e a. (2008). The aim of his sudy is o examine he voaiiy spiovers beween crude oi fuures reurns and oi company sock reurns in many major oi companies. This issue is sudied empiricay wih in a bivariae VARMA- GARCH and VARMA-AGARCH modes. The resus of he paper may shed on he imporance of he crude 357

3 Tansucha e a., Voaiiy spiover beween crude oi fuures reurns and oi company sock reurns oi on oi company sock. The remainders of he paper are organized as foows. The muivariae condiiona voaiiy modes are discussed in Secion 2. The daa are described in Secion 3, and he empirica resus are anayzed in Secion 4. Some concuding remarks are given in Secion Mehodoogy The purpose of his secion is o brief muivariae condiiona voaiiy mode incuding spiover effec, in which he condiiona variance of reurn i is specified o depend dynamicay on pas squared uncondiiona shocks and pas condiiona variance of each asse in he porfoio. The VARMA-GARCH mode of Ling and McAeer (2003), assumes symmery in he effec of posiive and negaive shocks on he condiiona voaiiy, is given by ( ) Y = E Y F + ε () ( L)( Y μ ) ( L) Φ =Ψ ε (2) ε = Dη (3) H W A B H r s = + ε + i, j = = (4) F is he pas informaion avaiabe up o ime, m is he oa of reurns o be where Y (,..., = y y m), anayzed and =,..., m. L is he ag operaor. ( )... q 2 Ψ ( L) = Im Ψ L... Ψ ql are poynomias in L. D = diag( hi, ), η (,..., η η m) p Φ L = Im Φ L Φ pl and = is a sequence of independeny and idenicay (iid) random vecors. H (,..., = h h m), W (,..., = ω ω m) 2 2, ε = ( εi,..., ε m), A and B are m m marices wih ypica eemens α ij and β ij, respecivey, for i, j =,..., m. A and β represen he ARCH effec and GARCH effec, respecivey. Spiover effecs or he independence of he condiiona variance beween WTI crude oi fuures reurns and oi company sock reurns are given in condiiona voaiiy for each reurn in he porfoio. Based on equaion (3), he VARMA-GARCH mode aso assumes ha he marix of condiiona correaions is given by ( ) reduces o he univariae GARCH mode of Boersev (986): p q 2 2 = ω+ αiε i + βih i i= i= h E ηη =Γ. If m =, equaion (4) (5) An exension of he VARMA-GARCH mode o accommodae asymmeric impacs of he posiive and negaive shocks, is he VARMA-AGARCH mode of McAeer e a. (2008), capures asymmeric spiover effecs from each of he oher reurns. An exension of (4) o accommodae asymmeries wih respec o ε i is given by r r s H W A = + + C I + B H ε ( η ) ε (6) = = = in which ε i = η h i for a i and, C are m m I η = diag I η is an m m marix, such ha, such ha ( ) ( ( i) ) I ( η ) i marices and ( ) 0, εi > 0 =, εi 0 I η is an indicaor variabe, and If m =, equaion (4) reduces o he asymmeric univariae GARCH, or GJR mode of Gosen e a. (992): If C = 0 wih A and r s 2 ( ( )) (8) h = ω+ α + γ I η ε + β h j j j j j j j= j= B being diagona marices for a hen VARMA-AGARCH reduces o: (7) 358

4 Tansucha e a., Voaiiy spiover beween crude oi fuures reurns and oi company sock reurns h r = ω + α ε + β h i i i, i, = = s (9) which is he consan condiiona correaion (CCC) mode of Boersev (990). As given in equaion (7), he CCC mode does no have asymmeric effecs of posiive and negaive shocks on condiiona voaiiy and voaiiy spiover effecs across differen financia asses, so i is inrinsicay univariae in naure. From (2), he condiiona correaion is εε = Dηη D, he condiiona covariance marix is ( εε ) E F =Ω = DΓ D. (0) Therefore, he condiiona correaion marix is defined as Γ= D Ω D. The parameers in mode (), (4), (6) and (9) can be obained by maximum ikeihood esimaion (MLE) using a join norma densiy: namey n ˆ θ = arg min ( og Q + ε Q ε) () θ 2 = where θ denoes he vecor of parameers o be esimaed on he condiiona og-ikeihood funcion, and Q denoes he deerminan of Q, he condiiona covariance marix. When η does no foow a join muivariae norma disribuion, he appropriae esimaors are defined as he Quasi-MLE (QMLE). 3. Daa In his paper we focus on voaiiy spiover modeing beween crude oi fuures reurn in WTI marke and he 0 oi company sock reurns. Six of hem are caed supermajor, six arges non sae-owned energy companies, which are composed of Exxon Mobi (XOM, US), Roya Duch She (RDS, The Neherands), Chevron Corporaion (CVX, US), ConocoPhiips (COP, US), BP (BP, UK) and Toa S.A. (TOT, French). The res of hem are Perobras (PBRA:Brasi), Lukoi (LKOH, Russia), Surgunefegas (SNGS, Russia), and Eni S.p.A. (ENI, Iay). A 3,202 price observaions are saring from 4 November 996 o 20 February 2009 and are obained from he DaaSream daabase services and expressed in oca currencies wih he ony excepion of WTI crude fuures prices, which are denominaed in USD per barre. The empirica resus of he uni roo ess for WTI crude oi fuures reurn and 0 oi company sock price reurns are avaiabe from he auhors upon reques. The Augmened Dickey-Fuer (ADF) and he Phiips- Perron (PP) es are used o expore he exisence of uni roos in he individua series. Under he nu hypohesis of a uni roo, boh ess provide arge negaive vaues for a cases presening ha a of he individua reurn series rejec he nu hypohesis a he % significan eve, which means a reurns series are saionary. 4. Empirica resus Since he univariae ARMA-GARCH nesed o VARMA-GARCH and ARMA-GJR nesed o VARMA- AGARCH wih condiiona variance specified in (5) and (8), univariae ARMA-GARCH and ARMA-GJR modes wi be esimaed. I aso makes sense o exend univariae o muivariae if he properies of univariae modes are saisfied. The coefficiens in he condiiona variance equaion resued from ARMA(,)-GARCH(,) are significan boh in he shor and ong run. However, he coefficien in he condiiona variance resued from he ARMA(,)-GJR(,) are a significan, bu wih PBRA ony in ong run. In addiion, a he univariae eve, he mos esimaes of he asymmeric effec in which negaive shocks are a greaer impac on voaiiy han posiive shocks are significan excep for TOT, LKOH and SNGS. The deai of he univariae esimaes of condiiona voaiiies and srucura properies of boh univarie modes, namey second momen and og-momen, based on WTI crude fuures reurns and oi company sock reurns are avaiabe from he auhors upon reques. The esimaes of consan condiiona correaions beween WTI crude oi fuures reurns and oi company sock reurns and Boersev-Woodridge (992) robus -raios using CCC mode based on esimaing univariae GARCH(,) modes are presened in Tabe. For he 0 oi company sock reurns, here are 0 condiiona correaion, wih he highes esimaed consan condiiona correaion being beween he sandardized shocks o he voaiiies in he WTI crude oi fuures and COP reurns and he owes being beween he sandardized shocks o he voaiiies in he WTI crude oi fuures and SNGS reurns. The cacuaed consan condiiona correaions are very ow. This can be inerpreed as he behavior of hose sandardized shocks o he voaiiies which are possiby deermined by oher variabes. 359

5 Tansucha e a., Voaiiy spiover beween crude oi fuures reurns and oi company sock reurns Tabe 2 Condiiona correaion from CCC mode beween WTI crude oi fuures reurn and oi company sock reurns WTI 0.72 BP COP CVX ENI LKOH PBRA RDS SNGS TOTAL XOM (9.05) (9.693) 0.34 (8.65) 0.5 (6.5) 0.02 (5.684) 0.64 (9.292) 0.9 (5.858) (3.578) 0.49 (7.683) Noes: () The wo enries for each parameer are heir respecive parameer esimaes and Boersev and Woodridge (992) robus - raios. (2) Enries in bod are significan a he 95% eve. Tabe 3 VARMA-GARCH Pane 3a. VARMA-GARCH: WTI_BP Pane 3f. VARMA-GARCH: WTI_PBRA (4.867) ϖ α WTI α BP β WTI β BP WTI BP Pane 3b. VARMA-GARCH: WTI_COP ϖ α WTI α COP β WTI β COP WTI COP Pane 3c. VARMA-GARCH: WTI_CVX ϖ α WTI α CVX β WTI β CVX WTI CVX Pane 3d. VARMA-GARCH: WTI_ENI ϖ α WTI α ENI β WTI β ENI WTI ENI Pane 3e. VARMA-GARCH: WTI_LKOH ϖ α WTI α LKOH β WTI β LKOH WTI ϖ α WTI α PBRA β WTI β PBRA WTI PBRA Pane 3g. VARMA-GARCH: WTI_RDS ϖ α WTI α RDS β WTI β RDS WTI RDS Pane 3h. VARMA-GARCH: WTI_SNGS ϖ α WTI α SNGS β WTI β SNGS WTI SNGS Pane 3i. VARMA-GARCH: WTI_TOTAL ϖ α WTI α TOTAL β WTI β TOTAL WTI TOTAL E Pane 3j. VARMA-GARCH: WTI_XOM ϖ α WTI α XOM β WTI β XOM WTI LKOH XOM Noes: () The wo enries for each parameer are heir respecive parameer esimaes and Boersev and Woodridge (992) robus - raios. (2) Enries in bod are significan a he 95% eve Corresponding muivariae esimaes for he VARMA(,)-GARCH(,) and VARMA(,)-AGARCH(,) modes using BHHH (Bernd, Ha, Ha and Hausman) agorihm and Boersev-Woodridge (992) robus -raio are repored in Tabe 2 and 3 respecivey. The esimaes of condiiona mean for VARMA-GARCH are avaiabe upon reques. In Pane 2a-2j, he ARCH and GARCH effecs for WTI fuures reurn and oi company sock reurns are saisicay significan in he condiiona voaiiies for he WTI fuures reurn and oi company sock reurns. Ineresingy, here is aso cear from abe 2 ha no evidence of voaiiy spiovers is observed boh one direcion and wo direcions (inerdependence). I means ha he pair of WTI fuures reurns and oi company sock reurns are affeced ony by is own reurns shor run (α) and ong run (β) shocks. The resus of he VARMA-AGARCH in Pane 3a-3j mirror hose in Pane 2a-2j. Like he previous Pane, he esimaes of condiiona mean for VARMA-AGARCH are avaiabe upon reques. Surprisingy, in Pane 3a-3j, he coefficiens of voaiiy spiovers are a saisicay insignifican. Therefore, each pair of reurns in porfoio are ony affeced by heir own previous shor run (ARCH effec) and ong run (GARCH effec) shocks, bu wih WTI of pair of WTI_ENI, PBRA of pair of WTI_PBRA and SNGS of pair of WTI_SNGS ony in ong run. The esimaes of he condiiona variance aso show ha asymmeric effecs are eviden in a cases, suggesing ha VARMA-GARCH is superior o VARMA-AGARCH. 360

6 Tansucha e a., Voaiiy spiover beween crude oi fuures reurns and oi company sock reurns Tabe 4 VARMA-AGARCH Pane 4a. VARMA-AGARCH: WTI_BP ϖ α WTI α BP γ β WTI β BP WTI BP Pane 4b. VARMA-AGARCH: WTI_COP ϖ α WTI α COP γ β WTI β COP WTI COP Pane 4c. VARMA-AGARCH: WTI_CVX ϖ α WTI α CVX γ β WTI β CVX WTI CVX Pane 4d. VARMA-AGARCH: WTI_ENI ϖ α WTI α ENI γ β WTI β ENI WTI ENI Pane 4e. VARMA-AGARCH: WTI_LKOH ϖ α WTI α LKOH γ β WTI β LKOH WTI Pane 4f. VARMA-AGARCH: WTI_PBRA ϖ α WTI α PBRA γ β WTI β PBRA WTI PBRA Pane 4g. VARMA-AGARCH: WTI_RDS ϖ α WTI α RDS γ β WTI β RDS WTI RDS Pane 4h. VARMA-AGARCH: WTI_SNGS ϖ α WTI α SNGS γ β WTI β SNGS WTI SNGS Pane 4i. VARMA-AGARCH: WTI_TOTAL ϖ α WTI α TOTAL γ β WTI β TOTAL WTI TOTAL Pane 4j. VARMA-AGARCH: WTI_XOM ϖ α WTI α XOM γ β WTI β XOM WTI LKOH XOM Noes: () The wo enries for each parameer are heir respecive parameer esimaes and Boersev and Woodridge (992) robus - raios. (2) Enries in bod are significan a he 95% eve 5. Concusion The empirica anaysis in his paper examined he voaiiy spiovers beween crude oi fuures reurns and oi company sock reurns by using receny muivariae GARCH mode, namey he CCC, VARMA- GARCH and VARMA-AGARCH mode. This paper invesigaes he WTI crude oi fuures reurns and sock reurns of en oi companies, composing of he group of supermajor oi companies, namey Exxon Mobi, Roya Duch She, Chevron Corporaion, ConocoPhiips, BP and Toa S.A., and oher arge oi and gas companies of he word, namey Perobras, Lukoi, Surgunefegas, and Eni S.p.A. The empirica resus presen ha he condiiona correaion beween WTI crude oi fuures reurns and oi company sock reurns of CCC mode are very ow. Surprisingy, he VARMA-GARCH and VARMA-AGARCH resus show ha here were no spiover effecs beween pair of reurns series. The evidence of asymmeric effecs of negaive and posiive shocks on condiiona variance suggess ha VARMA-AGARCH is superior o VARMA- GARCH modes. ACKNOWLEDGMENTS The auhors wish o hank Feix Chan and Abdu Hakim for providing he compuer programs. For financia suppor, he firs auhor acknowedges he Energy Conservaion Promoion Fund, Minisry of Energy, Facuy of Economics, Maejo Universiy and Facuy of Economics, Chiang Mai Universiy, he second auhor wishes o hank he Ausraian Research Counci, and he hird auhor is mos graefu o he Naiona Science Counci, Taiwan. REFERENCES Ågren, M. (2006), Does oi price uncerainy ransmi o sock markes? Deparmen of Economics, Uppsaa Universiy, Working Paper 2006:23. Basher, S. and Sadorsky, P. (2006), Oi price risk and emerging sock markes. Goba Finance Journa, 7, Boersev, T. (986), Generaized auoregressive condiiona heeroscedasiciy. Journa of Economerices, 3,

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