Lead Lag Relationships between Futures and Spot Prices

Transcription

1 Working Paper No. 2/02 Lead Lag Relaionships beween Fuures and Spo Prices by Frank Asche Ale G. Guormsen SNF-projec No. 7220: Gassmarkeder, menneskelig kapial og selskapssraegier The projec is financed by The Research Council of Norway INSTITUTE FOR RESEARCH IN ECONOMICS AND BUSINESS ADMINISTRATION BERGEN, JANUARY 2002 ISSN Dee eksemplar er fremsil eer avale med KOPINOR, Senergae 1, 0050 Oslo. Yerligere eksemplarfremsilling uen avale og i srid med åndsverkloven er sraffbar og kan medføre ersaningsansvar.

2 Lead Lag Relaionships beween Fuures and Spo Prices by Frank Asche Savanger Universiy College and Cenre for Fisheries Economics, Norwegian School of Economics and Business Adminisraion, Box 2557 Ullandhaug, N-4091 Savanger, Norway. Fax: (47) ; and Ale G. Guormsen (Corresponding auhor) Deparmen of Economics and Social Sciences, Agriculural Universiy of Norway, Box 5033, N-1432 Aas, Norway. Fax: ; Frank Asche is a professor a Savanger Universiy College and Cenre for Fisheries Economics, Norwegian School of Economics and Business Adminisraion. Ale G. Guormsen is an associae research professor a he Deparmen of Economics and Social Sciences a he Agriculural Universiy of Norway.

3 Lead Lag Relaionships beween Fuures and Spo Prices Absrac In his paper we examine he relaionship beween spo and fuures prices. This is radiionally done by esing for coinegraion wih he Engle and Granger mehodology, before one specifes an error correcion models in order o draw inference abou causaliy. This approach, alhough appealing for is simpliciy, is problemaic on a leas wo accouns. Firs, he approach is only valid given an exogeneiy assumpion, which is wha one wans o es, and second, given ha here are several conracs wih differen imes o expiraion, bivariae specificaions canno capure all he relevan informaion. We show ha boh problems can be avoided if he ess are carried ou in a mulivariae framework like he Johansen es. An empirical applicaion is carried ou on fuures prices for gas oil. Findings indicae ha fuures prices leads spo prices, and ha fuures conracs wih longer ime o expiraion leads conracs wih shorer ime o expiraion. Key Words: Fuures, spo, causaliy, mulivariae coinegraion, exogeneiy.

4 Inroducion The exisence of price discovery, marke sabiliy and marke efficiency associaed wih spo and fuures markes has been imporan opics since he genesis of fuures markes more han 100 years ago. Numerous papers have examined he relaionship beween spo and fuures prices for various ypes of commodiies as well as for financial asses. Empirical evidence o dae is mixed, alhough a majoriy of sudies indicae ha fuure markes have a price discovering role. Recen papers examining he price discovery role and he lead lag relaionship beween fuures and spo prices have o a large exen followed he wo-sep procedure oulined in Quan (1992), which is based on he price series being nonsaionary. i The firs sep is o es he exisence of a long-run relaionship beween he spo and fuures prices by invesigaing wheher he daa series are coinegraed. If he firs sep reveals a longrun relaionship, hen causaliy (lead-lag) can be esed o examine he discovery role of fuures prices. If no long-run relaionship is revealed, he invesigaion comes o an end because he wo imes series are generaed compleely independen (Quan 1992). When invesigaing he relaionship beween spo and fuure prices, he Engle and Granger es (Engle and Granger, 1987) has been he mos common ool o es for coinegraion. Condiioned on he exisence of a long-run relaionship, single equaion error correcion models (ECM) have been specified in order o draw inference abou causaliy. This approach, alhough appealing for is simpliciy, is problemaic on a leas wo accouns. Firs, single equaion ECMs are only valid given an exogeneiy assumpion (Banjeree e al, 1993). However, his is wha one wans o es. Moreover, given ha here are several conracs wih differen imes o expiraion, bivariae specificaions canno in general capure all he relevan informaion. This paper show ha boh problems can be avoided if he ess are carried ou in a mulivariae framework like he Johansen es (Johansen, 1988, 1991). The firs issue can 1

5 hen be addressed by modeling he relaionship beween he price of a fuure conrac and he spo price as a bivariae sysem. The exogeneiy assumpion underlying any single equaion model can hen be esed in addiion o he exisence of a long run relaionship. To ake ino accoun he fac ha a any ime several conracs are raded for he same produc, a mulivariae sysem mus be specified. I is hen possible o es several hypohesis wih respec o he price discovery process. For insance, in addiion o es only wheher fuures prices lead spo prices, i is of ineres o examine wheher some of he conracs lead ohers. Moreover, wih he srucure mos commonly observed for fuures prices, i can be shown ha a mos one price/conrac can be leading in he erm srucure. Anoher issue ha is ofen inadequaely addressed in he lieraure is he form of he long-run relaionships beween he fuure and spo prices, and paricularly if basis is consan so ha he prices move proporionally o each oher. Ofen his is assumed, a oher imes one jus regress he relaionship wihou paying aenion o his issue, or one invesigae he relaionships under boh condiions. This is because he favored mehod, Engle and Granger coinegraion ess and ECM models, does no allow saisical inference on he parameers in he long-run relaionship. This problem can also be avoided in he Johansen framework, as exploied in bivariae sysems by Kellard, Newbold, Rayner and Ennew (1999) and Haigh (2000). These ess are also easily exended o a mulivariae framework. Wih he possibiliy o es resricions on he parameers in he sysem, one can es for consan basis as well as for price leadership. The approach will be used o sudy fuures on Gas oil. Price leadership in he fuures marke for gas oil and oher oil derivaives as well as he crude price has been he focus in a number 2

6 of sudies including Herbs, McCormack and Wes (1987), Kawaller, Koch and Koch (1987), Chan (1992), Quan (1992), Schwarz and Szakmary (1994), Moosa and Alloughani, (1994), Gülen (1998), Girma and Paulson (1999) and Silvapulle and Moosa (1999). However here is also conflicing evidence wih respec o price leadership. The daa used in his paper is from he Inernaional Peroleum Exchange (IPE). The gas oil conrac was launched as he IPE's firs fuures conrac in 1981, and developed rapidly ino a benchmark for spo middle disillae across norh-wes Europe and beyond. The IPE's Gas Oil fuures conrac is a highly flexible and liquid conrac and is ofen referred o as heaing oil in Europe or he USA. In June 2001, volumes of Gas Oil fuures raded reached a daily high of 60,639 los. IPE claims ha he Gas Oil fuures have become very closely associaed wih he physical marke. The paper is organized as follows: The following secion will give an exposiion of he sandard heory on he spo-fuures price relaionship, in secion hree mulivariae empirical specificaions are presened and discussed, whereas he daa is presened in secion four. Secion five presen he resul and some concluding remarks are presened in he las secion Lead-lag relaionships beween fuures and spo prices. There are basically wo views on he price formaion process for commodiy fuures prices. In he firs he ineremporal relaionship beween cash and fuures prices of coninuously sorable commodiies is explained by he cos of carry for he commodiy (Kaldor, 1939; Working 1948, 1949; Brennan, 1958; Telser, 1958). In he second view one splis he fuures price ino an expeced risk premium and a forecas of a fuure spo price (Cooner, 1960; Dusak, 1973; Breeden, 1980; Hazuka, 1984). 3

7 The heory of ineremporal relaionship beween cash and fuures prices can be explained briefly wih he cos of carry condiion as a saring poin. This condiion can, for coninuously sorable commodiies be formulaed as T r w T (1) F Se where is he curren dae, T is he fuures conrac expiraion dae, w a sorage cos, r is he riskless money rae of ineres a, T F is he fuure price a, and S is he spo price a. This condiion says ha if you wan a commodiy a some ime T, you can eiher buy a fuure conrac wih delivery a ime T, or you can buy he commodiy in he spo marke and sore i unil T. A dispariy beween he lef-hand and righ-hand side of cos-of-carry equaion migh give rise o an arbirage opporuniy. Arbiragers can hen go long in he commodiy and shor he fuures conrac, and hence lock in a secure payoff. From equaion (1) i seems like he condiions also should hold he oher way around, i.e. ha he fuures price never should be less han he spo price plus sorage and ineres cos. However his is more problemaic since one can argue ha here is a value associaed wih having he commodiy. This value, he convenience yield, is based in he fac ha having he commodiy in sock provides flexibiliy regarding for insance unexpeced demand. Supporers of he second view on he price formaion process for commodiy fuures prices argues ha he basis can be expressed as a sum of an expeced premium and an expeced change in he spo price, T F S E ª P T º ¼ E ST S (2) here he expeced premium E P, T ª º ¼ is defined as he bias of he fuure price as a forecas of he fuure spo price. 4

8 T, E ª P T º ¼ F E ST (3) Fama and French (1988) argue ha he heory of sorage, equaion (1) and equaion (2) are alernaive bu no compeiive views of he basis, and ha variaion in expeced change in he spo price in (2) ranslaes ino variaion in he ineres rae and he marginal sorage cos in (1). Boh heories imply ha here should be a long run sable relaionship beween spo and fuures prices. In addiion, for he fuure price o be an unbiased predicor of subsequen spo price, i.e., E P, T Silber, 1983). ª º ¼equals zero, he fuure price should lead he spo price (Garbade and Several oher more ad hoc argumens for he fuures price o lead he spo price can be found in he lieraure. ii Silvapulle and Moosa (1999) argue ha fuures prices respond o new informaion more quickly han he laer due o lower ransacion coss and ease of shoring, while Newberry (1992) posulae ha fuures marke provide opporuniies for marke manipulaion. According o his argumen he fuures marke can be manipulaed eiher by he larger a he expense of he smaller or by he beer informed a he expense of he uninformed. There are also argumens for he opposie hypohesis, ha spo price lead fuures prices (Silvapulle and Moosa,1999; Quan, 1992; Moosa, 1996). Moosa (1996) presens a model where he change in he spo price will rigger acion from he hree kinds of marke paricipans, and hese acions will subsequenly change he fuures price. The heories reviewed above have in common ha hey are bivariae specificaions of he relaionship beween he spo price and he fuure price. They do no ake ino accoun he fac ha for mos fuures, several conracs are raded a he same ime. For a rader in he marke, buying a fuures conrac wih expiraion a ime is similar o buying a fuures conrac ha 5

9 expires a ime iand hen sore he commodiy from i o. Hence a similar relaionship as in equaion (1) also holds for wo fuures conracs wih differen ime o expiraion. r w T i F F e (4) T T i However, as menioned above, his condiion only says ha here should be a long run relaionship beween he prices, he condiion says nohing abou wheher any of he prices leads he oher. If he longes conrac predics he fuure spo price, his should also predic he price of any shorer fuure conracs. On he oher hand, some weighing beween convenience yield and e.g. low ransacion coss can lead a shorer conrac o be he price leader, and as above spo prices can be price leading if he convenience yield is high enough. I is of ineres o noe ha if equaion (1) holds for all fuure conracs, hen equaion (4) follows. This is analogue o Hall, Anderson and Granger s (1992) model of ineres raes. Empirical specificaion Mos prices series seem o be nonsaionary. Coinegraion analysis is herefore he preferred ool when analyzing relaionships beween prices. The use of coinegraion analysis and errorcorrecion models also enables one o disinguish beween shor-run and long-run deviaions from equilibrium indicaive of price discovery and long-run deviaions ha accoun for efficiency and sabiliy (Pizzi e al., 1998). Evidence of price changes in one marke generaing price changes in he oher marke so as o bring abou long-run equilibrium relaionship is given as s E E f e (5) 0 1 where s and f are logs of spo and fuures prices a ime, ; E 0 and E1 are parameers; and e is he deviaion from pariy. If s and f are coinegraed he error erm e will be saionary. This observaion forms he basis for he Engle and Granger es for coinegraion, 6

10 where e is esed for saionariy by performing ADF uni roo ess. Engle and Granger furher show ha if wo series, such as spo and fuures prices, are coinegraed, an appropriae mehodology for modeling he shor-erm dynamics of he sysem is an errorcorrecion model (ECM). In he fuures lieraure i has been sandard pracice o represen his by single equaions as ' s D T e ' f D T e (6) Thus, each ECM conains lagged residuals from he coinegraion regression (equaion (5)). A number of hypohesis is of ineres in relaion o equaions (5) and (6). If E0 0, E 1 1 he marke is efficien, while if E 1 1 he prices are proporional and he prices are predicable from each oher. If he T 1 0 in equaion (6) he spo price is weakly exogenous for he fuure price and herefore leads he fuure price, while if T 2 0 he fuure price leads he spo price. In addiion if (If T1 T 2 0 he spo and fuure prices are no coinegraed). The Johansen es In conras o he Engle and Granger approach, he Johansen es is a mulivariae approach. This can be represened as follows. Le X denoe an nu1 vecor, where he mainained hypohesis is ha X follows an unresriced vecor auoregression (VAR) in he levels of he variables X 31X ' X 0 (7) k k where each of he 3 i is a nun marix of parameers, P a consan erm and H are idenically and independenly disribued residuals wih zero mean and conemporaneous covariance marix :. The VAR sysem in (5) wrien in error correcion form (ECM) is; 7

11 ' X * ' X... * ' X 3X 0 (8) 1 1 k1 k1 k wih * I , i 1,..., k 1 and * I , i 1,..., k 1. Hence, 3 is i i he long-run level soluion o (7). If X is a vecor of I(1) variables, he lef-hand side and he firs (k-1) elemens of (8) are I(0), and he kh elemen of (8) is a linear combinaion of I(1) variables. Given he assumpions on he error erm, he kh elemen mus also be I(0); 3X k i ai(0). Hence, eiher X conains a number of coinegraion vecors, or 3 mus be a marix of zeros. The rank of 3, r, deermines how many linear combinaions of X are saionary. If r=n, he variables in levels are saionary; if r=0 so ha 3=0, none of he linear combinaions are saionary. When 0<r<n, here exis r coinegraion vecorsor r saionary i linear combinaions of X. In his case one can facor 3; 3 DE c, where boh D and E are nur marices, and E conains he coinegraion vecors (he error correcing mechanism in he sysem), and D he facor loadings or adjusmen parameers. Please noe ha he coinegraion vecors are idenified only up o a nonsingular ransformaion, so ha c PP 1 DE D E c ABc where P is an arbirary nonsingular rur marix. Furhermore, he coinegraion relaionships give nonlinear cross equaion resricions, so he sysem canno in general be esimaed efficienly in single equaions. Johansen suggess wo ess for he number of coinegraion vecors in he sysem, he maximal eigenvalue es and he race es. Boh ess have he null hypohesis ha here are a mos r coinegraion vecors. For he maximal eigenvalue es, he alernaive hypohesis is ha here are exacly r 1 coinegraion vecors, while he alernaive hypohesis in he race es is ha here exis more han r coinegraion vecors. iii The Johansen procedure allows a wide range of hypohesis esing on he coefficiens D and E, using likelihood raio ess (Johansen and Juselius, 1990). When esing hypohesis wih respec o basis, i is he 8

12 resricions on parameers in he coinegraion vecors E we wish o es. Informaion abou price leadership is formally esed as exogeneiy ess on he D coefficiens. I may here be worhwhile o se up a sysem ha conains he relevan informaion. Le us firs sar wih a sysem wih wo variables, a spo price s and a fuures price f. Assuming ha he prices are nonsaionary, bu coinegraed, wih one lag and suppressing he error erm, his can be represened as follows. ª ' sº ª a1 º ª s 1 º «> b1 b2@ f» «a» «2 f» ' ¼ ¼ 1 ¼ (9) If b 1 =-b 2, he prices will be proporional and basis consan. Normally, b 1 is normalized o be 1, so ha one ess wheher b 2 =-1 (or 1 if he erm is moved o he oher side of he equaliy operaor). The a s measure he impac of changes in basis on respecively he spo and fuure prices. If a 1 z0, a change in basis will be a leas parly correced by a change in he spo price, while if a 2 z0, a change in basis will be a leas parly correced by a change in he fuure price. I should hen be obvious ha if a 1 =0, here are no changes in he spo price due o changes in basis and all correcions will have o made by changes o he fuure price, and vice versa if a 2 =0. Hence, if a 1 =0 spo prices will lead fuures prices, if a 2 =0 fuure prices will lead spo prices and if a 1 za 2 z0 here will be no price leadership in his sysem. Boh a s canno simulaneously be zero, as here will hen be no long-run relaionship. When moving o a mulivariae sysem he main difference is ha and. is marices (a and b in equaion (9). In general, all long-run relaionships influence all he variables, and since here are cross equaion resricions, informaion is los if all equaions are no esimaed ogeher. Alhough he inuiion in a mulivariae sysem is equivalen o he bivariae example above, here are also some special issues. In a sysem wih n daa series here will be r 9

13 sochasic rends and n-r coinegraion vecors (Sock and Wason, 1988). If he daa series are nonsaionary one can a mos have n-1 coinegraion vecors. When all fuure prices are coinegraed wih he spo price, hey will all follow he same sochasic rend and here will be n-1 coinegraion vecors in he sysem. This implies ha E will be a nun-1marix, and hence one can es wheher all basises, or a subse of hem, are consan simulaneously. More imporan in our conex is i ha in a sysem wih n daa series and r sochasic rends here can a mos be r exogenous variables (Johansen and Juselius, 1994). Wih he srucure one expec o find in fuures markes (i.e. a long-run relaionship beween he spo price and he fuures price for all conracs), one expec o find n-1 coinegraion vecors and one sochasic rend. This is in common wih many oher financial sysems, see e.g. (Cox, Ingersoll and Ross, 1985; Hall, Anderson and Granger, 1992). Hence, here can a mos be one price ha leads he sysem. In his case i will also be valid o model he sysem as bivariae relaionships wih he exogenous variable on he righ hand side. This has wo imporan implicaions. Firs, if here are no exogenous variables in he sysem, he full sysem mus be esimaed. This also implies ha he full sysem mus be esimaed if one is o es for exogeneiy. Second, if he spo price is o be included in all relaionships, he spo price mus be exogenous if any prices are exogenous. In single equaion specificaions i mus hen be he righ hand side variable. If i is a fuures price ha is exogenous, his should be he righ hand side variable. Daa The daase used in his sudy consis of monhly observaions of fuures prices for gas oil markeed a IPE. The period covered includes he whole hisory of he conrac, i.e. April 1981 o Sepember Daa were obained from he Exchange s homepage ( 10

14 As a proxy for he fuures price, he conrac closes o delivery is used. This is a common pracice when cash prices are no readily available (Fama and French, 1987). Assuming risk neural and raional acors, he fuure price close o delivery should represen he expeced spo price when deliveries acually happen. To preven problems wih low rading volume he las day wih acive rading, prices quoed 5 days before are used in he analysis. Wih several days o he conrac expires, volume should sill be high enough. Fuures conracs wih respecively 1 monh o expiraion, 3 monh o expiraion and 6 monh o expiraion is used in he analysis. Empirical Resuls Before conducing any economeric analysis, he ime series properies of he daa mus be invesigaed. This is done wih Augmened Dickey Fuller (ADF) es. Lag lengh was chosen as suggesed by Banerjee (1993) by saring wih a generous parameerizaion and hen removing insignifican lags. Table 1 repors he resuls of he ADF ess. The es indicaes ha while prices in levels are nonsaionary, all prices are saionary in firs differences. The analysis will herefore proceed under he assumpion ha all price series are inegraed of order one. Tesing for Coinegraion Since he price series are all nonsaionary and inegraed of he same order, coinegraion analysis is he appropriae ool o invesigaing he relaionship beween he prices. We proceed by esing for coinegraion in he sysem conaining he spo price as well as he prices for hree fuure conracs. The lag lengh was again chosen o whien he error erm and as ess for auocorrelaion Lagrange muliplier ess (LM) for he presence of auocorrelaion up o he 12 h order are repored in able 2. The wo ess o deermine he rank of he 11

15 coefficien marix LH WKH WUDFH DQG HLJHQYDOXH WHVWV DUH DOVR UHSRUWHG LQ WDEOH 7KH maximum eigenvalue es as well as he race es suggess ha here are hree coinegraion vecors in he sysem, and accordingly only one sochasic rend. The conclusion mus herefore be ha spo prices and fuures prices wih differen ime o expiraion are coinegraed and hence here is a long run relaionship beween he prices. This resul is furher confirmed wih he resuls from he bivariae ess (able 3) indicaing ha all he prices are bilaerally coinegraed. For he fuures price o be an unbiased predicor of he spo price, he fuure and spo prices mus be proporional (i.e E 1 1 in equaion (5)). In he sysem a likelihood raio es for his hypohesis is disribued as $ 2 (3) and give a es saisic of 2.41 wih a p-value of Hence he hypohesis ha all he prices are proporional canno be rejeced. This resul was also confirmed in bivariae relaionships (es saisics in able 3). The es ha he prices are proporional and in addiion ha E 0 (in equaion (5)) are zero in all relaionships was also performed wih a likelihood raio es. The es ha is $ 2 (6)-disribued give a es saisic of wih and p-value of Hence he hypohesis was rejeced. Tes resuls so far have confirmed ha spo prices and fuures prices wih differen ime o mauriy follow he same sochasic rend, and move proporionally over ime. However, price leadership, or causal relaionship beween he prices is no ye invesigaed. A es for exogeneiy will provide such informaion. As discussed earlier, ess on he facor loading parameers will deermine wheher any of he variables can be considered as weakly exogenous in he sysem. The null hypohesis o be esed is ha he D marix in a paricular row is conaining only zeros, and is esed wih a likelihood raio es. Moreover, since here is only one sochasic rend in he sysem, here canno be more hen one exogenous price. 12

16 Resuls are repored in able 2, and indicae ha weak exogeneiy canno be rejeced for he fuures conrac wih 6 monhs o expiraion, while i is clearly rejeced for he wo oher fuures prices and he spo price. These resuls sugges ha he fuures conrac wih longes ime o expiraion is he driving facor in he price generaing process and ha i is his conrac ha binds he price series ogeher in he long-run. Again, he resuls were confirmed in he bivariae equaions. Also here weak exogeneiy could no be rejeced for he 6 monhs fuures conrac in any of he relaionship conaining 6 monh. In addiion weak exogeneiy could no be rejeced for he hree monh conrac in he bivariae equaions conaining hree monh and spo, and hree monh and one monh. And a las, weak exogeneiy canno be rejeced for he one monh conrac in he formulaion wih only one monh and spo. The conclusion seem herefore o be ha fuures prices leads spo prices, and ha fuures prices wih longer ime o expiraion leads fuures conracs wih shorer ime o expiraion, and hence i is always he longes conrac ha binds he price series ogeher in he long-run. Concluding Remarks Tess on long run relaionships and lead lag relaionships beween fuures and spo prices are in he lieraure mosly carried ou in a wo sep Engle and Granger approach. However, his approach has several shorcomings. In paricular, valid ess for lead lag relaionships can only be carried ou in a sysem framework. Moreover, one canno es hypohesis wih respec o he parameers in he long-run relaionship (he basis) in he Engle and Granger framework. Finally, one canno ake ino accoun ha here for mos commodiies are several conracs. In 13

17 his paper, i is shown ha all hese problems can be avoided if one use he Johansen procedure. Our empirical resuls clearly demonsrae ha gas oil fuures and gas oil spo price form a sable long run relaionship and ha he prices are proporional so ha he basis is consan. The resuls also indicae ha he fuure price leads he spo price, and in addiion, he fuure conracs wih longer ime o expiraion lead fuures conracs wih shorer ime o expiraion. Hence he longes conrac in our sysem (6 monh) is he leading indicaor of fuure spo price as well as for fuure fuures price for shorer conracs. 14

18 Bibliography Banerjee, A., Dolado, J., Galbraih, J. W. & Hendry, D. F. (1993). Co-inegraion, error correcion, and he economeric analysis of non-saionary daa, Oxford: Oxford Universiy Press. Breeden, D. T. (1980). Consumpion risks in fuure markes. Journal of Finance, 35: Brennan, M. J. (1958). The supply of sorage. American Economic Review, 48: Chan. K. (1992). A furher analysis of he lead-lag relaionship beween he cash marke and sock index fuures marke. Review of Financial Sudies, 5, Cox, J., Ingersoll, E., & Ross, S. (1985). A heory of he erms srucure of ineres raes. Economerica, 53, Cooner, P. H. (1960). Reurns o speculaors: Telser vs. Keynes. Journal of Poliical Economy, 68, Dusak, K. (1973). Fuures rading and invesor reurns: An invesigaion of commodiy marke risk premiums. Journal of Poliical Economy, 81, Engle, R. F., & Granger C. W. J. (1987). Co-inegraion and error correcion, represenaion esimaion and esing. Economerica, 55,

19 Fama, E. F., & French, K. R. (1987). Commodiy fuures prices: some evidence on forecas power, premiums, and he heory of sorage. Journal of Business, 60(1), Garbade, K. D., & Silber, W. L. (1983). Price movemens and price discovery in fuures and cash markes. Review of Economics and Saisics, 65, Girma, P. B., & Paulson, A. S. (1999). Risk arbirage opporuniies in peroleum fuures spreads. The Journal of Fuures Markes, 19(8), Gülen, S. G. (1998). Efficiency in he crude oil fuures marke. Journal of Energy Finance & Developmen, 3(1), Haigh, M. S. (2000). Coinegraion, unbiased expecaions, and forecasing in he BIFFEX freigh fuures marke. The Journal of Fuures Markes, 20(6), Hall, A.D., Anderson, H. M., & Granger, C. W. J. (1992). A coinegraion analysis of reasury bill yields. The Review of Economics and Saisics, 74(1), Hazuka, T. B. (1984). Consumpion beas and backwardaion in commodiy markes. Journal of Finance, 39, Herbs, A. F., McCormack, J. P., & Koch, T. W. (1987). Invesigaion of a lead-lag relaionship beween spo sock indices and heir fuures conracs. The Journal of Fuure Markes, 7,

20 Johansen, S., & Juselius, K. (1990). Maximum likelihood esimaion and inference on coinegraion - wih applicaions o he demand for money. Oxford Bullein of Economics and Saisics, 52, Johansen, S., & Juselius., K. (1994). Idenificaion of he Long-Run and he Shor-Run srucure: an applicaion o he IS-LM model. Journal of Economerics, 63, Johansen, S. (1991) Esimaion and hypohesis-esing of coinegraion vecors in gaussian vecor auoregressive models. Economerica, 59(6), Johansen, S. (1988). Saisical analysis of coinegraion vecors. Journal of Economic Dynamics and Conrol, 12, Kaldor, N., (1939). Speculaion and economic sabiliy. Review of Economic Sudies, 7, Kawaller, I., Koch, P., & Koch, T. (1987). The emporal price relaionship beween S&P 500 fuures and he S&P 500 index. Journal of Finance, 42, Kellard, N., Newbold, P., Rayner T., & Ennew C. (1999). The relaive efficiency of commodiy fuures markes. The Journal of Fuures Markes, 19(4), Moosa, I. A. (1996). An economeric model of price deerminaion in he crude oil fuures markes, in M. McAleer, P. Miller & Leong, K. (Eds), Proceedings of he Economeric Sociey Ausralian meeing (vol 3, pp ), Perh: Universiy of Wesern Ausralia. 17

21 Moosa, I. A., & Al-loughani, N. E. (1994). Unbiasedness and ime-varying risk premia in he crude-oil fuures marke. Energy Economics, 16(2), Newberry, D. M. (1992). Fuures markes: hedging and speculaion, in P. Newman and M. Milgae, & J. Eawell (Eds), The new palgrave dicionary of money and finance. 2, Pizzi, M. A., Economopoulos, A. J. & O Neill, H. M. (1998). An examinaion of he relaionship beween sock index cash and fuures markes: A coinegraion approach. The Journal of Fuure Markes, 18, Quan, J. (1992). Two sep esing procedure for price discovery role of fuures prices. The Journal of Fuures Markes, 12(2), Schwarz, T., & Szakmary. A. (1994). Price discovery in peroleum markes: Price discovery, coinegraion and he ime inerval of analysis. The Journal of Fuures Markes, 9, Silvapulle, P., & Moosa, I. A. (1999). The relaionship beween spo and fuures prices: evidence form he crude oil marke. The Journal of Fuures Markes, 19(2), Sock, J. H. & Wason, M. W. Tesing for common rends. Journal of he American Saisical Associaion, 83, Telser, L.G. (1958). Fuures rading and he sorage of coon and whea. Journal of Poliical Economy, 66,

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23 Table 1. Dickey-Fuller ess. Price levels Firs differences Spo ** 1 monh ** 3 monhs ** 6 monhs ** ** indicaes significance a a 1 percen level. Criical values a he five percen level is and a he one percen level Table 2. Mulivariae Johansen Tess. Variables H 0 :rank = p Max es a) Trace es a) LM b) Exogeneiy c) Spo P= =0 74.2** 152.3** 1.72 (0.06) (0.01)* 1 monh P<= ** 78.07** 1.59 (0.09) (0.00)** 3 monhs P<= * 27.43** 1.02 (0.43) (0.02)* 6 monhs P<= (0.67) 3.35 (0.34) a) Criical values for he coinegraion es can be found in Johansen and Juselius (1990). b) LM is a Lagrange muliplier es agains auocorrelaion up o welve lags for he equaion for he associaed variable in column 1. The es are disribued as F(12,208), p-values in parenheses c) The es is disribued as 2 (3).which have a criical value a 7.82 a a 5% level. ** indicaes saisical significance a 1% while * indicaes saisical significance a 5% level. p-values in parenheses. 20

24 Table 3. Bivariae Johansen Tess. Variables H 0 :rank = p Max Trace Cons LM c) Exogeneiy d) es a) es a) basis b) Spo P== ** 52.48** (0.25) 9.95 (0.00)** 1 Monh P<= (0.07) 1.38 (0.18) 1.62 (0.20) Spo P== ** 47.47** (0.14) (0.00)** 3 monhs P<= (0.10) 0.93 (0.52) 0.70 (0.40) Spo P== ** 40.63** (0.08) (0.00)** 6 monhs P<= (0.27) 0.60 (0.84) 0.78 (0.38) 1 monh P== ** 50.19** (0.25) (0.00)** 3 monhs P<= (0.12) 0.70 (0.75) 3.25 (0.07) 1 monh P== ** 50.36** (0.37) (0.00)** 6 monhs P<= (0.24) 0.54 (0.89) 2.05 (0.15) 3 monhs P== ** 56.5** (0.99) (0.00)** 6 monhs P<= (0.37) 0.34 (0.98) 2.76 (0.10) a) Criical values for he coinegraion es can be found in Johansen and Juselius (1990). b) The es is disribued as 2 (1), which have a criical value a 3.84 a a 5% level. c) LM is a Lagrange muliplier es agains auocorrelaion up o welve lags for he associaed variable in column 1. The es are disribued as F(12,221), p-values in parenheses d) The es is disribued as 2 (1), which have a criical value a 3.84 a a 5% level, ** indicaes saisical significance a 1% while * indicaes saisical significance a 5% level, p-values in parenheses. 21

25 Foonoes i If he daa series are saionary, one can es for he exisence of a long run relaionship wih radiional saisical ools. ii Silvapulle and Moosa (1999) presen an overview of he differen argumen used. iii Boh ess have non-sandard disribuions. Criical values for hese ess have been abulaed by Johansen and Juselius (1990). 22