What Do We Learn from the Price of Crude Oil Futures?

Transcription

1 Wha Do We Learn from he Price of Crude Oil Fuures? Ron Alquis Universiy of Michigan Luz Kilian* Universiy of Michigan and CEPR Firs draf: February 8, 007. This version: February 1, 008 Absrac: Despie heir widespread use as predicors of he spo price of oil, oil fuures prices end o be less accurae in he mean-squared predicion error (MPE) sense han no-change forecass. This resul is driven by he variabiliy of he fuures price abou he spo price, as capured by he oil fuures spread. This variabiliy can be explained by he marginal convenience yield of oil invenories. Using a wo-counry, muli-period general equilibrium model of he spo and fuures markes for crude oil we show ha increased uncerainy abou fuure oil supply shorfalls under plausible assumpions causes he spread o decline. Increased uncerainy also causes precauionary demand for oil o increase, resuling in an immediae increase in he real spo price. Thus he negaive of he oil fuures spread may be viewed as an indicaor of flucuaions in he price of crude oil driven by precauionary demand. An empirical analysis of his indicaor provides independen evidence of how shifs in he uncerainy abou fuure oil supply shorfalls affec he spo price of crude oil and how hey undermine he forecas accuracy of oil fuures prices. Our model is consisen wih a number of empirical regulariies and resuls obained by alernaive mehodologies. Key words: Crude oil; fuures marke; spo marke; spread; expecaions; forecasing abiliy; precauionary demand. JEL classificaion: C53, D51, G13, G15, Q31, Q43. Acknowledgemens: We hank aul Hymans for assising us in locaing some of he daa for his sudy. We also hank Ben Chabo, Lucas Davis, Ana-María Herrera, eve alan, and Ken Wes as well as seminar paricipans a he Universiy of Michigan and he Federal Reserve Bank of Dallas for helpful commens and suggesions. In addiion, we benefied from commens received a he. Louis Fed Conference on Macroeconomerics in Augus 007 and in he ECB Workshop on Forecasing Techniques in November 007. The firs auhor acknowledges he generous suppor of he Cener for Inernaional Business Educaion a he ephen M. Ross chool of Business, Universiy of Michigan. * Correspondence: Deparmen of Economics, Universiy of Michigan, 611 Tappan., Ann Arbor, MI lkilian@umich.edu. Phone: (734) Fax: (734)

2 1. Inroducion The surge in he price of crude oil since 00 has renewed ineres in he quesion of wha deermines he spo and fuures price of crude oil and has highlighed he imporance of being able o predic as accuraely as possible he evoluion of he spo price of oil (see, e.g., Greenspan 004a,b, 005; Bernanke 004, 006; Gramlich 004; Davies 007; Kohn 007). In his paper, we use insighs provided by a heoreical model of he spo and fuures marke for crude oil in conjuncion wih empirical analysis o shed ligh on he relaionship beween he spo price of crude oil, expecaions of fuure oil prices, he price of crude oil fuures, and he oil fuures spread (defined as he percen deviaion of he oil fuures price from he spo price of oil). The paper is organized as follows. In secion, we documen he use of oil fuures prices as predicors of spo prices a cenral banks and inernaional organizaions. Fuures-based forecass of he price of crude oil inform moneary policy decisions and affec financial markes percepions of he risks o price sabiliy and susainable growh. I is widely believed ha oil fuures prices can be viewed as effecive long-erm supply prices (see, e.g., Greenspan 004a) or as he expeced price of oil (see, e.g., Bernanke 004). We pu his common pracice o he es. Using a newly consruced daa se of oil fuures prices and oil spo prices ha includes daa up o February 007, we assess empirically wheher forecass based on he price of oil fuures are more accurae han forecass from alernaive models excluding fuures prices. We show ha forecass based on oil fuures prices and forecass based on he oil fuures spread end o be less accurae han forecass from alernaive easy-o-use models such as he no-change forecas under sandard loss funcions including he mean-squared predicion error (MPE). They also are more biased han he no-change forecas. The resul ha fuures prices are neiher unbiased predicors nor he bes possible predicors in he MPE sense is new and surprising because i conradics widely held views among policymakers and financial analyss. I also differs from some earlier empirical resuls in he academic lieraure based on shorer samples. Moreover, i conrass wih relaed resuls in he foreign exchange lieraure. Alhough he no-change forecas has been shown o work well in oher conexs such as exchange rae forecasing, here are imporan differences beween he foreign exchange marke and he crude oil marke. Forecas efficiency regressions for oil markes generae he expeced signs and magniudes for all coefficiens, whereas similar regressions for foreign exchange markes generae coefficiens of he wrong sign and magniude (see, e.g., Froo 1

3 and Thaler 1990). Thus, he superioriy of he random walk predicor of oil prices compared wih fuures prices is by no means expeced. In secion 3, we conduc a sysemaic evaluaion of he ou-of-sample predicive accuracy of a broader se of oil price forecasing approaches based on he forecas evaluaion period A robus finding across all horizons from 1 monh o 1 monhs is ha he nochange forecas ends o be more accurae han forecass based on oher economeric models and much more accurae han professional survey forecass of he price of crude oil. This makes he no-change forecas a naural benchmark. In secion 4 we show ha he cause of he large mean-squared predicion error (MPE) of fuures-based forecass relaive o he no change forecas is no so much ha hese forecass are so differen on average, bu raher he variabiliy of he fuures price abou he spo price, as capured by he spread of oil fuures. We documen ha here are large and persisen flucuaions in he oil fuures spread ha are unlike he flucuaions observed in he spread of foreign exchange fuures (see, e.g., Taylor 1989). In secion 5, we show ha hese differences can be linked o he exisence of a marginal convenience yield for crude oil ha is absen in foreign exchange markes. Oil invenories, unlike invenories of many financial asses, may serve o avoid inerrupions of he producion process or o mee unexpeced shifs in demand. This opion value is refleced in a convenience yield (see, e.g., Brennan 1991; Pindyck 1994, 001; Rouledge, eppi and pa 000; chwarz 1997). We sudy he implicaions of he marginal convenience yield for he oil fuures spread in he conex of a muli-period, wo-counry general equilibrium model of he spo and fuures markes for crude oil. We show ha shifs in he uncerainy abou fuures oil supply shorfalls may explain he excess variabiliy of oil fuures prices relaive o he spo price ha is responsible for heir poor predicive accuracy. In he model, an oil-producing counry expors oil o an oil-consuming counry ha uses oil in producing a final good o be raded for oil or consumed domesically. Oil imporers may insure agains uncerainy abou sochasic oil endowmens by holding above-ground oil invenories or buying oil fuures. Oil producers may sell oil fuures o proec agains endowmen uncerainy. The model absracs from oil below he ground. The spo and fuures prices of oil are deermined endogenously and simulaneously. Using comparaive saics, we esablish ha under plausible condiions increased uncerainy abou fuure oil supply shorfalls causes he oil fuures

4 spread o fall. uch uncerainy shifs also raise he curren real spo price of oil, as precauionary demand for oil invenories increases in response o increased uncerainy. Increased uncerainy abou fuure oil supply shorfalls in he model will cause he real price of oil o overshoo iniially wih no response of oil invenories on impac, followed by a gradual decline of he real price of oil, as invenories are gradually accumulaed gradually over ime. The model implies ha he oil fuures spread declines, as he componen of he real spo price of oil driven by precauionary demand for crude oil increases. Hence, he negaive of he oil fuures spread may be viewed as an indicaor of flucuaions in he spo price of crude oil driven by shifs in precauionary demand for oil. In secion 6, we evaluae hese predicions of our model empirically. Firs, we show ha he proposed indicaor moves as expeced during evens such as he Persian Gulf War ha a priori should be associaed wih large shifs in precauionary demand for crude oil. We also find evidence of shifs in he spread associaed wih he Asian financial crisis, wih 9/11 and wih he 003 Iraq War, for example. Our findings corroborae earlier resuls in he lieraure based on regression dummies as well as hisorical decomposiions derived from srucural vecor auoregressive (VAR) models. econd, our indicaor is highly correlaed wih an independen esimae of he precauionary demand componen of he spo price of crude oil proposed in Kilian (007a,b). Tha alernaive esimae is based on a srucural VAR model of he global crude oil marke and does no rely on daa from he oil fuures marke. We show ha he VARbased measure and he fuures-based measure have a correlaion as high as 79 percen during Third, we show ha he overshooing paern of he response of he real price of oil o a precauionary demand shock in he Kilian (007a) VAR model is consisen wih he predicions of our heoreical model. The concluding remarks are in secion 7.. Do Oil Fuures Prices Help Predic he po Price of Oil? I is commonplace in policy insiuions, including many cenral banks and he Inernaional Moneary Fund (IMF), o use he price of NYMEX oil fuures as a proxy for he marke s expecaion of he spo price of crude oil. 1 A widespread view is ha prices of NYMEX fuures 1 Fuures conracs are financial insrumens ha allow raders o lock in oday a price a which o buy or sell a fixed quaniy of he commodiy in a predeermined dae in he fuure. Fuures conracs can be reraded beween incepion and mauriy on a fuures exchange such as he New York Mercanile Exchange (NYMEX). The NYMEX offers insiuional feaures ha allow raders o ransac anonymously. These feaures reduce individual defaul risk and ensure homogeneiy of he raded commodiy, making he fuures marke a low-cos and liquid mechanism for 3

5 conracs are no only good proxies for he expeced spo price of oil, bu also beer predicors of oil prices han economeric forecass. Forecass of he spo price of oil are used as inpus in he macroeconomic forecasing exercises ha hese insiuions produce. For example, he European Cenral Bank (ECB) employs oil fuures prices in consrucing he inflaion and oupu-gap forecass ha guide moneary policy (see vensson 005). Likewise he IMF relies on fuures prices as a predicor of fuure spo prices (see. e.g., Inernaional Moneary Fund 005, p. 67; 007, p. 4). Fuures-based forecass of he price of oil also play a role in policy discussions a he Federal Reserve Board (see, e.g., Greenspan 004a,b; Bernanke 004; Gramlich 004). This is no o say ha forecasers do no recognize he poenial limiaions of fuures-based forecass of he price of oil. Neverheless, he percepion is ha oil fuures prices, imperfec as hey may be, are he bes available forecass of he spo price of oil. There are suble differences in how oil fuures prices are inerpreed by policymakers. In is sronges form, he price of oil fuures is viewed as he bes predicor of he spo price of oil. This inerpreaion is exemplified by Greenspan s (004a) remark ha oil fuures prices can be viewed as effecive long-erm supply prices. A weaker inerpreaion is ha oil fuures prices represen he expeced spo price of oil. Tha view is illusraed by Bernanke s (004) saemen ha fuures prices of $0 a barrel sugges ha raders expec oil prices o remain a ha level. Before sudying he heoreical suppor for hese saemens, in his secion we examine heir empirical suppor. We formally evaluae he predicive power of oil fuures prices for he spo price of oil since he creaion of oil fuures markes in he 1980s..1. Forecasing Models.1.1. The Benchmark Model Le (h) F denoe he curren nominal price of he fuures conrac ha maures in h periods, he curren spo price of oil, and E + ] he expeced fuure spo price a dae +h condiional on [ h informaion available a. A naural benchmark for forecass based on he price of oil fuures is provided by he random walk model wihou drif. This model implies ha changes in he spo price are unpredicable, so he bes forecas of he fuure spo price of crude oil is simply he curren spo price: hedging agains and for speculaing on oil price risks. The NYMEX ligh swee crude conrac is he mos liquid and larges volume marke for crude oil rading (NYMEX 007a). 4

6 (1) ˆ + h = h = 1, 3, 6, 9, 1 Below we consider wo ypes of forecasing models based on he price of oil fuures. The firs model simply reas he curren level of fuures prices as he predicor; he second model is based on he fuures spread..1.. Fuures Prices as Fuure po Prices The Greenspan (004a) quoe of he inroducion implies he forecasing model: () ˆ + = F h = 1, 3, 6, 9, 1. h ( h).1.3. Forecass Based on he Fuures pread An alernaive approach o forecasing he spo price of oil is o use he spread beween he spo price and he fuures price as an indicaor of wheher he price of oil is likely o go up or down (see, e.g., Gramlich 004). If he fuures price equals he expeced spo price, as saed by Bernanke (004), he spread should be an indicaor of he expeced change in spo prices, alhough no necessarily an accurae predicor of he change in spo prices in he MPE sense. The raionale for his approach is clear from dividing ( h F ) = E[ + h] by, which resuls in ( h) E[ + h] = F. We explore he forecasing accuracy of he spread based on several alernaive forecasing models. The baseline model is: (3) ˆ ( ( h ) + h 1 + ln( F / ) ) =, h = 1, 3, 6, 9, 1 To allow for he possibiliy ha he spread may be a biased predicor, i is common o relax he assumpion of a zero inercep: (4) ˆ ( ( h ) + h 1 +αˆ ln( F / ) ) = +, h = 1, 3, 6, 9,1 Alernaively, one can relax he proporionaliy resricion: (5) ˆ ( ) ( ) 1 ˆ ln( h + h + β F / ) =, h = 1, 3, 6, 9,1 Finally, we can relax boh he unbiasedness and proporionaliy resricions: (6) ˆ ( ) ( ) 1 ˆ h + h +αˆ βln( F / ) = +, h = 1, 3, 6, 9, 1... Daa Descripion and Timing Convenions..1. Daa Consrucion In secion.3, we will compare he real-ime forecas accuracy of models (1)-(6). Our empirical 5

7 analysis is based on daily prices of crude oil fuures raded on he NYMEX from he commercial provider Price-Daa.com. The ime series begins in March 30, 1983, when crude oil fuures were firs raded on he NYMEX, and exends hrough February 8, 007. Crude oil fuures can have mauriies as long as 7 years. Conracs are for delivery a Cushing, OK. Trading ends four days prior o he 5 h calendar day preceding he delivery monh. If he 5 h is no a business day, rading ends on he fourh business day prior o he las business day before he 5 h calendar day (NYMEX 007b). A common problem in consrucing monhly fuures prices of a given mauriy is ha an h-monh conrac may no rade on a given day. We idenify he h-monh fuures conrac rading closes o he las rading day of he monh and use he price associaed wih ha conrac as he end-of-monh value. For all horizons, we obain a coninuous monhly ime series based on a backward-looking window of a mos five days. For mauriies up o hree monhs, he backward-looking window is a mos hree days. Our approach is moivaed by he objecive of compuing in a consisen manner end-of-monh ime series of fuures prices for differen mauriies. This allows us o mach up end-of-monh spo prices and fuures prices as closely as possible. The daily spo price daa are obained from Daasream and refer o he price of Wes Texas Inermediae crude oil available for delivery a Cushing, OK. Figure 1 plos he monhly prices of oil fuures conracs for mauriies of 1 hrough 1 monhs and he spo price of crude oil saring in Noe ha conracs of longer mauriies only gradually became available over he course of he sample period.... The Choice of Mauriies in he Empirical Analysis The percepion ha fuures prices conain informaion abou fuure spo prices implicily relies on he assumpion ha fuures conracs are acively raded a he relevan horizons. In his subsecion we invesigae how liquid fuures markes are a each mauriy h. This quesion is imporan because one would no expec (h) F o have predicive conen for fuure spo prices, unless he marke is sufficienly liquid a he relevan horizon. Policymakers and he public widely believe ha he oil fuures marke provides effecive insurance agains risks associaed wih crude oil producion shorfalls and conveys he marke s Our approach differs from ha in Chernenko, chwarz, and Wrigh 004). Their approach is o rea fuures prices from a window in he middle of he monh as a proxy for he fuures price in a given monh. Ye anoher approach is o subsiue he price of a j-monh conrac for a given day for he missing price of he h-monh conrac on ha day where j h, (see Bailey and Chan 1993). 6

8 assessmen of he evoluion of fuure supply and demand condiions in he crude oil marke. If he marke were effecively pricing he possibiliy of, say, a shudown of he Iranian oil fields or he demise of he audi monarchy wihin he nex five years, one would expec acive rading a such long horizons. The evidence below, however, suggess oherwise. Figure shows he monhly rading volume corresponding o a fuures conrac wih a fixed horizon ha is closes o he las rading day of he monh. Volume refers o he number of conracs raded in a given monh. 3 As illusraed in Figure, over he pas 5 years, rading volume in he fuures marke has grown significanly, paricularly a he 1-monh and 3-monh horizon, and o a lesser exen a he 6-monh horizon. In 1989, he NYMEX inroduced for he firs ime conracs exceeding welve monhs and in 1999, a 7-year conrac was firs inroduced. Alhough such conracs are available, he marke remains illiquid a horizons beyond one year even in recen years. Trading volumes fall sharply a longer mauriies. This observaion is imporan for our forecas evaluaion because one would no expec forecass based on fuures wih long mauriies o provide accurae predicions, when only a handful of conracs are rading. Given he evidence in Figure, we herefore will resric ourselves o fuures conracs of up o one year in he empirical analysis below. In addiion, he evidence in Figure suggess ha he public and policymakers have overesimaed he abiliy of oil fuures markes o provide insurance agains long-erm risks such as poliical insabiliy in he Middle Eas or he developmen of oil resources in he Caspian ea. Policymakers rouinely rely on fuures prices for long mauriies in predicing fuure oil prices. For example, Greenspan (004a) explicily referred o he 6-year oil fuures conrac in assessing effecive long-erm supply prices. For similar saemens also see Greenspan (004b), Gramlich (004) and Bernanke (004). As our volume daa in Figure show, here is very lile informaion conained in fuures prices beyond one year, making i inadvisable o rely on such daa. This conclusion is also consisen wih prior sudies of he crude oil fuures marke beween 1983 and 1994 (see Neuberger 1999) and wih percepions of indusry expers. 4 3 In conras o open ineres, volume measures he oal number of conracs, including hose in a posiion ha a rader closes or ha reach delivery, and hus gives a good sense of he overall aciviy in he fuures marke. Our mehod of daa consrucion is consisen wih he convenions used in consrucing he monhly fuures prices. 4 According o sources wihin he oil indusry who wish o remain anonymous, oil companies are fully aware of how hin he marke is a longer horizons and do no rely on fuures price daa for such mauriies. The percepion is ha one rader signing a couple of conracs wih a medium-erm horizon may easily move he fuures price by several dollars on a given day. 7

9 .3. Real-Time Forecas Accuracy of Fuures-Based Forecasing Models Tables 1 hrough 5 assess he predicive accuracy of various forecasing models agains he benchmark of a random walk wihou drif for horizons of 1, 3, 6, 9, and 1 monhs. The forecas evaluaion period is The assessmen of which forecasing model is bes may depend on he loss funcion of he forecaser (see Ellio and Timmermann 007). We presen resuls for he MPE and he mean absolue predicion error (MAPE). We also repor he bias of he forecass, and we repor he number of imes ha a forecas correcly predics he sign of he change of he spo price based on he success raio saisic of Pesaran and Timmermann (199). In addiion o ranking forecasing models by each loss funcion, we formally es he null ha a given candidae forecasing model is as accurae as he random walk wihou drif. uiably consruced p-values are shown in parenheses Oil Fuures as Predicors of Oil po Prices The firs wo rows of Tables 1 hrough 5 documen ha he no-change forecas has lower MPE han he fuures forecas a he 1-monh, 6-monh, 9-monh and 1-monh horizon. Only a he 3- monh horizon is he fuures forecas more accurae, bu he improvemen in accuracy is no saisically significan. Moreover, based on he MAPE meric, he random walk forecas is more accurae a all horizons. In all cases, he random walk forecas is less biased han he fuures forecas. Nor do fuures forecass have imporan advanages when i comes o predicing he sign of he change in oil prices. Only a he 9-monh and 1-monh horizons is he success raio significan a he 10 percen level and 5 percen level, respecively, bu he improvemen is only.6 and 3.6 percenage poins. The observaion ha fuures prices are worse predicors of he price of oil han simple no-change forecass is imporan because i conradics commonly held views ha curren fuures prices are a good guide o he evoluion of fuure spo prices, as exemplified by he Greenspan (004a) and Bernanke (004) quoaions..3.. Oil Fuure preads as Predicors of Fuure po Prices Rows 3-6 in Tables 1-5 documen ha he no-change forecas has lower MPE han spreadbased forecass a horizons of 6, 9 and 1 monhs. A horizons 1 and 3 in some cases he spread models has lower MPE, bu he improvemen is never saisically significan and no one spread model performs well sysemaically. Based on he MAPE rankings, he no-change forecas is superior a all horizons. These resuls are broadly consisen wih he earlier evidence for he 8

10 fuures forecass. Finally, rows 3-6 reveal some evidence ha spread models may help predic he direcion of change a horizons of 9 and 1 monhs. The gains in accuracy are saisically significan, bu quie moderae. There is no such evidence a shorer horizons Relaionship wih Forecas Efficiency Regressions I is useful o compare our resuls for he spread model in Tables 1 hrough 5 o he closely relaed lieraure on forecas efficiency regressions (see, e.g., Chernenko e al. 004; Chinn, LeBlanc, and Coibion 005). Consider he full-sample regression model: ( h) ( ) Δ s = α + β f s + u, h = 1,3,6,9,1, + h + h where lower-case leers denoe variables in logs and u + hdenoes he error erm. Forecas efficiency in he conex of he oil fuures spread means ha he hypohesis H : α = 0, β = 1 0 holds. A rejecion of hese resricions is inerpreed as evidence of he exisence of a imevarying risk premium (see, e.g., Fama and French 1987, 1988; Chernenko e al. 004). 6 Chernenko e al. repor ha he hypohesis of forecas efficiency canno be rejeced a convenional significance levels. I is imporan o bear in mind ha such evidence does no necessarily mean ha oil prices are forecasable based on he spread in pracice. Firs, nonrejecion of a null hypohesis does no imply ha he null model is rue. In fac, we showed ha he forecasing model (3) ha imposes his null does no dominae he no-change forecass in ou-of-sample forecass. econd, as our forecasing resuls show, relaxing one or more of he resricions implied by forecas efficiency may eiher improve or worsen he forecas accuracy of he spread model, depending on he bias-variance rade-off. In paricular, such models require he esimaion of addiional parameers compared wih he no-change forecas, and he resuling loss in forecas precision may ouweigh he benefis from reduced forecas bias. Thus, here is no conradicion beween our resuls and he forecas efficiency resuls in he lieraure. In addiion, i can be shown ha he resuls in Chernenko e al. are no robus o updaing he sample. Despie differences in he iming convenions used in consrucing he monhly fuures price daa, we are able o replicae heir resuls qualiaively using our daa, bu heir 5 Moivaed by erm-srucure models, we also experimened wih models including a weighed average of spreads a differen horizons. These models consisenly performed so poorly ha no resuls will be repored. 6 uch ess implicily posulae ha he rader s loss funcion coincides wih he economerician s quadraic loss funcion. If ha is no he case, forecas efficiency ess end o be biased in favor of he alernaive hypohesis (see Ellio, Komunjer, and Timmermann 005). 9

11 sample period. For he full sample, however, we do rejec he hypohesis of forecas efficiency a horizons 6 and 1 (see Table 6). This paern is consisen wih he earlier forecasing resuls. This rejecion of forecas efficiency occurs despie he fac ha ˆα is close o zero and ˆ β fairly close o 1, as suggesed by heory, and very much unlike in he foreign exchange lieraure (see, e.g., Froo and Thaler 1990). 3. Wha is he Bes Predicor of he po Price of Oil? The preceding secion demonsraed ha simple no-change forecass of he price of oil end o more accurae in he MPE sense han forecass based oil fuures prices. This does no mean ha he no-change forecas is necessarily he bes predicor of he spo price. The firs par of his secion broadens he scope of forecasing mehods o include oher predicors. One alernaive approach o measuring marke expecaions is he use of survey daa. While economiss have used survey daa exensively in measuring he risk premium embedded in foreign exchange fuures (see Chinn and Frankel 1995), his approach has no been applied o oil fuures, wih he excepion of recen work by Wu and McCallum (005). Ye anoher approach is he use of more sophisicaed economeric forecasing models of he spo price of crude oil Oher Candidae Forecasing Models urvey Forecass Given he significance of crude oil o he inernaional economy, i is surprising ha here are few organizaions ha produce monhly forecass of spo prices. In he oil indusry, where he spo price of oil is criical o invesmen decisions, oil firms end o make annual forecass of fuure spo prices for horizons as long as 15-0 years, bu hese are no publicly available. The U.. Deparmen of Energy s Inernaional Energy Agency (IEA) uses a srucural economeric model of crude oil supply and demand o produce quarerly forecass of he spo price of oil, bu hese forecass are available only beginning in lae 004. The Economis Inelligence Uni has produced annual forecass since he 1990s for horizons of up o 5 years. None of hese sources provides monhly forecass. A sandard source of monhly forecass of he price of crude oil is Consensus Economics Inc., a U.K.-based company ha compiles privae secor forecass in a variey of counries. Iniially, he sample consised of more han 100 privae firms; i now conains abou 70 firms. Of ineres o us are he survey expecaions for he 3- and 1-monh ahead spo price of Wes Texas 10

12 Inermediae crude oil, which corresponds o he ype and grade delivered under he NYMEX fuures conrac. The survey provides he arihmeic average, he minimum, he maximum, and he sandard deviaion for each survey monh beginning in Ocober 1989 and ending in February 007. We use he arihmeic mean a he relevan horizon: (7) ˆ CF + h =, h h = 3, Economeric Forecass An alernaive o modeling expecaions of spo prices for crude oil is based on economeric models. One example of such economeric models is he random walk model wihou drif inroduced earlier. In his secion, we inroduce he random walk wih drif and he Hoelling model as addiional compeiors. Given ha oil prices have been persisenly rending upward (or downward) a imes, i is naural o consider a random walk model wih drif. One possibiliy is o esimae his drif recursively, resuling in he forecasing model: (8) ˆ ( 1 α ) = h = 1, 3, 6, 9, 1 + h + Alernaively, a local drif erm may be esimaed using rolling regressions: ˆ ) ( l (9) + h = (1 + Δs ) h = 1, 3, 6, 9, 1, l = 1, 3, 6, 9,1 where ˆ is he forecas of he spo price a +h; and ( l) 1+ Δs + is he geomeric average of he h monhly percen change for he preceding l monhs, i.e., he percen change in he spo price beween and -l+1. This model posulaes ha raders exrapolae from he spo price s recen behavior when hey form expecaions abou he fuure spo price. The local drif model is appealing in ha i may capure shor-erm forecasabiliy ha arises from local rends in he oil price daa. An alernaive approach is moivaed by Hoelling s (1931) model, which predics ha he price of an exhausible resource such as oil appreciaes a he risk free rae of ineres: (10) ˆ (1 ) + h = + i, h h = 3, 6, 1 where i h, refers o he ineres rae a he relevan mauriy h. 7 Alhough he Hoelling model 7 Assuming perfec compeiion, no arbirage, and no uncerainy, oil companies exrac oil a a rae ha equaes: (1) he value oday of selling he oil less he coss of exracion; () and he presen value of owning he oil, which, given he model s assumpions, is discouned a he risk free rae. In compeiive equilibrium, oil companies exrac crude oil a he socially opimal rae. 11

13 seems oo sylized o generae realisic predicions, we include his mehod given recen evidence ha he Hoelling model does well in forecasing he fuure spo price of oil (see Wu and McCallum 005). We use he Treasury bill rae as a proxy for he risk free rae Real-Time Forecas Accuracy of Oher Forecasing Approaches In his subsecion, we compare he real ime forecas accuracy of models (7)-(10) o ha of he no-change forecas in (). ecion.3 esablished ha he no-change forecas ends o be more accurae han models based on he price of oil fuures. An obvious quesion is wheher he nochange forecas can be improved upon, for example, by using informaion on ineres raes Hoelling Model Row 7 in Tables, 3, and 5 shows ha he random walk model has lower MPE han he Hoelling model a horizons of 3 and 6 monhs, whereas a he 1-monh horizon he ranking is reversed. This reversal is no saisically significan, however. Based on he MAPE, he nochange forecas is superior a all hree horizons. The Hoelling forecasing model has sysemaically lower bias a all hree horizons han he no-change forecas. I also is sysemaically beer a predicing he sign of he change in oil prices han fuures forecass, alhough we canno assess he saisical significance of he improvemen, given ha here is no variabiliy a all in he sign forecas Random Walk Models wih Drif The nex six rows in Tables 1-5 documen ha allowing for a drif in no case significanly lowers he MPE of he random walk model, when he drif is esimaed based on rolling regressions, and only in one case, when he drif is esimaed recursively. Allowing for a drif lowers he MAPE a some horizons and for some models, bu he gains are no sysemaic and differen models work well for differen horizons. Again, he Clark and Wes (005) es rejecs he null of no predicabiliy in several cases (mainly a he nine-monh horizon). As discussed earlier, ha rejecion does no necessarily ranslae ino accuracy gains in real ime forecasing, as evidenced by he MAPE rankings. In some cases, allowing for a drif also improves significanly he abiliy o predic he sign of he change of he oil price a longer horizons, bu only when he drif is esimaed recursively. In general, he resuls for he random walk wih drif are quie sensiive o 8 pecifically, we use he 3-monh, 6-monh, and 1-monh consan-mauriy Treasury bill raes from he Federal Reserve Board s websie hp://federalreserve.gov/releases/h15/daa.hm 1

14 he model specificaion and forecas horizon, and hey do no accoun for he specificaion mining implici in considering a large number of alernaive models wih drif (see Inoue and Kilian (004) and he references herein). There is no evidence ha such models dominae he no-change forecas Professional urvey Forecass The las row in Tables and 5 shows ha he consensus survey forecas has much higher MPE han he no-change forecas a boh he 3-monh and 1-monh horizons. I also has a larger bias and higher MAPE and here is no saisically significan evidence ha i is beer a predicing signs han a coin flip. The survey forecas is also inferior o he fuures forecass, suggesing ha survey respondens do no rely on fuures price daa alone in forming heir expecaions Why he No-Change Forecas is a Plausible Measure of he Expeced po Price The cenral resul of secion 3. is ha no-change forecass of he price of oil end o be more accurae han forecass based on economeric models and more accurae han survey forecass. 9 This resul is consisen wih views among oil expers. For example, Peer Davies, chief economis of Briish Peroleum, has noed ha we canno forecas oil prices wih any degree of accuracy over any period wheher shor or long (see Davies 007). The favorable forecasing performance of he no-change forecas also is consisen wih he observed high persisence of he nominal spo price of oil (see, e.g., Diebold and Kilian 000). The high auocorrelaion of commodiy prices in general has been widely recognized in he lieraure (see, e.g., Deaon and Laroque 199, 1996). Finally, i is imporan o sress ha he superior forecas accuracy of he random walk model wihou drif does no conradic heoreical resuls in he lieraure ha oil prices are endogenous wih respec o global macroeconomic condiions (see, e.g., Barsky and Kilian 00). The firs poin o keep in mind is ha macroeconomic deerminans such as U.. ineres raes, U.. inflaion, or global economic growh are bu one of many deerminans of he price of oil. For example, many of he major oil price increases in recen decades have been 9 This resul differs from a leas some earlier sudies. For example, Chernenko e al. (004) repor evidence ha fuures-based forecass have marginally lower MPE han he no-change forecas a horizons of 3, 6 and 1 monhs. In relaed work, Wu and McCallum (005) find ha fuures prices are generally inferior o he no-change forecas, bu repor ha spread regressions have lower MPE han he no-change forecas a shor horizons (also see Pagano and Pisani 006). These findings do no conradic our resuls. The differences in MPE rankings can be raced mainly o differences in he sample period. The sample period considered in our paper is longer han in any previous sudy. Furher sensiiviy analysis suggess ha evidence of accuracy gains, someimes obained in samples shorer han ours, ends o vanish when he full sample is examined. 13

15 associaed wih unforeseen poliical disurbances in he Middle Eas and rising concerns abou fuure oil supply shorfalls. Hence, one would no expec forecasing models based on macroeconomic fundamenals alone o be successful in pracice. The second poin o bear in mind is ha predicabiliy ha exiss in populaion may be difficul o exploi in real ime in finie samples. The link from macroeconomic fundamenals o he price of oil is complicaed and likely o be nonlinear. Even if he spo price of crude oil does no ruly follow a random walk, random walk forecass end o be aracive in erms of heir mean-squared predicion error (MPE) since he reducion in variance from excluding oher predicors in small samples will ypically more han offse he omied variable bias. Thus, he superior forecas accuracy of he no-change forecas does no invalidae economic models of he crude oil marke. 4. Why Is he MPE of Oil-Fuures Prices so Large Relaive o he No-Change Forecas? The preceding secion demonsraed ha under he MPE meric he bes predicor of he nominal price of oil is he no-change forecas. This secion examines in greaer deail he differences beween he no-change forecas and he forecas based on oil fuures prices. A formal analysis of wha precisely goes wrong wih he oil fuures forecas will help moivae he heoreical analysis of he oil spo and fuures markes in he nex secion. For his purpose i is convenien o express he deviaion of he fuures price from he no-change forecas in percenage erms as f ( h) s. There are wo possible reasons for he higher MPE of F relaive o. One is higher forecas bias; he oher is a higher forecas variance. In Table 7, we firs evaluae he possibiliy ha F is differen on average from. For exposiory purposes, we focus on he 3-monh and ( h ) 1-monh horizons. Our sample period is , as a coniguous ime series for he 1- monh spread becomes available only saring in Using heeroskedasiciy and auocorrelaion consisen (HAC) sandard errors, on average boh he 3-monh and 1-monh spread are saisically differen from zero a he 1% level. Alhough he rejecion is decisive, Table 7 shows ha he mean deviaion is comparaively small in magniude (abou 1% a he 3- monh horizon and below 5% a he 1 monh horizon). Whereas he bias of fuures prices relaive o he no-change forecas may seem small, he variabiliy abou he no-change forecas is no. As Table 7 shows, a any poin in ime, he discrepancy beween he fuures price and he spo price may be very large and go in eiher ( h ) 14

16 direcion. I is his variabiliy of he deviaion of fuures prices from spo prices raher han he differences in mean ha drives he larger MPE of fuures-based forecass and ha makes he use of such oil price forecass inadvisable. The ime-variaion in he spread is no only large, bu highly persisen. In Table 7, we measure his persisence by modeling he spread as an auoregression wih he lag order seleced by he Akaike Informaion Crierion. Based on he fied auoregressive models, we compue he sum of he auoregressive coefficiens as a measure of persisence as suggesed by Andrews and Chen (1994). The esimaed persisence for he 3- monh spread in he firs column is 0.74, whereas ha for he 1-monh spread is The evidence in Table 7 is imporan because i suggess ha he key o undersanding he poor predicive accuracy of oil fuures prices relaive o he no-change forecas is o undersand he causes of he excess variabiliy of oil fuures prices relaive o he spo price of oil. The exisence of such large flucuaions in he oil fuures spread may seem surprising a firs, considering he much lower variabiliy and persisence of he fuures spread in he widely sudied foreign exchange fuures marke. The spread of foreign exchange fuures prices over he spo exchange rae is well explained by he bilaeral ineres rae differenial because he spread capures he opporuniy cos of holding asses in one currency as opposed o anoher. This covered ineres rae pariy resul has been documened, for example, by Taylor (1989). Considering he ypical size of ineres rae differenials, he spread in major foreign exchange markes ends o be small. This poin is illusraed in Figure 3. The oil fuures spread is far more variable han he U..-U.K. foreign exchange fuures spread. In he nex secion we propose a heoreical explanaion of his discrepancy. We observe ha he difference beween he oil fuures price and he expeced spo price of oil is no accouned for by he ineres rae alone, bu ha i also reflecs he value ha firms derive from having ready access o oil, a fac commonly referred o as he convenience yield. The presence of his convenience yield makes he analysis of oil fuures markes fundamenally differen from he analysis of he marke for foreign exchange fuures. We propose a heoreical model ha explains he persisen and large flucuaions in he spread in erms of flucuaions in he marginal convenience yield. The model implies ha flucuaions in he marginal convenience yield can be direcly linked o shifing fundamenals in he form of expecaion shifs abou fuure oil supply shorfalls. Whereas concerns abou fuure supply shorfalls may in principle arise in any commodiy marke, here is reason o believe ha such concerns hisorically have been 15

17 paricularly relevan in he crude oil marke and may explain boh large and sharp flucuaions in he spread over ime. 5. A Two-Counry General Equilibrium Model of he Oil Fuures and Oil po Markes 5.1. Model Descripion The model in his secion can be viewed as a generalizaion of he analysis in Pindyck (1994, 001). There are wo counries, he Unied aes and audi Arabia. audi Arabia rades is oil endowmen wih he Unied aes in exchange for a consumpion good ha he Unied aes produces from oil o be delivered a he end of he period. The Unied aes consumes some of he final consumpion good and sells he res o audi Arabia. audi Arabia is reaed as an endowmen economy in recogniion of he fac ha capaciy consrains have been binding in global crude oil producion in recen years (see Kilian 008). The exisence of capaciy consrains implies ha exracing less oil oday does no permi more oil o be exraced in he fuure. Each period, audi Arabia receives a random oil endowmen ω. The oil endowmen in period is ω = ω+ ε wih probabiliy θ ; and ω ˆ = ω ε wih probabiliy 1 θ and ˆ ε = θε (1 θ) such ha E( ω ) = ω. The variance of he oil endowmen is σ ε. In each period, he Unied aes chooses: (1) nex period s above-ground invenory holdings of oil ( I ); () he number of oil fuures conracs ha deliver one barrel of oil nex period; (3) he number of risk-free one-period bonds ha yield (1 +, 1), and (4) he quaniy of oil o use in he producion of he consumpion good. audi Arabia chooses he number of oil fuures conracs and he number of risk-free bonds i wishes o hold. The price of he consumpion good in period is P and he spo price of oil is. The price of he consumpion good is he numeraire. 5.. The Unied aes Demand for Oil The Unied aes chooses he amoun of oil o use in he producion of he consumpion good; and he amoun of oil o sore as above-ground invenory. Impored oil can be ransformed ino he consumpion good using he producion funcion FZ ( ), where Z is he quaniy of oil he Unied aes uses in producing he consumpion good. We posulae ha F ( Z ) > 0, F ( Z ) < 0, F ( Z ) > 0, and lim F ( Z ) =. The Unied aes chooses Z such ha he marginal produc Z 0 r + 16

18 of oil equals he real price of oil in erms of he consumpion good (11) P = F ( Z ), which implies he demand schedule: Z P F P. 1 (, ) ( ) The resource consrain for crude oil is given by he ideniy (, ) ΔI ω Z P. Re-inerpreing equaion (11) as a demand funcion in Δ I, we obain he inverse ne demand funcion expressed as a funcion of he random audi oil endowmen and he change in invenories: P = F ( ω ΔI ) D( ω, ΔI ). If P is drawn on he verical axis and Δ I on he horizonal axis, D( ω, ΔI) is upward - sloping in Δ I No-Arbirage Condiion 1: The Oil Fuures Marke If we are willing o impose, in addiion, ha boh he Unied aes and audi Arabia are risk neural, as Bernanke (004) explicily assumed, hen by he no-arbirage condiion ha he expeced reurn from holding invenories mus equal he real price of oil oday, i follows ha [ ] [ ] E F P = E P Using a linear Taylor series approximaion, we obain ha [ ] F E + 1 Thus, he fuures price will be an approximaely unbiased predicor of he spo price No-Arbirage Condiion : The Bond Marke Under risk neuraliy, he real value of a bond oday mus equal he discouned real presen value of a bond omorrow: (1) = β (1 + r, + 1) E E P P = + 1 β (1 r, + 1) P P A linear Taylor series approximaion implies ha: 17

19 (1 ) 1 β (1 + r, + 1 ) 1 r, β No-Arbirage Condiion 3: The Marke for orage The disinguishing feaure of our model is he exisence of a marke for sorage. orage akes he form of holding above-ground oil invenories. The erm convenience yield in he lieraure refers o he benefis arising from access o crude oil in he form of invenories such as he abiliy o avoid disrupions of he producion process or he abiliy o mee unexpeced demand for he final good. The convenience yield is a commonly used modeling device (see, e.g., Brennan 1991; Fama and French 1988; Gibson and chwarz 1990; Pindyck 1994; Rouledge e al. 000; chwarz 1997). Is microeconomic foundaions have been discussed in Williams (1987), Ramey (1989), Lizenberger and Rabinowiz (1995), and Considine (1997), among ohers. We denoe he convenience yield by g = g( I, σ ε ). Le g (, ) 1 = g1 I σ ε denoe he marginal convenience yield associaed wih holding addiional above-ground invenories beween and + 1. Following he commodiy pricing lieraure, we impose ha g1 > 0, g11 < 0, and g 1 > 0, where g i denoes he derivaive of g wih respec o is i h argumen and g ij he cross-parial derivaive of g wih respec o he argumens i and j. As increases in he variance make producion shorfalls more likely, he marginal convenience yield from holding invenories is increasing in he variance. Throughou he paper we also posulae ha he Inada condiion ( σ ) lim g1 I, ε I 0 = holds, which ensures ha he U.. holds sricly posiive invenories. Wih g I (, ) 1 ε σ on he verical axis and above-ground invenory holdings on he horizonal axis, he inersecion of he g I σ curve and invenory holdings I describes he equilibrium in he marke for sorage. (, ) 1 ε Absracing from coss of sorage, no arbirage implies ha soring a barrel of oil above ground for one period and simulaneously selling shor a one-period fuures conrac is a risk-free sraegy: F F (1 + r ) g + E + E E = (1 + r ) g + E , + 1 1, P+ 1 P P+ 1 P+ 1 P P+ 1 Reurn from soring oil Reurn from selling fuures conrac By no arbirage, he reurns o his invesmen mus equal he reurn on invesing he same 18

20 amoun a he risk-free rae: ince [ ] F r, + 1 = (1 + r, + 1) g1 + E P P P. + 1 E F P+ 1 F P given equaion (1), we obain: F (1 + r ) (1 + r ) g (13), + 1, 1 1 P P + Equaion (13) shows ha he difference beween he capialized real spo price and he real fuures price is equal o he capialized marginal convenience yield A Permanen Mean-Preserving pread of Oil Endowmens In his subsecion, we derive wo comparaive saics resuls under risk neuraliy. The firs resul is ha an increase in uncerainy abou he fuure oil supply shorfalls immediaely raises he real spo price of oil; he second resul is ha under plausible assumpions his increase in uncerainy lowers he oil fuures spread. We model he increase in uncerainy as a mean-preserving increase in he spread of he oil endowmen shock. The hough experimen is an increase in ε. The mean preserving spread helps us absracs from changes in he condiional mean of oil supplies and focus on changes in he condiional variance. The moivaion for his modeling choice is bes seen by focusing on he example of he Persian Gulf War. Evens such as he invasion of Kuwai in Augus of 1990 have wo disinc effecs. Firs, hey cause a reducion in expeced oil supply. This oil supply shock represens a change in he condiional mean of oil supplies. I has been documened in he lieraure ha such a shock indeed occurred in 1990, bu ha his supply shock fails o explain he bulk of he movemens in he real price of oil in 1990/91. econd, here is an increase in uncerainy abou fuure oil supply shorfalls. Indirec evidence ha he price spike of 1990/91 was driven by increased uncerainy abou fuure oil supply shorfalls has been presened in Kilian (008). To keep he model racable, we model his increased uncerainy as an increase in he condiional variance of oil supplies, implicily absracing from he global business cycle or any oher change in he condiional mean Resul 1: An Increase in Uncerainy Increases he Real po Price We solve he no-arbirage condiion (13) for equaion (1) o obain P and subsiue for 1 ((1 r, + 1) P ) + from 19

21 [ ] [ ] P = F + β E g1( I, ) P σ ε + 1 E F P = E P by he no-arbirage condiion in he fuures marke. Using equaion (1) o subsiue for he real price of oil in erms of he marginal produc, we arrive a: [ ] F ( ω Δ I ) = βe F ( ω Δ I ) + g ( I, σε ), implying ha he Unied aes equaes he marginal benefis and marginal coss of hese invenory holdings. The mean-preserving spread drives a wedge beween he lef-hand and righhand side of his ineremporal marginal efficiency condiion. Because F (.) is convex, he mean-preserving spread increases E [ F ( ΔI )] by Jensen s inequaliy (Hirshleifer and ω Riley 199). I also increases he marginal willingness o pay for invenories, given by g (, ) 1 I σ ε. To re-esablish ineremporal marginal efficiency, he Unied aes mus increase is invenory holdings such ha equaliy is re-esablished. Figure 4 illusraes he dynamic adjusmen process of he real price of oil and of U.. oil invenories in response o an exogenous increase in uncerainy abou fuure oil supply shorfalls. Figure 4a plos he marginal convenience yield. Figure 4b shows he corresponding inverse U.. demand funcion for oil. In he model, dae invenory holdings are deermined by he quaniy of invenories he U.. decided o hold a ime 1. uppose ha we are a poin A in Figure 4a a he beginning of he period. When here is a mean-preserving increase in he endowmen spread, he marginal convenience yield schedule shifs upwards insananeously, because he U.. values each uni of invenory more han i did prior o he increase in uncerainy. We move along he invenory schedule from poin A o poin B. Consequenly, by he concaviy of is producion funcion, he Unied aes finds i opimal o increase is fuure invenory holdings relaive o las period s invenory holdings. Thus I 1 I and Δ I = I I 1 > 0. This implies a decrease in he real price of oil over ime, saring from poin B, as he Unied aes moves along he marginal convenience yield schedule owards poin C. The accumulaion of addiional invenories is associaed wih a decline in he real price of oil, as he marginal convenience yield falls. The real price of oil in he new long-run equilibrium will be higher han is level a 1, bu lower han is impac level. To summarize, we expec he real price of oil o overshoo in response o increased uncerainy abou fuure oil supply shorfalls, whereas invenories will be 0

22 accumulaed only gradually over ime. The overshooing resul for he real price of oil is analogous o he overshooing of he exchange rae in he Dornbusch (1976) model. I is driven by he assumpion ha invenories are predeermined and will no adjus fully o an increase in uncerainy on impac Resul : An Increase in Uncerainy Decreases he Oil Fuures pread By rearranging equaion (13), we obain an expression for he spread: (14) F g I = +. 1(, σ ) r, 1 (1 r, 1) ε + + P A sufficien condiion for he oil fuures spread o decrease in response o a mean-preserving spread is ha dr, + 1 d(1 + r, + 1) g1( I, σ ) ε dε dε P 1 dδi dσ F ε dδi (1 + r, + 1) g11( I, σε) g1( I, σε) g 1( I, σε) 0 F + dε dε + < F dε ince dr, + 1 dε 0, he firs wo erms in his expression are zero. The sign of he expression depends on he relaive magniudes of (1) he decrease in he marginal convenience yield associaed wih he increase in invenories riggered by he shock o he endowmen disribuion; and () he increase in he marginal convenience yield associaed wih he increase in riggered by he same shock. The spread declines if and only if σ ε (15) Δ dσ ε 1 F d I > g11 g1 dε g + 1 F dε. We can express boh d σ ε dε and d I dε expression (15) is equivalen o: λ(1 θ ) B (15 ) g1 >, θε (1 λ) where λ ( ) g g + F F g ( A g ),0< λ < 1; and Δ in erms of he model s parameers and show ha [ ] A= F ( ω ΔI) βe F ( ω+ 1 Δ I+ 1) > 0 B = βθ[ F ( ω + ε ΔI ) F ( ω + ˆ ε Δ I )] > Hence, for a given sock of invenories and increase in ε, he spread will decline, provided g 1 1