What Do We Learn from the Price of Oil Futures?

Transcription

1 Wha Do We Learn from he Price of Oil Fuures? Ron Alquis* Universiy of Michigan Luz Kilian Universiy of Michigan and CEPR Preliminary and Incomplee! Do No Quoe wihou Permission! Firs draf: February 28, This version: Augus 13, 2007 Absrac I is common o rely on prices of oil fuures o predic he pah of he spo price of oil. Based on a wo-counry, wo-period general equilibrium model of he spo and fuures markes for crude oil, we clarify he condiions under which oil fuures prices can predic he spo price, We documen ha hese condiions are violaed in he daa. Using a newly consruced daa se of monhly oil fuures prices and oil spo prices ha akes careful accoun of he exac daing of he underlying daily ime series, we find ha fuures-based forecass of oil prices end o be less accurae han forecass from alernaive easy-o-use mehods such as he no-change forecas. This resul does no mean, however, ha here is no useful informaion in oil fuures prices. Under plausible condiions our model implies a posiive correlaion beween he risk premium embodied in he price of oil fuures and he componen of he global spo price of oil driven by precauionary demand for oil. Under he random walk benchmark, his risk premium is observable. Is evoluion over ime suggess major shifs in precauionary demand during he Persian Gulf War and following he Asian crisis, for example. Our analysis provides independen evidence on how shifs in marke expecaions abou fuure oil supply shorfalls affec he spo price of crude oil. Key words: Crude oil; fuures marke; spo marke; risk premium; basis; 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, eve alan, and Ken Wes for helpful commens and suggesions. 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 [email protected].

2 1. Inroducion Prices of crude oil fuures are hough o convey useful real-ime informaion regarding shifs in marke expecaions abou fuure demand and supply condiions in he crude oil marke. I is common o rely on fuures prices of crude oil o infer he fuure pah of he spo price of crude oil, in paricular. uch forecass are a crucial inpu for he macroeconomeric models used a many cenral banks and a he Inernaional Moneary Fund. When macroeconomic forecass fail, heir failure can be ofen raced o inaccurae forecass of he price of crude oil. Fuuresbased forecass of he price of crude oil also play an imporan role in moneary policy decisions and affec financial markes percepions of he risks o price sabiliy and susainable growh. This paper examines he common pracice of predicing he spo price of crude oil based on he price of oil fuures. Based on a heoreical model of he spo and fuures markes for crude oil, we clarify he condiions under which prices of oil fuures can predic fuure spo prices. We documen ha hese condiions are violaed in he daa. Using a newly consruced daa se of monhly oil fuures prices and oil spo prices ha akes careful accoun of he exac daing of he underlying daily ime series, we show ha fuures-based forecass in pracice end o be less accurae han forecass from alernaive easy-o-use models such as he random walk model. This resul does no mean, however, ha here is no useful informaion in oil fuures prices. Our wo-counry, wo-period general equilibrium model of he fuures and spo markes for crude oil, implies ha oil fuures prices are informaive abou shifs in precauionary demand for crude oil, as refleced in he curren spo price of crude oil. pecifically, in he presence of capaciy consrains on crude oil producion, he risk premium implied by a random walk or no-change forecas of he spo price of oil is shown o be posiively correlaed wih he componen of he spo price ha is driven by precauionary demand for crude oil. Our resuls confirm ha he sharp spike in oil prices during he Persian Gulf War was mainly driven by an expecaions shif refleced in higher precauionary demand, corroboraing earlier resuls in Kilian (2007c) based on regression dummies as well as resuls in Kilian (2007a,b) based on hisorical decomposiions. They also confirm ha he emporary decline in oil prices following he Asian crisis and is reversal afer 1999 refleced flucuaions in precauionary demand. An independen empirical esimae of he precauionary demand componen of he spo price of crude oil has recenly been proposed by Kilian (2007a,b) for he period

3 Tha esimae was based on a srucural VAR model of he global crude oil marke. We show ha he VAR-based measure and he fuures-based measure have a correlaion of beween 62 percen and 80 percen during , depending on he mauriy of he fuures daa used. The correlaion monoonically increases in he horizon. aring in , however, he correlaion beween he risk premium and he VARbased esimae of he precauionary demand componen of he spo price vanishes. Whereas he VAR-based measure suggess an increase in concerns abou fuure oil supply shorfalls, especially in 2005 and 2006 (consisen wih an increase in geopoliical uncerainy, srong expeced demand for crude oil and expecaions of igh oil supplies), he fuures-based esimae suggess a seady decline in precauionary demand afer We show ha his divergence is consisen wih evidence of an unprecedened increase in speculaive aciviies in oil fuures markes saring in As increased demand for fuures from speculaors drives up fuures prices, he risk premium falls, creaing he misaken impression ha precauionary demand has fallen. We conclude ha oil fuures prices, alhough hey are no useful for predicing fuure spo prices and in fac are dominaed by simple no-change forecass, may conain useful informaion abou he deerminans of he curren spo price. They will no be reliable, however, unless major srucural shifs in he composiion of raders are accouned for. The remainder of he paper is organized as follows. In secion 2, we documen he use of prices of oil fuures as predicors of spo prices a cenral banks and inernaional organizaions. In secion 3, we inroduce a wo-period, wo-counry general equilibrium model of he spo and fuures markes for crude oil. In he model, an oil-producing counry expors oil o an oilconsuming counry ha uses oil in producing a final good o be raded for oil or consumed domesically. Boh oil producers and oil consumers may insure agains uncerainy abou sochasic oil endowmens by holding oil invenories or rading oil fuures. The spo and fuures prices of oil are deermined endogenously and simulaneously. Wihin his heoreical framework, we esablish he condiions under which he curren fuures price is he expeced spo price of oil, and we discuss he implicaions of our analysis for he specificaion of forecasing models. Wheher he condiions required for fuures prices o be accurae predicors are saisfied in pracice, is an empirical quesion ha we ake up in secion 4. We provide a sysemaic evaluaion of he predicive accuracy of he leading forecasing models based on he forecas 2

4 evaluaion period This period includes several major upheavals in he crude oil marke. A robus finding across all horizons from 1 monh o 12 monhs is ha he no-change forecas is he mos accurae forecas based on he mean-squared forecas error and he mean absolue forecas error. imple no-change forecass end o be more accurae han forecass based on fuures prices or he fuures spread. We also show ha professional forecass of he price of crude oil such as he 3-monh and 12-monh survey forecass provided by Consensus Economics Inc. are dominaed by boh he random walk model and fuures-based forecass. The poor forecasing accuracy of oil fuures prices is consisen wih he presence of a large and ime-varying risk premium embodied in he fuures price. In secion 5 we sudy he deerminans of his risk premium. In our heoreical model, flucuaions in he risk premium are driven by shifs in uncerainy abou fuure oil supply shorfalls. Our heoreical analysis implies a posiive correlaion beween he risk premium embodied in he fuures price and he componen of he spo price of oil driven by precauionary demand for crude oil. Thus, he risk premium may be viewed as an index of flucuaions in he price of crude oil driven by precauionary demand for oil. Given our evidence ha simple no-change forecass are mos accurae in forecasing he spo price of crude oil, we can express he empirical counerpar of his risk premium in erms of observables. We discuss he evidence for expecaions shifs in oil markes since 1989 and we compare he evoluion of his risk premium o he VAR-based esimae of he precauionary demand componen presened in Kilian (2007a,b). We also propose a measure of he erm srucure of risk premia ha conveys he marke s assessmen of he preponderance of shor-erm versus long-erm risks in he crude oil marke. The concluding remarks are in secion Oil Price Fuures Are Widely Used as Predicors of he Fuure po Price 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. In conras o forward conracs, fuures conracs can be reraded beween incepion and mauriy on a fuures exchange such as he New York Mercanile Exchange (NYMEX). A furher difference beween fuures and forward conracs is ha he holder of a fuures conrac realizes he gains or losses from holding ha conrac coninuously raher han a mauriy. 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 3

5 liquid mechanism for 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 2007a). I is commonplace in policy insiuions, including many cenral banks and he Inernaional Moneary Fund (IMF), o use he price of oil fuures as a proxy for he marke s expecaion of he spo price of crude oil. A widespread view is ha prices of NYMEX fuures conracs are good proxies for he expeced spo price of oil and beer predicors of oil prices han economeric forecass in paricular. Forecass of he spo price of oil are imporan inpus in he macroeconomic forecasing exercises ha hese insiuions produce. For example, he European Cenral Bank (ECB) employs he fuure oil price in consrucing he inflaion and oupu-gap forecass ha guide moneary policy (see vensson 2005). Likewise he IMF relies on fuures prices as a predicor of fuure spo prices (see Inernaional Moneary Fund (2007), p. 42). Fuures-based forecass of he price of oil also play a role in policy discussions a he Federal Reserve Board (see, e.g., Greenspan 2004a,b; Bernanke 2004; Gramlich 2004). 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. Given he prominence of fuures-based forecass of he price of oil in pracice, i is imporan no only o assess he empirical evidence for he forecasing abiliy of oil fuures prices (as we do in secion 4), bu o use economic heory o undersand he link beween he spo marke for crude oil and he fuures marke for crude oil. In secion 3, we propose a heoreical framework for hinking abou he relaionship beween he price of crude oil fuures and he expeced price of crude oil. Our analysis is based on a wo-counry, wo-period general equilibrium model. We explicily model he ineracion of oil producers in he Middle Eas and oil consumers in he Unied aes. The insighs provided by his model will also be used o guide and inform our empirical analysis in secions 4 hrough A Two-Counry General Equilibrium Model of he Oil Fuures and Oil po Markes The model in his secion provides explici microeconomic foundaions for Pindyck s (1994, 2001) analysis. Pindyck discusses how equilibrium prices and quaniies in generic spo and fuures markes are endogenously deermined by he ineracion of he spo marke, he marke for sorage, and he fuures marke. Our analysis builds on Townsend (1978). We exend he 4

6 framework used by Townsend in hree direcions. Firs, we add producion of a final good. The model posulaes ha one represenaive rader in he economy, he Unied aes, uses oil as an inpu in producing a final consumpion good. econd, he model allows he wo represenaive raders, he Unied aes and audi Arabia, o carry invenories of oil from he firs period o he second period. Third, he wo represenaive raders have access o a bond marke ha allows hem o save a a risk-free rae Model Descripion There are wo counries, he Unied aes and audi Arabia. In he firs period, audi Arabia rades is known oil endowmen ω 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 s second period oil endowmen is uncerain. There are wo saes of naure. Wih probabiliy θ, audi Arabia receives he random endowmen ω + ε in sae 1. Wih probabiliy 1 θ, i receives he endowmen ω ˆ ε in sae 2, where ˆ ε = εθ (1 θ) o ensure ha he endowmen shock has expecaion zero. The variance of he second period oil endowmen is σ 2. In he firs period, boh he Unied aes and audi Arabia choose: (1) invenory holdings o carry forward o he second period; (2) he number of oil fuures conracs ha deliver one barrel of oil in he second period; and (3) he number of risk-free bonds ha pay R in he second period. In addiion, he Unied aes chooses he quaniy of oil o be used as he inpu ino he producion of he consumpion good. The opimizaion problem for he Unied aes can be solved by backward inducion. In he second period, he Unied aes problem is max UY ( ) { Z } 2 s s.. 2s F (1 + R) Y = F( Z ) ( Z I ) + N ( ) + B, 2s 2s 1 2s 2s 2s U U U P2s P2s P2s P2s where Z is he quaniy of oil he Unied aes chooses in period and sae s = 1,2 ; U (.) is he 2s 1 In relaed work, Brio (1984) proposes a general equilibrium model of a closed economy in which fuures and spo prices of a generic commodiy are deermined endogenously. His model allows for producion risk, bu does no include invenories or savings. 5

7 Unied aes uiliy funcion defined over he consumpion good; Y2s is he quaniy of he consumpion good available o he Unied aes in period 2 and sae s ; F (.) is he sricly concave producion funcion ha generaes he consumpion good from oil; I U is he quaniy of oil he Unied aes hold as invenory; N U is he number of oil fuures conracs he Unied aes buy or sell in he firs period for delivery in he second period; 2s is he spo price of oil in sae s ; P 2s is he price of he consumpion good in sae s ; F 1 is he price of a fuures conrac ha delivers one barrel of oil in he second period; R is he risk-free ineres rae; and B U is he number of bonds he Unied aes hold. In he second period I U, N U, and BU are sae variables. In he firs period, he Unied aes chooses he quaniy of oil, invenories, he number of oil fuures conracs, and he number of bonds o maximize is uiliy: max U( Y1) + g( IU, σ) + β 1 ( U, U, U) (1 ) 2 ( U, U, U) { Z1, IU, NU, BU } θj I N B + θ J I N B s.. B Y = F( Z ) ( Z + I ), 1 U U P1 P1 where Z 1 is he quaniy of oil he Unied aes chooses in he firs period; Y 1 is quaniy of he consumpion good available o he Unied aes in period 1; g (.) is an increasing, sricly concave funcion in boh invenories and he variance of he oil endowmen ha measures he convenience yield accruing o he Unied aes from holding invenory beween period one and period wo; β ( 0,1) is he discoun facor; 1 is he spo price of oil period 1; P 1 is he price of he consumpion good in period one; and J s is he value funcion in sae s. audi Arabia s decision problem can be solved in he firs period, because i faces no decision in he second period. audi Arabia s problem is { I, N, B } s.. [ ] max VC ( ) + hi (, σ) + β θvc ( ) + (1 θ) VC ( ) A A A 1 A

8 C B 1 A 1 = ( ω A) P1 P1 I F (1 + R) C21 = ( ω+ ε + I ) + N ( ) + B P P P P F (1 + R) C ˆ 22 = ( ω ε + I ) + N ( ) + B P P P P A A A A A A where V (.) is audi Arabia s uiliy funcion defined over he consumpion good; C 1 is he quaniy of he consumpion good available o audi Arabia in he firs period; C 2s is he quaniy of he consumpion good available o audi Arabia in period wo and sae s = 1,2 ; h (.) is a sricly concave funcion in boh is argumens ha measures he convenience yield ha accrues o audi Arabia from holding oil invenories beween period one and period wo; I A is he quaniy of oil audi Arabia holds as invenory; and B is he number of bonds audi Arabia holds. These wo opimizaion problems joinly yield 15 equaions. There are six firs-order condiions and hree budge consrains for he Unied aes; and here are hree firs-order condiions and hree budge consrains for audi Arabia. In addiion, here are eigh markeclearing condiions: C1+ Y1 = F( Z1) C21 + Y21 = F( Z21) C22 + Y22 = F( Z22) Z1 = ω IU IA Z21 = ω+ ε + IU + IA Z ˆ 22 = ω+ ε + IU + IA NU + NA = 0 B + B = 0 U These 23 equaions allow us in principle o solve for he 22 endogenous variables, he six A consumpion variables ( Y1, Y21, Y22, C1, C21, C 22) ; he wo invenory holdings ( IU, I A) ; he wo fuures posiions ( NU, N A) ; he wo bond holdings ( BU, B A) ; he hree inpu choices A 1 F F1 F1 ( Z1, Z21, Z 22) ; and he seven relaive prices (,,,,,, R ). P P P P P P down he general equilibrium in he economy These condiions pin 7

9 The model has direc implicaions for he relaionship beween he fuures price and he expeced spo price of crude oil. Taking he firs-order condiion of U( Y 2s ) wih respec o U.. holdings of fuures conracs ( N U ), we obain ( ) F ( 1 ) ( 22 ) F β θu Y + θ U Y = 0. P21 P21 P22 P22 Rearranging and using he definiion of cov (.), his expression can be solved for oday s fuures price: (1) 2 2 cov U ( Y2), E U ( Y2) E P 2 P 2 F1 = +. U ( Y ) U ( Y ) E E 2 2 P 2 P 2 From he perspecive of modern asse pricing heory, he firs erm in expression (1) may be inerpreed as a risk premium. Under risk neuraliy, he covariance erm is zero, and using a firs-order Taylor series approximaion abou he mean, we obain: (1 ) F E[ ] 1 2 If he Unied aes are risk averse, in conras, hen expression (1) suggess ha here is no simple relaionship beween he fuures price of crude oil and he expeced spo price. Thus, he quesion of wheher fuures prices for crude oil can forecas he fuure spo price depends on he unknown preference srucure and is ulimaely an empirical quesion. ecion 4 will explore his empirical quesion in deail. In secion 5, we will reurn o he model proposed here and will develop more fully is implicaions for he fuures marke, he spo marke, and he evoluion of he risk premium over ime. Before we evaluae he forecas accuracy of fuures prices in pracice, however, i is useful o consider he implicaions of he possible presence of a risk premium for forecasing The Role of he Risk Premium in Forecasing Oil Prices The heoreical model in secion 3.1 suggess ha he presence of a risk premium in fuures prices of oil may undermine heir forecasing abiliy. This observaion has imporan 8

10 implicaions for he relaive performance of alernaive forecasing models. Le (h) F denoe he curren 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 informaion available a. [ h Expression (1) implies ha F will equal E + ] only under risk neuraliy. More generally, (h) [ h (h) [ h F and E + ] will differ. The difference by consrucion is he risk premium. hor of aking a sand on raders preferences, modeling he risk premium requires ha we specify he expeced fuure spo price and make assumpions abou how raders form expecaions. For any horizon h, he h-period ahead risk premium is given by (2) ( ) E [ + ] F ρ. ( h) h h The risk premium associaed wih holding he fuures conrac is expressed relaive o he curren spo price because he value of he fuures conrac is zero a incepion. 2 By solving equaion (2) for F (h), we obain: ( h) ( h) (3) F = E[ + h ] ρ which links he fuures price o he risk premium. Equaion (3) illusraes ha he fuures price differs from he expeced spo price if and only if here is a risk premium. Accommodaing he risk premium poses a problem in empirical work because expecaions of marke paricipans are no in general observable. One approach ha sideseps his problem is o assume ha markes are informaionally efficien and ha ex-pos realized reurns are a good proxy for ex-ane expeced reurns. This assumpion is implici in forecas efficiency regressions ha evaluae wheher fuures prices are raional expecaions of fuure 2 If he risk premium is posiive, he expeced reurn from holding a long fuures posiion is posiive ha is, he expeced reurn associaed wih buying he fuures conrac is posiive and oil users have an incenive o purchase a fuures conrac a he observed fuures price, while oil suppliers have an incenive o sell i; if he risk premium is negaive, he expeced reurn from holding a shor fuures posiion is posiive ha is, he expeced reurns associaed wih selling he fuures conrac is posiive and oil suppliers have an incenive o buy a fuures conrac and oil users o sell i. 9

11 spo prices. A rejecion of he resricions implied by his model is inerpreed as evidence of he exisence of a ime-varying risk premium (see, e.g., Fama and French 1987, 1988; Chernenko, chwarz, and Wrigh 2004). uch ess also posulae ha he rader s loss funcion coincides wih he economerician s quadraic loss funcion (see Ellio, Komunjer, and Timmermann 2005). Neiher assumpion is necessarily plausible in pracice. An alernaive approach is o use proxies for marke expecaions of he spo price such as survey expecaions. 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 (2005). The survey approach allows he researcher o idenify he ex-ane risk premium, dispensing wih he assumpion ha expecaions are necessarily model-consisen Alernaive Measures of he Expeced po Price of Oil Expeced Fuure po Prices from urveys Given he significance of crude oil o he inernaional economy, i is surprising ha here are few organizaions ha produce monhly forecass of fuure 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 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 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 widely used 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, bu i now conains abou 70 firms. Of ineres o us are he survey expecaions for he 3- and 12-monh ahead spo price of Wes Texas Inermediae crude oil, which corresponds o he ype and grade usually 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 We use he arihmeic mean a he relevan horizon: 10

12 (4) ˆ + =, h CF h Expeced Fuure po Prices from Economeric Models An alernaive o modeling expecaions of spo prices for crude oil is based on economeric models. In his secion, we consider hree ypes of economeric models: he random walk wihou drif, he random walk wih drif, and he Hoelling model. Treaing he condiional expecaion from any one of hese economeric models as a proxy for he marke expecaions, equaion (2) allows us o consruc he risk premium. The random walk forecas of he fuure spo price of crude oil is simply he curren spo price: (5) ˆ h = + Thus changes in he spo price are unpredicable. This parsimonious forecasing model is consisen wih he view of Peer Davies, chief economis of Briish Peroleum, ha we canno forecas oil prices wih any degree of accuracy over any period wheher shor or long (see Davies 2007). The random walk model has worked well in many oher asse pricing conexs. Even if he spo price of crude oil does no ruly follow a random walk, random walk forecass may be aracive in erms of heir mean-squared predicion error (MPE) since he reducion in variance from excluding oher predicors in small samples may more han offse he omied variable bias. Given ha oil prices have been persisenly rending upward (or downward) a imes, we also consider a random walk model wih drif. One possibiliy is o esimae his drif recursively, resuling in he forecasing model: (6) ˆ ( 1 α ) =. + h + Alernaively, a local drif erm may be esimaed using rolling regressions: 11

13 ˆ ) + h ( l (7) = (1 + Δs ) 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. A hird forecasing model is moivaed by Hoelling s (1931) model, which predics ha he price of an exhausible resource such as oil grows a he riskless rae of ineres. (8) ˆ (1 ) + h = + i, h where i h, refers o he ineres rae a he relevan mauriy h. 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; (2) and he presen value of owning he oil, which, given he model s assumpions, is discouned a he riskless rae. In compeiive equilibrium, oil companies exrac crude oil a he socially opimal rae. Alhough he Hoelling model 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 2005) Fuures Prices as Expeced Fuure po Prices Perhaps he mos common approach o consrucing oil price forecass is o rely on oil fuures prices. A widespread view is ha oil fuures prices are good proxies for expeced spo prices and beer predicors han economeric forecass in paricular, despie he possible presence of a risk premium. In is simples form, his forecasing model is: (9) ˆ + h = F ( h) As discussed in secion 3, in he presence of a risk premium, here is no necessarily a connecion beween he curren crude oil fuures price and he expeced spo price. From a heoreical perspecive, high fuures prices relaive o he curren spo price are consisen wih 12

14 increasing, consan, or falling spo prices (see Duffie 1989). Figure 1 shows a sylized example ha illusraes he hree cases. In each case, he fuures price of $50 exceeds he spo price of $40, ye, depending on he movemen of he risk premium, E + ] may be higher han, equal [ h o, or lower han he curren spo price of $40. Wihou furher assumpions, he fuures price is no a suiable predicor of he fuure spo price. The common pracice of basing oil price forecass on fuures prices may be defended, however, provided ha (1) he risk premium is approximaely consan; or (2) ha he risk premium is small if i is ime-varying. In ha case, he fuures price may sill conain useful informaion abou he fuure spo price and indeed may be he bes available predicor 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 oil prices are likely o go up or down. This approach is referred o, for example, in a speech by Federal Reserve Board Governor Edward Gramlich (2004). The raionale for using he spread o forecas he fuure spo price is clear from rearranging (2): F ( h) = E [ + h ] ( h) ρ The spread, F, by consrucion conains informaion abou boh he expeced percen ( h) change in he spo price and he risk premium. As wih all forecasing models based on fuures price daa, for he spread o be a good predicor of he change in he spo price, he risk premium mus be negligible. 4 As Figure 1 shows, a large posiive spread oday is consisen wih eiher rising, consan, or falling expeced spo prices, depending he magniude of he risk premium. We will explore he forecasing accuracy of he spread based on he forecasing models: 3 Prior empirical work provides no consensus abou he exisence of a risk premium in he crude oil marke or commodiy fuures markes more broadly. ome auhors have argued ha commodiy fuures prices, and crude oil fuures in paricular, conain no risk premium (see Chernenko e al. 2004); ohers have found evidence of a significan ime-varying risk premium in average commodiy fuures prices comparable in magniude o he equiy risk premium (see Goron and Rouwenhors 2006). 4 Alernaively, one could esimae he risk premium in real ime and purge he effec of he risk premium on fuures prices. This possibiliy is discussed in Chernenko e al. (2004) and Pagano and Pisani (2006). 13

15 ( ) (10) ˆ ( h) + h 1 + ( α βln( F / ) ) = +, (11) ˆ ( ( h ) + h 1 + β ln( F / ) ) =, (12) ˆ ( ( h ) + h 1 + ln( F / ) ) =, which differ in he exen o which he forecasing model is consrained o coincide wih efficien marke models (see, e.g., Chernenko e al. 2004). 4. Are Oil Prices Predicable? A Forecas Accuracy Comparison 4.1. Daa Descripion and Timing Convenions Our 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 28, Crude oil fuures can have mauriies as long as 7 years. Trading ends on he las rading day four days prior o he 25 h calendar day preceding he delivery monh. If he 25 h is no a business day, rading ends on he fourh business day prior o he las business day before he 25 h calendar day (NYMEX 2007b). In a ypical year, here are 252 rading days or 21 rading days each monh. Thus, for example, a 3-monh ahead fuures conrac corresponds o a conrac wih 63 days unil delivery. A common problem in consrucing monhly fuures prices a a given horizon is ha an h-monh conrac may no rade on a given day. One way of dealing wih his problem is o rea fuures prices from a window in he middle of he monh as a proxy for he fuures price for a given monh (see Chernenko e al. 2004). 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). Our approach is differen. A he end of a given monh, we idenify he conrac closes o he las rading day of he monh ha corresponds o he h-monh ahead fuures conrac and use he price associaed wih his 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 was hree days. Our approach is moivaed by he objecive of compuing in a consisen manner end-ofmonh ime series of fuures prices for mauriies ranging from one monh o five years. 14

16 4.2. 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 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 assessmen of he evoluion of fuure supply and demand condiions in he crude oil marke. As a recen aricle in he New Yorker saed: [T]raders don jus look a oday s supply and demand. They also ry o forecas he fuure. And if buyers hink here s a chance ha supply is going o be lower down he line because, say, Iranian oil fields will be shu down hey will be willing o pay a higher price oday in order o guaranee ha hey will have he oil hey need. (urowiecki 2007) If his percepion were correc, one would expec acive rading a long horizons. The evidence below, however, suggess oherwise. Figure 2 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. 5 As illusraed in Figure 2, over he pas 25 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 offered conracs exceeding welve monhs and in 1999, a 7-year conrac was firs inroduced (see Haigh e al. 2007). Alhough such conracs are available, he marke remains illiquid a horizons beyond one year even in recen years. Trading volume falls 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 2, we herefore will resric ourselves o fuures conracs of up o one year in he empirical analysis below. In addiion, he evidence in Figure 2 suggess ha he public and policymakers have 5 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. 15

17 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. For example, Greenspan (2004a) suggess ha oil fuures are pricing long-erm risks associaed wih he fuure supply of oil: More worrisome [han upgrading refinery capaciy] are he longer-erm uncerainies ha in recen years have been boosing prices in disan fuures markes for oil [ ] Prices for delivery in 2010 of ligh, low-sulphur crude rose o more han $35 per barrel when spo prices ouched near $49 per barrel in lae Augus. Rising geopoliical concerns abou insecure reserves and he lack of invesmen o exploi hem appear o be he key sources of upward pressure on disan fuure prices Given ha Greenspan s speech was made in Ocober of 2004 and referred o fuures prices for delivery in 2010, we may infer ha his assessmen of risks mus have been based on he 6-year fuures conrac. Greenspan (2004b) is even more explici. In referring o he 6-year oil fuures conrac, Greenspan saes ha: fuures prices a ha horizon can be viewed as effecive long-erm supply prices. As our volume daa in Figure 2 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 Forecas Evaluaion Crieria Tables 1 hrough 5 assess he predicive accuracy of he curren fuures price agains he benchmark of a random walk wihou drif for horizons of 1, 3, 6, 9, and 12 monhs. We also include he random walk wih drif, various random walk models wih local drif, he Hoelling model (o he exen ha ineres raes are available a he relevan mauriies), he consensus survey forecas (a he horizons for which survey forecass are available), and forecass from he regressions on he fuures spread discussed furher below. The forecas evaluaion period is We exploi he full se of available oil fuures price daa. The assessmen of 6 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. 16

18 which forecasing model is bes may depend on he loss funcion of he forecaser (see Ellio and Timmermann 2007). We presen resuls for he mean-squared predicion error (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 (1992). 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 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 12-monh horizon. Only a he 3-monh horizon he fuures forecas is 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 12-monh horizons, he success raio is significan a he 10 percen level and 5 percen level, respecively, bu he improvemen is only 2.6 and 3.6 percenage poins. These resuls are consisen wih he presence of a large and ime-varying risk premium in oil fuures prices. 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. For example, Federal Reserve Board Chairman Ben Bernanke in 2004 inferred from he level of fuures prices ha he marke expeced he preceding increase in spo prices o be long-lived: [P]robably more economically significan han near-erm uncerainy abou oil prices is he fac ha raders appear o expec igh condiions in he oil marke o coninue for some years, wih a bes only a modes decline in prices. This belief on he par of raders can be seen in he prices of oil fuures conracs. Throughou mos of he 1990s, marke prices of oil for delivery a daes up o six years in he fuure flucuaed around $20 per barrel, suggesing ha raders expeced oil prices o remain a abou ha level well ino he fuure. Today, fuures markes place he expeced price of a barrel of oil in he long run closer o $39, a near doubling. Thus, alhough raders expec he price of oil o decline somewha from recen highs, hey also believe ha a significan par of he recen 17

19 increase in prices will be long lived. (see Bernanke 2004) 7 Tha conclusion is quesionable for wo reasons. Firs, as we showed in secion 3, using longhorizon fuures prices is problemaic because few conracs are raded a hese horizons and hence hese prices convey lile informaion. econd, Bernanke s saemens rely on he assumpion ha he risk premium is eiher approximaely consan or small, which seems unlikely given he empirical evidence in Tables 1-5. Given he apparen imporance of he risk premium in deermining fuures prices, he naure of he risk premium will be furher documened and sudied in secion Oher Predicors of he po Price of Oil An obvious quesion is wheher he no-change forecas can be improved upon, for example, by using informaion on ineres raes. 8 Tables 2, 3, and 5 show ha he random walk model has lower MPE han he Hoelling model a horizons of 3 and 6 monhs, whereas a he 12-monh horizon he ranking is reversed. This reversal is no saisically significan, however. Based on he MAPE, he no-change 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. Allowing for a drif in no case significanly improves he MPE or MAPE of he random walk model, wheher he drif is esimaed based on rolling or recursive regressions. In some cases, allowing for a drif does improve significanly he abiliy o predic he sign of he change of he oil price. In general, he resuls for he random walk wih drif are quie sensiive o he model specificaion and forecas horizon, and hey do no accoun for he specificaion mining implici in considering a large number of alernaive models (see Inoue and Kilian (2004) and he references herein). There is no evidence ha such models dominae he no-change forecas. Finally, he consensus survey forecas has much higher MPE han he no-change forecas a he boh he 3-monh and 12-monh horizon. I also has a larger bias and higher 7 In he endnoes o his speech, Bernanke qualifies his commens by adding ha his conclusions are condiional on fuures prices being unbiased predicors of fuure spo prices and no conaining a significan risk premium. 8 The ineres rae daa are he 3-monh, 6-monh, and 12-monh consan-mauriy Treasury bill raes from he Federal Reserve Board s websie hp://federalreserve.gov/releases/h15/daa.hm 18

20 MAPE and here is no saisically significan evidence ha i is beer a predicing signs han a coin flip. The survey forecas also is inferior o he fuures forecass, suggesing ha survey respondens do no rely on fuures daa alone in forming heir expecaions Oil Fuure preads as Predicors of Fuure po Prices The preceding subsecion suggesed ha oil price forecass based on fuures prices, while clearly superior o he consensus survey forecas, are in urn ouperformed by simple no-change forecass. This subsecion considers forecasing models based on he fuures spread. Tables 1-5 show ha he no-change forecas has lower MPE han spread-based forecass a horizons of 6, 9 and 12 monhs. A horizons 1 and 3 in some cases one of 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, he no-change forecas is superior a all horizons. These resuls are consisen wih he earlier evidence for he fuures forecass, and he presence of a large and ime-varying risk premium. Tables 1 hrough 5 also show robus evidence ha he spread models help predic he direcion of change a horizons of 9 and 12 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 ineresing and 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. 2004; Chinn, LeBlanc, and Coibion 2005). Consider he full-sample regression model: ( h) ( ) Δ s = α + β f s + u, h = 1,3,6,9,12, + 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. Chernenko e al. repor ha he hypohesis of forecas efficiency canno be rejeced a convenional significance levels. Despie imporan differences in he iming convenions used in consrucing he monhly fuures price daa, we are able o replicae heir resuls qualiaively using our daa (see Table 6), alhough one p-value is close o he rejecion region. I is imporan o noe ha such evidence does no mean ha oil prices are forecasable based on he spread in pracice. Firs, non-rejecion of a null hypohesis does no imply ha he null model is rue. In fac, we showed ha he forecasing model (12) ha imposes his null does no dominae he no- 19

21 change forecass in ou-of-sample forecass. econd, as our 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. 5. Undersanding he Risk Premium The forecas accuracy comparison of secion 4 esablished ha he no-change forecas is he bes available predicor of he spo price of crude oil in pracice, a leas if he objecive is o minimize he MPE or he MAPE. Based on his benchmark for E[ + h], i is sraighforward o compue a direc measure of he risk premium in expression (2): ( ) E [ + ] F ρ. ( h) h h in erms of he observables and ( h F ). This pus us in a posiion o assess he magniude of he risk premium and he exen o which he risk premium has been flucuaing hisorically. Before assessing his evidence, i is useful o address he quesion of why he risk premium should be flucuaing over ime. The wo-counry, wo-period general equilibrium model of secion 3 sheds ligh on his quesion. In he model, he fundamenal driving he risk premium embodied in oil fuures prices is shifs in he uncerainy 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 paricularly relevan in he crude oil marke and may explain he exisence boh of large risk premia and of sharp flucuaions in risk premia over ime. I is imporan o noe ha unanicipaed shifs in uncerainy abou fuure oil supply shorfalls differ from acual supply shorfalls. In paricular, i is no necessary for any of he underlying expecaion shifs acually o be realized. In fac, a common siuaion in pracice is ha concerns abou possible shorfalls of oil producion driven, for example, by fears ha OPEC would reinsiue an oil embargo in he 1970s, ha Khomeini would aack moderae Gulf saes in he 1980s, or ha addam Hussein would invade audi Arabia in 1990 have evaporaed over 20

22 ime, only o be replaced by new and differen concerns such he nuclear hrea from Iran or he insabiliy of he audi hrone. This siuaion is no unlike ha of a peso problem in foreign exchange markes. As we will demonsrae below, a heoreical link can be esablished beween shifs in expecaions abou fuure oil supply and he basis of oil fuures defined by ( ( h ) ) basis = F. Under he random walk wihou drif model, E[ + h] =, so he risk premium ρ F = basis. Thus, flucuaions in he risk premium are direcly ( h) ( h) reduces o ( ) linked o shifs in uncerainy abou fuure oil supply shorfalls. The model also implies ha he spo price of oil increases in response o adverse expecaions shifs, which implies a posiive correlaion beween he random walk risk premium and he componen of he spo price of oil driven by concerns abou fuure oil supply shorfalls. In oher words, he model implies a posiive relaionship beween he risk premium and increases in he spo price of oil driven by precauionary demand for oil in response o shifing concerns abou fuure oil supply shorfalls. Thus, we can inerpre he random walk risk premium as an index of he expecaions-driven componen of oil prices and compare ha esimae o independenly consruced esimaes of his componen in he lieraure. In secion 5.1, we derive he comparaive saics resuls ha form he basis of he subsequen analysis Comparaive aics In his subsecion, we derive wo comparaive saics resuls. The firs resul is ha an increase in uncerainy abou he availabiliy of oil supplies in he second period raises he firs period s spo price; he second resul is ha his increase in uncerainy lowers he basis in he firs period. In boh cases, we model he increase in uncerainy as a mean-preserving increase in he spread of he second period oil endowmen shock. To derive he comparaive saics resuls, we make a simplifying assumpion. We assume ha boh he Unied aes and audi Arabia are risk neural and hence ha heir marginal uiliies are consans normalized o one. This assumpion makes he resuls ransparen, because i avoids inroducing assumpions abou he curvaure of he uiliy funcions associaed wih differen degrees of risk aversion. If we did no assume risk-neuraliy, he resuls would hinge 21

23 on raders risk preferences The Effec of an Increase in Uncerainy on he Firs-Period po Price From he Unied aes firs-order condiion, he marginal efficiency condiions, and he marke clearing condiions, we obain F'( ω I I ) g ( I, σ) = β[ θf'( ω+ ε + I + I ) + (1 θ) F'( ω ˆ ε + I + I )], U A I U U A U A U where he noaion g I U (.) denoes he parial derivaive of he funcion g (.) wih respec o U.. invenory holdings. From audi Arabia s firs order condiions, we obain he analogous condiion: F'( ω I I ) h ( I, σ) = β[ θf'( ω+ ε + I + I ) + (1 θ) F'( ω ˆ ε + I + I )], U A IA A U A U A where he noaion h I A (.) denoes he parial derivaive of he funcion h (.) wih respec o audi Arabia s invenory holdings. Toally differeniaing boh of hese expression wih respec o I U, I A, and ε yields wo equaions in wo unknowns, which can be compacly represened in marix noaion A giusi A us diu B = d, A A h IAI di A A B ε where A= [ F''( ω I ) ''( ) (1 ) ''( ˆ U IA + βθf ω+ ε + IU + IA + β θ F ω ε + IU + IA)] > 0 B = βθ[ F''( ω+ ε + I + I ) F''( ω ˆ ε + I + I )] > 0. U A U A olving for he change in U.. and audi oil invenories yields diu 1 dε A giusi A us B = dia A A h IAI B A dε 1 BhIAI A = > 0, gi ( ) usi h us IAI A g A IusI + h us IAI Bg A IusIus which shows ha boh he Unied aes and audi Arabia accumulae invenories in response o 9 As Varian (1985) and Barsky (1989) show, even in asse pricing models wih no producion, deriving unambiguous conclusions abou how asse prices change in general equilibrium requires srong assumpions on raders risk preferences and he disribuion of shocks. 22

24 1 a mean-preserving increase in he spread. ince = F'( ω IU IA) is a decreasing convex P funcion of U.. and audi invenories, he increase in invenories raises he firs-period spo price in real erms. Thus he firs implicaion of he model is ha an increase in uncerainy raises he spo price of oil in erms of he consumpion good The Effec of an Increase in Uncerainy on he Oil Fuures Basis We can express he oil fuures basis as a funcion of he marginal convenience yield, he real spo price of oil, and he risk-free ineres rae: F gi ( I, ) U U σ = R (1 + R). 1 P Toally differeniaing he righ-hand side of his equaion, we obain he expression 2 diu dia dσ g [ g F''( ω) + g F'( ω)] + g F''( ω) + g F'( ω) (1 + R) ε ε ε, 2 dε dε 1 [ F''( ω)] P1 2 dr dr IU IUIU IU I IUσ U d d d where we use he shorhand 2 I (, ) U IU U 1 g = g I σ and F( ω) = F( ω I I ). Assuming ha dr dε 0, he 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 (2) he increase in he marginal convenience yield associaed wih he increase in σ riggered by he same shock. Algebraically, he basis will decline if and only if 2 dσ diu dia IUσ ω > IUI ω + U I ω U I ω U g F'( ) [ g F'( ) g F''( )] g F''( ), dε dε dε I follows ha a sufficienly large increase in uncerainy will cause he basis o decrease. Thus, one would expec a negaive correlaion beween he basis and he componen of he spo price driven by precauionary demand for oil a leas during major shifs in uncerainy. A decrease in he basis (or equivalenly an increase in he random walk risk premium) seems he more likely, he smaller he decrease in he marginal convenience yield associaed wih an increase in invenory holdings. In radiional models ha incorporae he marginal convenience yield such as Brennan U A 23

25 (1958), Telser (1958), and Fama and French (1988) an increase in invenory holdings has an unambiguously posiive effec on he spo price because of he decreasing reurns o holding invenories. As invenory holdings increase, he marginal convenience yield declines, raising he basis. Our conclusion is differen. The reason is ha we follow Pindyck (2001) in incorporaing a direc effec from increased uncerainy on he marginal convenience yield, which raises he value of holding invenories when uncerainy is high and pushes up he marginal convenience yield for each uni of invenory. The disincion is ha he indirec effec hrough invenories reflecs he accumulaion of addiional invenories in response o he increase in uncerainy; 2 whereas he effec operaing hrough σ capures he noion ha each uni of invenories now has greaer value, as uncerainy has increased. This increase in he value of invenories reflecs increased demand for oil in he Unied aes in response o greaer uncerainy. We refer o his demand as precauionary demand for crude oil Using he Model o Idenify Expecaions hifs The model of secion 3 suggess ha flucuaions in he basis (or equivalenly in he risk premium implied by he random walk model) are indicaive of flucuaions in he spo price of oil driven by precauionary demand for crude oil. ricly speaking, his link holds if and only if a change in demand for oil invenories is confroned wih an inelasic supply of oil. In he model, his inelasiciy is represened in he form of an endowmen srucure. While his assumpion may be unrealisic for he early 1980s, hroughou much of he sample ha we consider below his is a reasonable assumpion. Kilian (2007c) documens ha capaciy consrains in world crude oil producion have been binding since he early 1990s. ince he risk premium a he 12- monh horizon becomes available only in , we will focus on he period Table 7 summarizes he ime series properies of he risk premium implied by our analysis in secion 4. For exposiory purposes, we focus on he 3-monh and 12-monh horizon. Table 7 confirms, firs of all, ha he risk premium ends o be large in magniude and ha he fuures price is a biased predicor of he spo price. Using heeroskedasiciy and auocorrelaion consisen (HAC) sandard errors, boh he 3-monh and 12-monh risk premium are saisically differen from zero a he 1% level. To ge a sense of he average magniude of he risk premium, Table 7 also presens he mean absolue deviaion. This measure shows ha, on average, he magniude of he risk premium is subsanial. Equaion (3) allows us o ge a sense of he economic significance of he esimaed risk premium. Taking he spo price of crude oil o be 24

26 $65, abou is level in lae March 2007, he minimum (maximum) value of he 3-monh ahead risk premium implies ha he fuures price can rade a a premium (discoun) of as much as $19 ($27). The mean implies ha i rades a abou a $3 premium. omewha smaller values are obained for he 12-monh risk premium. Overall, hese calculaions sugges ha he magniude of he risk premium can be economically significan. Even if here is a risk premium, fuure prices may sill provide unbiased forecass as long as i is consan and one includes an inercep in he forecasing model. As Table 7 shows, however, here is srong evidence of persisen ime variaion in he risk premium ha will cause fuures prices o be biased predicors of spo prices. We capure his ime variaion by modeling he risk premium 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 measure of persisence as suggesed by Andrews and Chen (1994). The sum of he auoregressive coefficiens for he 3-monh risk premium is 0.68, whereas ha for 12-monh risk premium is This evidence confirms ha here is considerable persisence in he risk premium. The long-horizon risk premium is more persisen han he shor-horizon risk premium. I is even more ineresing o idenify he episodes associaed wih shifs in he risk premium and hence expecaions. Figure 3 plos he random walk risk premium for by horizon. The plo confirms ha he sharp spike in oil prices during he Persian Gulf War was mainly driven by an expecaions shif refleced in higher precauionary demand, corroboraing earlier resuls in Kilian (2007c) based on regression dummies represening expecaions shifs as well as resuls in Kilian (2007a,b) based on hisorical decomposiions from srucural VAR models. The plo also confirms ha he emporary decline in oil prices following he Asian crisis and is reversal afer 1999 refleced flucuaions in precauionary demand. In addiion, he plo suggess a persisen decline in precauionary demand in recen years, a poin ha we will discuss in more deail below The Term rucure of Risk Premia Furher informaion may be obained from he erm srucure of risk premia. The erm srucure is informaive abou wheher he marke expecs higher risks o oil prices a long horizons han a shor horizons. Figure 4 plos he (demeaned) difference beween he 12-monh and 3-monh risk premium. A posiive value of his erm srucure indicaes ha he marke expecs risks o 25

27 increase over ime, whereas a negaive value indicaes a decline in he compensaion required for risks associaed wih fuure uncerainy. For example, he oubreak of he Persian Gulf War of Augus 1990 was preceded by expecaions of increasing risks. As he spo price jumped upon he invasion of Kuwai, he erm srucure urned sharply negaive, indicaing a greaer shor-erm risk han long-erm risk. By April 1991, afer he war had ended, he erm srucure urned posiive again. imilarly, he Iraq War of early 2003 was associaed wih a negaive spike in he erm srucure, whereas he mos recen period (as well as he period leading up o he 2003 Iraq War) was characerized mosly by a posiive erm srucure, indicaing he expecaion of increasing risks. Wars are no he only periods characerized by a negaive erm srucure. There also was an episode from lae 1993 unil lae 1996, during which he marke expeced risks o decline a longer horizons. The inermien period of appears volaile, bu he erm srucure is less persisen han in earlier periods Alernaive Measures of Precauionary Demand hifs The index of expecaions-driven oil price increases proposed in his paper is no he only possible approach. Recenly, an alernaive measure of he componen of he spo price of crude oil ha is driven by shocks o precauionary demand has been proposed by Kilian (2007a,b). Unlike he measure developed in his paper, ha esimae was based on a srucural VAR decomposiion of he price of crude oil. The srucural represenaion of he underlying rivariae auoregressive model is Az 0 24 = α + Az + ε, i i i= 1 where ε denoes he vecor of serially and muually uncorrelaed srucural innovaions and z a vecor variable including he percen change in global crude oil producion, a (suiably derended) measure of real economic aciviy, as i relaes o indusrial commodiy markes, and he real price of oil (in ha order) a monhly frequency. Le e denoe he reduced form VAR innovaions such ha e = A ε. The srucural innovaions are derived from he reduced form 1 0 innovaions by imposing exclusion resricions on 1 A 0. The idenifying assumpions are ha (1) crude oil supply will no respond o oil demand shocks wihin he monh, given he coss of adjusing oil producion and he uncerainy abou he sae of he crude oil marke; ha (2) 26

28 increases in he real price of oil driven by shocks ha are specific o he oil marke will no lower global real economic aciviy wihin he monh; and ha (3) innovaions o he real price of oil ha canno be explained by oil supply shocks or shocks o he aggregae demand for indusrial commodiies mus be demand shocks ha are specific o he oil marke. As documened by Kilian (2007a), he laer shock by consrucion capure flucuaions in precauionary demand for oil driven by fears abou he availabiliy of fuure oil supplies. From he srucural moving average decomposiion, one can consruc a ime series of he componen of he real price of oil ha can be aribued o shifs in he precauionary demand for crude oil in response o shifing concerns abou he fuure oil supply shorfalls. While i is no possible o compare his VAR-based measure o he fuures-based measure for he enire sample period of considered in Kilian s work, given he limied availabiliy of oil fuures daa, we may compare hese wo independenly obained measures for he period , which includes several major oil price spikes. Table 8 shows ha he wo measures in general are highly correlaed nowihsanding he differences in heir mehod of consrucion. From hrough , he correlaion ranges from 62% a he 3-monh horizon o 80% a he 12 monh horizon. The fi improves monoonically wih he horizon, consisen wih he view ha shifs in precauionary demand are primarily concerned wih expecaions beyond he shor run. Table 8 also shows, however, ha saring in 2002 he posiive correlaion beween he basis and he VAR-based esimae of he precauionary demand componen of he spo price vanishes. Whereas he VAR-based measure suggess an increase in concerns abou fuure oil supply shorfalls, especially in 2005 and 2006 (consisen wih an increase in geopoliical uncerainy, srong expeced demand for crude oil and expecaions of igh oil supplies), he fuures-based esimae suggess a raher implausible seady decline in precauionary demand afer This paern is refleced in a near-reversal of he correlaions in Table 8 relaive o he pre-2002 sample. This reversal is also clearly seen in Figure 5. aring in 2002, he basis and he VAR-based esimae of he precauionary demand componen of he spo price begin o move in opposie direcions Explaining he Breakdown The fac ha he heoreical model of secion 3 generaes economically implausible predicions afer 2001 and predicions ha depar from independen esimaes of precauionary demand, 27

29 suggess ha a srucural change may have occurred around 2001/2002 ha is beyond he scope of he heoreical model in secion 3. Indeed, i has been suggesed in he financial press ha he naure of he oil fuures markes has changed in recen years, as hedge funds and oher invesors wih no ies o he oil indusry aemped o capialize on rising oil prices. Verifying his claim is difficul. By is naure, he NYMEX marke for crude oil fuures is anonymous, and i is commensuraely difficul o pin down exacly he exen o which he hedging or he speculaive moive of rading predominaes. The Commodiy Fuures Trading Commission (CFTC) collecs daa ha speak o his issue, however. In order o monior he amoun of speculaion in commodiy fuures markes, he CFTC requires ha raders who hold posiions in he fuures marke repor he naure of heir business. Is weekly Commimens of Traders (COT) repor records he posiions of raders in every marke for which 20 or more raders hold posiions a or above a hreshold required by he Commission. These daa comprise 70-90% of he oil fuures conracs raded on he NYMEX (CFTC 2007). The CFTC uses hese repors o classify he raders ino commercial and noncommercial. Commercial raders are eniies ha use fuures conracs in he commodiy as defined by he CFTC s regulaions (CFTC 2007). The precise wording from CFTC regulaion 1.3(z) reads: Bona fide hedging ransacions and posiions shall mean ransacions or posiions in a conrac for fuure delivery on any conrac marke, or in a commodiy opion, where such ransacions or posiions normally represen a subsiue for ransacions o be made or posiions o be aken a a laer ime in a physical markeing channel, and where hey are economically appropriae o he reducion of risks in he conduc and managemen of a commercial enerprise (CFTC 2007) More succincly, a rader is considered commercial by he CFTC as long as i is engaged in business aciviies hedged by he use of fuures. uch raders are idenified as hedgers. 10 Among he ypes of firms classified as commercial by he CFTC are merchans, manufacurers, producers, and commodiy swaps and derivaive dealers (see Haigh, Harris, Overdahl, and Robe 2007). Non-commercial raders are all oher raders, such as hedge funds, floor brokers and raders, and non-reporing raders, and are idenified as speculaors. To guaranee ha raders are classified accuraely, he CFTC can re-classify a rader a is discreion if i has addiional informaion abou how he rader uses he fuure marke. 10 Appendix 1 conains all of secion 1.3(z). 28

30 The CFTC records he open ineres of each ype of rader for shor and long posiions. Open ineres is he oal number of long posiions ousanding in a fuures conrac, which is equal o he oal number of shor posiions in a fuures conrac, and measures he number of ousanding conracs ha exis a a poin in ime (see Hull 2006). The open ineres held by an individual rader is he rader s posiion. When a rader opens a new posiion, he seller wries a new conrac, increasing open ineres by one. If he rader closes his posiion a or prior o delivery, he conrac is erminaed and open ineres decreases by one. For non-commercial raders, he CFTC also records he number of conracs associaed wih a spread posiion. A spread posiion enails he simulaneous purchase of one conrac and he sale of anoher wih he inenion of exploiing he relaive price differenial beween he wo conracs. For example, a rader may have a long posiion in he near crude oil conrac and a shor posiion in he longerm crude oil conrac in anicipaion of rising spo prices in he near erm and declining spo prices in he long erm. These wo posiions offse one anoher and hence coun as a single spread posiion. These daa are likely o be reliable. Firms ha use he fuures marke o hedge price risk can deduc he posiions as a business expense from heir axes, so misreporing he naure of one s business has significan legal implicaions and is considered ax fraud. Moreover, alhough hedge funds in paricular have an incenive o conceal heir posiions among a variey of differen brokers, he CFTC moniors and enforces a regulaion ha considers muliple posiions subjec o common ownership as a single posiion (see CFTC 2007). These insiuional mechanisms reduce he scope for misreporing among firms acive in he crude oil fuures marke. Moreover, here is no incenive for firms o misrepor hemselves as non-commercial firms, so any increase in such posiions is likely o be genuine. A naural measure of he relaive imporance of speculaive aciviies is he number of noncommercial spread posiions expressed as a percenage of he reporable open ineres posiions. Figure 6 shows a marke increase in he percen share of he noncommercial spread posiions afer , suggesing ha speculaion has recenly inensified. In fac, Figure 6 suggess ha here have been spikes in speculaive aciviy, whenever he spo price of oil moved persisenly (or predicably) up or down, noably in 1990/91 during he Persian Gulf War, when he price of oil collapsed afer he Asian Crisis, and when i recovered in However, he recen increase in he non-commercial spread posiion is clearly unprecedened in he sample. 29

31 The percenage in quesion has more han ripled since This evidence maers because, as increased demand for oil fuures from speculaors drives up fuures prices, he basis increases, and he random walk risk premium falls, creaing he misaken impression ha precauionary demand has fallen. This breakdown is expeced, as our heoreical model in his secion does no allow for speculaion. Whereas he VAR-based approach appears immune from he presence of speculaors in he oil fuures marke, he fuuresprice based approach breaks down saring in We conclude ha oil fuures prices (or relaed variables such as he basis or he spread), alhough hey are no useful for predicing fuure spo prices and in fac as predicors are dominaed by simple no-change forecass, may conain useful informaion abou he deerminans of he curren spo price. They will no be reliable, however, unless major srucural shifs in he composiion of raders are accouned for. 6. Conclusion In his paper, we inroduced a wo-counry, wo-period general equilibrium model of boh he spo marke and he fuures marke for crude oil o provide fresh insighs abou he inerpreaion of oil fuures prices and relaed saisics such as he fuures spread or basis. The key insighs can be summarized as follows: Our heoreical model illusraes ha prices of oil fuures would be expeced o forecas spo prices only under cerain resricive condiions. How well hese forecass work in pracice herefore is an empirical quesion and depends on he properies of he risk premium. Using a newly consruced daa se of monhly oil fuures prices and oil spo prices ha akes careful accoun of he exac daing of he underlying daily ime series, we documened ha prices of crude oil fuures are no useful predicors of he spo price of crude oil in pracice. We showed ha he presence of a large and ime-varying risk premium invalidaes such forecass. For example, given a spo price of $60, he fuures price may deviae as much as $43 from he expeced spo price or as lile as $0. Many users of fuures-based forecass are aware of hese caveas and undersand ha fuuresbased forecass may be poor, bu sill believe ha fuures-based forecass provide he bes available forecas of spo prices of crude oil. We showed his no o be he case. Fuures-based forecass are inferior o simple and easy-o-use forecasing mehods such as he no-change forecas. uch forecass are also more accurae han commercial survey-based forecass. Given our evidence ha simple no-change forecass are mos accurae in forecasing he spo 30

32 price of crude oil, we can express he empirical counerpar of he risk premium in he heoreical model in erms of observables. In our heoreical model, flucuaions in his risk premium are driven by shifs in he uncerainy abou fuure oil supply shorfalls. Our heoreical analysis implies a posiive correlaion beween he risk premium and he componen of he spo price of oil driven by precauionary demand for crude oil. Thus, he risk premium may be viewed as an index of flucuaions in he price of crude oil driven by precauionary demand for oil. The esimaed random walk risk premia sugges major shifs in precauionary demand for oil during he Persian Gulf War and following he Asian crisis, for example. These resuls provide independen evidence on how shifs in marke expecaions abou fuure oil supply shorfalls affec he spo price of crude oil. They are also consisen wih relaed evidence in he lieraure obained by alernaive mehodologies (see Kilian 2007a,b,c). The abiliy of he risk premium o capure shifs in precauionary demand sharply deerioraes afer 2002, however, consisen wih evidence of an unprecedened increase in speculaive aciviies in he oil fuures marke. This breakdown is expeced, as our heoreical model does no allow for speculaion and increased speculaive rading will end o depress he observed risk premium. Thus, while fuures price daa can be useful in idenifying expecaions shifs in general, our resuls sugges cauion in inerpreing oil fuures daa in he absence of furher informaion abou he marke srucure. We also proposed a erm srucure of random walk risk premia as a measure of he marke s expecaion of wheher risks in he crude oil marke are increasing or decreasing in he forecas horizon. This measure suggess, for example, ha fuures raders have been expecing risks o increase a longer horizons for he mos par since mid Finally, we showed ha oil fuures markes are oo illiquid a horizons beyond one year o provide effecive insurance agains risks of fuure oil supply shorfalls a medium and long-erm horizons. 31

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36 Table 1: 1-Monh Ahead Recursive Forecas Error Diagnosics ˆ MPE MAP E uccess Raio Bias (p-value) (p-value) (p-value) N.A. + 1 (1) F (0.809) (1) ( 1+ ( ˆ α + ˆ βln( F / ) )) (0.352) (1) ( 1+ ˆ β ln( F / ) ) (0.246) (12) ( 1+ ln( F / )) (0.807) (1 + ˆ α) (0.527) (1) (1 s ) +Δ (0.450) (3) (1 s ) +Δ (0.828) (6) (1 s ) +Δ (0.797) (9) (1 s ) +Δ (0.903) (0.770) (0.822) (0.742) (0.776) (0.525) (0.946) (0.750) (0.570) (0.696) (0.898) (0.529) (0.984) (0.898) (0.497) (0.646) (0.265) (0.499) (0.509) (12) (1 +Δ s ) (0.281) (0.130) Noes: The forecas evaluaion period is The iniial esimaion window is For regressions based on 6-monh fuures prices he esimaion window begins in ; for he 9-monh ( h) fuures price in ; for he 12-monh fuures price in F is he fuures price ha maures in h () l periods; i m, is he m monh ineres rae; and Δ s denoes he railing geomeric average of he monhly percen change for l monhs. p-values are in parenheses. All p-values refer o pairwise ess of he null of a random walk wihou drif. Comparisons of nonnesed models wihou esimaed parameers are based on he DM-es of Diebold and Mariano (2005) wih N(0,1) criical values. Nesed model comparisons wih esimaed parameers are based on Clark and Wes (2006). For he rolling regression esimaes of he random walk wih drif we use N(0,1) criical values under quadraic loss; for recursive esimaes under quadraic loss and for all esimaes under absolue loss we use boosrap criical values as described in Clark and Wes. The sign es in he las column is based on Pesaran and Timmermann (1992). 35

37 Table 2: 3-Monh Ahead Recursive Forecas Error Diagnosics ˆ MPE MAPE uccess Raio Bias (p-value) (p-value) (p-value) N.A. + 3 (3) F (0.347) (1 + i ), (0.715) (3) ( 1+ ( ˆ α + ˆ βln( F / ) )) (0.948) (3) ( 1+ ˆ β ln( F / ) ) (0.999) (12) ( 1+ ln( F / )) (0.348) (1 + ˆ α) (0.493) (1) (1 s ) +Δ (0.684) (3) (1 s ) +Δ (0.947) (6) (1 s ) +Δ (0.860) (9) (1 s ) +Δ (0.510) (12) (1 s ) +Δ (0.439) CF, (0.997) Noes: ee Table (0.920) (0.632) (0.999) (0.999) (0.920) (0.500) (0.816) (0.829) (0.669) (0.545) (0.459) (0.999) (0.648) N.A (0.996) (0.992) (0.648) (0.716) (0.418) (0.376) (0.509) (0.044) (0.032) (0.338) 36

38 Table 3: 6-Monh Ahead Recursive Forecas Error Diagnosics ˆ MPE Bias MAP E uccess Raio (p-value) (p-value) (p-value) N.A. + 6 (6) F (0.716) (1 + i ), (0.713) (6) ( 1+ ( ˆ α + ˆ βln( F / ) )) (0.926) (6) ( 1+ ˆ β ln( F / ) ) (0.997) (12) ( 1+ ln( F / )) (0.721) (1 + ˆ α) (0.486) (1) (1 s ) +Δ (0.769) (3) (1 s ) +Δ (0.851) (6) (1 s ) +Δ (0.622) (9) (1 s ) +Δ (0.293) (12) (1 s ) +Δ (0.413) (0.906) (0.708) (0.960) (0.997) (0.910) (0.487) (0.828) (0.858) (0.752) (0.988) (0.596) (0.483) N.A (0.983) (0.703) (0.483) (0.022) (0.501) (0.641) (0.374) (0.091) (0.450) Noes: ee Table 1. 37

39 Table 4: 9-Monh Ahead Recursive Forecas Error Diagnosics ˆ MPE Bias MAPE uccess Raio + 9 (p-value) (p-value) (p-value) N.A. (9) F (0.887) (0.926) (0.080) (9) ( 1+ ( ˆ α + ˆ βln( F / ) )) (0.802) (0.684) (0.035) (9) ( 1+ ˆ β ln( F / ) ) (0.901) (0.850) (0.026) (12) ( 1+ ln( F / )) (0.898) (0.948) (0.080) (1 + ˆ α) (0.526) (0.528) (0.000) (1) (1 +Δ s ) (0.849) (0.883) (0.611) (3) (1 +Δ s ) (0.638) (0.725) (0.210) (6) (1 +Δ s ) (0.301) (0.561) (0.427) (9) (1 +Δ s ) (0.162) (0.312) (0.442) (12) (1 +Δ s ) (0.270) (0.351) (0.729) Noes: ee Table 1. 38

40 Table 5: 12-Monh Ahead Recursive Forecas Error Diagnosics ˆ MPE MAPE uccess Raio Bias (p-value) (p-value) (p-value) N.A (12) F (0.898) (1 + i ), (0.408) (12) ( 1+ ( ˆ α + ˆ βln( F / ) )) (0.849) (12) ( 1+ ˆ β ln( F / ) ) (0.967) (12) ( 1+ ln( F / )) (0.916) (1 + ˆ α) (0.502) (1) (1 s ) +Δ (0.294) (3) (1 s ) +Δ (0.469) (6) (1 s ) +Δ (0.291) (9) (1 s ) +Δ (0.197) (12) (1 s ) +Δ (0.191) CF, (0.979) Noes: ee Table (0.767) (0.804) (0.768) (0.950) (0.789) (0.562) (0.93) (0.941) (0.918) (0.862) (0.622) (0.954) (0.021) N.A (0.032) (0.004) (0.021) (0.001) (0.002) (0.421) (0.932) (0.967) (0.746) (0.122) 39

41 Table 6: Asympoic p-values for Forecas Efficiency Regressions Horizon H : 1 0 H : 0, monh monh monh Noes: For he 3- and 6-monh regressions, he sample period is For he 12-monh regression, he sample is All - and Wald-ess have been compued based on HAC sandard errors. 40

42 Table 7: Time eries Feaures of he Random Walk Risk Premium 3 Monh 12 Monh Mean sa. (p-value) 2.97 (0.00) 3.28 (0.00) Mean Abs. Dev Min Max Persisence Noes: The sample for he Consensus-based risk premia is ; he sample for he 3-monh random walk and Hoelling-based risk premia is ; and ha for he 12-monh random walk and Hoelling-based risk premia is , ( h) reflecing he daa consrains. The HAC -saisic is for H0 : ˆ ρ = 0. The measure of persisence is he sum of he auoregressive coefficiens proposed by Andrews and Chen (1994). 41

43 Table 8: Conemporaneous Correlaion of Random Walk Risk Premium and Precauionary Demand Componen of po Price of Crude Oil (Percen) Horizon NOTE: Compued based on Figure 5. 42

44 Figure 1: Why $ F ( h) ( h ) F > Does No Imply Rising po Prices = 50 a. Increasing Prices E [ ] = 60 +h = 40 Incepion () Mauriy (+h) Monhs b. Consan Prices $ ( h ) F = 50 = 40 E [ ] = 40 +h Incepion () Mauriy (+h) Monhs c. Falling Prices $ ( h ) F = 50 = 40 E [ ] = 20 +h Incepion () Mauriy (+h) Monhs 43

45 Figure 2: Volume of NYMEX Fuures Conracs No. of Conracs (1,000) No. of Conracs (1,000) No. of Conracs (1,000) 50 1M Fuures Conrac M Fuures Conrac 3Y Fuures Conrac M Fuures Conrac M Fuures Conrac 4Y Fuures Conrac M Fuures Conrac Y Fuures Conrac Y Fuures Conrac ource: Price-daa.com 44

46 Figure 3: Random Walk Risk Premium by Horizon Monh 6 Monh 9 Monh 12 Monh Percen

47 Figure 4: Term rucure of Random Walk Risk Premia 12-Monh Risk Premium 3-Monh Risk Premium Percenage Poins

48 Figure 5: Random Walk Risk Premium by Horizon and Precauionary Demand Componen of po Price Horizon: 3 monhs Precauionary Demand Componen of po Price Horizon: 6 monhs Precauionary Demand Componen of po Price Horizon: 9 monhs Precauionary Demand Componen of po Price Horizon: 12 monhs Precauionary Demand Componen of po Price

49 Figure 6: hare of Non-Commercial pread Posiions in Reporable Open Ineres: Oil Fuures Marke hare of Non-commercial pread Posiions Average Percen Noes: Daa are end-of-monh observaions. Commercial firms are engaged in business aciviies ha can be hedged in he fuures marke. Non-commercial firms are all oher firms. Percenages refer o he share of reporable posiions, which comprise 70-90% of all posiions. 48

50 Appendix 1 CFTC Rule 1.3(z) Bona Fide Hedging Transacions and Posiions 11 (z) Bona fide hedging ransacions and posiions (1) General definiion. Bona fide hedging ransacions and posiions shall mean ransacions or posiions in a conrac for fuure delivery on any conrac marke, or in a commodiy opion, where such ransacions or posiions normally represen a subsiue for ransacions o be made or posiions o be aken a a laer ime in a physical markeing channel, and where hey are economically appropriae o he reducion of risks in he conduc and managemen of a commercial enerprise, and where hey arise from: (i) The poenial change in he value of asses which a person owns, produces, manufacures, processes, or merchandises or anicipaes owning, producing, manufacuring, processing, or merchandising, (ii) The poenial change in he value of liabiliies which a person owns or anicipaes incurring, or (iii) The poenial change in he value of services which a person provides, purchases, or anicipaes providing or purchasing. Nowihsanding he foregoing, no ransacions or posiions shall be classified as bona fide hedging unless heir purpose is o offse price risks incidenal o commercial cash or spo operaions and such posiions are esablished and liquidaed in an orderly manner in accordance wih sound commercial pracices and, for ransacions or posiions on conrac markes subjec o rading and posiion limis in effec pursuan o secion 4a of he Ac, unless he provisions of paragraphs (z) (2) and (3) of his secion and 1.47 and 1.48 of he regulaions have been saisfied. (2) Enumeraed hedging ransacions. The definiions of bona fide hedging ransacions and posiions in paragraph (z)(1) of his secion includes, bu is no limied o, he following specific ransacions and posiions: (i) ales of any commodiy for fuure delivery on a conrac marke which do no exceed in quaniy: (A) Ownership or fixed-price purchase of he same cash commodiy by he same person; and (B) Twelve monhs' unsold anicipaed producion of he same commodiy by he same person provided ha no such posiion is mainained in any fuure during he five las rading days of ha fuure. (ii) Purchases of any commodiy for fuure delivery on a conrac marke which do no exceed in quaniy. 11 ee Elecronic Code of Federal Regulaions a hp://ecfr.gpoaccess.gov. 49

51 (A) The fixed-price sale of he same cash commodiy by he same person. (B) The quaniy equivalen of fixed-price sales of he cash producs and by-producs of such commodiy by he same person; and (C) Twelve monhs' unfilled anicipaed requiremens of he same cash commodiy for processing, manufacuring, or feeding by he same person, provided ha such ransacions and posiions in he five las rading days of any one fuure do no exceed he person's unfilled anicipaed requiremens of he same cash commodiy for ha monh and for he nex succeeding monh. (iii) Offseing sales and purchases for fuure delivery on a conrac marke which do no exceed in quaniy ha amoun of he same cash commodiy which has been bough and sold by he same person a unfixed prices basis differen delivery monhs of he conrac marke, provided ha no such posiion is mainained in any fuure during he five las rading days of ha fuure. (iv) ales and purchases for fuure delivery described in paragraphs (z)(2)(i), (ii), and (iii) of his secion may also be offse oher han by he same quaniy of he same cash commodiy, provided ha he flucuaions in value of he posiion for fuure delivery are subsanially relaed o he flucuaions in value of he acual or anicipaed cash posiion, and provided ha he posiions in any one fuure shall no be mainained during he five las rading days of ha fuure. (3) Non-enumeraed cases. Upon specific reques made in accordance wih 1.47 of he regulaions, he Commission may recognize ransacions and posiions oher han hose enumeraed in paragraph (z)(2) of his secion as bona fide hedging in such amoun and under such erms and condiions as i may specify in accordance wih he provisions of uch ransacions and posiions may include, bu are no limied o, purchases or sales for fuure delivery on any conrac marke by an agen who does no own or who has no conraced o sell or purchase he offseing cash commodiy a a fixed price, provided Tha he person is responsible for he merchandising of he cash posiion which is being offse. 50