Copyright(c) Shoko Nakano 2007 All Rights Reserved. FORWARD DISCOUNT BIAS: IS IT A RISK PREMIUM ON CRUDE OIL? August 10, 2007

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1 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. FORWARD DISCOUNT BIAS: IS IT A RISK PREMIUM ON CRUDE OIL? Augus 10, 2007 SHOKO NAKANO Gradua School of Economics, Hiosubashi Univrsiy, 2-1 Naa, Kuniachi, Toyo , Japan Minisry of Economy, Trad, and Indusry, 3-1 Kasumigasi, Chiyoda-u, Toyo , Japan Absrac This papr invsigas h forward discoun bias in Ligh Sw Crud Oil fuurs, also nown as Ws Txas Inrmdia (WTI) crud oil fuurs, lisd on h Nw Yor Mrcanil Exchang. W confirm ha h currn forward-spo diffrnial is a biasd forcas of fuur changs in h spo pric. Using survy forcas daa, w drmind ha h saisically significan causs of h forward discoun bias wr (i) h corrlaion bwn forcas rrors and h currn forward-spo diffrnial, and (ii) h avrag lvl of forcas rrors. Addiionally, w found ha, consisnly afr h firs half of 2003, hr xisd a subsanial avrag amoun of ris prmium h currn forward-spo diffrnial was nin prcnag poins highr on avrag han wha h avrag forcasr had xpcd. JEL Classificaion: G13; G14; Q40 Kywords: Crud oil; Forward discoun bias; Survy Forcas; Ris prmium naano-shoo@mi.go.jp. Viws xprssd in his papr ar hos of auhors and do no ncssarily rflc hos of Minisry of Economy, Trad, and Indusry. 1

2 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. 1. INTRODUCTION Is h forward discoun a biasd prdicor of h fuur chang in h spo pric? This is on of h olds qusions in Financial Economics, spcially in h Inrnaional Financ liraur. Mos sudis found i o b a biasd prdicor, and h rsul is rfrrd o as h forward discoun puzzl. This papr conducs h unbiasdnss s for crud oil fuurs, spcifically for h Ligh Sw Crud Oil fuurs lisd on h Nw Yor Mrcanil Exchang, nown also as Ws Txas Inrmdia (WTI) crud oil fuurs. This papr uss survy daa on spo pric xpcaions of WTI crud oil, sinc survy daa allow us o dcompos forward discoun bias ino componns aribuabl o h ris prmium and xpcaional rrors. Wihou spo pric xpcaions, on canno drmin whhr h bias is vidnc of a ris prmium or of a violaion of raional xpcaion. Th liraur on forign xchang ras nds o disagr abou h answr. Som sudis, for xampl Bilson (1981), assum ha invsors ar ris nural, so ha h sysmaic componn of pric changs in xcss of h forward discoun is inrprd as vidnc of a failur of raional xpcaions. Ohrs, howvr, such as Hsih (1984), aribu h sam sysmaic componn o a im-varying ris prmium ha sparas h forward discoun from xpcd dprciaion. In ordr o show h caus of h forward discoun bias as clarly as possibl, his papr follows Froo and Franl (1989) 2

3 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. and uss survy daa, spcifically h on publishd by Consnsus Economics Inc., which survyd an sima of h spo pric of WTI for hr monhs a a rgular inrval of on monh sinc Novmbr Addiionally, w allow h avrag lvl of ris prmium o chang discrly and xamin whhr h chang is causd by hdging prssur, a phnomnon firs addrssd by Kyns (1930). Froo and Franl (1989) hav conducd h unbiasdnss s for forign xchang ras using survy daa and found a subsanial avrag lvl of h ris prmium. Thir Figurs I IV also suggs ha h avrag lvl of h ris prmium changd discrly. To capur such discr changs, his papr mploys an simaion mhod dvlopd by Bai and Prron (1998). Our findings, sad blow, ar (1) ha h WTI crud oil fuurs prics ar a biasd prdicor of h fuur spo pric; (2) ha h bias is vidnc of (i) h corrlaion bwn h forward discoun and forcas rrors, and (ii) h avrag lvl of forcas rrors; (3) ha a subsanial ris prmium mrgd, ha is, h forward discoun was nin prcnag poins highr on avrag han wha an avrag forcasr had xpcd afr h arly 2003; and (4) h subsanial amoun of h ris prmium is no causd by hdging prssur. Th rs of his papr is organizd as follows: w conduc h unbiasdnss s in Scion 2; giv an ovrviw of h daa, including h survy daa in Scion 3

4 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. 3; invsiga whhr h ris prmium xplains h forward discoun, and also whhr h avrag lvl of h ris prmium is causd by hdging prssur in Scion 4; xamin whhr forcas rrors xplain h forward discoun in Scion 5; and sa our conclusions in Scion UNBIASEDNESS TEST In his scion, w xamin forward mar unbiasdnss for WTI crud oil fuurs prics using his rgrssion: S + = α + β F + ) + η+ (,. (1) S + is h prcnag incrmn of h spo pric (h chang in h log of h spo pric of WTI Crud Oil) ovr priods, F is h currn -priod, + forward discoun (h log of h fuurs pric minus h log of h spo pric), and η + is a random rror (mar paricipans xpcaional rrors). Th null hypohss o s whhr h ralizd spo ra is qual o h forward ra plus a random rror rm ar ha β =1 and α = 0. Fuurs prics ar compud by rolling ovr h prics of four-monh-o-mauriy conracs; hrfor, h in (1) indicas four monhs. As a proxy for h spo pric, h slmn pric a h day 4

5 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. of mauriy is usd. Thrfor, h in (1) indicas h mauriy da. 1 Th sampl priod is Fbruary 1996 hrough Novmbr Eq. (1) is simad using OLS. Th rsuls ar prsnd in Tabl 1. Th simas α and β ar 0.04 and 0.12, rspcivly. Th β is significanly lss han on, suggsing ha h forward discoun of WTI crud oil fuurs is a biasd prdicor of h fuur chang in h spo pric. [Tabl 1 Hr] Th rsul ha β 1 indicas ihr (a) ha h mar paricipans xpcaional rrors ar corrlad wih h forward discoun, or (b) ha h ris prmium is corrlad wih h forward discoun (ha is, h im-varying ris prmium xiss). In ordr o idnify hs facors, Froo and Franl (1989) usd h sima of mar xpcaion, Sˆ, and dcomposd h cofficin β ino 1 + (h null hypohsis) minus a rm arising from any failur of raional xpcaions, br, minus anohr rm arising from ris prmium, b : rp β = 1 b (2) r b rp 1 In ordr o avoid h informaion ovrlap problm causd by srial corrlaion in h rrors, w us Andrw (1991) s Hrognous Auocorrlaion Consisn, HAC, simaors. 5

6 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. b b r rp cov( η +, F, + ) = ; var( F ) var( rp =, + ) + cov( Sˆ var( F +, +, rp ) ) ; rp F, + +. = ˆ For xampl, if hr ar no sysmaic prdicion rrors in h sampl, hn b r = 0. On h ohr hand, if h ris prmium is uncorrlad wih h forward discoun, b rp = 0. Thus, (2) indicas ha h sima of mar xpcaion mas i possibl o clarly dcompos h caus ha β 1 ino forcas rrors and im-varying ris prmiums. 3. SURVEY DATA This papr uss survy daa collcd by Consnsus Economics Inc. Each monh, Consnsus Economics survys svral hundrd conomic and financial forcasrs. Ovr fify of hm compld his survy qusion, giving simas for h spo pric in boh hr and wlv monhs of WTI (USD pr barrl). 2 This papr uss h hr-monh survy forcas daa. 3 2 Th forcas daa of WTI crud oil is availabl a rgular on-monh inrvals bginning Novmbr For xampl, in h survy conducd on Jun 13, 2005, a forcasr providd his/hr sima for h spo pric of WTI crud oil for h nd of Spmbr 2005 as h sima in hr monhs. Trading of h WTI crud oil fuurs rminas a h clos of businss on h hird businss day prior o h 25h calndar day of h monh prcding h dlivry monh. Thus, h WTI crud oil 6

7 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. Figur 1 shows h man of h hr-monh survy forcass (hin lin), boh h highs and lows forcass (dod lins), h slmn prics of h fourh conrac of WTI crud oil fuurs (hin lin wih diamond), and h ralizd spo prics of WTI crud oil (bold lin). Th da on h horizonal axis is appndd basd on h da of forcas. For xampl, h valus shown on May 2003 ar h man of h survy forcass mad on May 12, 2003 (USD 24.9 pr barrl), h fuurs pric on h sam da (USD 26.5 pr barrl), and h ralizd spo pric a h day of mauriy in Spmbr 2003 (USD 26.9 pr barrl). Th rason why h ralizd spo pric is shown on May 2003 is ha h spo pric was forcasd on May 12, Hnc, h vrical diffrnc bwn h ralizd spo pric and h hr-monh survy forcas shows h survy-masurd forcas rrors of h forcas mad on h appndd da. Similarly, h diffrnc bwn h fuurs pric and h survy forcas shows h survy-masurd ris prmium paid on h appndd da. [Figur 1 Hr] From 1995 hrough 1998, crud oil prics wr rlaivly sabl. Fuurs dlivrd during Ocobr 2005 was rminad on Spmbr 20, 2005, and was h fourh conrac on Jun 13, Thrfor, w us h hr-monh survy forcas, which is consisn wih h fourh conrac in h WTI crud oil fuurs. 7

8 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. prics and survy forcass wr vry clos, suggsing ha h avrag lvl of h ris prmium was almos zro. Th ralizd spo prics wr oscillaing around hm wihin a vry narrow rang. Amid such circumsancs, h Asian currncy crisis in July 1997 brough a dclin in oil prics. Alarmd by h dclin, bginning in March 1998, boh OPEC and non-opec counris sard wihholding oupu. This coopraiv wihholding causd oil prics o mov slighly upward in h firs quarr of Afr 2003, oil prics incrasd unprcdndly bcaus of uncrainy in Iraq, incrasing dmand in China, and ohr facors. During his priod, h ralizd spo and fuurs prics wr consanly highr han h man of h survy forcass. This suggss ha hr xisd boh h avrag lvl of forcas rrors and h avrag lvl of ris prmium. 4. DOES THE RISK PREMIUM EXPLAIN ANY OF THE FORWARD DISCOUNT BIAS? This scion xamins whhr h forward discoun bias can b xplaind by h ris prmium using h survy forcas daa. W dfin S + as h unobsrvabl mar-xpcd spo pric and ε as h random masurmn rror in h survys. W also assum ha h man of all survy rsponss is an simad ru 8

9 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. invsor xpcaion, ha is, Sˆ S + ε. 4 Undr his assumpion, w rgrss + = + h masur of xpcd chang ovr priods agains h forward discoun: S ˆ = a + b + ε for j = 1, K, m+ 1. (3) + j ( F, + ) Th probabiliy limi of h cofficin b in (3) is ˆ Cov( S +, F, + ), and h Var( F ), + probabiliy limi of h cofficin β in (1) is ˆ Cov( S +, F, + ) Cov( η +, F, + ) +. Using (2), w can xprss cofficin b as Var( F ) Var( F ), +, + Cov( η+, F, + ) b = β = 1 brp. (4) Var( F ), + Hnc, h null hypohsis ha h ris prmium is uncorrlad wih h forward discoun is ha b = 1, ha is, = 0. This mans ha hr is no im-varying b rp ris prmium. Th null hypohsis ha hr is no avrag lvl of h ris prmium is ha a = 0. Th null hypohsis ha h ris prmium is idnically zro ( ˆ F ) is ha boh a = 0 and b = 1. To xamin discr changs in S + =, + h avrag lvl of ris prmium, w a ino accoun h mulipl srucural bras in h consan rm ( j = 1,, m + 1), and s h possibl srucural 4 This is analogous o h raional xpcaion approach, which uss x-pos pric changs rahr han survy daa and assums ha h rror in masuring ru xpcd pric chang is random. 9

10 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. bras using h mhod of Bai and Prron (1998). Th rsuls of (3) ar prsnd in h firs row in Tabl 2. W firs xamin h rsuls for h im-varying ris prmium. Th sima b is 1.17, and is no saisically diffrn from on. This indicas ha h rason why h hypohsis ha β = 1 in (1) was rjcd is no bcaus of h im-varying ris prmium. Nx, w xamin h avrag lvl of h ris prmium. From h consan rm in (3), on srucural bra is dcd in May Bfor May 2003, h consan rm was 0.02 ( ); and afr Jun 2003, i bcam 0.09 ( a ). a1 2 Whil h consan rm a 1 is no significanly diffrn from zro, h consan rm a 2 is diffrn wih a 1% significanc lvl. I indicas ha afr h bra da h avrag lvl of h ris prmium xisd. Spcifically, h forward discoun was nin prcnag poins highr on avrag han wha an avrag forcasr xpcd. [Tabl 2 Hr] To drmin who paid h avrag lvl of ris prmium, w add a variabl ha can capur hdging prssur, q, in (3). (S Appndix for h concp of hdging prssur, h dfiniion of hdging prssur in his papr, and h rgrssion quaion wih h hdging prssur variabl.) Th rsuls afr 10

11 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. conrolling h ffcs from hdging prssur ar shown in h scond row in Tabl 2. A srucural bra is dcd in January Bfor January 2003, h consan rm was 0.02 ( ); afr h bra da i bcam 0.09 ( a ). Ths a1 2 simas ar significan and almos h sam as h simas in (3). Thrfor, w can conclud ha h avrag lvl of h ris prmium is no causd by h hdging prssur DO EXPECTATIONAL ERRORS EXPLAIN ANY OF THE FORWARD DISCOUNT BIAS? In his scion, w s whhr hr ar sysmaic xpcaional rrors ha can xplain h finding of bias in h forward discoun. Among facors ha inducd h rjcion in Tabl 1, h porion arising from h corrlaion bwn h forcas rrors and h forward discoun (h cofficin b in (2)) is obaind by r rgrssing h xpcaional prdicion rror, ˆ + ) ( S S +, on h forward discoun: 6 5 Considring (A2) in Appndix as 2SLS, a h firs sag, w rgrss h variabl on q q, + S h variabl. Th simad cofficin for a h firs sag is 0.25 (is sandard dviaion, 0.08). This significan ngaiv cofficin mans ha, whn hr is slling (buying) hdging prssur, h WTI crud oil fuurs nd o significanly dclin (incras). Combining his rsul wih h rsuls from (A2), w can considr ha h hdging prssur is significan bu is no h main caus of h avrag of h ris prmium. 6 Th rror rm in (5) is h masurmn rror in h survys lss h unxpcd chang in h = ε η v + + spo ra, ha is,. F 11

12 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. ( ˆ, for j = 1, K, m + 1. (5) S + + ) = d j + br ( F + ) + v+ Th null hypohsis ha h forcas rror is uncorrlad wih h forward b r b r discoun is ha =0. A finding ha >0, for xampl, mans ha an invsor could hav mad xcss profi by bing lowr in absolu magniud han h forward discoun. Th null hypohsis ha hr is no avrag lvl of h forcas rror is ha d = 0. Addiionally, h null hypohsis ha hr is no sysmaic forcas rror is ha boh d = 0 and b =0. r Th simaion rsuls ar prsnd in Tabl 3. Th sima of b r is 0.89, which is significanly diffrn from zro. This suggss ha h forward discoun bias is causd by h corrlaion bwn h forcas rror and h forward discoun. A srucural bra is no dcd from h consan rm. Th sima of h consan rm is 0.09 hroughou all h sampl priod, which is significanly diffrn from zro. Ths simaion rsuls suggs ha sysmaic forcas rrors aros du o (i) h corrlaion bwn h forcas rror and h forward discoun ( b >0 ), and (ii) h avrag lvl of undrsimaion ( d < 0 ). r [Tabl 3 Hr] W canno rjc h hypohsis ha hr is no sysmaic prdicion 12

13 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. rror. Howvr, his finding dos no ncssarily man ha invsors ar irraional, as a sysmaic prdicion rror can mrg whil raional invsors incorpora uncrainy abou shifs in h disribuion of conomic shocs ino hir forcass, ha is, whil larning. Sinc 2003, suspc vns in such shifs hav occurrd conscuivly. Ths ar, for xampl, h uncrainy in Iraq and h mor-han-xpcd growh of h Chins conomy. In h ligh of larning, i is rasonabl o assum ha hs conscuivly occurring suspc vns ar sufficin o induc h sysmaic prdicion rrors. 6. CONCLUSION This papr has invsigad h forward discoun bias in h Ligh Sw Crud Oil fuurs, also nown as h WTI crud oil fuurs, lisd in Nw Yor Mrcanil Exchang. W confirmd ha (1) h forward discoun was a biasd forcas of h fuur chang in h spo pric. W hn found ha (2) h saisically significan causs of h forward discoun bias wr (i) h corrlaion bwn forcas rrors and forward discoun, and (ii) h avrag lvl of forcas rrors. W could no find h im-varying ris prmium wih saisical significanc. Howvr, w found ha (3) hr xisd a subsanial avrag amoun of ris prmium afr 2003, h forward discoun was consisnly nin prcnag poins highr on avrag han wha h avrag forcasr xpcd. (4) Th subsanial amoun of h ris 13

14 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. prmium is no causd by hdging prssur. Appndix. WHO PAID THE AVERAGE LEVEL OF RISK PREMIUM? Hr, w ry o drmin who paid h avrag lvl of ris prmium by adding, in (3), a variabl ha can capur hdging prssur, ha is, hdg dmand from hdgrs in h fuurs mar. Hdging prssur was firs xprssd by Kyns (1930) o xplain h fuurs pric bias and was dvlopd by Hirshlifr (1990), D Roon al. (2000). In many paprs, h hdgrs n shor posiion is usd as a proxy for hdging prssur. 7 Following his approach, w compos a hdging prssur variabl, q, using h larg radr s posiions publishd by h Commodiy Fuurs Trading Commission (CFTC). Spcifically, i is composd of h shor and long posiions a h WTI crud oil mar in NYMEX: numbr of q = shor hdg posiions numbr of long oal numbr of hdg posiions hdg posiions. (A1) Hdging prssur a da affcs a fuurs pric quod a da. Thrfor, h spcificaion including hdging prssur is as follows. 7 For xampl, Chang,. al. (1985) and Sandrs,. al. (2004) hav usd h hdgrs n shor posiion as a proxy for hdging prssur. Addiionally, hr ar rar paprs ha hav usd h disaggrgad (non-public) vrsion of h Commimns of Tradrs (COT) daa of h Commodiy Fuurs Trading Commission (CFTC),.g., Haigh,. al. (2007). 14

15 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. Sˆ S a b F S cq + = j + (, + ) + + ε for j = 1,, m+ 1 K. (A2) In his spcificaion, h ffcs from hdging prssur ar rmovd from h cofficins a j and b. Thrfor, if w find srucural bras in (A2) similar o hos ha w found in (3), w may conclud ha h hdging prssur is no h caus of h avrag lvl of h ris prmium. 15

16 Copyrigh(c) Shoo Naano 2007 All Righs Rsrvd. Rfrnc Bai, J., and Prron, P, Esimaing and sing linar modls wih mulipl srucural changs. Economrica 66, Bilson, J., Th spculaiv fficincy hypohsis. Journal of Businss LIV, Chang, E., Rurns o spculaors and h hory of normal bacwardaion. Th Journal of Financ Vol. 40 No. 1, Commodiy Fuurs Trading Commission, 1962-(ongoing). Th Commimns of Tradrs. Washingon, DC. Consnsus Economics Inc., 1984-(ongoing). Consnsus Forcass. London. D Roon, F., Nijman, T., and Vld, C., Hdging prssur ffcs in fuurs mars. Th Journal of Financ Vol. LV No. 3, Froo, K., and Franl, J., Forward discoun bias: Is i an xchang ris prmium? Th Quarrly Journal of Economics Vol. 104 No. 1, Haigh, M., Harris, J., Ovrdahl, J., and Rob, M., Mar Growh, Tradr Paricipaion and Pricing in Enrgy Fuurs Mars. Manuscrip, Commodiy Fuurs Trading Commission, Washingon, D.C. Hirshlifr, D., Hdging prssur and fuurs pric movmns in a gnral quilibrium modl. Economrica Vol. 58 No. 2, Hsih, D., Tss of raional xpcaions and no ris prmium in forward xchang mars. Journal of Inrnaional Economics XVII, Kyns, J., A Trais on Mony, Vol. 2. London, MacMillan. Sandrs, D., Boris, W., and Manfrdo, M., Hdging, funds, and small spculaors in h nrgy fuurs mars: An analysis of h CFTC s Commimns of Tradrs rpors. Enrgy Economics 26,

17 α S + = α + β ( F, + ) + η + α β

18 Sˆ Sˆ + = a j + b ( F, + ) + = a j + b ( F, + + ε ) ) + c q + ε j j = 1, K, m + = 1, K, m a1 a2

19 ˆ ( S + + ) = d j + b r ( F, + ) + v + j = 1, K, m + 1 d br

20