Usefulness of the Forward Curve in Forecasting Oil Prices

Transcription

1 Usefulness of he Forward Curve in Forecasing Oil Prices Akira Yanagisawa Leader Energy Demand, Supply and Forecas Analysis Group The Energy Daa and Modelling Cener Summary When people analyse oil prices, he forward curve is ofen referred o as i reflecs he average view among marke paricipans. In his paper, o wha exen he forward curve provides useful informaion in forecasing oil prices was analysed quaniaively. Alhough he usefulness of he forward curve is confirmed in forecasing oil prices, he effec in reducing forecas error is small. Addiionally, he forward curve is acually useful for one week ahead and for one monh ahead in daily and weekly forecass, respecively. However, he forward curve is scarcely useful in long-erm forecas. 1. Trend of crude oil price and is forward curve Crude oil price 1 exceeded $7/bbl on 9h June 29 for he firs ime in seven monhs and he price was $72.68/bbl on 11h June. The high price, which rose by $14/bbl only in jus one monh, is one of he concerns for he vulnerable global economy. Oil supply and demand balance was far from igh in general ha oil sock in he Unied Saes ouched he highes level in he las 19 years. However, i is said ha he expecaion of recovery of he global economy, he side effec by he easy-money policy, ec. lead o his rapid rise of he oil prices. 1 Ligh Swee Crude Oil lised a New York Mercanile Exchange, or NYMEX, fron monh, so called WTI price. Closing price. 1

2 Figure 1: Crude oil price $/bbl /3 7/3 1/4 7/4 1/5 7/5 1/6 7/6 1/7 7/7 1/8 7/8 1/9 Source: Deparmen of Energy, Unied Saes The forward curve, a curve of fuures price over conrac monh, is now in conango. I is said ha he conango is an indicaion ha he marke expecs higher prices in he fuure. Figure 2: Forward curve (on 9h June 29) $/bbl /9 8/9 9/9 1/9 11/9 12/9 1/1 2/1 3/1 4/1 5/1 6/1 Conrac monh Source: NYMEX The forward curves of oil price have so far ofen in backwardaion. The forward curves, however, form differen shapes depending on he period. For example, in January 29, he forward curve was fairly seep and i was said ha he forward curve was showing ha he oil prices would rise in he fuure. 2

3 Figure 3: Change of forward curves Price difference from fron monh ($/bbl) Fron monh Conango Backwardaion Jan 29 April 29 June 29 July 28 Oc 28 April 28 Jan 28 6h 12h Conrac Source: NYMEX I is widely hough ha forward curve reflecs he average view of fuure oil prices among marke paricipans. Addiionally, he forward curve provides informaion on he fuure in a coninuous, immediae and precise manner. Hence, he forward curve is also regarded as one of predicors in forecasing oil prices. Then o wha exen does forward curve provide useful informaion forecasing oil prices? In his paper, he usefulness of he forward curve is analysed quaniaively using ime series models of oil prices. The conrac for December 217 is he furhes ransacion a NYMEX. While abou 9% of he ransacion volume is concenraed o he neares few monhs, he volume of back monhs is exremely lile. For insance, he conrac for December 217 ransaced only hree unis on 19h June 29 (Figure 4). The prices of he nex hree monhs (second fron monh o fourh fron monh) in addiion o fron monh are aken as forward curve in his paper because prices of back monhs migh no be so reliable. This makes long-erm forecass of over a year o be virually ou of focus of he analysis. 3

4 Figure 4: Volume by conrac monh and cumulaive share (on 9h June 29) Volume (1, unis) Volume 37 Share in cumulaive volume /9 1/9 1/1 4/1 6/1 12/17 Conrac Monh Share in cumulaive volume (%) Source: NYMEX 2. Inquiry of usefulness of forward curve and Granger causaliy 2.1 Saionariy of oil prices For quaniaive analysis, he saionariy of oil prices should be considered iniially. The bigges problem in non-saionary cases is having a uni roo of characerisic equaion. AR(1) which has a uni roo is called random walk and i is known ha is bes forecas is he laes value. In oher words, if i is assumed ha oil price is random walk, immediaely we have a conclusion ha neiher he forward curve nor any informaion excep for he laes value is useful in forecasing is fuure value. I is hough ha generally, here is some srucure behind oil price and many people ry o forecas i by invesigaing he srucure. Then i is assumed ha oil price is saionary hereafer considering his siuaion, ec., alhough i migh no be suiable for quaniaive analysis Usefulness of forward curve and Granger causaliy Hereafer he usefulness of he forward curve in oil price forecas is analysed using Granger causaliy. Granger causaliy is used o deermine wheher using pas informaion of z, or, z 3, z 2, z 1, reduces predicion mean squared error, or PMSE of x. In oher words, wheher z is useful o forecas x on he average can be deermined from Granger causaliy. Granger causaliy is quie defined mahemaically and ha gives people an unnaural impression someimes comparing i wih he general undersanding of causaliy. The definiion, however, 2 Augmened Dickey-Fuller es did no rejec null hypohesis ha oil price is non-saionary even a 1% level of significance. This resul, however, does no mean oil price is judged o be non-saionary. 4

5 is very suiable for he inquiry of he usefulness of forward curve in oil price forecas. In Granger (Granger=Sargen) es, i is esed wheher v ˆ 2, PMSE of x a x 1 1 a 2 x 2 a p x p b1 z 1 b2 z 2 b p z p v is less han u ˆ 2, PMSE of x a x 1 1 a 2 x 2 a p x p u or no. If v ˆ 2 is less han u ˆ 2 significanly, z is said o Granger-cause x. 3. An empirical analysis 3.1 Usefulness of he forward curve in oil price forecas Here, wheher prices of he second, hird and fourh fron monh (hereafer F2, F3, F4 respecively) are useful in oil price forecas or no is analysed. Then F2, F3 and F4 are esed wheher hey Granger-cause he price of fron monh or no. Analysis was done for daily, weekly and monhly daa and vecor auoregressive (VAR) models were buil for each. Regression period is shown in Table 1. Table 1: Regression period Sar of period End of period Number of samples Daily 4 January 24 2 June 29 1,357 Weekly The fis week in The fifh week in 283 January 24 May 29 Monhly January 24 May The lag lengh of each model was chosen referring o he Akaike informaion crierion, or AIC; 5-lags for daily, 4-lags for weekly and 3-lags for monhly models. The summary of he models is shown in 5. Appendix: Summary of he models. Mos of monhly models are considered no reasonable judging by he sign of heir coefficiens, ec. Also weekly models wih boh F2 and F3 and wih all of F2, F3 and F4 are considered no reasonable 3. Aferwards, he Granger es was done using he models. The null hypohesis is ha price(s) of back monh(s) do no Granger-cause he price of fron monh. If his null hypohesis is rejeced, he price(s) of back monh(s) do Granger-cause oil prices and he usefulness of forward curve in oil price forecas is proven saisically. Resuls of he es are shown in Table 2. 3 Hereafer, heir resuls are shown bu ou of consideraion. 5

6 Null Hypohesis F2 does no Grangercause oil price. Table 2: Resuls of Granger es (P value) F3 does no... F4 does no... F2 and F3 do no... F3 and F4 do no... F2, F3 and F4 do no... Daily.3 ** **.9 **. ** Weekly.5 **.9 **.9 **.1 **.6 **.5 ** Monhly * Noe (1): **: Significan a 1% level, *: significan a 5% level. Noe (2): Srike-hrough shows he models are considered no reasonable. In eigh models, four daily models and four weekly models, he null hypoheses were rejeced. Therefore, i was shown ha he forward curve is useful in forecasing he daily and weekly oil prices in some cases. On he oher hand, as here were scarcely available reasonable models for he monhly basis, he usefulness of he forward curve in oil price forecas could no be deermined. 3.2 Effec of using he forward curve in he forecas Then o wha exen is he forward curve useful in forecas? Sandard errors, which show he accuracy of he forecass, are shown in Table 3. Table 3: Sandard errors Reference Wih F2 Wih F3 Wih F4 Wih F2 and F3 Wih F3 and F4 Wih F2, F3 and F4 Daily Weekly Monhly Noe: Srike-hrough shows he models are considered no reasonable. To ge he inuiive image, forecas errors for one period ahead a he beginning of each monh are shown as samples in Figure 5 and Figure 6. 6

7 Figure 5: Errors in forecas for one period ahead, daily, wih F2, F3 and F Wih F2, F3 and F4 Reference $/bbl /24 7/24 1/25 7/25 1/26 7/26 1/27 7/27 1/28 7/28 1/29 Figure 6: Errors in forecas for one period ahead, weekly, wih F $/bbl Wih F2 Reference -14 1/24 7/24 1/25 7/25 1/26 7/26 1/27 7/27 1/28 7/28 1/29 Like in he beginning of 29 in weekly forecas wih F2, we can see some cases in which forecas errors are fairly reduced. As a collecive impression, however, reducion of errors is limied compared wih he degree of forecas errors. Considering he resul in he previous secion, we have o say ha alhough he forward curve is saisically useful in forecasing oil price forecas, he effec in reducing forecas error is small. 3.3 Usefulness of he forward curve in forecas for furher period ahead So far, he usefulness of he forward curve in forecas for one period ahead is discussed. Then how furher is forward curve useful? Resuls of Granger ess are shown in Table 4 and Table 5. 7

8 Null hypohesis Table 4: Resuls of Granger es (P value), daily F2 does no Granger cause oil price. F3 does no... F4 does no... F2 and F3 do no... F3 and F4 do no... F2, F3 and F4 do no... Forecas for 1 period ahead.3 ** **.9 **. ** 2 periods.12 * **.3 **. ** 3 periods.29 * **. **. ** 4 periods.18 * **. **. ** 5 periods.26 * **. **. ** 6 periods.17 * **. **. ** 7 periods **. **. ** 8 periods **. **. ** Null hypohesis Table 5: Resuls of Granger es (P value), weekly F2 does no Granger cause oil price. F3 does no... F4 does no... F2 and F3 do no... F3 and F4 do no... F2, F3 and F4 do no... Forecas for 1 period ahead.5 **.9 **.9 **.1 **.6 **.5 ** 2 periods.5 **.16 *.16 *. **.1 **. ** 3 periods.13 * **. **. ** 4 periods.6 **.17 *.16 *. **. **. ** 5 periods.4 **.6 **.5 **. **. **. ** 6 periods.6 **.6 **.5 **. **. **. ** 7 periods *. **. **. ** 8 periods **. **. ** Noe (1): **: Significan a 1% level, *: significan a 5% level. Noe (2): Srike-hrough shows he models are considered no reasonable. The null hypohesises price(s) of back monh(s) do no Granger-cause oil price in forecas for 6 periods ahead in daily and 7 periods ahead in weekly prices were rejeced. However, if we see he forecas accuracy of he resul of he weekly models, he coefficien of deerminaion, or R 2, exceeds abou.9 by four period ahead. Considering comprehensively, i should be said ha he forward curve is useful for one week ahead and for one monh ahead in daily forecas and weekly forecas, respecively. To see he effec by using he forward curve in oil price forecas, forecas errors a he beginning of each monh are shown in Figure 7 and Figure 8. 8

9 Figure 7: Errors in forecas for five periods ahead, daily, wih F $/bbl Wih F2 Reference -1 1/24 7/24 1/25 7/25 1/26 7/26 1/27 7/27 1/28 7/28 1/29 Figure 8: Errors in forecas for four periods ahead, weekly, wih F $/bbl Wih F2 Reference -2 1/24 7/24 1/25 7/25 1/26 7/26 1/27 7/27 1/28 7/28 1/29 In boh resuls, he collecive endency is no so much differen from forecas for one period ahead. The effec of using he forward curve is limied compared wih he degree of forecas errors. 4. In closing When people analyse oil prices, he forward curve is ofen referred o as i reflecs average view of he fuure prices among marke paricipans. Alhough he usefulness of he forward curve in forecasing oil prices is confirmed in daily and weekly bases, he effec in reducing forecas error is small. Addiionally, he forward curve is acually useful for one week ahead and for one monh ahead in daily forecas and weekly forecas, respecively. However, he forward 9

10 curve is scarcely useful in long-erm forecass. The reasons why he forward curve is useful only in shor-erm forecas and is effec is limied are he following: No informaion on unexpeced evens in he fuure is considered, The forecas of prices ends o be inaccurae because he equilibrium price is a cross of wo uncerainness, namely supply and demand, and The price inelasic supply and demand curve of oil leads o huge flucuaion of prices even wih sligh changes in supply and/or demand. Addiionally as he naure of he forecas iself, he following hings could be lised. In forecass, people end o sick o pas rends and pas forecass, In forecass, here is Keynesian beauy cones effec, and Correcion of forecass is generally done slowly. This ime, he prices of back monhs were included in he models direcly. However, his leads o risks of muli-correlaion if we hink abou he naure of daa. To capure informaion provided by he forward curve beer, he applicaion of principal componen analysis before building VAR models should be considered. 1

11 5. Appendix: Summary of he models Exogenous variables Table 6: Summary of he daily models (Equaions of price of fron monh) Equaions (Endogenous variables) F1 F1, F2 F1, F3 F1, F4 F1, F2, F3 F1, F3, F4 F1, F2, F3, F4 F1(-1) (33.82) (7.83) (9.585) (11.145) (3.346) (7.99) (3.2) F1(-2) (.85) (.928) (.48) (.377) (.755) (.33) (.676) F1(-3) (1.842) (2.55) (1.817) (1.513) (3.195) (1.9) (3.93) F1(-4) (1.11) (1.673) (1.389) (1.293) (1.83) (1.287) (1.676) F1(-5) (-2.195) (-3.753) (-3.9) (-2.641) (-5.247) (-3.918) (-5.27) F2(-1) (2.21) (5.27) (5.15) F2(-2) (-.669) (-1.969) (-1.913) F2(-3) (-2.98) (-1.76) (-1.55) F2(-4) (-1.366) (-.645) (-.513) F2(-5) (3.34) (3.41) (3.188) F3(-1) (.899) (-4.78) (2.95) (-3.283) F3(-2) (-.26) (2.36) (-.289) (1.651) F3(-3) (-1.293) (1.24) (-1.498) (.738) F3(-4) (-1.67) (.368) (-.223) (.124) F3(-5) (2.474) (-2.424) (2.46) (-1.651) F4(-1) (.499) (-1.836) (.628) F4(-2) (-.81) (.311) (-.295) F4(-3) (-.921) (1.177) (.193) F4(-4) (-.95) (-.88) (.185) F4(-5) (2.39) (-1.72) (.289) Consan (1.779) (1.351) (1.61) (1.743) (1.27) (.561) (1.269) R Noe (1): F1, F2, F3 and F4 refer price of fron monh, he second fron monh, he hird fron monh and he fourh fron monh respecively. Noe (2): F1(-1) refers price of F1 in he previous erm. Noe (3): Number in parenheses refers value. 11

12 Exogenous variables Table 7: Summary of he weekly models (Equaions of price of fron monh) Equaions (Endogenous variables) F1 F1, F2 F1, F3 F1, F4 F1, F2, F3 F1, F3, F4 F1, F2, F3, F4 F1(-1) (19.519) (4.989) (6.61) (7.39) (1.646) (3.454) (1.393) F1(-2) (-.979) (-2.782) (-2.491) (-2.32) (-3.57) (-2.722) (-2.997) F1(-3) (-.48) (-1.335) (-1.356) (-1.46) (-.947) (-.654) (-1.155) F1(-4) (-1.453) (2.842) (2.593) (2.535) (.91) (.73) (.867) F2(-1) (-1.382) (1.39) (1.118) F2(-2) (2.715) (1.696) (1.431) F2(-3) (1.9) (-.94) (.64) F2(-4) (-3.114) (.9) (-.61) F3(-1) (-1.514) (-1.242) (.224) (-.798) F3(-2) (2.431) (-.94) (1.367) (-.455) F3(-3) (1.82) (.491) (-.665) (-.729) F3(-4) (-3.7) (-.67) (.56) (.952) F4(-1) (-1.51) (-.325) (.462) F4(-2) (2.261) (-1.52) (.159) F4(-3) (1.123) (.848) (.87) F4(-4) (-3.3) (-.853) (-1.259) Consan (1.931) (1.635) (1.833) (1.938) (.838) (.653) (1.45) R Noe (1): F1, F2, F3 and F4 refer price of fron monh, he second fron monh, he hird fron monh and he fourh fron monh respecively. Noe (2): F1(-1) refers price of F1 in he previous erm. Noe (3): Number in parenheses refers value. 12

13 Table 8: Summary of he monhly models (Equaions of price of fron monh) Exogenous variables Equaions (Endogenous variables) F1 F1, F2 F1, F3 F1, F4 F1, F2, F3 F1, F3, F4 F1, F2, F3, F4 F1(-1) (1.87) (-1.15) (-.159) (.315) (-2.974) (-1.895) (-2.917) F1(-2) (-.982) (1.75) (1.56) (1.417) (-.77) (.871) (-.411) F1(-3) (-1.962) (-1.38) (-1.36) (-1.426) (-1.355) (-1.42) (-1.178) F2(-1) (2.159) (2.854) (2.31) F2(-2) (-1.825) (.984) (.831) F2(-3) (1.111) (.34) (.324) F3(-1) (1.913) (-2.355) (1.948) (-1.4) F3(-2) (-1.7) (-1.444) (.176) (-.474) F3(-3) (1.72) (.346) (.297) (-.86) F4(-1) (1.89) (-1.68) (.893) F4(-2) (-1.656) (-.444) (-.8) F4(-3) (1.86) (.29) (.154) Consan (2.917) (2.171) (2.321) (2.411) (.14) (.146) (.362) R Noe (1): F1, F2, F3 and F4 refer price of fron monh, he second fron monh, he hird fron monh and he fourh fron monh respecively. Noe (2): F1(-1) refers price of F1 in he previous erm. Noe (3): Number in parenheses refers value. References Taku Yamamoo (1988), `Time-series Analysis of Economy, Sobunsha Publishing. Conac: repor@ky.ieej.or.jp 13