Effectiveness of Oil Futures Contracts for Hedging International Crude Oil Prices

Effectiveness of Oil Futures Contracts for Hedging International Crude Oil Prices Amir H. Alizadeh, Sharon Lin and Nikos Nomikos Faculty of Finance C...
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Effectiveness of Oil Futures Contracts for Hedging International Crude Oil Prices

Amir H. Alizadeh, Sharon Lin and Nikos Nomikos Faculty of Finance Cass Business School, City University 106 Bunhill Row London EC1Y 8TZ, UK. Emails: A.Alizadeh @city.ac.uk, [email protected] [email protected]

Abstract This paper examines the effectiveness of hedging different international crude oil price fluctuations using crude oil futures contracts traded at the New York Mercantile Exchange (NYMEX) and the International Petroleum Exchange (IPE) in London using a multivariate error correction model with a GARCH error structure. Using both constant and dynamic hedge ratios over the period October 1993 to April 2003, it is found that in and out-of-sample hedging effectiveness are different across different crude markets. In general, the most effective futures contract to hedge physical crude oil prices is found to be the IPE Brent crude oil futures contract with variance reductions varying between 44.41% and 79.47% in sample and 32.13% and 90.99% out-of-sample. Differences in hedging effectiveness between physical crude prices are attributed to quality, grade and delivery locations of the oil as well as how each type of crude is priced in the market. Results have important implications in terms of choice of instrument for risk management strategies of crude oil traders, refineries and oil producers.

Keywords: Hedging, International Crude oil, oil futures, VECM, GARCH.

1. INTRODUCTION Crude oil is without doubt the most important physical commodity as it provides energy for all kinds of human activity. The primary crude oil distillates, gasoline, aviation fuel, heating oil and fuel oil are indispensable for transportation, industrial and residential uses. As a result, it is not surprising that crude oil is the world's most actively traded commodity. It is also for that reason that issues regarding crude oil risk management are of great importance. Traditionally, oil prices were determined through long-term contracts. From the 1970’s onwards and primarily after the first oil shock, oil prices became more volatile. Nowadays there are primarily two major markets which act as benchmarks for the pricing of crude oil and its refined products on an international basis: the West Texas Intermediate (WTI) in the United States and the Brent Blend in London. These are the major “marker” crudes that set the pace in international prices which are quoted on the basis of a premium or discount on these marker prices. These premia or discounts reflect the quality characteristics of the different crude types as well as regional and global supply and demand conditions. The major marker crudes are also used as the underlying assets of futures contracts traded at organised exchanges. More specifically, WTI is the base grade for the “light sweet crude”, on the New York Mercantile Exchange (NYMEX) and Brent is the basis for the Brent contract at London’s International Petroleum Exchange (IPE). The main body of literature on physical and derivatives oil markets concentrates on issues such as price discovery and market interrelationships. For example, the issue of price discovery and efficiency has been investigated by Crowder and Hamed (1993) who find that WTI futures are unbiased forecasts of the realised spot prices. Other studies investigate the causal relationship between oil spot and futures prices. For example, Silvapulle and Moosa (1999) report that oil spot and futures prices react simultaneously to the arrival of new information to the market. A number of studies also investigate linkages between physical and futures crude oil markets in different geographical locations. For instance, Ewing and Harter (2000) provide evidence that Brent blend and Alaska North Slope crude oil prices move together over time and react similarly to shocks in the world oil market. Similarly, Lin and Tamvakis (2001) investigate the information transmission mechanism between WTI and Brent futures and find that there are price and volatility spillovers between the two markets

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with the WTI market being the dominant in terms of information discovery. The findings of these studies indicate that oil markets around the world are linked and prices move together over time. The relationship between Brent and WTI has also been investigated by Milonas and Henker (2001). They model the Brent and WTI futures spread as a function of the convenience yields of the two contracts. They use convenience yields as surrogates for supply and demand conditions in the two markets and find that they can explain the variation in the inter-crude spread. This also indicates that regional supply and demand imbalances are an important factor in determining oil futures prices. In this study, we investigate the effectiveness of cross hedging the most widely traded crudes across major supply and demand areas. In particular, we assess the hedging effectiveness of the IPE Brent and NYMEX WTI contracts on Brent, WTI, Bonny, OPEC Basket, Arabian Light, Iranian Light, Ural and Tapis. Arab Light and Iranian Light are exported crudes from the Middle East. OPEC Basket is the index price based on crude oil varieties from OPEC countries. Ural and Brent are major crudes in Europe while Tapis and WTI are major crudes for South East Asia and North America respectively. Examination of the cross-sectional variability of hedge ratios and measures of hedging effectiveness across the different types of crude is of considerable interest to participants in the crude oil market since they can benefit from using optimal hedge ratios that minimise their freight rate risk. This study then, by investigating the hedging effectiveness of crude oil futures contract, sheds some light to these important issues. We model the spot and futures returns as a vector error correction model (VECM) (Engle and Granger, 1987 and Johansen, 1988) with a GARCH error structure (Bollerslev, 1986). The VECM models the long-run relationship between spot and futures prices and the GARCH error structure permits the second moments of their joint distribution to change over time; the time-varying hedge ratios are then calculated from the estimated covariance matrix of the model. The structure of this paper is as follows; the next section presents an overview of the literature in futures hedging; Section 3 describes the minimum-variance hedge ratio methodology and section 4 illustrates the empirical model that is used in this study; Section 5 presents the statistical properties of the data and section 6 offers empirical results and evaluates the hedging effectiveness of the proposed strategies. Finally, section 7 concludes this study.

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2. LITERATURE REVIEW Earlier studies in the literature (see for e.g. Johnson, 1960; Stein, 1961 and Ederington, 1979) derive hedge ratios that minimise the variance of returns on the hedged portfolio based on the principles of portfolio theory. Let ∆St and ∆Ft represent changes in spot and futures prices between period t and t-1. Then the variance-minimising hedge ratio is the ratio of the unconditional covariance between cash and futures price changes to the variance of futures price changes; this is equivalent to the slope coefficient, γ*, in the following regression ∆St = γ0 + γ*∆Ft + ut ;

ut ∼ iid(0, σ2)

(1)

Within this specification, the higher the R2 of equation (1) the greater the effectiveness of the minimum-variance hedge. Examples of empirical studies involved in estimating minimum risk hedge ratios and measures of hedging effectiveness include: for T-bill futures, Ederington (1979) and Franckle (1980); for oil futures, Chen et al. (1987); for stock indices, Figlewski (1984) and Lindahl (1992); for currencies, Grammatikos and Saunders (1983). The major conclusion of these studies is that commodity and financial futures contracts perform well as hedging vehicles with R2’s ranging from 80% to 99%. This method of calculating hedge ratios is demonstrated by Myers and Thompson (1989) and Kroner and Sultan (1993) to be lacking in several respects. The first objection is related to the implicit assumption in equation (1) that the risk in spot and futures markets is constant over time. This assumption contrasts sharply with the fact that many asset prices are characterised by time-varying distributions which implies that optimal, risk-minimising hedge ratios should be time-varying. A second problem is that equation (1) is potentially mispecified because it ignores the existence of a long-run cointegrating relationship between spot and futures prices (Engle and Granger, 1987). These issues raise concerns regarding the risk reduction properties of the hedge ratios generated from equation (1). These problems have been addressed in several commodity and financial futures markets (see e.g. Kroner and Sultan, 1993 and Gagnon and Lypny, 1995 and 1997) but there is no evidence, as yet, from energy futures markets.

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Given the relative absence of research in this market, this paper aims to fill this gap in the literature. The cointegration relationship between crude oil prices and IPE and NYMEX futures is used to model the spot and futures returns as a vector error correction model (VECM) (Engle and Granger, 1987 and Johansen, 1988) with a multivariate generalised autoregressive conditional heteroscedasticity error structure (GARCH) (Baba et al. 1987). This framework meets the earlier criticisms of possible model misspecifications and time varying γt∗ since the VECM models the long-run relationship between spot and futures prices and the multivariate GARCH error structure permits the second moments of their joint distribution to change over time. The time-varying hedge ratios are then calculated from the estimated covariance matrix of the model.

3. HEDGING AND TIME-VARYING HEDGE RATIOS Market participants in futures markets choose a hedging strategy that reflects their individual goals and attitudes towards risk. In particular, consider the case of an oil refinery that wants to secure its exposure to crude oil price fluctuations. The return on the refinery's portfolio of spot and futures crude oil positions can be denoted by:

RH,t = RS,t - γtRF,t

(2)

where RH,t is the return on holding the portfolio between t-1 and t; RS,t is the return on holding the spot position between t-1 and t; RF,t is the return on holding the futures position between t-1 and t; and γt is the hedge ratio, i.e. the number of futures contracts that the hedger must sell for each unit of spot commodity on which he bears price risk. The variance of the returns of the hedged portfolio, conditional on the information set available at time t-1, is given by

Var(RH,t | Ωt-1 ) = Var(RS,t | Ωt-1) – 2 γt Cov(RS,t,RF,t | Ωt-1) + γ 2t Var(RF,t | Ωt-1)

(3)

where Var(RS,t|Ωt-1), Var(RF,t|Ωt-1) and Cov(RS,t,RF,t |Ωt-1) are, respectively, the conditional variances and covariance of the spot and futures returns. The optimal hedge ratio is defined

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as the value of γt which minimises the conditional variance of the hedged portfolio returns i.e., min [Var(RH,t|Ωt-1)]. Taking the partial derivative of equation (3) with respect to γt, γt

setting it equal to zero and solving for γt, yields the optimal hedge ratio conditional on the information available at t-1, as follows (see e.g. Baillie and Myers, 1991)

γ t* | Ω t −1 =

Cov( RS,t , RF,t |Ω t -1 ) Var(R F,t |Ω t -1 )

=

Cov(∆S t , ∆Ft |Ω t -1 ) Var(∆Ft |Ω t -1 )

(4)

where returns are defined as the logarithmic differences of spot and futures prices. The conditional minimum-variance hedge ratio of equation (4) is the ratio of the conditional covariance of spot and futures price changes over the conditional variance of futures price changes.1 Moreover, the conditional hedge ratio nests the conventional hedge ratio, γ* of equation (4); if we replace the conditional moments in equation (4) by their unconditional counterparts then we get the conventional hedge ratio. Because the conditional moments can change as new information arrives in the market and the information set is updated, timevarying hedge ratios may provide superior risk reduction compared to static hedges. Whether this is the case in the oil futures market is a matter of empirical investigation.

4. TIME-VARYING HEDGE RATIOS AND ARCH MODELS To estimate γt* in equation (4), the conditional second moments of spot and futures prices are measured using the family of ARCH models, introduced by Engle (1982). For this purpose, we employ a VECM model for the conditional means of spot and futures returns with a multivariate GARCH error structure. The error correction part of the model is necessary because spot and futures prices share a common stochastic trend, and the multivariate GARCH error structure permits the variances and the covariance of the price series to be

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It can be shown that, provided expected returns to holding futures contracts are zero, the minimum-variance hedge ratio of equation (4) is equivalent to the utility-maximising hedge ratio. A proof of this result is available in Benninga et al. (1984) and Kroner and Sultan (1993).

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time-varying. Therefore, the conditional means of spot and futures returns are specified using the following VECM

∆Xt = µ +

⎛ ε S, t ⎞ ⎟ |Ωt-1 ∼ IN(0,Ht) ; εt = ⎜⎜ ⎟ ⎝ ε F,t ⎠

p−1

∑ Γi∆Xt-i + ΠXt-1 + εt i =1

(5)

where Xt = (St Ft)′ is the vector of spot and futures prices, Γi and Π are 2x2 coefficient matrices measuring the short- and long-run adjustment of the system to changes in Xt and εt is the vector of residuals (εS,t εF,t)′ which follow a multivariate normal conditional distribution with mean zero and time-varying covariance matrix, Ht. The existence of a long-run relationship between spot and futures prices is investigated in the VECM of equation (5) through the λmax and λtrace statistics (Johansen, 1988) which test for the rank of Π 2. If rank (Π)=1, then there is a single cointegrating vector and Π can be factored as Π = αβ′, where α and β′ are (2x1) vectors. Using this factorisation, β′ represents the vector of cointegrating parameters and α is the vector of error correction coefficients measuring the speed of convergence to the long run steady state. The significance of incorporating the cointegrating relationship into the statistical modelling of spot and futures prices is emphasised in studies such as Kroner and Sultan (1993), Ghosh (1993), Chou et al. (1996) and Lien (1996); hedge ratios and measures of hedging performance may change sharply when this relationship is unduly ignored from the model specification. The conditional second moments of spot and futures returns are specified as a GARCH(1,1) model (Bolleslev, 1986) using the following augmented Baba et al. (1987) (henceforth, BEKK) representation (see Engle and Kroner, 1995):

H t = A' A+ Β' H t -1 Β+ Γ' ε t −1 ε ′t −1 Γ

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(6)

The Johansen (1988) procedure provides more efficient estimates of the cointegrating vector compared to the Engle and Granger (1987) two step approach (see Gonzalo, 1994). Moreover, Johansen’s tests are shown to be fairly robust to the presence of non-normal innovations (Cheung and Lai, 1993) and heteroskedastic disturbances (Lee and Tse, 1996); this is particularly important since spot and futures prices in this study share these characteristics (see the next section for a discussion on this).

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where A is a 2x2 lower triangular matrix, B and Γ are 2x2 full parameterised coefficient matrices 3. In this representation, the conditional variances are a function of their own lagged values and their own lagged error terms, while the conditional covariance is a function of lagged covariances and lagged cross products of the εt′s. Moreover, this formulation guarantees Ht to be positive definite almost surely for all t and, in contrast to the constant correlation model of Bolleslev (1990), it allows the conditional covariance of spot and futures returns to change signs over time.4 Preliminary evidence on our data set with the conditional normal distribution reveals substantial excess kurtosis in the estimated standardised residuals even after accounting for second moment dependencies. As demonstrated in Bollerslev and Wooldridge (1992), this invalidates traditional inference procedures. Therefore, they suggest using Quasi-Maximum Likelihood (QML) estimation, which yields an asymptotically consistent covariance matrix.

5. DATA DESCRIPTION AND CRUDE OIL PRICES We investigate the cross hedging performance of major international crude prices such as Iranian Light, African Bonny, Arab Light, Russian Ural, OPEC Basket, Malaysian Tapis, WTI Cushing and Brent Physical, against two crude oil futures contracts, namely IPE Brent and NYMEX WTI. Weekly crude oil physical prices are downloaded from Datastream for the period 20 October 1993 to 30 April 2003. While Brent, WTI, Bonny, Ural and Tapis are mostly traded in spot markets, Iranian Light and Arab Light have limited spot trades and are primarily traded on long-term basis. They are sold by the concept of “term contract” and the pricing formula is “marker price” (in this case, Brent spot) plus “DFL” (Dated for Front Line”, a term used to reflect crude oil grade differential and demand-supply differentials for different calendar periods. African Bonny and Russian Ural, two major exported crudes are also priced as differentials to Brent spot, while Malaysian Tapis is light sweet crude in South

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Although coefficient matrices B and Γ can be restricted to be diagonal for a more parsimonious representation of the conditional variance (see as well Bollerslev et al., 1994), we use a full parameterisation form in order to be able to investigate any volatility spillover effects. Moreover, a GARCH(1,1) model is used because of the substantial empirical evidence that this model adequately characterises the dynamics in the second moments of spot and futures prices; see Kroner and Sultan (1993), Gagnon and Lypny (1995, 1997), Tong (1996) and Bera et al. (1997) for evidence on this. 4 For a discussion of the properties of this model and alternative multivariate representations of the conditional covariance matrix see Bollerslev et al. (1994) and Engle and Kroner (1995).

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East Asia which is used as a Marker for other Asian and Australian crudes and is not directly priced against the Brent. We also use two widely traded crude oil futures contracts in the International Petroleum Exchange (IPE) and the New York Mercantile Exchange (NYMEX). The underlying crude for futures contracts traded in the IPE is Brent (BFO since 2001) deliverable in Sullom Vue (North Sea), while the underlying crude for NYMEX futures contract is WTI crude deliverable in Cushing Oklahoma. IPE crude oil futures contracts are traded for all the deliveries within the next 12 consecutive months, then quarterly up to a maximum twenty-four months and then half yearly up to a maximum thirty-six months. Each contract is traded until the close of business on the third business day prior to the 15th calendar day of the month preceding the delivery month. If the 15th calendar day of the month is a non-business day, trading shall cease at the close of business on the business day immediately preceding the 15 day prior to the first day of the delivery month if such fifteenth day is a banking day in London. If the fifteenth day is a nonbanking day in London (including Saturday), trading shall cease on the business day immediately preceding the next business day prior to the fifteenth day. Open outcry trading takes place daily at IPE from 10:02 GMT until 19:30 GMT, while the electronic trading takes place from 02:00 GMT to 22:00 GMT. NYMEX futures contracts are traded for all the deliveries within the next 30 consecutive months as well as for specific long-dated deliveries such as 36, 48, 60, 72 and 84 months from delivery. Each contract is traded until the close of business on the third business day prior to the 25th calendar day of the month preceding the delivery month. If the 25th calendar day of the month is a non-business day, trading shall cease on the third business day prior to the last business day preceding the 25th calendar day. For instance, the last trading day for the June 2001 futures contract is 22 May 2001 (i.e. 3 working days before the 25th of May). Open outcry trading takes place daily at NYMEX from 10:00 NY time (15:00 GMT) until 14:30 NY time (19:30 GMT). IPE and NYMEX crude oil futures prices are for the contract which is closer to maturity until five working days before the expiration of the contract in which case we switch to the next available month. The choice of the nearest contract to maturity is motivated by the fact that is

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invariably characterised by large volume and liquidity. Additionally, there is evidence that trading volume declines significantly during the last 5 trading days of a WTI contract as traders close or roll over their positions to next month (see Lin and Tamvakis, 2001)

Figure 1 presents the historical values of a number of physical crudes along with WTI and IPE futures over the period October 1993 to April 2003. Two observations can be made here. First it can be seen that prices of physical and derivative crude oil move close together in a way that they seem to be almost identical. Second, although the price series move together in the long run there are short term deviations between the physical and derivative prices which are mainly due to regional short-term supply and demand imbalances as well as quality differentials between the different crudes. Descriptive statistics of the international crude oil prices, and the two crude oil futures contracts under investigation are reported in Table 1. It can be seen that all weekly price changes are negatively skewed and have excess kurtosis (leptokurtic); that is a common characteristic of returns on financial assets. These results are also confirmed by Jarque-Bera (1980) normality tests, which indicate significant deviations from normality. Furthermore, the unconditional volatility of crude oil price changes, measured by the standard deviation, varies from 3.6% for Tapis to 5.8% for Ural. In general, it seems that futures returns are less volatile compared to those of physical crudes, with the exception of Tapis and OPEC. The reason for the latter is because OPEC crude is a basket and is expected to be smoother, while Tapis is a sweet crude which is priced independently from Brent or WTI and sold in the Far East. Ljung-Box (1978) portmanteu tests for 6th order autocorrelation in the series reveal that there is no serial autocorrelation in the return series. Also, Engle’s (1982) tests for 6th order ARCH effects indicate that 6 out of 10 return series show significant conditional heteroscedasticity. The exceptions are OPEC basket, WTI physical and the two futures contracts. Finally, Phillips and Perron (1988) unit root tests reveal that both physical and futures crude oil prices in all markets are nonstationary, I(1) variables, while their first differences are stationary, I(0). According to the previous discussion on the use of nonstationary series, our findings here imply that VECM-GARCH models could be used to model the mean of spot and futures prices, provided that they are cointegrated.

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To investigate which futures contracts, IPE Brent or NYMEX WTI, are potential candidates as hedging instruments for international crude prices, the strength of co-movements between these crude oil prices and crude futures in NYMEX and IPE is examined through correlation analysis of log differences (returns). Reported results in Table 2 indicate that correlation coefficients between crude oil price changes and returns on crude futures contracts vary significantly from 56.5% between Arab Light and NYMEX futures to 93.1% and 89.3% between WTI Cushing and NYMEX futures, and dated Brent and IPE futures, respectively. This is expected since WTI and dated Brent are underlying crudes for NYMEX and IPE futures respectively, whereas, Arab Light and Tapis are locally priced crudes which are not directly related to Brent or WTI. Correlation between other crudes and futures contracts are reasonably high, indicating the potential of using crude futures contract for hedging international physical crude prices. This is because the degree of correlation between returns in the spot and futures can be regarded as the hedging effectiveness of the futures instrument in reducing the variance of the portfolio of spot and futures contracts, when a constant hedge ratio is used. For example, the correlation coefficient of 87.2% between African Bonny and IPE crude futures indicates a 76% (=0.8722) reduction in the variance of the portfolio of Bonny and IPE futures compared to the variance of the unhedged portfolio.

6. ESTIMATION RESULTS Having identified that physical and futures crude oil prices are I(1) variables, cointegration techniques are used next to examine the existence of a long-run relationship between these series. The lag length (p) in the VECM of equation (5), chosen on the basis of SBIC (Schwarz, 1978), is presented in Table 3 for physical crude prices against the two crude futures contracts5. The estimated λmax and λtrace statistics show that all physical crude prices stand in a long-run relationship with each of the crude futures contracts, thus justifying the use of a VECM in modelling physical and futures prices in a multivariate framework. The normalised coefficient estimates of the cointegrating vector, i.e. β′=(1 β1 β2) in the same table, represent the long-run relationship between spot and futures prices. The last column of Table 3 reports the results of likelihood ratio tests on the hypothesis that physical and futures

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This refers to the lag length of an unrestricted VAR in levels as follows; Xt =A0+AiXt-1+A2Xt-2+ … +ApXt-p+ εt. A VAR with p lags of the dependent variable can be re-parameterised in a VECM with p-1 lags of first differences of the dependent variable plus the levels terms.

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prices stand in a one-to-one relationship; that is, the cointegrating vector is the lagged basis (the difference between log of physical and futures prices). It can be seen that, the hypothesis has been rejected at the 5% significance level in all cases with the exception of Bonny-IPE Brent, Brent-IPE Brent, and Tapis-NYMEX WTI. The same hypothesis is valid for WTI Cushing-NYMEX WTI at the 1% significant level. The rejection of the hypothesis is because, in this study, the underlying assets for futures contracts are different form the asset in the spot market and as a result price differences may not converge to represent the basis. Therefore, we use the unrestricted cointegrating vectors in the joint estimation of the conditional mean and the conditional variance. The results of VECM-GARCH are presented in Table 4 and Table 5 for physical crudes and IPE Brent futures, and Physical crudes and NYMEX WTI futures, respectively. The diagnostic tests for each VECM-GARCH model are also presented at the lower panels of Tables 4 and 5. Tests on the standardised residuals, εt/ h t , and standardised squared residuals, ε 2t /ht, indicate that the selected models are well specified and there are no signs of autocorrelation or ARCH effects. Sign- and size-biased tests for asymmetric impact of news on volatilities based on Engle and Ng (1993) reject any form of leverage effect on volatility due to shocks with different sign and/or size. Several observations merit attention. First, in most cases, the speed of adjustment of spot and futures prices to their long-run relationship, measured by the αj, (j = Spot, Futures) estimated coefficients, are negative and significant in the equation for the spot prices while, in the futures equation they are insignificant. This implies that in response to a positive deviation from their long-run relationship at period t-1, i.e. St-1 > Ft-1, the spot price in the next period will decrease in value while the futures price will remain unresponsive and suggests that petroleum futures are weakly exogenous to spot bunker prices. This is because prices for futures petroleum contracts are determined by supply and demand in the oil market. The exception to the above is model for OPEC basket price where the results indicate that both IPE and NYMEX futures adjust to any disequilibrium in the next period, while spot prices do not adjust. This observation is important as it indicates the significance of changes in OPEC basket prices to the world oil market.

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Second, the degree of persistence of volatility of spot prices measured as β ii2 + γ ii2 is higher than degree of persistence of futures market volatility. In other words, volatility of spot prices for international crude oils seems to be more persistent than crude oil futures prices. This is also expected as futures prices tend to respond faster to news in the market than prices for physical crude and consequently may absorb shock faster than spot prices. Finally, since we use the fully parameterised BEKK specification, we allow for both variances and covariances (correlations) between spot and futures returns to be time-varying. Such specification is found to be superior in terms of log-likelihood to the diagonal BEKK specification. Furthermore, significance of some of the off diagonal elements in Β and Γ matrices indicate that there may be some spillover and feedback effects between spot and futures price volatilities.6 For example, in cases where IPE Brent futures are used as hedging instrument (Table 4), we observe that γ21 is significant in African Bonny, Dated Brent, Iranian Light, Russian Ural and WTI Cushing models. This in turn indicates that futures market volatility is transmitted to spot market for these international crude oils. The results of volatility spill over effects seem to be opposite when NYMEX futures is used in bivariate VECM-GARCH models as in most cases γ12 is found to be significant which indicates that spot market volatility affects volatility of NYMEX futures prices.

6.1.

In-sample comparisons of hedging effectiveness

Following estimation of the VECM-GARCH models, measures of the time-varying variances and covariances are extracted and used to compute the time-varying hedge ratios of equation (4). Figure 2 plots constant and time-varying hedge ratios for African Bonny price and IPE crude futures during the estimation period. The variation in the hedge ratio indicates that the portfolio of spot and futures contracts (hedge ratios) must be revised frequently, in order to achieve optimum hedging performance. To formally compare the performance of each type of hedge, portfolios implied by the computed hedge ratios each week are constructed and the variance of the returns of these portfolios over the sample are calculated. In mathematical form, we evaluate: 6

For instance, significance of γ21 indicates the volatility spill over from futures to spot prices, while γ12 measures the spill over from spot to futures prices.

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Var(∆St - γ *t ∆Ft)

(7)

where γ*t are the computed hedge ratios. For each physical crude, we consider 4 different hedge ratios; the hedge ratios from the VECM-GARCH model of equation (5), the OLS hedge of equation (1), the hedge ratio generated from a VECM with constant variances and a naive hedge by taking a futures position which exactly offsets the spot position (i.e. setting γ *t = 1). The variance of the hedged portfolios is then compared to the variance of the unhedged position, i.e. Var(∆St). The larger the reduction in the unhedged variance, the higher the degree of hedging effectiveness. The hedged portfolio variance results using IPE Brent and NYMEX WTI futures for the period 20 October 1993 to 24 April 2002 are presented in panels A and B of Table 6, respectively. The same table also presents the incremental variance improvement of the VECM-GARCH hedge ratio relative to the other models. It can be seen that, in all cases, hedging based on the VECM-GARCH models outperforms all the other hedges considered as indicated by the positive variance improvement figures of time-varying hedge ratios over competing model (conventional and VECM). Comparisons of IPE Brent hedging effectiveness against physical crudes reveals a variance reduction of 77.33%, 78.76%, 75.88%, 79.47% and 73.35% for African Bonny, Brent, Iranian Light, OPEC Basket, and Russian Ural, respectively. In contrast, the hedging effectiveness for Arab Light and Asian Tapis is only 47.60% and 44.41%, respectively. This is expected, as both these crudes are locally priced with no direct link to Brent prices. The hedging results when NYMEX crude futures are used are qualitatively similar. VECM-GARCH hedge ratios outperform alternative strategies in all cases and the maximum variance reduction is achieved in the case of WTI Cushing physical. Again, hedging effectiveness is consistently above 60% for all crudes with the exception of Arab Light and Asian Tapis where hedging effectiveness is only 38.70% and 45.33%, respectively. Overall, IPE crude oil futures seem to provide better portfolio variance reduction compared to NYMEX crude futures for all physical crudes with the exception of WTI Cushing and Tapis; on average, IPE Brent outperforms NYMEX in terms of variance reduction by around 6%. This result can be attributed to the fact that most of the crudes considered in this study are priced against Brent and, as a result, they share more common characteristics with IPE Brent than NYMEX WTI.

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6.2.

Out-of-sample comparison of hedging effectiveness

As hedgers are more concerned with how well they can do in the future using alternative hedging strategies, out-of-sample performance might be a more realistic way to evaluate the effectiveness of the estimated hedge ratios. For that, we use the last 52 observations of the sample (or after 1 May 2002, representing a period of one year) and estimate the conditional model using only the data up to this date. Then, we perform one-step ahead forecasts of the covariance, E(hSF,t+1 |Ωt), and the variance of the futures returns, E(hFF,t+1|Ωt) which are used to estimate the one-step-ahead hedge ratios, similar to equation (4), as follows E(γ*t+1 |Ωt) = E(hSF,t+1 |Ωt)/ E(hFF,t+1|Ωt)

(8)

The following week (8 May 2002), this exercise is repeated, with the new observation included in the estimation period. The data set is continuously updated and models are estimated to obtain forecasts for the hedge ratios until the end of our data set (30 April 2003). The results of the out-of-sample hedging effectiveness using IPE and NYMEX futures contracts are presented in panels A and B of Table 7, respectively. Overall, out-of-sample hedging results seem to be better than in sample results. For example, with the exception of Arab Light and Asian Tapis, out of sample variance reductions vary between 79.58% and 90.99% when IPE crude futures is used and between 73.55% and 87.57% when NYMEX crude futures is used. As expected, the best results are achieved when hedging Physical Brent using IPE futures and when hedging WTI Cushing using NYMEX futures, i.e. when the crude to be hedged is the underlying asset of the futures contract. The variability of the degree of hedging effectiveness across the different international crudes, reflects the fact that the performance of cross hedging commodity prices depends on the closeness of the underlying commodity in a futures market with the commodity to be hedged. For example, Graff et al (1998) consider the seasonal hedging effectiveness of different agricultural commodity futures for those commodities with no futures contracts in a number of geographical locations across the US. They report that when Feeder Steers prices are hedged against Feeder Cattle futures the seasonal hedging effectiveness is above 90%. However, the effectiveness of hedging Millfeed using corn futures is reported to range

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between 17% to 61%. In fact their results suggest that the greater the degree of substitution between the underlying commodity in the futures market and the commodity in the cash market, the higher is the effectiveness of the hedging practice as the two prices move close together over time resulting in higher correlations. Similarly, Kavussanos and Nomikos (2000) find that freight rate risk is reduced more effectively in those shipping routes which are more heavily represented in the freight futures index contract. Furthermore, Wilson (1989) finds that the effectiveness of soybean, soybean meal and soybean oil futures in reducing the price risk of spot sunflower prices ranges between 9% and 46%. Finally, Alizadeh et al. (2004) find that hedging fuel oil prices using IPE and NYMEX crude and product contracts does not achieve high percentage variance reduction due to local conditions in demand and supply in local fuel oil markets and create differences in the prevailing basis between spot and futures prices. However, in contrast to the in-sample results, hedging strategies using constant hedge ratios perform better than those based on time-varying hedge ratios. The only exception is when WTI is hedged using NYMEX and IPE futures as well as when Tapis is hedged using IPE Brent in which case GARCH based hedges perform better than other hedges. Despite this, time-varying hedge ratios still eliminate a considerable proportion of the total risk in international crude oil prices. For instance, excluding Tapis and Arab Light, using IPE futures contracts eliminates between 80% and 90% of the total risk in international crude oil prices. The fact that hedging strategies based on VECM-GARCH models do not perform well out of sample is also in line with other studies in the literature. For example, Kroner and Sultan (1993) report low percentage variance improvements of the GARCH hedge relative to the constant (OLS) hedge, ranging only between 4.64% and 0.96% for 5 currencies, while Gagnon and Lypny (1995 and 1997) find that GARCH improves hedging performance by only 1.87% and 0.70% for the Canadian interest rate and Canadian stock index futures, respectively. Similarly, Bera et al. (1997) estimate 2.74% and 5.70% variance improvements. Finally, Kavussanos and Nomikos (2000) report variance reductions for individual freight routes using freight futures contracts (BIFFEX) ranging between 0.43% and 5.7%. Following the results above, a question that arises is how these hedging results compare with that in other markets. The range of variance reductions achieved for international crude prices is between 44.41% and 79.47% in sample, and 32.13% and 86.89% out-of-sample. This is

15

comparable, if not superior, with the variance reductions over the unhedged position evidenced in other markets; 57.06% for the Canadian Interest rate futures (Gagnon and Lypny, 1995), 69.61% and 85.69% for the corn and soybean futures (Bera et al., 1997) and 97.91% and 77.47% for the SP500 and the Canadian Stock Index futures contract (Park and Switzer, 1995 and 1997).

7. SUMMARY AND CONCLUSIONS This paper examined the performance and effectiveness of IPE and NYMEX crude oil futures contracts in managing fluctuations of international physical crude prices. Both in and out-ofsample hedging performances are examined for each type of crude, considering both constant and dynamic hedge ratios. In general, the most effective futures contract to hedge physical crude oil prices is found to be the IPE-Brent crude futures with variance reductions varying between 44.41% and 79.47% in sample and 32.13% and 90.99% out-of-sample. Differences in hedging effectiveness between physical crude prices might be due to quality, grade and delivery locations of the oil as well as how each type of crude is priced in the market. For example, most crude prices considered in this study are priced at premium or discount against Brent, therefore, one should expect any change in Brent price to be transmitted directly to the price of regional crudes such as West African Bonny, Iranian Light and Russian Ural. On the other hand, results indicate that for those crudes which are not directly priced against this benchmark crude hedging effectiveness can be relatively poor. In addition, it is found that most physical crude prices tend to adjust to any disequilibrium in the long run relationship between spot and futures prices; that is futures prices drive spot prices. However, when spot prices for OPEC basket are considered, it is found that both NYMEX and IPE crude oil futures tend to adjust to any disequilibrium in the long run relationship between OPEC basket and futures prices. Results have important implications in terms of choice of instrument for risk management strategies of crude oil traders, refineries and oil producers. In fact, we found that a large proportion of fluctuations in crude prices, which is linked to Brent crude price fluctuations can be removed using IPE or NYMEX futures contract. However, the remaining risk can only be eliminated using other means such as dated for front line swaps or other futures contracts

16

on oil products. The latter approach is suggested since part of the remaining risk in crude oil prices may be due to grade differentials.

17

References Alizadeh, A., Kavussanos, M., and Menachof, D. (2004): “Hedging Against Bunker Price Fluctuations Using Petroleum Futures Contracts,” Applied Economics, in press. Baba, Y. Engle, R. Kraft, D. and Kroner, K. (1987), ‘Multivariate Simultaneous Generalised ARCH’, Unpublished Manuscript, University of California, San Diego. Baillie, R. and Myers, R. (1991), ‘Bivariate GARCH Estimation of the Optimal Commodity Futures Hedge’, Journal of Applied Econometrics 6, 109-124. Benninga, S. Eldor, R. and Zilcha, I. (1984), ‘The Optimal Hedge Ratio in Unbiased Futures Markets’, The Journal of Futures Markets 4, 155 - 159. Bera, A. and Jarque, C. (1980), ‘Efficient Tests for Normality, Heteroskedasticity, and Serial Independence of Regression Residuals’, Economic Letters 6, 255-259. Bera, A., Garcia, P. and Roh, J. (1997): “Estimation of Time-Varying Hedge Ratios for Corn and Soybeans: BGARCH and Random Coefficients Approaches,” Office for Futures and Options Research, 97-06. Bollerslev, T. (1986), ‘Generalised Autoregressive Conditional Heteroskedasticity’, Journal of Econometrics 31, 307- 327. Bollerslev, T. and Wooldridge, J. M. (1992), ‘Quasi-Maximum Likelihood Estimation of Dynamic Models with Time Varying Covariances’, Econometric Reviews 11, 143 - 172. Bollerslev, T., Engle, R. F. and Nelson, D. B. (1994), ‘ARCH Models’, In ‘Handbook of Econometrics’, eds Engle and McFadden, pp 2959 - 3038. North Holland. Chen, K. C., Sears R. S. and Tzang, D., (1987), ‘Oil Prices and Energy Futures’, The Journal of Futures Markets, 7, 501 - 518. Cheung, Y. and Lai, K. (1993): “ Finite Sample Sizes of Johansen’s Likelihood Ratio tests for Cointegration,” Oxford Bulletin of Economics and Statistics, 55: 313 - 328. Chou, W., Denis, K. and Lee, C. (1996), ‘Hedging with the Nikkei Index Futures: The conventional versus the Error Correction Model’, The Quarterly Review of Economics and Finance 36, 495 - 505. Crowder, W. and Hamed, A. (1993): “ A Cointegration Test for Oil Futures Market Efficiency,” The Journal of Futures Markets, 13: 933 – 941 Ederington, L. H., (1979), ‘The Hedging Performance of the New Futures Markets’, The Journal of Finance 34, 157 - 170. Engle, R. F. (1982), ‘Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation’, Econometrica, 50, 987-1008. Engle, R. F. and Granger, C. W. (1987), ‘Cointegration and Error Correction: Representation, Estimation, and Testing’, Econometrica, 55, 251 - 276. Engle, R. F. and Kroner, K. F. (1995), ‘Multivariate Simultaneous Generalised ARCH’, Econometric Theory 11, 122 - 150. Engle, R. F. and Ng, V. K. (1993): “Measuring and Testing the Impact of News on Volatility,” Journal of Finance, 48: 1749 - 1778. Ewing, B. and Harter, C. (2000): “Co-movements of Alaska North Slope and UK Brent Crude Oil Prices,” Applied Economic Letters, 7: 55. - 558 Figlewski, S. (1984), ‘Hedging Performance and Basis Risk in Stock Index Futures’, Journal of Finance, 39, 657 - 669. Franckle, C. T. (1980), ‘The Hedging Performance of the New Futures Markets: Comment’, The Journal of Finance 35, 1273 - 1279. Gagnon, L. and Lypny, G. (1995), ‘Hedging Short-Term Interest Risk Under Time-Varying Distributions’, Journal of Futures Markets, 15, 767 - 783.

18

Gagnon, L. and Lypny, G. (1997), ‘The benefits of Dynamically Hedging the Toronto 35 Stock Index’, Canadian Journal of Administrative Science, 14, 52 - 68. Ghosh, A. (1993), ‘Hedging with Stock Index Futures: Estimation and Forecasting with Error Correction Model’, The Journal of Futures Markets 13, 743 - 752. Gonzalo, J. (1994): “Five Alternative Methods of Estimating Long-Run Equilibrium Relationships,” Econometrica, 60: 203 - 233. Graff, J. Schroeder, T. Jones, R. and Dhuyvetter, K. (1998), ‘Cross-Hedging Agricultural Commodities’ Mimeo Kansas State University, Agricultural Experiment Station and Cooperative Extension Service, Manhattan, Kansas. Grammatikos, T. and Saunders, A. (1983), ‘Stability and the Hedging Performance of Foreign Currency Futures,’ The Journal of Futures Markets, 3, 295 - 305. Johansen, S. (1988), ‘Statistical Analysis of Cointegrating Vectors’, Journal of Economic Dynamics and Control 12, 231 - 254. Johansen, S.(1991): “Estimation an hypothesis testing of cointegration vectors in Gaussian vector autoregression models”, Econometrica, Vol. 59, pp. 1551-1580. Johnson, L. (1960), ‘The Theory of Hedging and Speculation in Commodity Futures’, Review of Economic Studies 27, 139 - 151. Kavussanos, M.G. and Nomikos, N. (2000b), ‘Hedging in the freight futures market’, Journal of Derivatives, Vol. 8, No 1, Fall 2000, pp. 41- 58. Kroner, K. and Sultan, J. (1993), ‘Time-Varying Distributions and Dynamic Hedging with Foreign Currency Futures’, Journal of Financial and Quantitative Analysis 28, 535 - 551. Lee, T. and Tse, Y. (1996): “ Cointegration Tests with Conditional Heteroskedasticity,” Journal of Econometrics, 73: 401 - 410. Lien, D. (1996), ‘The Effect of the Cointegration Relationship on Futures Hedging: A Note’, The Journal of Futures Markets 16, 773 - 780. Lin, X. S. and Tamvakis, M. (2001): “Spillover Effects in Energy Futures Markets,” Energy Economics, 23: 43 - 56. Lindahl, M. (1992), ‘Minimum Variance Hedge Ratios for Stock Index Futures: Duration and Expiration Effects’, Journal of Futures Markets 12, 33 - 53. Ljung, M. and Box, G. (1978), ‘On a Measure of Lack of fit in Time Series Models. Biometrika 65, 297-303. Milonas, N. and Henker, T. (2001): “Price Spread and Convenience Yield Behaviour in the International Oil Market,” Applied Financial Economics, 11: 23 - 36. Myers, R. and Thompson, S. (1989), ‘Generalised Optimal Hedge Ratio Estimation’, American Journal of Agricultural Economics 71, 858 - 868. Osterwald-Lenum, M. (1992), ‘A Note with the Quantiles of the Asymptotic Distribution of the ML Cointegration Rank Test Statistics. Oxford Bulletin of Economics and Statistics 54, 461 - 472. Phillips, P. and Perron, P. (1988), ‘Testing for a Unit Root in Time Series Regressions’, Biometrica 75, 335 - 346. Schwarz, G. (1978), ‘Estimating the Dimension of a Model’, Annals of Statistics 6, 461 464. Silvapulle, P. and Moosa, I. (1999): “The Relationship between Spot and Futures Prices: Evidence from the Crude Oil Market,” The Journal of Futures Markets, 19: 175 - 193. Stein, J. (1961), ‘The Simultaneous Determination of Spot and Futures Prices’, The American Economic Review 51, 1012 - 1025. Tong, W. (1996), ‘An examination of Dynamic Hedging’, Journal of International Money and Finance, 15, 19-35. Wilson, W. W. (1989) ‘Price discovery and hedging in the Sunflower Market’, The Journal of Futures Market, Vol. 9, No 5, pp. 377-391.

19

Table 1: Summary Statistics of weekly changes in log spot and futures prices; Sample Period: 20 October 1993 – 24 April 2002 Mean

Variance

Skewness

Kurtosis

Normality J-B

Autocorrelation Q(6)

ARCH (6)

PP(4) levels

PP(4) 1st diffs

-0.2842 [0.010] -0.012 [0.916] -0.2822 [0.010] -0.2977 [0.007] -0.3580 [0.001] -0.4924 [0.000] -0.3080 [0.003] -0.3605 [0.001] -0.3233 [0.003] -0.3239 [0.005]

1.0686 [0.000] 1.2861 [0.000] 1.1467 [0.000] 1.2804 [0.000] 1.3647 [0.000] 2.4724 [0.000] 1.1711 [0.000] 1.1752 [0.000] 2.092 [0.000] 1.6226 [0.000]

30.340 [0.000] 34.261 [0.000] 33.829 [0.000] 41.292 [0.000] 49.185 [0.000] 146.67 [0.000] 36.257 [0.000] 39.360 [0.000] 99.296 [0.000] 62.437 [0.000]

7.814 [0.252] 6.549 [0.365] 5.804 [0.445] 8.053 [0.234] 5.531 [0.477] 9.522 [0.146] 8.498 [0.204] 8.782 [0.186] 3.562 [0.735] 9.159 [0.164]

2.721 [0.001] 2.090 [0.016] 2.559 [0.009] 4.092 [0.000] 1.522 [0.112] 2.021 [0.021] 3.869 [0.000] 0.840 [0.609] 0.944 [0.502] 1.475 [0.129]

-1.844

-22.59

-1.603

-24.68

-1.758

-23.03

-2.043

-23.03

-1.600

-22.51

-1.309

-21.62

-2.045

-22.85

-1.490

-25.03

-1.591

-23.87

-1.514

-24.28

African Bonny

0.0006

0.052

Arabian Light

0.0009

0.054

Brent Physical

0.0007

0.051

Iranian Light

0.0006

0.058

OPEC Basket

0.0008

0.045

Indonesian Tapis

0.0007

0.036

Russian Ural

0.0007

0.057

WTI Cushing

0.0007

0.050

IPE Crude Futures

0.0007

0.046

NYMEX Crude Futures

0.0007

0.048

• • •

N = 446 is the number of observations Values in [ ] are exact significance levels. $ 3 and ( α$ 4 -3) respectively; their asymptotic Skew and Kurt are the estimated centralised third and fourth moments of the data, denoted α

• • • •

$ 3 ∼ N(0,6) and T ( α$ 4 -3) ∼ N(0,24). distributions under the null are T α J-B is the Jarque - Bera (1980) test for normality; the statistic is χ2(2) distributed. Q(6) is the Ljung-Box (1978) Q statistics for 6th order sample autocorrelation; the test is χ2(6) distributed. ARCH(6) is the Engle (1982) test for 6th order ARCH effects; ; the test is χ2(6) distributed. PP is the Phillips and Perron (1988) unit root test; the truncation lag for the test is set to 4.

20

Table 2: Correlation matrix of prices changes of international crude prices and exchange trade futures contracts; Sample Period: 20 October 1993 – 24 April 2002 Iran Light

African Bonny

Arab Light

Russian Ural

OPEC Basket

Malysian WTI Tapis Cushing

Brent Physical

NYMEX IPE Brent Futures Futures

Iran Light

1.00000

African Bonny

0.96746

1.00000

Arab Light

0.60124

0.63067

1.00000

Russian Ural

0.98556

0.96150

0.58951

1.00000

OPEC Basket

0.90796

0.93062

0.66967

0.90023

1.00000

Malysian Tapis

0.60696

0.61417

0.56118

0.59464

0.72780

1.00000

WTI Cushing

0.78318

0.79424

0.56322

0.77695

0.85302

0.61517

1.00000

Brent Physical

0.96840

0.99488

0.63165

0.96074

0.93457

0.61468

0.80377

1.00000

NYMEX Futures

0.80514

0.81352

0.58519

0.79627

0.86957

0.65747

0.93103

0.82233

1.00000

IPE Brent Futures

0.87238

0.88642

0.63274

0.86042

0.89338

0.64821

0.79098

0.89430

0.81690

21

1.00000

Table 3: Johansen test for cointegration between bunkers and futures prices Sample Period: 20 October 1993 – 24 April 2002

∆Xt =

p−1

∑ Γi∆Xt-i + αβ′Xt-1 + εt

εt = ⎛⎜ ε S,t ⎞⎟ |Ωt-1 ∼ IN(0,H)

;

⎝ ε F,t ⎠

i =1

λmax test

λtrace test

CV

Lags IPE crude futures vs African Bonny 2 Arab Light

2

Brent Physical

2

Iranian Light

3

OPEC Basket

2

Indonesian Tapis

2

Russian Ural

2

WTI Cushing

2

H0: Statistic

IPE crude futures vs African Bonny 3 Arab Light

3

Brent Physical

3

Iranian Light

3

OPEC Basket

3

Indonesian Tappis

3

Russian Ural

3

WTI Cushing

3

53.07 2.74 28.39 3.08 82.16 3.24 28.34 2.96 23.83 3.04 42.84 1.77 51.24 2.89 60.19 2.13

r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1

56.13 2.74 31.47 3.08 85.40 3.24 28.35 2.96 26.88 3.04 44.62 1.77 54.13 2.89 62.32 2.13

r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1

52.58 3.60 38.89 3.53 61.99 3.51 28.51 3.68 37.94 3.27 49.74 2.57 38.44 3.67 189.3 3.62

r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1

56.18 3.60 42.41 3.53 65.51 3.52 32.19 3.68 41.20 3.27 52.31 2.57 42.12 3.68 192.9 3.62

β2)

(1

-1.003

0.006)

0.519 [0.471]

(1

-1.101

0.410)

15.00 [0.000]

(1

-1.016

0.043)

3.895 [0.089]

(1

-1.010

0.116)

17.20 [0.000]

(1

-1.013

0.075)

12.58 [0.000]

(1

-0.968

0.150)

23.59 [0.000]

(1

-1.007

0.078)

30.73 [0.000]

(1

-0.955

-0.202)

34.79 [0.000]

(1

-1.058

0.239)

27.25 [0.000]

(1

-1.178

0.712)

16.62 [0.000]

(1

-1.081

0.323)

29.32 [0.000]

(1

-1.096

0.446)

17.84 [0.000]

(1

-1.078

0.339)

18.57 [0.000]

(1

-1.029

0.096)

1.912 [0.167]

(1

-1.069

0.336)

24.93 [0.000]

(1

-1.006

0.018)

4.362 [0.038]



$ ) tests the null hypothesis of r cointegrating vectors against the alternative of r+1. λmax(r,r+1) = -Tln(1- λ r +1



λtrace(r) = -T

n

LR test -1 0) p-value

Nomalised

H0: Statistic

r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1 r=0 r=1

β1

(1 Stat

(1

$

∑ ln(1 - λ i ) tests the null that there are at most r cointegrating vectors against the alternative that the number

i =r +1

of cointegrating vectors is greater than r. ♦ 5% critical values for λtrace and λmax tests are 19.96 and 9.24, and 15.67 and 9.24, respectively. Critical values are from Osterwald-Lenum (1992), Table 1*. β′ = (1 β1 β2) are the coefficient estimates of the cointegrating vector where the coefficient of St-1 is normalised to be unity, β1 • is the intercept term and β2 is the coefficient on Ft-1.

23

Table 4: Results of VEC-GARCH models for physical crude oil and IPE crude oil futures prices. Sample Period 20 October 1993 to 24 April 2002

∆St =

p−1

p−1

bs,i∆Ft-i + δszt-1 + εS,t ∑ as,i∆St-i + ∑ i =1

εt = ⎛⎜ ε S,t ⎞⎟ |Ωt-1 ∼ IN(0,Ht) ⎝ ε F,t ⎠

i =1

∆Ft =

p−1

∑ aF,i∆St-i + i =1

j=S,F

aj,1 bj,1

p−1

′ ′ ′ ⎛ hSS,t hSF,t ⎞ ⎛α11 α12 ⎞ ⎛α11 α12 ⎞ ⎛ β11 β12 ⎞ ⎛ β11 β12 ⎞ ⎛γ 11 γ 12 ⎞ ⎛γ γ ⎞ ⎟ = ⎜⎜ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ Ht =⎜⎜ H ε t−1ε t′−1 ⎜⎜ 11 12 ⎟⎟ + + t 1 ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ h h ⎝ β21 β22 ⎠ ⎝γ 21 γ 22 ⎠ ⎝γ 21 γ 22 ⎠ ⎝ SF,t FF,t ⎠ ⎝ 0 α22 ⎠ ⎝ 0 α22 ⎠ ⎝ β21 β22 ⎠

∑ bF,i∆Ft-i + δFzt-1 + εF,t i =1

African Bonny

Arab Light

Brent Physical

Iranian Light

Spot Futures 0.171 0.182 [0.061] [0.016]

Spot Futures -0.148 0.106 [0.007] [0.016]

Spot Futures 0.157 0.194 [0.114] [0.020]

Spot Futures 0.118 0.165 [0.209] [0.017]

Spot -0.023 [0.762]

Futures 0.163 [0.044]

Spot -0.049 [0.505]

Futures 0.076 [0.421]

Spot 0.198 [0.036]

Futures 0.165 [0.022]

Spot 0.198 [0.036]

Futures 0.165 [0.022]

-0.188 -0.253 [0.068] [0.004]

0.222 [0.000]

-0.183 [0.087]

-0.178 -0.256 [0.114] [0.003]

0.007 [0.918]

-0.211 [0.008]

0.182 [0.003]

-0.064 [0.421]

-0.241 [0.030]

-0.243 [0.005]

-0.241 [0.030]

-0.244 [0.005]

-0.196 [0.000]

-0.269 [0.003]

aj,2

0.050 0.063 [0.585] [0.345]

bj,2

-0.004 -0.031 [0.972] [0.722]

δj αkk

k=1,2

βkk

k=1, 2

γkk

k=1,2

OPEC Basket

Asian Tapis

Russian Ural

WTI Cushing

-0.147 0.072 [0.024] [0.217]

-0.165 [0.000]

-0.032 [0.332]

-0.243 [0.003]

0.095 [0.169]

-0.082 0.035 [0.049] [0.257]

0.015 [0.794]

0.161 [0.011]

-0.079 [0.057]

0.100 [0.048]

-0.127 [0.021]

0.059 [0.147]

-0.127 [0.021]

0.059 [0.147]

0.004 0.001 [0.352] [0.640] 0.008 [0.015]

0.033 [0.647]

0.005 [0.435] 0.007 [0.028]

0.006 [0.046]

-0.000 [0.901] 0.007 [0.129]

0.007 0.003 [0.076] [0.114] 0.008 [0.001]

0.003 [0.321]

0.001 [0.366] 0.007 [0.000]

0.001 [0.998]

-0.003 [0.959] 0.013 [0.290]

0.007 [0.039]

0.002 [0.222] 0.007 [0.001]

0.007 [0.039]

0.002 [0.222] 0.007 [0.001]

0.942 0.101 [0.000] [0.314] 0.044 0.866 [0.592] [0.000]

0.963 [0.000] 0.030 [0.341]

0.002 [0.959] 0.957 [0.000]

0.966 [0.000] 0.003 [0.980]

0.232 [0.045] 0.724 [0.000]

0.937 0.054 [0.000] [0.226] 0.042 0.907 [0.428] [0.000]

0.949 [0.000] 0.040 [0.005]

0.081 [0.044] 0.896 [0.000]

0.930 [0.000] 0.058 [0.404]

0.091 [0.334] 0.878 [0.000]

0.932 [0.000] 0.051 [0.467]

0.042 [0.346] 0.929 [0.000]

0.932 [0.000] 0.051 [0.467]

0.042 [0.346] 0.929 [0.000]

0.428 0.079 [0.000] [0.349] -0.423 0.051 [0.007] [0.740]

0.191 [0.008] -0.068 [0.293]

-0.084 [0.428] 0.264 [0.000]

0.478 [0.000] -0.420 [0.003]

0.034 [0.724] 0.132 [0.307]

0.456 0.055 [0.000] [0.419] -0.441 0.063 [0.000] [0.546]

0.305 [0.002] -0.191 [0.111]

-0.033 [0.787] 0.212 [0.026]

0.231 [0.002] -0.065 [0.400]

0.002 [0.983] 0.243 [0.017]

0.430 [0.000] -0.431 [0.000]

0.074 [0.322] 0.049 [0.632]

0.430 [0.000] -0.431 [0.000]

0.074 [0.322] 0.049 [0.632]

24

Diagnostic Tests of VEC-GARCH models for physical crude oil and IPE crude oil futures prices. (cont.)

Diagnostic Tests African Bonny j=S,F

Arab Light

Brent Physical

Iranian Light

OPEC Basket

Asian Tapis

Russian Ural

WTI Cushing

Spot Futures 0.015 0.014

Spot 0.081

Futures 0.001

Spot 0.014

Futures 0.016

Spot Futures 0.011 0.017

Spot 0.000

Futures 0.025

Spot 0.083

Futures 0.001

Spot 0.014

Futures 0.017

Spot 0.014

Futures 0.017

J-B test

2.747 31.76 [0.253] [0.000]

8.518 [0.014]

24.03 [0.000]

2.043 [0.360]

18.926 [0.000]

8.064 27.432 [0.018] [0.000]

22.76 [0.000]

34.40 [0.000]

81.91 [0.000]

35.24 [0.000]

7.389 [0.025]

26.03 [0.000]

7.389 [0.024]

26.03 [0.000]

Q(6)

4.623 3.041 [0.592] [0.804]

3.622 [0.728]

4.153 [0.656]

5.038 [0.539]

3.176 [0.786]

4.644 3.201 [0.590] [0.783]

5.364 [0.498]

3.511 [0.743]

11.699 [0.069]

2.679 [0.847]

5.089 [0.532]

3.661 [0.722]

5.088 [0.532]

3.661 [0.722]

ARCH(6)

10.291 8.803 [0.112] [0.184]

9.005 [0.173]

8.101 [0.230]

9.477 [0.148]

6.277 [0.393]

12.220 8.928 [0.057] [0.177]

4.267 [0.640]

6.140 [0.407]

1.339 [0.969]

5.418 [0.491]

9.732 [0.136]

9.158 [0.165]

9.732 [0.136]

9.158 [0.165]

SBIC LL

-5250.6 2631.4

R-bar square

Sign Bias Test Positive Size Bias Negative Size Bias Joint test

1.292 [0.197] -1.618 [0.106] 0.426 [0.670] 2.063 [0.104]

0.573 [0.567] -1.307 [0.192] 1.523 [0.124] 2.720 [0.044]

-4878.3 2445.2 1.630 [0.103] -2.018 [0.044] -0.313 [0.754] 1.678 [0.171]

0.715 [0.475] -1.970 [0.049] 0.392 [0.695] 1.983 [0.116]

-5330.4 2671.3 1.145 [0.252] -1.427 [0.154] 0.670 [0.503] 2.075 [0.103]

0.284 [0.776] -1.139 [0.255] 1.144 [0.253] 1.628 [0.182]

-5109.9 2561.0 1.074 [0.283] -1.555 [0.120] 1.161 [0.246] 3.064 [0.029]

-5440.5 2726.3

0.260 [0.795] -1.297 [0.195] 1.556 [0.120] 2.509 [0.058]

1.561 [0.109] -1.113 [0.266] -0.091 [0.927] 1.395 [0.244]

-5198.2 2605.2

1.008 [0.314] -0.770 [0.442] 1.157 [0.248] 2.254 [0.081]

1.281 [0.201] -0.591 [0.555] -0.313 [0.755] 0.764 [0.514]

-5088.5 2550.3

0.769 [0.442] -0.795 [0.427] 0.735 [0.462] 1.089 [0.353]

0.871 [0.384] -1.036 [0.301] 1.266 [0.206] 2.606 [0.051]

0.718 [0.473] -1.318 [0.188] 1.595 [0.111] 3.062 [0.028]

-5088.5 2550.3 0.871 [0.384] -1.036 [0.300] 1.266 [0.206] 2.606 [0.051]

0.718 [0.473] -1.318 [0.188] 1.595 [0.111] 3.062 [0.028]

Notes: • Values in [ ] are exact significance levels. All models are estimated using QML estimation (see Bollerslev and Wooldridge, 1992) • See the notes in Table 1 for the definitions of the statistics. LL is the maximum value of the log-likelihood function.



The test statistic for the Engle and Ng (1993) tests is the t-ratio of b in the regressions;

u 2t

+

= a + b S t-1 εt-1 + β′z0t + et (positive size bias test) where

u 2t

u 2t

-

= a + b St-1 + β′z0t + et (sign bias test);

are the squared standardised residuals, ε2t/ht, ,

u 2t

-

= a + b St-1 εt-1 + β′z0t + et (negative size bias test);

S-t-1 is a dummy variable taking the value of one when εt-1 is negative and

S+t-1 = 1 - S-t-1 , β′ is a constant parameter vector β = (β01, β02)′ and z0t is a vector of parameters that explain the variance under the null hypothesis; in the case of a 2 + GARCH(1,1) model, z0t = ( ht-1, ε2t-1). The joint test is based on the regression u t = a + b1 St-1 + b2 St-1 εt-1 + b3 S t-1 εt-1 + β′z0t + et . The test statistic for the joint test H0: b1 = b2 = b3 = 0,

zero otherwise,

is an LM statistic distributed as χ2(3) with 5% critical value of 7.81.

25

Table 5: Results of VEC-GARCH models for physical crude oil and NYMEX crude oil futures prices. Sample Period 20 October 1993 to 24 April 2002

∆St =

p−1

p−1

bs,i∆Ft-i + δszt-1 + εS,t ∑ as,i∆St-i + ∑ i =1

εt = ⎛⎜ ε S,t ⎞⎟ |Ωt-1 ∼ IN(0,Ht)

p−1

′ ′ ′ ⎛ hSS,t hSF,t ⎞ ⎛α11 α12 ⎞ ⎛α11 α12 ⎞ ⎛ β11 β12 ⎞ ⎛ β11 β12 ⎞ ⎛γ 11 γ 12 ⎞ ⎛γ γ ⎞ ⎟ = ⎜⎜ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ Ht =⎜⎜ H ε t−1ε t′−1 ⎜⎜ 11 12 ⎟⎟ + + t 1 ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎟ h h ⎝ β21 β22 ⎠ ⎝γ 21 γ 22 ⎠ ⎝γ 21 γ 22 ⎠ ⎝ SF,t FF,t ⎠ ⎝ 0 α22 ⎠ ⎝ 0 α22 ⎠ ⎝ β21 β22 ⎠

⎝ ε F,t ⎠

i =1

∆Ft =

∑ aF,i∆St-i + i =1

p−1

∑ bF,i∆Ft-i + δFzt-1 + εF,t i =1

African Bonny

Arab Light

Brent Physical

Iranian Light

Spot Futures 0.207 0.269 [0.014] [0.000]

Spot Futures -0.121 0.133 [0.067] [0.032]

Spot Futures 0.175 0.270 [0.046] [0.001]

Spot Futures 0.167 0.247 [0.034] [0.000]

Spot -0.093 [0.327]

Futures 0.096 [0.334]

Spot -0.041 [0.475]

Futures -0.020 [0.795]

Spot 0.240 [0.002]

Futures 0.262 [0.000]

bj,1

-0.251 -0.330 [0.011] [0.000]

0.177 [0.015]

-0.170 [0.006]

-0.233 [0.014]

-0.330 [0.000]

-0.227 -0.325 [0.021] [0.000]

0.116 [0.188]

-0.108 [0.251]

0.152 [0.000]

-0.038 [0.546]

-0.287 [0.001]

-0.323 [0.000]

aj,2

0.191 0.238 [0.033] [0.001]

0.042 -0.0001 [0.461] [0.989]

0.222 [0.007]

0.260 [0.001]

0.230 0.230 [0.013] [0.000]

0.285 [0.000]

0.352 [0.000]

0.079 [0.148]

0.064 [0.369]

0.213 [0.005]

0.240 [0.000]

bj,2

-0.188 -0.301 [0.043] [0.000]

-0.018 [0.798]

-0.068 [0.359]

-0.236 [0.008]

-0.321 [0.000]

-0.262 -0.316 [0.026] [0.000]

-0.247 [0.001]

-0.366 [0.000]

0.020 [0.582]

-0.094 [0.087]

-0.263 [0.003]

-0.342 [0.000]

δj

-0.172 0.037 [0.008] [0.520]

-0.145 [0.000]

-0.024 [0.488]

-0.179 [0.014]

0.059 [0.356]

-0.097 0.013 [0.017] [0.692]

-0.007 [0.900]

0.111 [0.042]

-0.087 [0.001]

0.060 [0.138]

-0.161 [0.000]

0.001 0.010 [0.837] [0.035] 0.014 [0.006]

0.0000 [0.990]

0.001 [0.839] 0.010 [0.000]

0.0009 [0.776]

-0.007 [0.219] -0.012 [0.001]

0.008 0.009 [0.217] [0.031] 0.022 [0.000]

0.000 [0.986]

-0.001 [0.749] 0.007 [0.000]

0.0007 [0.800]

-0.002 [0.038] 0.007 [0.034]

1.082 0.243 [0.000] [0.000] -0.158 0.651 [0.000] [0.000]

0.904 [0.000] 0.117 [0.081]

0.065 [0.212] 0.882 [0.000]

1.039 [0.000] -0.079 [0.433]

0.206 [0.001] 0.727 [0.000]

1.019 0.233 [0.000] [0.006] -0.093 0.593 [0.615] [0.000]

1.027 [0.000] -0.044 [0.263]

0.239 [0.000] 0.758 [0.000]

0.967 [0.000] 0.002 [0.935]

0.043 0.422 [0.790] [0.001] 0.144 -0.358 [0.107] [0.003]

0.299 [0.005] -0.244 [0.044]

-0.186 [0.099] 0.406 [0.000]

0.014 [0.915] -0.179 [0.113]

-0.406 [0.000] 0.351 [0.000]

0.320 -0.124 [0.000] [0.087] -0.378 0.186 [0.002] [0.054]

0.229 [0.011] -0.077 [0.326]

-0.294 [0.004] 0.408 [0.000]

0.299 [0.000] -0.055 [0.140]

j=S,F

aj,1

αkk

k=1,2

βkk

k=1, 2

γkk

k=1,2

26

OPEC Basket

Asian Tapis

Russian Ural

WTI Cushing Spot

Futures

0.008 [0.827]

-0.812 [0.000]

0.191 [0.190]

0.007 [0.016]

0.006 [0.003] 0.001 [0.842]

0.011 [0.000]

0.009 [0.000] 0.006 [0.000]

0.170 [0.005] 0.858 [0.000]

0.965 [0.000] -0.013 [0.552]

0.045 [0.001] 0.932 [0.000]

0.335 [0.005] 0.629 [0.000]

-0.518 [0.000] 1.470 [0.000]

0.351 [0.000] -0.391 [0.000]

0.400 [0.000] -0.426 [0.000]

0.140 [0.006] 0.005 [0.938]

0.448 [0.000] -0.540 [0.000]

0.399 [0.000] -0.378 [0.001]

Diagnostic Tests of VEC-GARCH models for physical crude oil and IPE crude oil futures prices. (cont.) Diagnostic Tests African Bonny

Iranian Light

OPEC Basket

Spot Futures 0.026 0.061

Spot 0.071

Futures 0.014

Spot 0.022

Futures 0.063

Spot Futures 0.030 0.067

Spot 0.015

Futures 0.058

Spot 0.078

Futures 0.015

Spot 0.038

Futures 0.072

Spot 0.056

Futures 0.000

J-B test

6.980 17.57 [0.031] [0.000]

5.413 [0.067]

8.273 [0.016]

8.674 [0.013]

21.89 [0.000]

2.856 13.03 [0.239] [0.001]

28.94 [0.000]

19.81 [0.000]

133.5 [0.000]

8.314 [0.016]

1.756 [0.415]

11.28 [0.003]

14.32 [0.001]

12.32 [0.002]

Q(6)

2.532 1.732 [0.865] [0.942]

2.667 [0.849]

3.237 [0.779]

3.163 [0.788]

2.319 [0.888]

3.689 1.514 [0.718] [0.959]

4.435 [0.618]

2.870 [0.825]

5.767 [0.450]

3.819 [0.701]

3.184 [0.785]

2.371 [0.883]

5.131 [0.527]

9.172 [0.164]

ARCH(6)

11.07 8.580 [0.086] [0.198]

5.837 [0.442]

6.787 [0.341]

11.03 [0.087]

8.396 [0.211]

14.38 7.835 [0.026] [0.250]

2.551 [0.862]

6.340 [0.386]

1.107 [0.981]

4.767 [0.574]

13.34 [0.038]

7.242 [0.299]

3.528 [0.740]

4.056 [0.669]

SBIC LL

-5040.6 2526.4

j=S,F

R-bar square

Sign Bias Test Positive Size Bias Negative Size Bias Joint test

1.730 [0.084] -1.483 [0.138] 0.203 [0.839] 2.305 [0.076]

0.795 [0.427] -0.380 [0.704] -.0691 [0.489] 0.243 [0.865]

Arab Light

-4767.2 2389.7 1.299 [0.195] -1.481 [0.139] -0.769 [0.442] 0.790 [0.500]

0.841 [0.400] -0.369 [0.712] -0.676 [0.500] 0.269 [0.848]

Brent Physical

-5090.3 2551.2 1.429 [0.153] -1.119 [0.263] 0.574 [0.566] 2.244 [0.082]

0.866 [0.387] -0.412 [0.680] -0.659 [0.510] 0.277 [0.842]

-4911.3 2461.7 1.475 [0.141] -1.891 [0.059] 1.016 [0.310] 3.773 [0.011]

-5346.3 2679.3

0.955 [0.340] -0.798 [0.425] -0.414 [0.679] 0.337 [0.799]

See the notes in Table 4

27

1.649 [0.100] -1.290 [0.198] -0.475 [0.635] 1.193 [0.312]

0.038 [0.970] 0.209 [0.834] -0.264 [0.791] 0.069 [0.977]

Asian Tapis

-5193.0 2602.6 -0.219 [0.826] -0.207 [0.837] -0.450 [0.652] 0.296 [0.828]

1.077 [0.282] -0.517 [0.606] -0.602 [0.547] 0.419 [0.739]

Russian Ural

-4912.5 2462.3 0.981 [0.327] -0.939 [0.348] 1.183 [0.237] 2.811 [0.039]

0.554 [0.580] -0.604 [0.546] -0.487 [0.627] 0.143 [0.934]

WTI Cushing

-5706.1 2859.1 0.770 [0.442] -0.043 [0.966] 1.019 [0.307] 1.647 [0.177]

0.488 [0.625] -0.497 [0.619] 0.250 [0.803] 0.282 [0.839]

Table 6: In-sample hedging effectiveness of international crude prices s using exchange traded futures contracts Sample Period 20 October 1993 to 24 April 2002

Panel A: In-sample hedging effectiveness of international crude prices against IPE Brent futures Variance Comparisons Unhedged portfolio Naïve hedge Conventional hedge VECM Time-varying hedge

African Bonny 0.002780 0.000643 0.000642 0.000643 0.000630

Arab Light 0.002920 0.001860 0.001740 0.001740 0.001530

Brent Physical 0.002690 0.000581 0.000580 0.000581 0.000571

Iranian Light 0.003480 0.000909 0.000873 0.000874 0.000839

OPEC Basket 0.001980 0.000450 0.000419 0.000421 0.000407

Asian Tapis 0.001280 0.001270 0.000765 0.000767 0.000712

Russian Ural 0.003300 0.000916 0.000901 0.000902 0.000879

WTI Cushing 0.003300 0.000916 0.000901 0.000902 0.000879

44.41% 43.97% 7.03% 7.25%

73.35% 4.01% 2.40% 2.47%

73.35% 4.01% 2.40% 2.47%

Percentage Variance improvement of Time-Varying Hedge relative to other hedges Unhedged portfolio Naïve hedge Conventional hedge VECM

77.33% 1.99% 1.82% 1.90%

47.60% 17.74% 12.07% 12.07%

78.76% 1.65% 1.55% 1.74%

75.88% 7.65% 3.87% 3.92%

79.47% 9.70% 3.00% 3.34%

Panel B: In-sample hedging effectiveness of international crude prices against NYMEX WTI futures Variance Comparisons Unhedged portfolio Naïve hedge Conventional hedge VECM Time-varying hedge

African Bonny 0.002780 0.001020 0.000987 0.000990 0.000961

Arab Light 0.002920 0.002170 0.001920 0.001920 0.001790

Brent Physical 0.002690 0.000953 0.000921 0.000926 0.000890

Iranian Light 0.003480 0.001270 0.001270 0.001270 0.001220

OPEC Basket 0.001980 0.000583 0.000499 0.000501 0.000468

Asian Tapis 0.001280 0.001350 0.000747 0.000747 0.000700

Russian Ural 0.003300 0.001270 0.001270 0.001270 0.001260

WTI Cushing 0.002520 0.000334 0.000334 0.000333 0.000333

45.33% 48.16% 6.28% 6.32%

61.82% 0.79% 0.79% 0.79%

86.77% 0.29% 0.22% 0.03%

Percentage Variance improvement of Time-Varying Hedge relative to other hedges Unhedged portfolio Naïve hedge Conventional hedge VECM

65.43% 5.78% 2.61% 2.88%

38.70% 17.51% 6.77% 6.77%

66.90% 6.54% 3.36% 3.81%

64.94% 3.94% 3.94% 3.94%

28

76.39% 19.79% 6.38% 6.67%

Table 7: Out of-sample hedging effectiveness of international crude prices s using exchange traded futures contracts Sample Period 1 May 2002 to 30 April 2003

Panel A: Out of-sample hedging effectiveness of international crude prices against IPE Brent futures Variance Comparisons Unhedged portfolio Naïve hedge Conventional hedge VECM Time-varying hedge

African Bonny 0.002490 0.000259 0.000264 0.000266 0.000262

Arab Light 0.002770 0.002140 0.001860 0.001870 0.001880

Brent Physical 0.002420 0.000210 0.000214 0.000219 0.000218

Iranian Light 0.003070 0.000557 0.000579 0.000582 0.000599

OPEC Basket 0.001920 0.000291 0.000236 0.000240 0.000252

Asian Tapis 0.001490 0.001120 0.000715 0.000705 0.000691

Russian Ural 0.003060 0.000598 0.000607 0.000612 0.000625

WTI Cushing 0.002850 0.000584 0.000616 0.000605 0.000581

53.61% 38.29% 3.30% 1.90%

79.58% -4.53% -2.88% -2.17%

79.62% 0.61% 5.68% 4.08%

Percentage Variance improvement of Time-Varying Hedge relative to other hedges Unhedged portfolio Naïve hedge Conventional hedge VECM

89.47% -1.17% 0.56% 1.51%

32.13% 12.15% -1.08% -0.53%

90.99% -3.87% -2.12% 0.27%

80.48% -7.62% -3.45% -2.97%

86.89% 13.38% -6.73% -4.95%

Panel B: Out of-sample hedging effectiveness of international crude prices against NYMEX WTI futures Variance Comparisons Unhedged portfolio Naïve hedge Conventional hedge VECM Time-varying hedge

African Bonny 0.002490 0.000598 0.000549 0.000558 0.000584

Arab Light 0.002770 0.002470 0.001980 0.002000 0.002190

Brent Physical 0.002420 0.000527 0.000476 0.000487 0.000495

Iranian Light 0.003070 0.000767 0.000763 0.000772 0.000799

OPEC Basket 0.001920 0.000482 0.000350 0.000358 0.000372

Asian Tapis 0.001490 0.001280 0.000731 0.000724 0.000770

Russian Ural 0.003060 0.000747 0.000737 0.000741 0.000756

WTI Cushing 0.002850 0.000383 0.000381 0.000381 0.000354

48.30% 39.81% -5.32% -6.44%

75.30% -1.24% -2.53% -1.99%

87.57% 7.56% 7.00% 6.95%

Percentage Variance improvement of Time-Varying Hedge relative to other hedges Unhedged portfolio Naïve hedge Conventional hedge VECM

76.55% 2.41% -6.42% -4.72%

20.94% 11.34% -10.61% -9.50%

79.55% 6.01% -3.95% -1.59%

73.97% -4.21% -4.74% -3.55%

29

80.64% 22.84% -6.10% -3.88%

OPEC Basket NYME X IP E Brent

30 M aly s ian Tapis NY M E X IP E B rent

20/04/02 20/10/02 20/04/03

20/10/02 20/04/03

20/04/03

20/10/00

20/04/00

20/10/99

20/04/99

20/10/98

20/10/02

20/10/00

20/04/00

20/10/99

20/04/99

20/10/98

20/04/98

20/10/97

20/04/97

20/10/96

20/04/96

20/04/02

7

20/10/01

22

20/04/02

7 IP E B rent

20/04/01

F: African Bonny

20/10/01

12

20/04/98

22

20/04/01

17

12 20/10/97

D: African Bonny

20/10/01

17 IP E B rent

20/04/01

27

20/10/00

32

27 NY M E X

20/04/00

37

32 NY M E X

20/10/99

R us s ian U ral

20/04/99

37 20/04/97

A fric an B onny

20/10/98

IP E B rent

20/04/98

E: Iranian Light

20/10/97

C: Iranian Light

20/04/97

IP E B rent

20/10/96

27

20/04/96

32

27 20/10/95

A: Iranian Light

20/10/96

37

32

20/04/96

37 20/04/95

7

20/10/95

12

7 20/10/94

17

12

20/04/95

17

20/04/94

20/10/93

$/bbl

22

20/10/94

22 $/bbl

20/04/03

20/10/02

20/04/02

20/10/01

20/04/01

20/10/00

20/04/00

20/10/99

20/04/99

20/10/98

20/04/98

20/10/97

20/04/97

20/10/96

20/04/96

20/10/95

27

20/04/94

20/10/93

20/04/03

20/10/02

20/04/02

20/10/01

20/04/01

20/10/00

20/04/00

20/10/99

20/04/99

20/10/98

20/04/98

20/10/97

20/04/97

20/10/96

20/04/96

20/04/95

27

20/10/95

7

20/10/95

20/10/94

32

20/04/95

12

7 20/04/95

37

32

20/10/94

22 $/bbl 17

12

20/10/94

20/04/94

20/10/93

$/bbl 37

20/04/94

20/10/93

20/04/03

20/10/02

20/04/02

20/10/01

20/04/01

20/10/00

NY M E X

20/04/00

17

20/04/94

NY M E X

20/10/99

A rab Light

20/04/99

20/10/93

$/bbl

Iran Light

20/10/98

20/04/98

20/10/97

20/04/97

20/10/96

20/04/96

20/10/95

20/04/95

20/10/94

20/04/94

20/10/93

$/bbl

Figure 1: Plot of historical international crude oil prices against NYMEX and IPE Brent futures contracts B: African Bonny

22

31 17/02/2002

17/11/2001

17/08/2001

17/05/2001

17/02/2001

17/11/2000

17/08/2000

17/05/2000

17/02/2000

17/11/1999

17/08/1999

17/05/1999

17/02/1999

17/11/1998

17/08/1998

17/05/1998

17/02/1998

17/11/1997

17/08/1997

17/05/1997

17/02/1997

17/11/1996

17/08/1996

17/05/1996

17/02/1996

1.1

17/11/1995

17/08/1995

17/05/1995

17/02/1995

17/11/1994

17/08/1994

17/05/1994

17/02/1994

17/11/1993

Figure 2: Time-Varying and Constant Hedge Ratios for Bonny using IPE Futures

1.5

Time-Varying Hedge Ratio

1.3

Constant Hedge Ratio

0.9

0.7

0.5