Back Matter

Appendix I: Rules for Pricing of Crude Oil Futures Contracts

Appendix Table 1.

Crude Oil: Size of Market

(New York Mercantile Exchange)

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Source: New York Mercantile Exchange.Note: Contracts are for 1,000 barrels.
Appendix Table 2.

Comparison of Alternative Weighting Schemes for Futures Prices: Mean Absolute Errors

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Note: Forecasts are for the period December 1985 to October 1990.

This appendix outlines the procedures for determining the “settlement price” (SP) for crude oil futures contracts on the New York Mercantile Exchange. The SP is a daily price at which the clearing house clears all trades and settles all accounts between clearing members for each contract month. Since the SP is used to determine both the margin calls and invoice prices for deliveries, there are some very precise rules for its determination. 18/ By the same token, it is the best guide to the market’s views as to the future course of prices.

There are essentially two sets of rules, contingent on the volume of trade, for determining the SP. One set of rules applies if at the opening of business on any trading day, a given delivery month has more than 10 percent of the total open interest for all delivery months of the futures contracts. 19/ The second set of rules applies if the volume criterion is not met. These two sets of rules are considered below:

A. When the volume criterion is met:

(i) The SP is the weighted average of the transactions prices during the closing range; this range is defined as the last five minutes of trading before the end of the trading session. The weights are given by the number of contracts traded. For instance, suppose for January 1992 delivery, during the trading range n1 contracts are traded at price p1 and n2 contracts for p2. The settlement price would then be equal to (p1n1 + p2n2)/N, where N = n1 + n2.

The reason for having this procedure is that in the so-called “open cry” system of trading in the futures markets, at any given time there would be a range of prices at which transactions would be occurring. To call any one of those prices the “settlement” price would thus be quite arbitrary. The procedure adopted ensures that a set of representative prices is taken; by taking only the last few minutes of trading the objective is to have the prices reflect the latest information available to the market.

(ii) If there are no transactions in the closing range, the SP is the last trade price, unless a bid higher or offer lower than the last trade price is made in the closing range. Such higher bid or lower offer is then called the SP.

B. When the volume criterion is not met:

(i) For these delivery months, the SP is the price relationship between any given delivery month and the current delivery month. The price relationship itself is based on the last “spread transaction” executed in the closing range between such months. Spread transaction is a trade involving the simultaneous purchase of one futures contract against the sale of another futures contract. 20/ For instance, on February 1, 1991, a trader may sell March 1991 contract, the current delivery month, and buy March 1992 contract. The difference in the prices of these two contracts would thus determine the “price relationship” and the SP for March 1992.

(ii) If there is no such spread transaction in the closing range, the relationship would be established by the last such spread transaction executed that day unless a bid higher or offer lower than the last transaction is made in the closing range, in which case the last bid or offer for such spread is the SP.

(iii) If there are no spread transactions and no bids or offers made during any particular trading day, the spread differential for that day is taken to be the spread differential of the settlement prices for the preceding business day.

In addition to the above two sets of rules, there is a provision in the Rules that allows the Settlement Price Committee to establish the SP under specific circumstances. 21/ There are essentially two such circumstances: (a) if the SP, determined according to either set of rules, is inconsistent with transactions that occurred during the closing range in other delivery months; or (b) if the SP is inconsistent with market information known to the Committee. In either of these two circumstances the Committee may establish the SP at a level consistent with other transactions or market information. In such an event the Committee is required to prepare a written record of the basis for any SP so established.

It appears that after the outbreak of hostilities in the Middle East, the Committee had to intervene a number of times to set the SP, especially for some of the distant months for which trade volume was very limited. It should be noted that the Committee may determine the SP for one month with the SP for the following month determined by rules (A) or (B) and the Committee again determining the SP for the month following that. Given that the decisions of the Committee have serious financial implications for traders and other users of the futures market, the settlement prices so determined invariably reflect a consensus view, not only of the Committee members but also of the major traders.

APPENDIX II: The Relationship Between the “West Texas” and Other Crude Oil Prices 22/

This Appendix analyses the relationship between the spot price of “West Texas Intermediate” oil and the “average” price of crude oil. The latter, as used by the International Monetary Fund, is an arithmetic average of three other spot crude prices including “Dubai”, “UK Brent”, and “Alaskan North Slope” prices. The movement in the differential between the average and the West Texas price, in addition to being of some interest in its own right, also has a direct bearing on the projection of the average price. The Appendix first discusses some a priori considerations relating to the behavior of the differential and then presents some statistical evidence based on daily data on the various crude prices from November 1988 to November 1990, in all over 500 observations. The results indicate that, in general, there is a fairly clear negative relationship between the differential and the level of “West Texas” spot price.

1. Magnitude of the differential

This section examines some of the factors likely to determine the magnitude of the differential between the West Texas crude oil price (WT) and the “average” price (AP) based on the three other crudes and changes in it overtime. These factors include quality differences between the different types of crudes, the degree of substitution between them, the extent to which substitution possibilities change with changes in the price and transportation costs. Each of these factors is discussed in turn below:

1.1 Quality differences

There are several dimensions along which the four crudes differ, with the two most important being the sulphur content of oil and its weight. 23/ In terms of refinery operations, the lighter the oil and the lower its sulphur content, the easier it is to refine it to produce a wide variety of end products. Conversely, the heavier oil would be more expensive to refine and the range of end products available from it would be relatively limited. This difference means that, other things given, the lighter oil will be at a premium relative to the heavier oil.

Of the four crudes, WT is the lightest and has the lowest sulphur content, followed by U.K. Brent; the third in terms of this ranking is Dubai with Alaskan being the heaviest. For any given level of demand, it might be expected that the relative f.o.b. prices of the four crudes would reflect their relative quality. This would suggest that the WT price would be higher than the AP. 24/ There may be, of course, circumstances relating to the capacity of specific refineries, or a sudden upsurge in the demand for a particular end product, which lead to an increase in the demand for one of the heavier crudes, increasing its price relative to the others. Any such factor is, however, likely to be transitory with the normal ranking of the prices reestablishing itself within a short period of time.

1.2 Substitution possibilities

The quality differences noted above suggest that in general the differential will be positive (that is WT price will exceed AP). This does not mean, however, that the differential will be constant over time regardless of the level of prices. The extent to which the differential changes with respect to the level of crude prices depends on the extent to which substitution possibilities themselves change. Suppose, for instance, that at a relatively low price substitution between the different crudes is small. Initially, in such a situation an exogenous increase in demand for WT would increase its price, without affecting the prices of the other crudes, leading to an increase in the differential. As WT price increases, however, the substitution possibilities may change: that is, it may become more profitable to buy the cheaper crudes and make adjustments in the refinery operations than to continue to buy a specific crude. In such a situation, the differential in proportionate terms (that is, relative to WT price) would narrow. Indeed if the switch to the cheaper grades is large enough, say due to supply constraints on WT, the absolute differential may also decline.

The above argument suggests that in a period of scarcities with prices relatively high, consumers are less likely to be concerned about quality or grade differences than in a period of relative abundance and relatively low prices. 25/ It might also be argued, however, that it is not only the level of prices but also their rate of change which is important. If prices are rising very fast, consumers would want to ensure their supplies quickly in anticipation of continuing increase. In such a situation also, they may pay less attention to the precise grade, leading to a negative relationship between the differential and the rate of change of prices.

1.3 Transportation costs

As the names of the crudes suggest, each of them originates in a very different geographical location. The price quotations for all four are f.o.b.(although there is a marked difference in the distance between the oilwells and the f.o.b. points). 26/ There will thus be a difference in the f.o.b. prices depending solely on how far the f.o.b. point was from the location of the major consumer markets. For instance, the farther the supply source from the market, other things given, the lower is likely to be the f.o.b. price. On the basis of this argument, it might be expected that since WT is closest to a major consumer market, there would be a positive differential between it and the average price.

To the extent that transportation costs reflect changes in the prices of crudes, some association between WT and the differential might also be expected. For instance, if there is an increase in the demand for all crudes, then an equi-proportionate increase in all crude prices, and in transportation costs, will lead to an increase in the differential in absolute terms but not in proportionate terms. If transportation costs do not increase proportionately, however, the c.i.f. price of, say, the Dubai crude will become less than the WT c.i.f. price. This will lead to a relative increase in the demand for Dubai crude leading to an increase in its f.o.b. price. Thus, the transportation cost factor means that even if all crudes were perfect substitutes, an increase in demand and prices will lead to a narrowing of the differential in both absolute and proportionate terms.

2. Empirical evidence

The statistical evidence on the relationship between the differential and the average price is based on daily observations on the various prices from November 1988 to December 1990. The reason for using daily observations, rather than at a lower frequency, is that the crude spot oil market (as well as the associated futures market) has been highly volatile over the last several years, so that the differential itself is likely to have varied considerably even from day to day.

It is also worth noting that prior to mid-1989, the average price for the IMF’s WEO forecasts was based on a weighted average of different crudes. Since then a simple unweighted average has been used. For the purpose of the analysis below, a consistent, unweighted, series for the average price was computed, based on the three crudes discussed earlier.

Appendix Table 3 provides some basic statistics on the mean prices and their variances for each of the crudes, the average price, and the differential between the average and the WT price. In order to isolate any seasonal factors, the values are presented on a quarterly basis as well as for the period as a whole. There are three features worth noting in this table: first, the remarkable volatility in all crude prices even before the events in the Middle East which affected the prices in the second half of 1990. Prices increased by nearly a third between the fourth quarter of 1988 and second quarter of 1989, fell by nearly 10 percent in the following year, and nearly doubled following the Middle East crisis. Secondly, there does not appear to be any statistically significant difference in the volatility of different crude prices (according to the standard F-test) or any marked seasonal component. Thirdly, although the turning points in the prices are virtually identical, the magnitude of the change in prices is different. This is reflected in a marked variation in both the absolute differential, as well as in the differential as a percentage of the average price. Thus the differential varied between nearly 19 percent in quarter 2, 1990, to barely 4 percent in the last quarter.

Appendix Table 3.

Crude Oil Prices and Differentials, 1988-90 1/

(In U.S. dollars per barrel)

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Based on daily observations; data for 1988 Q4 are for November 1st to December 30th 1988, and 1990 Q4 are for October 1st to November 30th 1990. All prices are in U.S. dollars per barrel except for differential, which is both in dollar/barrel and percentage change. Numbers in brackets are the standard deviations.

Next consider the relationship between the differential and the average price. An analysis of the behavior of these variables using daily data suggested a fairly clear negative relationship between the percentage differential and the average price. To obtain a quantitative indication of this relationship, a first order correlation matrix was computed both for this set of variables as well as the three crudes constituting the average price and the WT price. The results of this exercise are provided in Appendix Table 4. The first half of the matrix shows that the daily prices of different crudes are virtually perfectly correlated. This does not, of course, imply that prices change in an equi-proportionate manner. This can be seen readily in the second half of the correlation matrix which shows a statistically significant correlation between the differential in absolute and percentage terms (DI and DIP respectively) and WT and AP. It is also worth noting that there is somewhat of a closer relationship between the level of prices and the differential in percentage terms than with the differential in absolute terms, supporting the discussion in Section 2. The last section of the matrix considers each of the three crudes constituting AP separately. The divergence of each of these three prices from AP is computed (this is given by the variables DALAP, DDUAP and DUKBAP, respectively); these variables are then correlated with the crude prices as well as with the differentials. The results further highlight the marked differences in the three crude prices. For instance, when WT increases, the divergence between Dubai and AP also increases; this is the reverse of the situation with regard to the other two crude prices.

Appendix Table 4.

Crude Oil Prices and Differentials: Correlation Matrix

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Note: Correlation are based on 517 daily observations for the period October 1988 to November 1990. All prices are in dollars per barrel. AL, DU, UKB and WT denote prices of Alaskan, Dubai, U.K. Brent and West Texas crudes, respectively. AP is the average price of the first three crudes. DI and DIP denote the differential between AP and WT in absolute and percentage terms. The last three variables DALAP, DDUAP and DUKBAP denote the divergence of each of the three crudes from AP.

In order to obtain an indication of the quantitative relationship between the differential and WT, a regression analysis was undertaken with DI or DIP as the dependent variables and WT (or AP) as the independent variables. The standard OLS estimation of this regression would, however, be inappropriate. This is because since DI (and DIP) are defined in terms of AP and WT, the error term in the regression would be correlated with the explanatory variables, yielding biased and inconsistent estimates of the parameters. Consistent estimates can be obtained by using the Instrumental Variable (IV) technique, as is done below. The main instruments used were the lagged values of the independent variables themselves. Since preliminary analysis had shown a high degree of autocorrelation in the error term, this was also taken into account in the regression analysis.

The results of the estimation are provided in Appendix Table 5. All results indicate a highly significant negative relationship between the differential and WT as well as AP. The results for the absolute differential suggest, for instance, that a dollar per barrel increase in WT price would be accompanied, on average, by a ten cent fall in the differential. Similarly the results for the proportionate differential suggest that a 10 percent increase in the price would be accompanied, on average, by a two percentage point fall in the differential.

Appendix Table 5.

Instrumental Variable Estimates

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The dependent variables are DI and DIP, absolute and the proportionate differential, respectively. AP and WT denote average price and West Texas price; the instruments are lagged values of these variables. All regressions axe corrected for first-order serial correlation by using he maximum likelihood iterative technique. T-ratios are in brackets.

Two additional tests were undertaken to further explore the statistical relationship between WT price and the differential. One set examined whether there was any threshold effect; the results indicated that for WT price below $20 a barrel, the differential declined at a slightly slower rate compared to a price above $20 but this result was not statistically significant. Secondly, the relationship between the differential and the rate of change in WT price was examined. Here the results indicated that with the level of WT price taken into account, there was a weak negative relationship between the differential and the rate of change of the WT price.

The above results suggest that when using WT futures price to forecast the average spot price, it would be appropriate to adjust the differential by taking into account the expected WT price. The results provide an indication of the magnitude of the adjustment which may be necessary. It should be emphasized, however, that the results provide an indication of the average adjustment; given the considerations noted above, exceptional market developments concerning any of the four crudes should also be taken into account in computing the precise value of the adjustment.


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I am grateful to Bijan Aghevli, Peter Wickham, Charles Adams, William Perraudin and Blair Rourke for helpful comments. Raja Hettiarachchi provided excellent computing assistance.


Each barrel includes roughly 42 gallons of oil. See Appendix Table 1 for detailed information on the size of the market.


For details, see Hirschfeld (1983).


See, for instance, Anderson et al (1990).


See, for example, Hampton (1991).


The delivery point is the town of Cushing in Oklahoma, U.S.A. The six other deliverable grades include two Algerian grades, two Nigerian grades, a Norwegian grade, and UK Brent Blend.


See, for instance, Petroleum Intelligence Weekly (1988). According to data provided by Petroleum Database Services, which has individual computer models of all U.S. refineries, the extra profit from five of the six deliverable crudes, relative to WTI, exceeded the NYMEX value adjustment by 15 to 70 cents a barrel during the second quarter of 1988. North Sea Brent Blend, the most readily available substitute crude, was the only grade that appeared unattractive to buyers at Cushing since it showed little or no extra profit compared to WTI, but the NYMEX adjustment method still penalized Brent with a slight premium.


It is worth noting that the delivery date was changed in 1985 when it was based on the fifth day, prior to the twenty-fifth calendar day. An earlier study by Ma (1989) for the period 1984-86 apparently used the same delivery date. Given the extreme sensitivity of prices near the maturity date, the difference of even a couple of days can be important. For a somewhat different methodology, see, for instance, Dominguez (1987).


An related model could be that of a random walk with drift; there was, however, no empirical support for the drift factor.


As noted above, given the variable number of trading days, the last 20 days in the month were utilized.


See, for instance, Box and Jenkins (1976) pp. 85-91, and Granger and Newbold (1986) pp. 25-28.


See, for instance, Box and Jenbuis (1976) pp. 85-91 and Granger and Newbold (1986) pp. 25-28)


In the tests below, given the ‘adjustments’ applied to forecasts obtained from econometric models, there was no attempt made to separate the econometric and the judgemental forecasts. c.f. McNees (1990).


These two factors are particularly relevant when considering comparison made, for instance, by Choe (1990).


The forecasts by the USEA have often been in terms of constant dollars--they were converted into nominal dollars using the expected inflation rate.


For a succinct summary of this literature, see, for instance, Granger and Newbold (1986) pp. 266-276.


For a rationale of this type of weighting scheme, see Granger and Newbold (op. cit.), p. 269.


Thus, for instance, for the six-month ahead forecast, the error variance using futures and time series models were 0.03577 and 0.04267 respectively (using V=1). The error variance of the combined forecast was 0.03447.


These rules are set out in the New York Mercantile Exchange’s Rule Guide. The rules for energy contracts (for crude oil, gasoline as well as fuel oil) are given by Rule 6.52. The rules are set by the Exchange and approved by the Commodity Futures Trading Commission.


Open interest is defined as the total number of futures contracts, long or short, that have been entered into and not yet liquidated by an offsetting transaction or fulfilled by delivery. The term is interchangeable with “open contracts” and “open commitments”.


There are a number of different types of spread transactions: the intra-market spread--consisting of buying one month and selling another month in the same commodity; the intercommodity spread--consisting of a long position in one commodity and a short position in a related commodity; and the intramarket spread--consisting of buying a commodity at one exchange and selling the same commodity at another exchange. For the determination of the crude oil SP, it is the first of these spread transactions which is relevant.


This committee consists of three members including a floor trader, a floor broker, and an oil market expert.


The analysis focuses on the relationship between the “average” price of crude oil as used in the forecasts of the International Monetary Fund, and the West Texas price.


The combination of these two characteristics determines the “sweetness” of the oil--the lighter the oil and the lower the sulphur content, the “sweeter” it is.


Of course, to the extent that one-third of the weight in the average price is that of Brent, which is similar to WT, the differential between WT and the average would be somewhat less than if, say, an average of only Dubai and Alaska was used.


This is a phenomenon found in a very wide variety of primary commodity markets.


West Texas is f.o.b. Midland Texas; Dubai is f.o.b. Dubai; U.K. Brent is U.K. Brent ports and Alaskan North Slope is f.o.b. Gulf of Mexico ports. (See, for instance, Petroleum Market Intelligence (1990).) This suggests that both Alaskan and UK Brent f.o.b. prices would contain elements reflecting transportation costs.