Hedging ratios and effectiveness for diesel fuel and gasoline the northern plains

Hedging Ratios and Effectiveness for Diesel Fuel and Gasoline in the Northern Plains

Dennis M. Conley

Agribusinesses must cope with the risk of price changes when retailing refined &ls. Hedging price risk with energy futures contracts is a possibility. Information is needed on the local basis, hedge ratios, and hedging effectiveness. The results vary by location. 01994 by

John Wiley & Sons, Inc.

Over the past 20 years, any person who bought gasoline for a car or diesel fuel for a farm tractor probably remembers periods of changing and sometimes very high fuel prices. A number of memorable price shocks have occurred. The first one was in 1973 when the Organization of Petro- leum Exporting Countries (OPEC) asserted their economic power and placed restrictions on crude

oil supplies. Prices doubled and outages were com- mon at gasoline stations in certain states. Similar price shocks came in 1979, again because of geo- political events, and most recently in August of 1990 with the Persian Gulf War. Probably less re- membered was the dramatic price decline in early 1986 when crude oil prices fell by more than half. The prices for crude oil and the refined fuels

that come from it, such as gasoline and diesel fuel, are influenced by a number of factors including the fundamentals of supply and demand; efforts by producing countries to affect prices; and geo- political events like war and regional disputes that threaten the normal worldwide flow of fuels. Crude oil and fuel prices can and do respond quickly to significant new information and world-

............................................................................................................... This article is Journal Series No. 10362, Agricultural Research Division, IANR, University of Nebraska. The author appreciates the useful

comments from Marvin Hayenga and an anonymous journal reviewer.

Dennis M. Conley is Associate Professor of Agribusiness, Department of Agricultural Economics, 307 Filley Hall, University of Nebraska-Lincoln, Lincoln, NE 68583-0922. ...............................................................................................................

Agribusiness, Vol. 10, No. 4, 305-317 (1994) 0 1994 by John Wiley & Sons, Inc.

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CCC 0742-4477/94/040305-13

Conley

wide events. All of this leads to price variability, which, at times, can be either modest or dramatic, and which creates a price risk for the agribusiness owning refined fuels. The focus of this study was to evaluate hedging as a method for managing the price risk.

Hedging refined fuel prices with energy futures contracts is a relatively new method of price risk management compared to using futures contracts to hedge agricultural commodity prices. Energy futures were established on the New York Mercan- tile Exchange (NYMEX) in November of 1978 with the introduction of the heating oil futures contract. Crude oil futures started in 1983 followed by unleaded gasoline futures in 1984. Heating oil and unleaded gasoline contracts are both 42,000 US gallons with the delivery point being the New York Harbor. Prices are quoted in dollars and cents per gallon, for example, $0.4825 per gallon. Crude oil is reputed to have the world's largest volume of trade compared to any cash commodity. A crude oil futures contract is 1,000 US barrels with the delivery point being Cushing, Oklahoma. Prices are quoted in dollars and cents per barrel, for example, $18.45 per barrel.

In searching the literature, few studies were found that discussed energy futures. Abkenl did an analysis of intramarket spreads in heating oil futures. Ma2 evaluated the forecasting efficiency of energy futures prices during 1980-1986 for crude oil, heating oil, and leaded gasoline. Cho and McDougall3 tested the theory of storage for crude oil, heating oil, and gasoline futures markets using direct and indirect tests. Only two articles were found that discussed energy hedging, one in a

trade periodical and the other in a journal. The trade article" illustrated how airlines and bus companies could hedge fuel costs in energy mar-

kets. The journal articles used a crude oil hedging example in measuring hedging effectiveness to il- lustrate valid and invalid comparisons of effectiveness. No studies were found that estimated hedge ratios and hedging effectiveness for diesel fuel and gasoline.

Objectives

The general objectives of this study were to measure price and basis variability for No. 2 diesel fuel and unleaded regular gasoline at selected terminal cities in the Northern Plains region of the United States, and evaluate hedging with futures contracts as a method for reducing the risk exposure from price variability. The Northern Plains was chosen because it is primarily an agricultural region with large farms that are dependent on refined fuel for operations. The region is also a

great distance from East, West, and Gulf Coast re- fineries, and the larger urban population centers in the United States. One terminal city from each of the four states in the Northern Plains was chosen to represent the location where agribusinesses store and distribute refined fuels to customers. The cities were Scott City, Kansas; Lincoln, Ne- braska; Bismarck, North Dakota; and Rapid City, South Dakota. The futures contracts used to hedge cash products were heating oil, unleaded regular gasoline, and crude oil. The time period covered by the study was from January 1, 1988 to December 31, 1992.

The study had three specific objectives. The first objective was to calculate average price and basis levels, and their associated variability, at each of the four terminal cities. This provided information for a spatial comparison across the Northern

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Northern Great Plains

Plains region. Of interest were answers to the question, how similar or different were these statistics across the region? The second objective was to estimate hedge ratios for the cash products of diesel fuel and gasoline using heating oil, gasoline, and crude oil futures contracts. The estimated hedge ratios showed the proportion of a cash position that should be offset by an opposite position in the futures market. The traditional hedging rule recommends an equal and opposite position in futures contracts to offset the physical cash position. This results in a hedge ratio of one. While an equal and opposite position is an easy hedge to execute, such a position may not result in reducing revenue variability by the greatest amount, The third objective was to measure the effective reduction in variability of revenue achieved by hedging the cash products at each city. The hedging effectiveness measured the reduction in variance of revenue that resulted from maintaining a hedged position versus an unhedged position. An unhedged position has the agribusiness assuming the revenue risk associated with price level variability, whereas a hedged position assumes the risk of basis variability.

Methodology

The methods used in this study were based on the modern portfolio theory of hedging developed by Markowitz6 and initially applied by Johnson? and Stein.8 Consistent with the traditional theory of hedging, the primary motivation was risk reduction. Brown9 provided a summary discussion of these earlier applications, and he subsequently re- formulated the portfolio model to focus on returns. The purpose was to avoid some of the

theoretical and statistical problems encountered in using price levels as originally done by Johnson and Stein. Brown’s model estimated a hedge ratio equating the changes in value of the futures position with the opposite changes in value for the spot position. He also found the use of price changes gave results very close to those when using returns. Myers and Thompson10 advocated a generalized optimal hedge ratio estimate taking into account the conditional covariance between spot and futures price, and the conditional variance of the futures price. The emphasis was on the use of conditional moments versus uncondi- tional ones implicit in the usual simple regression approaches. Consistent with Brown, they observed that using price changes may be an appropriate estimator of the optimal hedge ratio under certain conditions. The empirical example they presented for corn, soybeans, and wheat supported the use of price changes. Witt, Schroeder, and Hayengall compared three analytical approaches for estimating hedge ratios. They suggested the appropriate hedge ratio was related to the underlying objective function of the hedger; the relationship between cash and futures prices; and whether the hedge was a storage hedge or an anticipatory hedge. They also recommended the price change model when the hedger was risk averse and wanted to minimize the variance of returns; when the cash- futures price relationship was linear; and when the hedge was for storage. Lence, Kimle, and Hay- engal2 elaborated further that the static minimum variance hedge ratio represented the optimum ratio for a myopic agent who was extremely risk averse, and when futures prices were unbiased, regardless of the risk attitude of the myopic deci- sion maker. Another reason cited for estimating the static minimum variance hedge ratio, as com-

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pared to a dynamic minimum variance ratio, was that it is tractable enough to use in real-world sit- uations.

Static minimum variance hedge ratios are tradi- tionally estimated using a price change model as specified in the following equation:

Hedge Ratio

The risk-minimizing hecde ratio derived for this study followed from the research background of the above prior studies. The framework for the hedge was that the agribusiness supplier wanted to protect a continuous and varying inventory position from economic loss due to adverse price changes in the local market. Refined fuel inventories are not stored for extended periods of time like grain, but instead serve as short-term buffer stocks at all levels in the flow from the refinery through the pipeline to distributors and retail outlets. The retail agribusiness maintains a continuous physical inventory to serve customer demand, but the inventory level varies as fuel sales draw it down and then as the retailer subsequently refills it. Based on industry sources, the average ownership period is 4 weeks in rural areas, which is the same as a physical turnover rate of every 4 weeks. Given this operating environment, the duration of the hedge period used in this study was 4 weeks with the periods sequentially ordered in time over the years of 1988-1992 to reflect a continuous inventory hedge. The futures position was adjusted every week to match the physical inventory, and the hedge was rolled forward every 4 weeks to a new contract month. The hedger was assumed to be risk averse and would not intentionally maintain a speculative position in either the cash or futures market.

where E(R) is the expected revenue from the hedgers cash X , and futures X , positions. The terms E(C,+, - C,) and E(F,+, - F,) are the expected changes in cash and futures prices, respectively, from the time t when the hedge is placed to time t + 1 when it is lifted.

In order to handle the draw down in physical inventory over the 4-week period, a variable WTS modifies both right-hand-side terms in Eq. 1. Equation 2 reflects the operating environment as follows:

4

E ( R ) = C WTS, . X c . E(C,+, - C,) w = l

4

w = l

where WTS, are the weekly weights of 1.0, 0 . 7 5 , 0.50, and 0.25 to reflect the declining level of physical inventory X , over the 4-week period, and the corresponding adjustment in the futures position X F . In the first week, the physical inventory is l .OX, and in the second week it is 0 .75XC, etc.

The same holds for the futures positions. The terms E(CW+, - C,) and E(Fw+I - F,) are the expected weekly changes in cash and futures prices, respectively. Equation 2 can be rewritten as shown in Eq. 3:

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E ( R ) = Xc.E ( Cm+l - C,)* -k XF'E (Fm+l - Frn)*

sion of cash price changes on futures price changes for N hedging periods as follows: (3)

where (C,+, - C,)*N =

a + P (L+l - U * N + EN (6) 4

Equation 6 was estimated using ordinary least E(C,+I - C,)* = c WTS, . E(Cw+l - C,) w = l

squares, and any autocorrelation indicated by the Durbin-Watson statistic was corrected with a first-order lag. The estimated models all had con-

and

stant variance for the error term. 4

E(F,+, - F,)* = c WTS, . E ( F w + , - F, ) . w = l

Hedging Eflectiveness The arithmatic result is the same when the weights WTsw are applied to the Price changes rather than the Physical

cash and futures The measure of hedging effectiveness comes from comparing the variance of revenue in a hedged PO- sition to the variance of revenue from an unhedged position.

X c and futures position X F . From Eq. 3 the variance of the revenue is

Var (R) = X$ U$ + X$ U$

-k x C ' F aCF (4)

where a$ and US are the variance of the weighted cash and futures price changes, respectively, and uCF is their covariance. Given the hedgers objective of minimizing the variance of revenue, the first derivative of Eq. 4 with respect to X, is set equal to zero resulting in the minimum variance hedge ratio:

H E = (Vur ( U ) - Vur (H*))lVur ( U ) (7 )

where hedging effectiveness HE is the variance of an unhedged position Vur( U ) minus the variance of a hedged position Vur(H*), using the minimum variance hedge ratio of p* = fi estimated from Eq. 6. Thus the numerator of Eq. 7 gives the reduction in the absolute level of variance when hedging is applied. The numerator divided by the variance of an unhedged position Vur(U), gives the relative reduction in variance from hedging. Equa- tion 7 simplifies to

The proportion of the cash position Xc that should be hedged with an opposite futures position XF is equal to the ratio of the covariance of cash and futures price changes to the variance of the futures price changes. This hedge ratio is equiva- lent to the P coefficient in a simple linear regres-

H E = 1 - (Vur (H*)lVur ( U ) ) = R2 (8)

which is the same as the R2 statistic, referred to as the coefficient of determination, for Eq. 6. Thus, hedging effectiveness refers to the reduction in variance of revenue as a proportion of total

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variance that results from maintaining a hedged position rather than an unhedged position. l3

Data

The data used to calculate the basis figures and estimate the hedge ratios came from the period of January 1, 1988 through December 31, 1992. Both the cash and futures price time series were found to be stationary when the autocorrelation function was plotted as a correlogram. The cash prices at the four terminal cities were the weekly average of wholesale rack prices for the branded products of No. 2 diesel fuel and unleaded regular gasoline. Rack prices are those paid by the reseller to the wholesaler at the pipeline terminal where the product is pumped into a truck. At the retail level an analogous term is the pump price. A branded product has a brand name associated with it such as Amoco or Texaco, while an unbranded product has no such name association even though it is supplied by a known oil company. No state or fed- eral taxes, or special fund charges were included in the rack prices.

The futures prices were the Friday closing prices for heating oil, unleaded regular gasoline, and crude oil which were all traded on the New York Mercantile Exchange. The New York Harbor is the delivery point for heating oil and gasoline futures contracts, and Cushing, Oklahoma is the delivery point for West Texas Intermediate (WTI) crude oil futures traded on the NYMEX. Crude oil futures were included as a possible cross-hedging contract for both diesel fuel and gasoline because of the closer proximity of the four cities in the Northern Plains to Cushing, Oklahoma versus the more distant New York Harbor. Cash prices and

basis figures in the Northern Plains were hypothe- sized to be more influenced by supply and demand conditions for crude oil at Cushing than the same conditions for heating oil and gasoline at the New York Harbor. Thus, using crude oil futures prices might result in a lower variability of the basis, and a higher level of hedging effectiveness.

The futures prices were for the second nearest contract month to the current cash month. This was done because trading in an energy futures contract expires on the last trading day of the pre- ceding month. For example, a February 1988 futures contract would expire during January 1988, thus the February futures prices were viewed as being heavily influenced by cash market conditions in the month of January. The second nearest month would be March 1988 and those futures prices would be used for the hedge.

Retail agribusinesses selling refined fuels to customers, or jobbers who sell and distribute to other resellers, can calculate basis figures, hedge ratios, and hedging effectiveness for their own locations. A minimum 3-year history of weekly cash prices at the retail pump or at the pipeline rack would need to be collected. Futures prices for heating oil, gasoline, and crude oil are available in newspapers such as the Wall Street Journal. Futures prices can be also acquired from private sources that sell data as well as from New York Merchantile Exchange publications. The basis figures, hedge ratios, and measures of hedging effectiveness could then be calculated as described in previous sections.

Results

The results that follow are organized into four sec-

tions. The first gives statistics on price levels for

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Northern Great Plalns

Table I. Futures and Cash Price Statistics, 1988-1992. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c/gal)

. . . . . . . . . . . . . . . . . . Futures Prices

Heating Oil Gasoline Crude Oil

Diesel Fuel Cash Scott City Lincoln Bismarck Rapid City

Gasoline Cash Scott City Lincoln Bismarck Rapid City

Standard Average Deviation

.......................................................

56.71 11.42 58.79 10.27 48.00 9.43d

59.07 59.60 61.73a.b 6.E. 33a7b4

63.94 64.19 67.87a-b 68.67a3b

11.76 11.75 11.72 12.35

10.71 10.71 10.45 11.418

Minimum Maximum ...............................

38.31 36.74 30.12

42.48 41.97 44.01 48.76

103.82 96.10 89.93

106.12 106.86 107.81 108.45

45.93 99.43 46.36 98.66 5 1.41 98.91 50.75 105.92

"Significantly different than for Scott City, at the 5% level. bSignificantly different than for Lincoln, at the 5% level. cSigniticantly different than for Bismarck, at the 5% level.

Slgnifcantly different and less than the standard deviation for heating oil futures prices, at the 5% level. cSipifkantly different than for gasoline futures prices, at the 5% level.

selected terminal locations in the Northern Plains and for the corresponding products in the futures markets. The second section contains measures of average basis levels and variability by terminal locations. The third and fourth sections give the hedge ratios and measures of hedging effectiveness, respectively.

Cash and Futures Price Statistics

Table I gives weekly average price levels and measures of variability for the selected cash and futures markets. Friday closing prices for the second nearest futures month to the cash month were

used to calculate the futures price entries for heating oil, gasoline, and crude oil. These statistics are displayed in the top three lines of Table I. On the top line, the average futures price for heating oil was 56.71 $/gal. over the period of January 1, 1988 through December 31, 1992. The standard deviation is a measure of price dispersion from the average, which for heating oil indicated that 68% of the time, prices were within plus or minus 11.42 $/gal. of the average price of 56.71 $/gal. Over the 1988-1992 time period heating oil futures prices ranged from a minimum of 38.31 $/gal. to a maximum of 103.82 $/gal., which occurred during the Persian Gulf War period.

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A similar interpretation applies to the unleaded regular gasoline and crude oil futures prices. Crude oil was converted from a dollar per barrel price to cents per gallon for ease of comparing fu-

tures prices and basis figures. The normal conver- sion factor is 42 gallons of refined product per barrel of crude oil. The differences between the crude oil price and gasoline and diesel prices reflected the costs of refining, distribution, and mar- keting.

Cash price statistics are given in the bottom two- thirds of Table I. Weekly average rack prices for branded products over the 1988-1992 period were used to calculate the entries for each terminal city. The average cash price for diesel fuel was lowest in Scott City, Kansas at 59.07 $/gal., followed by Lincoln at 59.60 @/gal., but the Lincoln price was not a statistically significant difference. The prices for Bismarck and Rapid City were higher and significantly different than for Scott City and Lin- coln. The Rapid City price was the highest and even significantly different than Bismarck’s average price. A similar low to high relationship ex- isted for average gasoline prices. Figure 1 shows the price levels for the first week of each month at the Lincoln terminal, and the price variability over the 1988-1992 time period.

The standard deviations of diesel fuel cash prices in Table 1 were statistically the same in all four cities even though Rapid City looked higher at 12.35 $/gal. The same relationships held for gasoline cash prices. When comparing cash and futures prices, diesel fuel cash prices for the first three cities had standard deviations close to the one for heating oil futures at 11.42 $/gal. While the standard deviation for Rapid City appeared higher when compared to diesel futures it was not significantly different. Similar comparisons of cash

I10

1W

90

C

m - o m

b

O W

- 70

c

50

40

no _ _ 1988 1990 lsal 1592 1993

Year

FigIIre 1. Diesel fuel and gasoline terminal prices at Lincoln, 1988-1992.

and futures price variability held for gasoline prices. In this case, Rapid City was significantly higher, but not by much.

Basis Statistics

The motivation for hedging diesel fuel and gasoline cash prices with offsetting futures contracts is to reduce, if not eliminate, financial losses due to changes in cash prices. While hedging may reduce losses from cash price changes, there still remains basis risk depending on the relationship between cash and futures prices. The basis is defined here as the cash price at a terminal city m i n u s the futures price quoted on the New York Mercantile Ex- change with a positive value indicating how many cents per gallon the terminal city price is over the futures price. The basis is determined by supply and demand conditions at the terminal city, and by expected supply and demand as reflected in the futures markets, plus a price differential for handling and distribution from a delivery point for a futures contract to the terminal city.

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I I I I I @) :A8 1663 lae0 1991 1892 1993

Year

Figure 2. Diesel fuel and gasoline terminal basis at Lincoln, 1988-1992.

Figure 2 shows the basis for the first week of each month at the Lincoln terminal, and its variability over the 1988-92 period. Table I1 gives the weekly basis statistics for No. 2 diesel fuel at the four cities when calculated using either heating oil

or crude oil futures prices. The average basis for Scott City was 2.36 $/gal. indicating that diesel fuel cash prices at Scott City were an average of 2.36 $/gal. over the heating oil futures price for the second nearest month to the cash market. Co- incidental with the increasing price levels shown in Table I, the basis also increases from the low of 2.36 $/gal. at Scott City to a high of 7.62 $/gal. at Rapid City. The average basis using crude oil futures went from a low of 11.06 $/gal. at Scott City to a high of 16.33 $/gal. for Rapid City. The higher crude oil basis values reflect a price difference that includes a refining cost for converting crude oil into diesel fuel. In addition, the delivery point of Cushing, Oklahoma for crude oil futures is different than the New York Harbor for heating oil.

All of the average basis figures were significantly different than zero. The average basis for Scott City and Lincoln were not significantly different

Table 11. Basis Statistics for No. 2 Diesel Fuel, 1988-1992. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(c/gal)

Average Staudard Minimum Maximum Basis Deviation Basis Basis

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Heating Oil Futures

Scott City 2.36 4.41 - 12.20 25.87 Lincoln 2.89 4.57 - 12.34 27.22 Bismarck 5.02a.h 5.07a%h -11.83 30.43 Rapid City 7.62a3h3r 6.22 a,h-c -9.26 27.09

Crude Oil Futures Scott City 11.06 5.07 2.22 35.20 Lincoln 11.60 5.17 2.08 36.55 Bismarck 13.734’ 5.42 3.12 39.76 Rapid City 16.33a7b9c 6.20a2b3c -2.00 37.34

*Significantly different than for Scott City, at the 5% level. bSiglllfcantly different than for Lincoln, at the 5% level. CSignificantly different than for Bismarck, at the 5% level.

Conley

I Table Ill. Basis Statistics for Unleaded Regular Gasoline, 1988-1992. I [ .......................................... - ..........................

.~

([/gal)

Average Standard Minimum Maximum Basis Deviation Basis Basis

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gasoline Futures

Scott City 5.16 4.96 -9.21 18.66 Lincoln 5.40 4.82 -8.35 20.68 Bismarck 9.08a.b 5.67a3b -5.24 27.37 Rapid City 9 .884' 6.66ah.c -6.89 27.98

Crude Oil Futures Scott City 15.94 6.02 4.47 32.28 Lincoln 16.19 6.05 4.94 33.97 Bismarck 19. 86a3b 6.24 8.00 36.12 Rapid City 20.66 a,b 6.39 8.25 36.93

~~~~~ ~~~~ ~~

.Si@kantly different than for Scott City, at the 5% level. bSipficantly different than for Lincoln, at the 5% level. ~SigniFcantly different than for Bismarck, at thr 5% level.

when using either heating oil or crude oil futures. However, the basis for Bismarck and Rapid City were different when compared to Scott City and Lincoln, and Rapid City was significantly different than Bismarck. The standard deviation of the basis increased

from Scott City to Rapid City for both heating oil and crude oil futures. Contrary to expectations, crude oil futures prices did not provide any lower variability in the basis figures when compared to using heating oil futures. Consistent with the motivation for hedging, the standard deviations of the basis at each city were significantly less than the standard deviations for the cash prices. From Table I the standard deviation of diesel fuel prices at Scott City was 11.76 @/gal., and in Table I1 the corresponding heating oil basis figure was 4.41 $/gal. The interpretation is that without hedging, cash prices will vary within a range of plus or minus 11.76 $/gal. 68% of the time. With hedging,

cash price changes wil l be offset by changes in heating oil futures prices, and the hedger will be faced with a basis that varies by plus or minus 4.41 @/gal. 68% of the time. A similar interpretation applies when using crude oil futures to offset cash price changes.

The weekly basis statistics for unleaded regular gasoline are given in Table 111. All average basis figures were significantly different than zero. The basis for Scott City was 5.16 $/gal. closely followed by Lincoln at 5.40 $/gal. The figures were significantly higher for Bismarck at 9.08 $/gal. and Rapid City at 9.88 $/gal. The standard deviation of the basis for each city was approximately half the standard deviation for the corresponding cash prices given in Table I, and the differences were statistically significant. As was the case for diesel fuel, the range of exposure to price changes would be reduced by about half when hedging with gasoline futures. Crude oil futures followed a


Table 1V. Hedge Ratios for No. 2 Diesel Fuel and Unleaded Regular Gasoline, 1988-1992.

Futures Contracts ....................................................

Heating Oil Crude Oi l .................................................... Diesel Fuel

Scott City 0.70 1.72 Lincoln 0.68 1.68 Bismarck 0.60 1.28' Rapid City 0.41 1.078

................................................... Regular Gasoline Crude Oil

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gasoline

Scott City 0.60 0.98' Lincoln 0.62 1.26' Bismarck 0.39 0.838 Rapid City 0.23 0.74a

~

.Hedge ratio is not different than 1.00 at the 5% level of statistical sigdkance.

similar basis pattern across cities, as for gasoline futures, but did not sigmficantly lower the basis variability compared to using gasoline futures.

Hedge Ratios and Hedging Efiectiveness

The hedge ratios for diesel fuel and gasoline are given in Table IV. In estimating the ratios, heating oil and gasoline futures prices were in cents per gallon, and crude oil futures prices were in dollars per barrel. The ratios show the quantity of futures product that should be used to offset one gallon of diesel fuel or gasoline. For example, at Scott City, 0.70 gallons of heating oil futures would be sold to hedge one gallon of physical diesel fuel owned in inventory. Given the operating

environment described earlier where the physical inventory declines over the 4-week period due to sales, and the futures position is adjusted to cor- respond with the physical inventory, then the hedge ratio of 0.70 minimizes the variance of revenue from both the cash and futures positions. Crude oil futures are a cross-hedging contract since the oil is not a refined product similar to diesel fuel and gasoline, but the interpretation of the ratio is the same. For example, the Scott City ratio indicates that 1.72 barrels of crude oil futures should be used to hedge one gallon of diesel fuel in inventory. All ratios were tested using the t test to see if

they were statistically different than one at the 5% level of significance. The hedge ratios using heating oil and gasoline futures contracts were all less than one. In contrast, the ratios when using crude oil futures to offset diesel fuel positions at Scott City and Lincoln were greater than one. The remaining entries for crude oil were not significantly different than one.

Measures of hedging effectiveness are given in Table V which shows the reduction in variance of revenue when hedging is used compared to not hedging. At Scott City, the variance was reduced by 37% when diesel fuel cash prices were hedged with heating oil futures. A nearly equal reduction in variance occurred for Lincoln at 34%. Bis- marck was less at 3070, and Rapid City only real-

ized an 18% reduction in revenue variance when hedging. Crude oil futures were less effective at hedging than were heating oil futures. A similar pattern of hedging effectiveness occurred for gasoline as for diesel fuel across cities and between futures contracts. Hedging gasoline inventories at Bismarck and Rapid City was essentially ineffective.

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-~

Table V. Hedging Effectiveness of the Hedge Ratios for No. 2 Diesel Fuel and Unleaded Regular Gasoline,

1988-1992. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Futures Contracts ~~ ~

Heating O i l Crude O i l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diesel Fuel

Scott City 0.37 0.25 Lincoln 0.34 0.23 Bismarck 0.30 0.17 Rapid City 0.18 0.14

................................................... Regular Gasoline Crude Oil

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gasoline

Scott City 0.23 0.11 Lincoln 0.25 0.17 Bismarck 0.11 0.09 Rapid City 0.05 0.08

Summary and Conclusions

The average price levels for diesel fuel and gasoline varied across the four terminal cities reflect- ing differing geographic locations relative to origination of supply, and local supply-demand conditions. The largest significant difference in prices was about 5@/gal. between Scott City, Kan- sas and Rapid City, South Dakota for both diesel fuel and gasoline. By comparison Lincoln’s average price was about 0.5@/gal. higher than Scott City but it was not si@icantly different.

Given this range in price levels across the four cities, the average basis also showed a similar pattern. The diesel fuel basis for Scott City was 2.36dgal. using heating oil futures while Rapid City’s basis was si@icantly higher at 7.62@/gal. The average gasoline basis was 5.16$/gal. com-

pared to 9.88@/gal. for the two cities, respectively. Again, the Lincoln basis was only 0.5dgal. higher than for Scott City, and not significantly different.

The hedge ratios for diesel fuel and gasoline did not support the traditional hedging rule of one gallon of futures product to offset one gallon of physical inventory. The ratios were all less than one in each of the four cities. Ratios using crude oil futures as a cross-hedge for diesel fuel were greater than one in Scott City and Lincoln, and were essentially equal to one for the remaining cities and products.

The measure of hedging effectiveness was low for all cities and products. The high for diesel fuel was at Scott City with a reduction in variance of 37% to a low at Rapid City of 18%. Gasoline hedging effectiveness ranged from 23% to 5% for the same respective cities. A slightly higher level of hedging effectiveness was achieved using heating oil and gasoline futures rather than crude oil futures.

When reviewing the above results three conclusions were drawn. One was that hedging worked only moderately in Scott City, Lincoln, and Bis- marck for diesel fuel by reducing revenue variability by about one-third. Hedging gasoline in Scott City and Lincoln was even less effective, reducing revenue variability by only about one- fourth. Hedging was ineffective in Rapid City for both products. A second conclusion was that the traditional hedging rule of one gallon of futures for one gallon of cash product did not work in all applications across cities and products. Crude oil futures could serve as a cross-hedge contract, but it does not work as well as the refined products. The third conclusion was that the basis, hedge ratios, and hedging effectiveness were not uniform across the four cities. The statistics for Scott City

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and Lincoln were essentially the same, but Bis- marck and Rapid City were substantially different. If an agribusiness wants to evaluate the

effectiveness of futures contracts to hedge, then it will need to estimate these statistics for its particu- lar terminal location.

References

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Heating Oil Futures,” The Journal of Futures Markets,

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6. H.M. Markowitz, Portfolio Selection: Efficient Diver-

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cultural Economics, 71(4), 858 (1989).

11. H.J. Witt, T.C. Schroeder, and M.L. Hayenga, “Compar-

ison of Analytical Approaches for Estimating Hedge Ra-

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Futures Markets, 7(2), 135 (1987).

12. S.H. Lence, K.L. Kimle, and M.L. Hayenga, “A Dynamic

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8. J.L. Stein, “The Simultaneous Determination of Spot and Lexington, MA., 1989.

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Hedging ratios and effectiveness for diesel fuel and gasoline the northern plains