FACULTY WORKING PAPER NO. 1344 Oil Prices and Energy Futures K. C. Chen R. Stephen Sears Dah-nein Tzang College of Commerce and Business Administration Bureau of Economic and Business Research University of Illinois, Urbana-Champaign BEBR FACULTY WORKING PAPER NO. 1344 College of Commerce and Business Administration University of Illinois at Urbana-Champaign March 1987 Oil Prices and Energy Futures K. C. Chen, Assistant Professor Department of Finance R. Stephen Sears, Assoicate Professor Department of Finance Dah-nein Tzan Chicago State University Abstract Oil price volatility has increased dramatically in the last few years. Energy futures can play a vital role in hedging the oil price volatility faced by producers, refiners and consumers. The empirical evidence in this research shows a strong correlation between futures price movements and spot prices in the crude oil, heating oil and leaded gasoline markets. The hedging results show that a substantial portion of the price risk can be removed through the use of energy futures while at the same time enhancing the hedger's portfolio return. Digitized by the Internet Archive in 2011 with funding from University of Illinois Urbana-Champaign http://www.archive.org/details/oilpricesenergyf1344chen Oil Prices and Energy Futures Prior to the 1970's, the oil industry was highly concentrated and vertically integrated. Many firms produced the crude oil, moved the crude to their refineries, and then distributed refined products such as heating oil and gasoline. During this time, prices were relatively low and stable. The oil industry went through major structural changes in the 1970's. As a result of these changes and a variety of other factors, there was a dramatic increase in the price volatility in oil prices which, in turn, affected the financial risk exposure of oil producers and users. Some of the possible measures which may aid in hedging this risk include: (1) a revision of the process by which oil prices are set; (2) long-term contracting between producers, refiners and consumers; (3) using the energy futures markets. Among these solutions, the use of energy futures markets would appear to be very promising. The purpose of this paper is to provide an ex post empirical analysis of the hedging potential of energy futures for three widely traded commodities: crude oil, heating oil and leaded gasoline. The analysis indicates the desirability of energy futures in reducing the price risk of energy products as well as in improving the risk-return performance of the hedger's position. The results also show that, in general, hedging effectiveness increases with the hedger's holding period and the nearer the contract's time to delivery. Section 1 contains a brief summary of the theoretical basis for determining hedge ratios and hedging effectiveness. A description of -2- the data base and empirical results regarding the hedging effectiveness of energy futures is presented in Section II. Section III summarizes the findings. I. Alternative Approaches to Hedging and Their Effectiveness Several hedging approaches have been discussed in the academic literature. In this section, we review briefly two of these approaches that will be used in our analysis. A. Minimum Risk Hedging Following the early works of Johnson (1960) and Stein (1961), Ederington (1979), Makin (1978), and McEnally and Rice (1979) have shown that the optimal minimum risk hedge ratio (HR*) and the hedging effectiveness of this ratio is related to the covariance between spot and futures price changes and the variance in futures price changes. Mathematically, the minimum risk hedge ratio is found as the solution to the following problem: 2 2 2 2 ? min: a (Ap ) = x a (As ) +x_a"(Af ) + 2x x.cov( As , Af ) (1) t s tf t st tt X f where: As , Af , Ap = the price change during period t of the spot, futures, and a portfolio of spot and futures, respectively. x = the proportion of the portfolio held in futures contracts. x = the proportion of the portfolio held in the spot s commodity and = 1 , by assumption. a = variance of price changes. The solution yields the optimal minimum risk hedge ratio HR*: x * = HR* = -cov(As ,Af )/a 2 (Af ) (2) -3- The value of HR* is equivalent to the negative of the slope coefficient of a regression of As against Af . When HR* < 0, a short position in futures is indicated; when HR* > 0, a long position in futures is required. For example, an HR* of -1.5 (1.5) indicates that the hedger should sell (buy) $1.50 in futures for every $1.00 held in the spot commodity. Many studies (e.g., Cicchetti, Dale and Vignola (1981), Franckle (1980), Grammatikos and Saunders (1983), Hill, Liro and Schneeweis (1983), Hill and Schneeweis (1982), Kuberek and Pefley (1983), Maness (1981), Marmer (1986), Overdahl and Starleaf (1986) and Senchack and Easterwood (1983)) have employed this "risk minimization" approach in the analysis of a variety of futures contracts. Determining hedge ratios in this manner assumes that the hedger' s objective is to receive the maximum amount of price change reduction. Literature ( Energy Futures: Trading Opportunities for the 1980's (1984)) describing the oil industry suggests that the objective of price change risk minimiza- tion is a reasonable assumption for many producers and refiners who are primarily in the business of production or delivery of oil and its refined products and must make commitments to buy and sell in an uncer- tain price environment. The hedging effectiveness of a minimum risk hedged position is 2 measured by the R of the regression of As against Af . The higher 2 the R value, the higher is the correlation between As and Af and the greater is the reduction in price change variance as a proportion of total variance that results from maintaining a hedged (x ±0) rather than an unhedged (x =0) position. -4- B. Risk-Return Hedging The risk minimization approach does not consider the return dimen- sion of hedging. Research by Anderson and Danthine (1980, 1981) Kopenhaver (1984), Nelson and Collins (1985) and Working (1953a, 1953b) have emphasized the need for a risk-return approach to hedging. Recent research by Howard and D' Antonio (1984, 1986) has extended these earlier efforts and developed an optimal risk-return hedge ratio and a risk- return measure of hedging effectiveness. The desirable feature of a risk-return approach is that it enables hedgers with different risk tolerances to hedge in an optimal fashion. The principal differences between the Howard and D'Antonio (1984) analysis and the more traditional risk-minimization approach include: (1) the use of returns rather than price changes (2) the incorporation of a risk-free asset i (e.g., Treasury Bill) in the analysis. The risk-return approach can be visualized in Figure 1. In Figure 1, the investor (hedger) has the choice of putting money into three assets: the risk-free asset (i), the spot commodity (s) and a futures contract on the spot commodity. The curved portion of Figure 1 represents the risk (a) and expected return (r) combinations for alternative spot- futures portfolios. Point i(s) represents the risk and return position 2 of a portfolio containing only the risk-free asset (spot) commodity. Assuming that the investor is seeking the greatest expected return for a given level of risk, all optimal portfolios lie on the straight line running from point i through the tangent portfolio point t and beyond. Portfolio t represents the optimal combination of spot and futures. -5- The investor would invest in this portfolio and borrow (at rate i) or invest (at rate i) to move to the desired point along the line. The exact position taken in the futures portion of portfolio t will depend upon the risk-free rate, the expected returns and standard deviations of returns for the spot and futures and the correlations between those returns. The optimal level of futures (hedge ratio) associated with portfolio t is found as the solution to the following problem: max: (r - i)/a P P X f (3) where: r , i = expected return on a portfolio of spot and futures and the risk free asset i, respectively. a = standard deviation of returns. P Figure 1 Risk-Return Hedging Analysis The solution (see Howard and D'Antonio (1984)) yields the optimal risk-return hedge ratio b* : x f = b* = (X-p)/ytt(1-X P ) (4) -6- where: X = (7 f /cr f )/((7 -i)/o ) t 1 s s it = a c /a f s Y - P f /P s p = correlation between spot and futures returns r ,r = expected one-period returns for spot and futures, respectively. a , a r = standard deviation of returns for spot and futures, respectively, s f p ,p f = current price per unit for spot and futures, respectively. The risk-return hedging effectiveness of futures can be measured by comparing the increase in portfolio expected returns for a port- folio which contains futures to one without futures at the same risk level. Figure 1 illustrates how this can be done. In Figure 1 the optimal risk-return hedge ratio b* measures the slope of line (i-t) and can be interpreted as the excess (in excess of risk-free return i) return per unit of risk available with the use of futures. The slope of line (i-s) measures the excess return per unit of risk available by investing in the spot only. Dividing the slope of line (i-t) by the slope of line (i-s) gives the increase in excess return per unit of risk of using futures and measures the hedging effectiveness (HE(b*)) of the optimal risk-return hedge ratio: / HE(b*) = /(l-2Xp+X 2 )/(l-p 2 ) (5) For example, an HE(b*) value of 1.20 means that the hedger can enhance the portfolio's excess return by twenty percent while maintaining the same risk level. -7- With regard to the risk-return approach and equations (4) and (5), several comments are in order. First, although the minimum risk hedge ratio (HR*) and the risk-return hedge ratio (b*) have the same inter- pretation, in general the numerical values of two ratios will be dif- ferent, even for the same spot-futures analysis. Second, the hedging effectiveness measures for the two ratios are different. For HR* , which is estimated using price changes, hedging effectiveness is measured by 2 R (correlation between spot and futures price changes). For b* , which is estimated using returns, X (the risk-return parameter) and p (corre- lation between spot and futures returns) are both important. Third, although HR* is usually derived using price changes, its hedging effec- tiveness can also be gauged on a risk-return basis by: HE(HR*) = //(1-p 2 ) (6) since HR* is derived under the assumption that r f = X = 0. Thus, equa- tions (5) and (6) enable a comparison of the "risk-return" effectiveness of b* and HR* , respectively. Finally, it is instructive to note that the risk-return approach is an ex ante method; b* may not have the highest ex post risk-return effectiveness. Having discussed these methods, we now turn to the empirical analysis and the evidence regarding the hedging effectiveness of energy futures. II. Empirical Analysis The purpose of the empirical analysis is to examine, ex post , the hedging effectiveness of energy futures. The analysis will begin with a description of the data base and sample period. Next, empirical results will be presented regarding hedge ratios determined using the risk -8- minimization and risk-return approaches. Finally, the ex post risk- return hedging effectiveness of these two approaches will be compared. A. The Data Currently, three corammodity exchanges in the United States trade energy-related futures: New York Mercantile Exchange (NYMEX), New York Cotton Exchange (NYCE) and the Chicago Board of Trade (CBOT). Futures volume and open interest figures indicate particularly heavy trading in three commodities: NYMEX Heating Oil, No. 2 (introduced in 1978), NYMEX Gasoline, Leaded Regular (introduced in 1981) and NYMEX Crude Oil, Light 3 Sweet (introduced in March, 1983). Whereas producers are primarily concerned with fluctuations in crude oil prices, refiners and consumers are also concerned with the volatility in the prices of refined prod- ucts such as heating oil and leaded gasoline. For this reason, all three commodities and their related futures contracts will be examined in the empirical analysis. Futures contracts on each of the three commodities call for delivery of 1000 barrels (1 barrel = 42 gallons). Currently, futures contracts trade as far out as 15 consecutive months for heating oil and leaded gasoline and 18 consecutive months for crude oil. Futures prices are quoted by the gallon for heating oil and leaded gasoline and by the barrel for crude oil. The sample period extends from July 20, 1983 - March 31, L986. The July 20, 1983 date is chosen to provide for seasoning in the crude oil market and to provide for a common sample period for all three commodi- ties. Figure 2 presents the weekly price series (per barrel) for these three commodities over the sample period. As Figure 2 indicates, 60 75 Time (in weeks) Figure 2 150 Weekly prices per barrel for Heating Oil (+) , Leaded Gas (*) and Crude Oil (O) for the period July 20, 1983-March 31, 1986. -10- energy prices were quite volatile and on average were declining over the sample period. Because many of the distant futures contracts have limited data, only the six nearby monthly contracts for each of the three commodities are used in the analysis. Futures prices for the six nearby monthly contracts as well as for each of the three commodities are gathered from the Wall Street Journal on a weekly basis using Wednesday closing prices. Although the sample includes 141 weekly spot prices for each commodity, some futures contracts do not have full data for all 141 weeks because on any given Wednesday a particular contract may not trade, Previous analyses of futures hedging indicate that hedging results can be affected by both the length of the investment horizon as well as 4 the time to delivery of the futures contract. While the choice of any particular hedging horizon provides information about the correlation between spot and futures price changes, its choice necessarily involves an assumption about the period of time for which the hedger desires coverage for the risk of unexpected price changes. Choosing an appropriate hedging horizon in energy futures is par- ticularly interesting because, unlike many commodities, the energy market deals with a product (oil well) whose production may extend for 10-20 years (or longer). Because existing futures contracts go out only 15-18 months, producers and refiners cannot hedge (at one time) the full value of all future production. Thus, an important decision is at what point should the hedge be placed? Because much of the oil trade operates on monthly delivery cycles, one possibility is to "stack" hedges for the next few months' deliveries. That is, use -11- futures contracts to place hedges for several months at a time, then as deliveries are made, establish new hedges to cover new future deliveries. However, because the trading is very thin in contracts beyond six months, this strategy seems advisable only for nearby pro- duction. Ideally, an empirical analysis of energy futures would examine hedging horizons ranging from one week to about six months. However, because the crude oil futures market is so new, data limitations restrict this study to hedges of just a few weeks. With this in mind, the data sets are partitioned so as to examine one and two week hedges across contracts separated into six monthly periods representing time to delivery (closest to delivery = one month; farthest to delivery = six months). Partitioning the sample in this manner produces twelve data sets for each of the three commodities. B. Risk Minimization Hedging Results As discussed in Section 1(A), the risk minimization hedge ratio (HR*) can be estimated via the following regression: 48 t = a : + a 2 Af t ♦ e £ (7) where: As , Af = s -s ,(s -s „) and f -f ,(f -f ) for one t t t t-1 t t-2 t t-1 t t-2 (two) week hedges. a.,a 9 = regression parameters where HR* = -a e = residual terra t Table I presents the statistical results of this regression for the one week hedging horizon while Table II presents the results for the two week k < 5 horizon. -12- It is instructive to note several things regarding the results in Tables I and II. First, all hedge ratios are negative and signifi- cantly different from zero. Thus, over the period examined, the risk- minimization hedging strategy was a short position in energy futures 2 for both one week and two week investment horizons. Second, the R values are highly significant, especially for the crude oil and leaded gas contracts, and indicate substantial risk reduction potential through hedging across all commodities, contracts and investment hori- 2 zons. Interestingly, the R values for heating oil are considerably lower than the other two commodities. One factor that may account for this result is the greater seasonality present in heating oil. 2 Third, the R values indicate that, in general, hedging effective- ness declines with time to delivery for both the one week and two week investment horizons. Thus the closer to expiration a contract is, the more effective it is in hedging energy price risk. This result is con- sistent with the general findings of earlier studies of other commodities: Treasury Bills (Cicchetti, Dale and Vignola (1981) and Ederington (1979)), GNMAs (Ederington (1979) and Hill, Liro and Schneeweis (1983)), foreign currencies (Hill and Schneeweis (1982)), corporate debt (Kuberek and Pefley (1983)), certificates of deposit (Overdahl and Starleaf (1986)), and corn and wheat (Ederington (1979)). Manner's (1986) 2 study of Canadian dollars reports mixed results regarding R and time to delivery. 2 Fourth, in general, the R values are higher for the two week hedging horizon (Table II) which indicates the greater hedging effec- tiveness for the longer (two week) investment period. This relationship 2 between R and the hedging period is similar to the findings of other -13- studies of futures: Treasury Bills (Cicchetti, Dale and Vignola (1981) and Ederington (1979)), Canadian dollars (Marnier (1986)), certificates of deposit (Overdahl and Starleaf (1986)), GNMAs (Ederington (1979) and Hill, Liro and Schneeweis (1983)) and corn and wheat (Ederington (1979)) Fifth, many of the risk minimization hedge ratios are significantly different: from one, and, in general, the magnitude of the hedge ratios increases as the hedging period increases from one week to two weeks. This indicates the desirability of the risk-minimization approach in these cases vis a vis a commonly used naive strategy of hedging the spot commodity dollar for dollar with the futures contract. Studies by Cicchetti, Dale and Vignola (1981), Ederington (1979), Franckle (1980), Hill and Schneeweis (1982) and Marmer (1986) generally found hedge ratios to be an increasing function of hedging horizon. On the other hand, Miller's (1982) study of live hog futures found an inverse relationship between the length of the hedging horizon and the magni- tude of the hedge ratio. Maness (1981), Miller and Luke (1982) and Overdahl and Starleaf (1986) found no particular relationship between these two variables. Finally, it is instructive to note that our objective is to present ex post evidence of the hedging potential of energy futures. The hedge ratios presented in Tables I and II are average relationships over the sample period and may vary from period to period. C. Risk-Return Hedging Results The calculation of the risk-return hedge ratios is accomplished by first converting each data set from prices into percentage return equivalents: -14- r = (s /s^ , )-l and r c = (f„/f^ , )-l for one week returns (8) s , t C t-I r , t C t-1 r = (s /s^ ~)-l and r c = (f\ /f ~)-l for two week returns (9) s , t t t— A r , t t t-Z From the series of returns, ex-post average returns and the associated statistics required for Equation (4) can be computed. The risk-free rate i is calculated as the return on a one (two) week Treasury bill for the one (two) week investment horizon. Tables II and III present the results for b* , p and X for the one and two week investment horizons. Consistent with the risk-minimization (price changes) results, there is a strong correlation between spot and futures returns and the correlation declines, in general, with time to delivery for both the one week and two week investment horizon data sets. Furthermore, the correlation in returns increases, in general, with investment horizon. However, unlike the risk minimization horizon results (but similar to the results presented in Howard and D'Antonio (1986), not all of the risk-return hedge ratios are negative. If 1 - Xp > (see Equation 4), then b* > when X > p and b* < when X < p. In general, we observe these results in Tables III and IV. However, the data in Tables III and IV indicate considerable variation in the value of X (particularly for the heating oil results), the return/risk parameter. Because b* is affected not only by p, but also return/risk (X), this can produce considerable changes in both the magnitude as well as the sign (when 1-Xp<0) of b*. Thus, the determination of b* can be quite sensitive to the relative values of the parameters (particularly X) affecting its value. -15- D. Risk-Return Hedging Effectiveness — Risk-Minimization vs. Risk-Return Using Equations (5) and (6), the risk-return effectiveness measures for the risk-return hedge ratios (b*) and the risk-minimization hedge ratios (HR*) are calculated for the one wee-k and two week investment horizons data sets. These results are presented in Tables V and VI. The results reveal some interesting aspects regarding the _ex post hedging effectiveness of these two hedging approaches. First, all of the effectiveness numbers are greater than one, indicating a risk- return benefit to hedging with energy futures. Second, an examination of both tables reveals that, on the whole, the risk-return effectiveness of both HR* and b* decline with time to delivery. That is, the most effective hedge (whether risk-minimization or risk-return) from a risk-return perspective is the nearby (one month) contract. Exceptions to this (see Table V) are the crude and heating oil one week HE(b*) results. The HE(HR*) results are not particularly surprising since the risk-return effectiveness measure (equation (6)) increases directly when the correlation in returns increases. The results also indicate that the risk-return effectiveness improves with the length of the hedging period. With the exception of leaded gas, the two week results (Table VI) are higher than the one week results (Table V). Finally, in most cases, the ex post risk-return effectiveness for the risk-minimization ratios is greater than the risk- return ratios. This result is comparable to the finding by Howard and D'Antonio (1986) that, ex post , the risk-return approach may not provide the highest performance. Thus, although the risk-return hedge approach -16- would have improved the risk-return performance of the hedger's port- folio, the performance would have been even better by following a risk minimization approach. III. Conclusion Oil price volatility has increased dramatically in the last few years. Energy futures can play a vital role in hedging the oil price volatility faced by producers, refiners and consumers. The empirical evidence in this research shows a strong correlation between futures price movements and spot prices in the crude oil, heating oil and leaded gasoline markets. The hedging results show that a substantial portion of the price risk can be removed through the use of energy futures while at the same time enhancing the hedger's portfolio return. -17- Bibliography Anderson, R. , and Danthine, J. (1980): "Hedging and Joint Production," Journal of Finance , 35: 487-98. Anderson, R. , and Danthine, J. (1981): "Cross Hedging," Journal of Political Economy , 89: 1182-96. Chang, J. S. K. , and Shanker, L. (1986): "Hedging Effectiveness of Currency Options and Currency Futures," The Journal of Futures Markets , 6: 289-305. Cicchetti, P., Dale, C. , and Vignola, A. (1981): "Usefulness of Treasury Bill Futures as Hedging Instruments," The Journal of Futures Markets , 1: 379-87. ~~ Ederington, L. (1979): "The Hedging Performance of the New Futures Markets," Journal of Finance , 34: 157-70. Energy Futures: Trading Opportunities for the 1980s (1984): Tulsa: Tulsa: Pennwell Publishing Company. Franckle, C. (1980): "The Hedging Performance of the New Futures Market: Comment," Journal of Finance , 35: 1273-79. Grammatikos, T. , and Saunders, A. (1983): "Stability and the Hedging Performance of Currency Futures," The Journal of Futures Markets , 3: 295-305. Hayenga, M. , and DiPietre, D. (1982): "Hedging Wholesale Meat Prices: Analysis of Basis Risk," The Journal of Futures Markets , 2: 131-40. Hill, J., Liro, J., and Schneeweis, T. (1983): "Hedging Performance of GNMA Futures Under Rising and Falling Interest Rates," The Journal of Futures Markets , 3: 403-13. Hill, J., and Schneeweis, T. (1982): "The Hedging Effectiveness of Foreign Currency Futures," The Journal of Financial Research , 3: 95-104. Hirschfeld, D. (1983): "A Fundamental Overview of the Energy Futures Market," The Journal of Futures Markets , 3: 75-100. Howard, C. , and D'Antonio, L. (1984): "A Risk-Return Measure of Hedging Effectiveness," Journal of Financial and Quantitative Analysis , 19: 101-12. Howard C. , and D'Antonio, L. (1986): "Treasury Bill Futures as a Hedging Tool: A Risk-Return Approach," The Journal of Financial Research, 9: 25-40. -18- Johnson, L. (1960): "The Theory of Hedging and Speculation in Commodity Futures," Review of Economic Studies , 27: 139-51. Kahl, K. , and Tomek, W. (1982): "Effectiveness of Hedging in Potato Futures," The Journal of Futures Markets , 2: 9-18. Koppenhaver, G. (1984): "Selective Hedging of Bank Assets with Treasury Bill Futures Contracts," Journal of Financial Research , 7: 105-19. Kuberek, R. , and Pefley, N. (1983): "Hedging Corporate Debt with U.S. Treasury Bond Futures," The Journal of Futures Markets , 3: 345-53. Makin, J. (1978): "Portfolio Theory and the Problem of Foreign Exchange Risk," Journal of Finance , 33: 517-34. Maness, T. (1981): "Optimal versus Naive Buy-Hedging with T-Bill Futures," The Journal of Futures Markets , 1: 393-403. Marmer, H. (1986): Portfolio Model Hedging with Canadian Dollar Futures: A Framework for Analysis," The Journal of Futures Markets , 6: 83-92. McEnally, R. , and Rice, M. (1979): "Hedging Possibilities in the Flotation of Debt Securities," Financial Management , 8: 12-18. Miller, S. (1982): "Forward Pricing Feeder Pigs," The Journal of Futures Markets , 2: 333-40. Miller, S. , and Luke, D. (1982): "Alternative Techniques for Cross- Hedging Wholesale Beef Prices," The Journal of Futures Prices , 2: 121-29. Nelson, R. , and Collins, R. (1985): "A Measure of Hedging' s Performance," The Journal of Futures Markets , 5: 45-56. Overdahl, J., and Starleaf, D. (.1986): "The Hedging Performance of the CD Futures Market," The Journal of Futures Markets , 6: 71-82. Senchack, A., and Easterwood, J. (1983): "Cross Hedging CD's with Treasury Bill Futures," The Journal of Futures Markets , 3: 429-38. Schwartz, E. , Hill, J., and Schneeweis, T. (1986): Financial Futures: Fundamentals, Strategies and Applications , Richard D. Irwin, Homewood , Illinois. Stein, J. (1961): "The Simultaneous Determination of Spot and Futures Prices," American Economic Review , 51: 1012-25. Working, H. (1953a): "Futures Trading and Hedging," American Economic Review , 48: 314-43. Working, H. (1953b): "Hedging Reconsidered," Journal of Farm Economics , 35: 544-61. D/108 -19- Footnotes K* Financial exposure to oil price volatility also extends to many governmental units as evidenced in the recent decline in crude oil prices in 1985-1986. For example, it has been estimated that for every $1 drop in the price per barrel of crude oil, the states of Alaska and Texas will lose $150 million and $70 million, respectively, in current tax revenues ( USA Today , March 14, 1986, p. 10a). "As Howard and D'Antonio (1984) point out, their zero margin requirement assumption implies that a portfolio containing only futures cannot be represented in Figure 1 because both the expected return and standard deviation of such a portfolio would be infinite. Futures contracts on unleaded gasoline were recently introduced. Because of their limited data base, these contracts are not included in the analysis. 4 Prior empirical studies of hedging in futures markets have used a variety of hedging period lengths. In general, studies of financial futures have used shorter investment horizons than studies of agriculturally-related products whose analyses employ storage and/or planting/harvest periods. The table below gives a partial bibliography of prior studies, the commodities examined and the hedging periods used. Study Chang and Shanker (1986) Cicchetti, Dale and Vignola (1981) Ederington (1979) Franckle (1980) Grammatikos and Saunders (1983) Hill, Liro and Schneeweis (1983) Hill and Schneeweis (1982) Hayenga and Pietre (1982) Howard and D'Antonio (1986) Kahl and Tomek (1982) Kopenhaver (1984) Kuberek and Pefley (1983) Maness (1981) Marmer (1986) McEnally and Rice (1979) Miller (1982) Miller and Luke (1982) Overdahl and Starleaf (1986) Senchack and Easterwood (1983) Commodity foreign currencies Treasury Bills Treasury Bills, GNMAs , corn and wheat Treasury Bills foreign currencies GNMAs foreign currencies beef Treasury Bills potatoes Treasury Bills Treasury Bonds and corporate debt Treasury Bills Canadian dollars corporate debt hogs beef certificates of deposit certificates of deposit Hedging Period(s) 1 week 2 and 4 weeks 2 and 4 weeks 2 and 4 weeks 2 weeks 1 week 1, 2 and 4 weeks 2 months 1 week 4, 5 and 6 months 3 months 4 weeks 5 days to 60 days 1 , 2 and 4 weeks 1 week 6 and 10 months 3, 6 and 12 months 1, 2 and 13 weeks 3 and 6 months -20- Even though the regressions are expressed in difference form, some of the regressions required correction for first order autocorrelation of the residuals. While this correction preserves the desirable econometric properties of the coefficients, its correction implies that R values (a relative goodness of fit measure) are not strictly comparable, per se. This is because the dependent variable is no longer the same across the corrected regressions. Each regression was also estimated via the random coefficient approach (see Grammatikos and Saunders (1983) for discussion). While the random coefficient hedge ratios are very similar to those presented in Tables I and II, some regressions showed evidence of non- stationarity. These results are not presented here and are available upon request from the authors. Results for y and tt which also determine b* are not presented here, but are available upon request from the authors. In general, Y (p c /p ) is close to 1.00 and the effects of tt (a c /a ) are ts rs incorporated in X. 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