- Email: [email protected]
Fuel price risk management using futures
Journal of Air Transport Management 5 (1999) 39 — 44
Fuel price risk management using futures Vadhindran K. Rao* Business Administration Department, Embry-Riddle University, 600 S. Clyde Morris Blvd., Daytona Beach, FL 32114, USA
Abstract The primary objective of this study is to investigate whether an ongoing policy of hedging jet fuel price risk using heating oil futures contracts reduces the volatility of quarterly pretax income of an average major airline in the US. The results indicate that, after controlling for trend, seasonality, and persistence of shocks, hedging has the potential to reduce the unexplained volatility of the average airline’s quarterly income by over 20%. Thus, the results suggest that the usefulness of hedging is not restricted to protecting weak airlines incapable of withstanding an increase in fuel prices. Also, airlines should not eschew hedging merely because of the possibility of incurring opportunity costs if fuel prices go down rather than up; hedging appears to pay off in the long run by providing a more stable earnings stream. Further, the results also point to the importance of selecting an appropriate futures contract and timing the hedging transactions properly. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Airline management; Fuel price risk; Hedging
1. Introduction Airline earnings are highly volatile and therefore, airline stocks trade at relatively low Price/Earnings (P/E) ratios (see Fig. 1). It is commonly believed that one of the most important sources of volatility in airline earnings are fuel prices. In fact, airlines’ exposure to this risk is believed to be greater than their exposures to either interest rate or foreign exchange risk (Quinn, 1996). Airlines are often urged to protect themselves from fuel price fluctuations by making use of various types of derivative instruments. The primary objective of this study is to investigate the hedging effectiveness of one such instrument, namely heating oil futures. The main question addressed is whether an ongoing strategy of anticipatory long hedges applied using heating oil futures contracts reduces the volatility of quarterly profits of an average large airline in the United States. Major airlines consume over 2.5 billion gallons of fuel a year; therefore, an increase of even a single cent in the
* Tel.:#1 904 226 6246; fax:#1 904 226 6696; e-mail: [email protected]. erau.edu. The average quarterly pretax income of the ten largest extant US airlines combined over the period 1988—97 is $136 million while the standard deviation is $1228 million.
price of fuel means an increase of over $25 million in annual operating expenses. Further, fuel costs account for over 10% of the operating expenses of an airline. Consequently, industry experts often advocate fuel price risk hedging by airlines. For example, in an article explaining the uses of various alternative derivative instruments to manage jet fuel price risk, Ubhi, 1996—97 asserts that ‘‘2 an airline that could protect itself against price increases would, in addition to managing its costs and protecting its revenues, have a significant marketing edge over its competitors . . .’’ The intuition underlying input price risk hedging using futures in a single-period framework is straightforward. Suppose that the hedging strategy is implemented using heating oil futures, a strategy often recommended owing to the strong correlation between the price of heating oil and the price of jet fuel. An airline can protect itself from an increase in fuel prices by entering into an anticipatory long hedge — for example, going long on heating oil futures at the start of the period being hedged, and entering into an offsetting contract at the end of the period. Any increase in operating costs resulting from an increase in the price of jet fuel is then likely to be offset, at least partially, by a profit on the futures position. Of course, if prices go down, then the decrease in costs will be offset by losses on the futures position. From a single period perspective, hedging using futures can enable an
0969-6997/99/$ — see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 6 9 9 7 ( 9 8 ) 0 0 0 3 5 - 0
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V.K. Rao / Journal of Air Transport Management 5 (1999) 39—44
Fig. 1. The chart shows the time series of combined quarterly pretax income of the top ten major airlines in the US over 1988—1997.
airline to ‘‘lock in’’ its cost of fuel for the coming period, or at least reduce the level of uncertainty regarding the effective cost of fuel for the period, and thereby possibly reduce the uncertainty associated with operating costs and earnings for the period. While the point that hedging using futures can protect an airline’s current period earnings against increases in the price of fuel is important, typically, the objective of a hedging corporation is not to merely reduce uncertainty about earnings in the current period, but to reduce the volatility of earnings over time. A top level executive from Lehman Brothers, New York is quoted in Quinn, 1996 as saying in the context of foreign currency risk faced by major US airlines: ‘‘To the extent that US airlines can manage these exposures, producing less volatility in earnings estimates, shareholders will be more comfortable and their multiples could increase.’’ Therefore, an interesting question is how effective an ongoing hedging strategy using futures is likely to be in reducing the volatility of airline earnings. Accordingly, this study uses actual quarterly revenue, cost and income data for the period 1988—97 of ten US airlines to construct an ‘‘average’’ airline, and the focus of the study is the impact of an ongoing quarterly hedging strategy applied using heating oil futures on the volatility of quarterly pretax income of this average airline. The issue of hedging effectiveness is important for more reasons than one. For one thing, the cost of implementing a fuel price risk hedging program could be as high as 1% of an airline’s fuel budget. Therefore, an airline needs to know the potential benefits from hedging to determine if it is worth the cost. The usefulness of hedging can also be questioned on grounds other than the cost of implementation. For instance, it is possible that operating revenues are positively related to fuel price changes, either because of
market power enjoyed by the airline whereby it has the ability to pass on fuel price increases to consumers, or because of a positive relationship between energy prices and demand for air travel. In such cases, an airline is at least partially hedged against fuel price increases. In fact, it is even possible that the relationship between earnings and futures price change is positive rather than negative. If so, the conventional strategy of a long hedge would serve to increase rather than decrease the volatility of earnings. Another case in which the conventional hedging strategy would be inappropriate if there are so many uncorrelated random factors impacting on airline earnings that there may be no discernible relationship between an airline’s earnings and fuel price. In such a case, again, hedging may increase rather than decrease the volatility of earnings. Further, hedging using futures is a double-edged sword. A hedging corporation can incur substantial opportunity costs if fuel prices go down rather than up. For these or other reasons, US airlines, unlike their European counterparts, have not been very active hedgers. As mentioned by Adams, 1997, most major airlines in the US hedge barely 15% of their fuel requirements. It seems worthwhile to examine whether such a policy is justified.
2. Theoretical framework The theoretical framework for analyzing the fuel price risk hedging decision faced by an airline is described below. The model is initially developed in a single-period framework. Each futures contract is assumed to be for one gallon of heating oil. For simplicity, entering into a futures contract is assumed to be costless, and the
V.K. Rao / Journal of Air Transport Management 5 (1999) 39—44
marking-to-market feature is ignored. At the beginning of the period, the information set of the airline consists of the joint probability distribution of its pretax income and futures price change for the period. The airline can take a position in heating oil futures at the beginning of the period so as to change the distribution of its pretax (post-hedge) income so as to better suit the decision maker’s risk preferences. The sole decision variable faced by the airline is the number of futures contracts it should buy or sell. At the end of the period, the airline closes its futures position by entering into an offsetting contract; also, its pre-hedge income is revealed, and its post-hedge income is just the sum of its pre-hedge income and profits (or losses) on its futures transactions. In symbols, n "n #X (*f ), (1) F S where n is the random pretax pre-hedge income of an S airline, n the random pretax post-hedge income, f the F random per gallon futures price of heating oil at the end of the period, F the known per gallon futures price of heating oil at the beginning of the period, *f"f !F , the change in the futures price over the period and X the number of futures contracts bought at the beginning of the period, the sole decision variable in the model. In general, the optimal futures position would depend on the relationship between income and futures price change, the expected change in futures price and the risk preferences of the decision maker. Therefore, the optimal hedge has a pure hedging as well as a speculative component. (See Duffie (1989), Chapter 4 for a simple meanvariance model that makes this point). However, as in Ederington (1979) and Koppenhaver (1985), the effectiveness of a hedging strategy using futures can be gauged by determining the maximum possible percentage reduction in risk that can be achieved. Therefore, for the purpose of the empirical analysis, it is assumed that the objective of the airline is to minimize the variance of income. Accordingly, differentiate the variance of post-hedge income Var +n ,#X Var +*f ,#2X Cov +n , *f , (2) S S with respect to X, set the derivative equal to zero, and solve for X to obtain the minimum variance hedge: !Cov +n , *f , S X" . Var +*f ,
(3)
Hedging effectiveness may then be measured as Var +n , +4 , H.E."1! Var +n , S
(4)
For reasons that will become apparent later, the analysis focuses on pretax income rather than net income.
41
where H.E. denotes the measure of hedging effectiveness, and n denotes post-hedge income corresponding to +4 the minimum variance hedge. Using Eq. (3), it is seen that (Cov +n , *f ,) S H.E." . (5) Var +*f , Var (n ) S Assuming that the variables, n and * f are jointly S independently and identically normally distributed, H.E. can be estimated as the coefficient of determination (or R) in the simple linear regression of pre-hedge income, n , on change in futures price, *f. Note that, under this S assumption, following the minimum variance policy would not only reduce uncertainty of earnings in the coming period, but also reduce volatility of earnings over time. 2.1. Measuring hedging effectiveness: A refinement A problem with the approach outlined above is that it ignores the predictable variability of earnings due to factors such as the seasonal nature of airline demand as well as the upward trend in airline earnings. It seems desirable to measure the impact of hedging on the volatility of income after factoring out all predictable variation in the expected level of income. Accordingly, the measure of hedging effectiveness used in this study is calculated as follows: 1. The residuals from the regression of n on the followS ing explanatory variables is estimated: ¹IME, a trend variable that takes the value 1 in the first quarter of the sample period and is incremented by a unit every subsequent quarter; dummy variables, Q , Q , and Q , representing calendar quarters 2, 3 and 4, respectively, and income during the previous quarter. n "a #a ¹IME #a Q #a Q S R R R R #a Q #a n #e . (6) R S R\ R The dummy variables help account for seasonal variation in airline demand. The trend variable may be interpreted as allowing for the growth of the airline. Lagged income is included to allow for the possibility that shocks to airline earnings may dissipate only gradually. The residuals from this regression may be viewed as representing the unpredictable component of income. 2. Next, these residuals are regressed on change in futures price: e "b #b *f #u . R R R
(7)
As explained later, not including a lagged dependent variable in the model results in autocorrelation among the residuals.
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V.K. Rao / Journal of Air Transport Management 5 (1999) 39—44
The R of this regression is the percentage decrease in the unpredictable variability of income from following a minimum variance hedging strategy, and is therefore an appropriate measure of hedging effectiveness. Further, the minimum variance hedging quantity is given by !b , the negative of the coefficient of *f in Eq. (7). This approach to measuring hedging effectiveness is superior to one based on a simple regression of income on futures price change in that, unlike the latter, it allows the conditional mean of income to change over time. However, the approach has the following drawbacks: (a) It assumes that the conditional variances of income and futures price changes are constant over time; (b) it imposes the requirement that the quantity of futures contracts bought each quarter should be the same; and (c) the optimal hedge determined by this method could not have been implemented by an airline as the estimation is based on data pertaining to the entire sample period. While these objections have merit, it should be noted that the objective of this study is to obtain a first pass estimate of the potential effectiveness of fuel price risk hedging, rather than to present airline managers with a recipe for effective hedging. 2.2. Data and hedging strategies Data about the spot price of jet fuel as at the end of each month over 1988—97 were gathered from various issues of the Monthly Energy Review (published by the Energy Information Administration, US Dept. of Energy). Quarterly airline data, gathered from various issues of ¹he Airline Monitor (published by ESG Aviation Services), consist of total operating revenues, total operating costs, pretax income, cost per gallon of fuel consumed, and total number of gallons of fuel consumed in each quarter for the period 1988—97 for 10 of the largest US airline companies, namely, Alaska Air Group, America West, AMR Corp., Continental Airlines, Delta Air Lines, NWA Inc., Southwest Airlines, Trans World Airlines, UAL Corp., and US Airways Inc. The operating and financial statistics of the ‘‘average’’ airline are constructed as a weighted average of the statistics pertaining to these 10 companies with the weights based on the quantity of fuel consumed by an airline in each quarter. As mentioned earlier, the study focuses on pretax income rather than net income. The main reason for this is to avoid the complications associated with determining an appropriate tax rate for calculating after-tax profits/losses on futures positions for this fictional average airline. Table 1 contains sample statistics, namely the sample mean and standard deviation, pertaining to the average airline’s quarterly pretax income, operating revenues, operating costs, and per gallon fuel costs. The standard
Table 1 Summary statistics for the average airline, quarterly data, 1988—97 Op. revenues Op. costs Pretax Fuel cost (000,000s of $) (000,000s of $) income per gallon (000,000s of $) (cents) Mean 2443.02 Std dev 452.46
2358.99 382.93
38.03 177.06
61.80 9.88
deviation of per gallon cost of fuel shows that fluctuations of as much as 10 cents from one-quarter to the next are not uncommon. The hedging strategy is based on heating oil futures traded on the New York Mercantile Exchange (NYMEX). Data on futures prices were obtained from a CD-ROM titled ‘‘Historical data’’ sold on a commercial basis by the firm ¹urtle ¹rader. A description of the hedging strategy is as follows. The airline is assumed to hedge for one quarter at a time. Two alternative heating oil futures contracts are considered for the purpose of implementing the hedge: (a) the contract expiring in the month immediately following the quarter being hedged (hereafter referred to as Contract A) and (b) that expiring in the first month of the quarter being hedged (hereafter referred to as Contract B). The study examines a total of three hedging plans: two based on Contract A and one on Contract B. Plan 1 consists of taking a position in the heating oil futures Contract A at the end of the previous quarter and entering into an offsetting contract at the end of the quarter being hedged. In other words, Plan 1 consists of entering into an anticipatory hedge at the end of the previous quarter using Contract A. For example, under Plan 1, an airline whose income is negatively correlated with futures price changes and is seeking to hedge for the quarter January 1987 to March 1987 would buy the futures contract maturing in April 1987 in end-December 1986 and sell the contract in end-March 1987. Plan 2 consists of entering into an anticipatory hedge using Contract A three months prior to the quarter being hedged and offsetting the position at the beginning of the quarter. Plan 3 is identical to Plan 2 except that Contract B is used instead of Contract A.
3. Results Table 2 contains the results from regressing each airline’s per gallon cost of fuel for a quarter on each of four independent variables, namely (i) the average spot price of jet fuel in that quarter (an average of the spot prices that prevailed on the last day of each month during the quarter), (ii) the futures price of Contract A as at the end of the quarter, (iii) the futures price of Contract A as at
V.K. Rao / Journal of Air Transport Management 5 (1999) 39—44
Table 3 Empirical regression models to explain variation in pretax income, op. rev. and op. costs
Table 2 R of regressions Dependent variable: Quarterly fuel cost per gallon Independent variables
Independent variables
Spot price Futures price of jet fuel of Contract A as of end of quarter
Futures price Futures price of Contract A as of Contract B as of beg. of quarter of beg. of quarter
97.49%
87.94%
28.58%
43
74.59%
Intercept TIME
Note: All regressions are significant at the 1% level. Quarter 2
the beginning of the quarter and (iv) the futures price of Contract B as at the beginning of the quarter. Observe that the strong correlation between the spot price of jet fuel and the average airline’s cost of fuel confirms anecdotal evidence regarding the lack of hedging activity on the part of most US airlines. Further, note that (ii) is the price at which an airline implementing an anticipatory long hedge would execute the offsetting transaction (of selling the futures contract) as per Plan 1. Similarly, (iii) is the selling futures price according to Plan 2, and (iv) the selling futures price according to Plan 3. The higher the degree of correlation of either (ii), (iii) or (iv) with the airline’s cost of fuel, more effectively can the airline lock in its cost of fuel in advance by implementing the corresponding plan. The results suggest that Plans 2 and 3 are likely to perform better than Plan 1. However, hedging effectiveness ultimately depends on the relationship not between spot and futures prices but between income and futures price change, and this is examined next. Table 3 contains regression results of simple models to estimate the unpredictable component of the average airline’s income, operating revenues, and operating costs for the sample period 1988—97. The results show that all the dependent variables exhibit seasonality, and that pretax income and operating revenues also exhibit a statistically significant upward trend. An analysis of the residuals using the Breusch—Godfrey test does not reveal any autocorrelation patterns among the residuals. Further, the R’s of the models are also quite high. Thus, the models provide a good fit to the data. For example, the model for quarterly income explains over 75% of the variation in the variable. The balance may be interpreted as random or unpredictable variability. Table 4 contains results showing the effectiveness of each of the three hedging plans. Hedging effectiveness, as For all the three dependent variables, the Durbin—Watson statistic indicates the presence of autocorrelation among the residuals if a lagged value is not included as an explanatory variable. However, if a lagged value is included, then the Breusch—Godfrey test statistic is consistent with the hypothesis of no autocorrelation of up to the fourth-order among the residuals. Note that the Durbin—Watson statistic cannot be used in lagged dependent variable models, and hence the use of the Breusch—Godfrey test. See Thomas, 1997 pp. 304—306 for a discussion of relevant issues and details of the test.
Quarter 3 Quarter 4 Lagged dep. var. R of Regression Breusch—Godfrey
Dependent variables: (in millions of $) Pretax income
Op. rev.
Op. costs
!5.25 (0.905) 2.49 (0.077) 94.33 (0.029) 29.56 (0.537) !252.68 (0.000) 0.74 (0.000)
727.62 (0.003) 16.73 (0.004) 152.55 (0.000) 143.43 (0.000) !108.37 (0.012) 0.55 (0.001)
174.73 (0.170) 2.22 (0.364) 72.41 (0.009) 92.62 (0.001) 61.26 (0.025) 0.89 (0.000)
76.85% 5.76
98.44% 3.66
98.00% 2.79
Notes: (a) P-values in parentheses. (b) The Breusch-Godfrey test statistic follows a Chi-square distribution with 4 degrees of freedom under the null hypothesis of no autocorrelation of up to the fourth order. The critical values at the 10% and 5% level of significance are, respectively, 7.779 and 9.488.
Table 4 Regression results: estimating hedging effectiveness Independent variables
Intercept Change in futures price (in cents) R of regression Durbin—Watson
Dependent variable (in millions of $) Unpredicatable component of pretax income Plan 1
Plan 2
Plan 3
!0.93 (0.947) 0.41 (0.692)
4.72 (0.697) !4.09 (0.002)
5.63 (0.658) !2.60 (0.009)
0.42% 2.18
23.21% 2.13
16.81% 1.91
Notes: (a) P-values in parenthesis. (b) The critical lower and upper values for the Durbin—Watson statistic at the 5% level of significance are respectively 1.44 and 1.54. The results are consistent with the null hypothesis of no autocorrelation.
described in the previous section, is measured by the R in the regression of the unpredictable component of pretax income (the residuals from the pretax income regression reported in Table 3) on futures price change. In the case of Plan 1, there is no significant relationship between futures price change and income. However, in the case of Plan 2, the results indicate that hedging reduces the random variation of pretax income by over 23%. Further, the low p-value of the slope coefficient is strong evidence in favor of hedging effectiveness. The results for Plan 3 are similar though weaker; hedging
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V.K. Rao / Journal of Air Transport Management 5 (1999) 39—44
according to this plan reduces the random variation of income by about 17%.
4. Conclusion Volatile jet fuel prices and the sensitivity of airline earnings to fuel prices make the issue of fuel price risk hedging an important one. The main objective of this study is to investigate the effectiveness of hedging fuel price risk using heating oil futures contracts in dampening the volatility of the average airline’s pretax income. To this end, an average airline is constructed by combining the operating and financial statistics of a sample of 10 large US airlines, and regression analysis is performed using quarterly revenue, cost, income and fuel price data over the period 1988—97. The study examines 3 hedging plans with the difference between the plans based on the timing of the hedge as well as on using heating oil futures contracts expiring at different times in relation to the quarter being hedged. The results indicate that an ongoing policy of hedging according to one of the plans reduces the unexplained volatility of quarterly income by over 23%. Thus, the results indicate that hedging fuel price risk is not necessarily a strategy whose usefulness is restricted to weaker airlines which cannot withstand fuel price increases. While it is of course true that a hedging airline incurs opportunity costs if fuel prices go down rather than up, the results demonstrate that, over the long haul, the benefits in terms of more stable earnings can be substantial. Another contribution of this study is that it highlights the importance of selecting an appropriate futures contract for the purpose of implementing the hedge. In the case of the fictional average airline used in this study, it is seen that using the futures contract maturing immediately after the quarter being hedged (Contract A) is more effective than using the contract maturing at the beginning of the quarter being hedged (Contract B). Further, it
is also important to time the hedging transactions correctly. In the case of this study, it is seen that initiating the hedge three months prior to the quarter being hedged and closing the position at the start of the quarter being hedged (Plan B) is highly effective; while initiating the hedge at the start of the quarter being hedged and closing the position at the end of the quarter being hedged (Plan A) is found to be quite ineffective. While the results appear to strongly testify to the usefulness of hedging, a possible objection is that the results pertain to a fictional ‘‘average’’ airline. The income of this fictional airline is likely to be less noisy as random fluctuations across airlines are likely to offset one another. As a result, the relationship between this airline’s earnings and futures price changes is likely to be stronger, thereby potentially overstating the benefits from hedging. The point has merit, and underlines the need for each airline to carefully examine the relationship between its earnings and futures price changes before deciding on an appropriate strategy. However, the results of this study strongly point to the likelihood of the existence of substantial benefits from an ongoing hedging policy.
References Adams, J., 1997. Airlines struggle with fuel price turbulence. Corporate Finance 147, 25—26. Duffie, D., 1989. Futures Markets. Prentice-Hall, Englewood Cliffs, NJ. Ederington, H.L., 1979. The hedging performance of the new futures markets. The Journal of Finance 34, 157—170. Koppenhaver, G.D., 1985. Bank funding risks, risk aversion, and the choice of futures hedging instrument. The Journal of Finance XL, 241—255. Nikkhah, S., 1987. How end users hedge fuel costs in energy markets, Futures, 66—67. Quinn, L., 1996. Balancing act. Airfinance Journal. 18—21. Thomas, R.L., 1997. Modern Econometrics: An Introduction. AddisonWesley, Essex, England. Ubhi, H., 1996/97. Jet fuel price risk management. Air Finance Annual 60—62.
Fuel price risk management using futures Vadhindran K. Rao* Business Administration Department, Embry-Riddle University, 600 S. Clyde Morris Blvd., Daytona Beach, FL 32114, USA
Abstract The primary objective of this study is to investigate whether an ongoing policy of hedging jet fuel price risk using heating oil futures contracts reduces the volatility of quarterly pretax income of an average major airline in the US. The results indicate that, after controlling for trend, seasonality, and persistence of shocks, hedging has the potential to reduce the unexplained volatility of the average airline’s quarterly income by over 20%. Thus, the results suggest that the usefulness of hedging is not restricted to protecting weak airlines incapable of withstanding an increase in fuel prices. Also, airlines should not eschew hedging merely because of the possibility of incurring opportunity costs if fuel prices go down rather than up; hedging appears to pay off in the long run by providing a more stable earnings stream. Further, the results also point to the importance of selecting an appropriate futures contract and timing the hedging transactions properly. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Airline management; Fuel price risk; Hedging
1. Introduction Airline earnings are highly volatile and therefore, airline stocks trade at relatively low Price/Earnings (P/E) ratios (see Fig. 1). It is commonly believed that one of the most important sources of volatility in airline earnings are fuel prices. In fact, airlines’ exposure to this risk is believed to be greater than their exposures to either interest rate or foreign exchange risk (Quinn, 1996). Airlines are often urged to protect themselves from fuel price fluctuations by making use of various types of derivative instruments. The primary objective of this study is to investigate the hedging effectiveness of one such instrument, namely heating oil futures. The main question addressed is whether an ongoing strategy of anticipatory long hedges applied using heating oil futures contracts reduces the volatility of quarterly profits of an average large airline in the United States. Major airlines consume over 2.5 billion gallons of fuel a year; therefore, an increase of even a single cent in the
* Tel.:#1 904 226 6246; fax:#1 904 226 6696; e-mail: [email protected]. erau.edu. The average quarterly pretax income of the ten largest extant US airlines combined over the period 1988—97 is $136 million while the standard deviation is $1228 million.
price of fuel means an increase of over $25 million in annual operating expenses. Further, fuel costs account for over 10% of the operating expenses of an airline. Consequently, industry experts often advocate fuel price risk hedging by airlines. For example, in an article explaining the uses of various alternative derivative instruments to manage jet fuel price risk, Ubhi, 1996—97 asserts that ‘‘2 an airline that could protect itself against price increases would, in addition to managing its costs and protecting its revenues, have a significant marketing edge over its competitors . . .’’ The intuition underlying input price risk hedging using futures in a single-period framework is straightforward. Suppose that the hedging strategy is implemented using heating oil futures, a strategy often recommended owing to the strong correlation between the price of heating oil and the price of jet fuel. An airline can protect itself from an increase in fuel prices by entering into an anticipatory long hedge — for example, going long on heating oil futures at the start of the period being hedged, and entering into an offsetting contract at the end of the period. Any increase in operating costs resulting from an increase in the price of jet fuel is then likely to be offset, at least partially, by a profit on the futures position. Of course, if prices go down, then the decrease in costs will be offset by losses on the futures position. From a single period perspective, hedging using futures can enable an
0969-6997/99/$ — see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 9 - 6 9 9 7 ( 9 8 ) 0 0 0 3 5 - 0
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V.K. Rao / Journal of Air Transport Management 5 (1999) 39—44
Fig. 1. The chart shows the time series of combined quarterly pretax income of the top ten major airlines in the US over 1988—1997.
airline to ‘‘lock in’’ its cost of fuel for the coming period, or at least reduce the level of uncertainty regarding the effective cost of fuel for the period, and thereby possibly reduce the uncertainty associated with operating costs and earnings for the period. While the point that hedging using futures can protect an airline’s current period earnings against increases in the price of fuel is important, typically, the objective of a hedging corporation is not to merely reduce uncertainty about earnings in the current period, but to reduce the volatility of earnings over time. A top level executive from Lehman Brothers, New York is quoted in Quinn, 1996 as saying in the context of foreign currency risk faced by major US airlines: ‘‘To the extent that US airlines can manage these exposures, producing less volatility in earnings estimates, shareholders will be more comfortable and their multiples could increase.’’ Therefore, an interesting question is how effective an ongoing hedging strategy using futures is likely to be in reducing the volatility of airline earnings. Accordingly, this study uses actual quarterly revenue, cost and income data for the period 1988—97 of ten US airlines to construct an ‘‘average’’ airline, and the focus of the study is the impact of an ongoing quarterly hedging strategy applied using heating oil futures on the volatility of quarterly pretax income of this average airline. The issue of hedging effectiveness is important for more reasons than one. For one thing, the cost of implementing a fuel price risk hedging program could be as high as 1% of an airline’s fuel budget. Therefore, an airline needs to know the potential benefits from hedging to determine if it is worth the cost. The usefulness of hedging can also be questioned on grounds other than the cost of implementation. For instance, it is possible that operating revenues are positively related to fuel price changes, either because of
market power enjoyed by the airline whereby it has the ability to pass on fuel price increases to consumers, or because of a positive relationship between energy prices and demand for air travel. In such cases, an airline is at least partially hedged against fuel price increases. In fact, it is even possible that the relationship between earnings and futures price change is positive rather than negative. If so, the conventional strategy of a long hedge would serve to increase rather than decrease the volatility of earnings. Another case in which the conventional hedging strategy would be inappropriate if there are so many uncorrelated random factors impacting on airline earnings that there may be no discernible relationship between an airline’s earnings and fuel price. In such a case, again, hedging may increase rather than decrease the volatility of earnings. Further, hedging using futures is a double-edged sword. A hedging corporation can incur substantial opportunity costs if fuel prices go down rather than up. For these or other reasons, US airlines, unlike their European counterparts, have not been very active hedgers. As mentioned by Adams, 1997, most major airlines in the US hedge barely 15% of their fuel requirements. It seems worthwhile to examine whether such a policy is justified.
2. Theoretical framework The theoretical framework for analyzing the fuel price risk hedging decision faced by an airline is described below. The model is initially developed in a single-period framework. Each futures contract is assumed to be for one gallon of heating oil. For simplicity, entering into a futures contract is assumed to be costless, and the
V.K. Rao / Journal of Air Transport Management 5 (1999) 39—44
marking-to-market feature is ignored. At the beginning of the period, the information set of the airline consists of the joint probability distribution of its pretax income and futures price change for the period. The airline can take a position in heating oil futures at the beginning of the period so as to change the distribution of its pretax (post-hedge) income so as to better suit the decision maker’s risk preferences. The sole decision variable faced by the airline is the number of futures contracts it should buy or sell. At the end of the period, the airline closes its futures position by entering into an offsetting contract; also, its pre-hedge income is revealed, and its post-hedge income is just the sum of its pre-hedge income and profits (or losses) on its futures transactions. In symbols, n "n #X (*f ), (1) F S where n is the random pretax pre-hedge income of an S airline, n the random pretax post-hedge income, f the F random per gallon futures price of heating oil at the end of the period, F the known per gallon futures price of heating oil at the beginning of the period, *f"f !F , the change in the futures price over the period and X the number of futures contracts bought at the beginning of the period, the sole decision variable in the model. In general, the optimal futures position would depend on the relationship between income and futures price change, the expected change in futures price and the risk preferences of the decision maker. Therefore, the optimal hedge has a pure hedging as well as a speculative component. (See Duffie (1989), Chapter 4 for a simple meanvariance model that makes this point). However, as in Ederington (1979) and Koppenhaver (1985), the effectiveness of a hedging strategy using futures can be gauged by determining the maximum possible percentage reduction in risk that can be achieved. Therefore, for the purpose of the empirical analysis, it is assumed that the objective of the airline is to minimize the variance of income. Accordingly, differentiate the variance of post-hedge income Var +n ,#X Var +*f ,#2X Cov +n , *f , (2) S S with respect to X, set the derivative equal to zero, and solve for X to obtain the minimum variance hedge: !Cov +n , *f , S X" . Var +*f ,
(3)
Hedging effectiveness may then be measured as Var +n , +4 , H.E."1! Var +n , S
(4)
For reasons that will become apparent later, the analysis focuses on pretax income rather than net income.
41
where H.E. denotes the measure of hedging effectiveness, and n denotes post-hedge income corresponding to +4 the minimum variance hedge. Using Eq. (3), it is seen that (Cov +n , *f ,) S H.E." . (5) Var +*f , Var (n ) S Assuming that the variables, n and * f are jointly S independently and identically normally distributed, H.E. can be estimated as the coefficient of determination (or R) in the simple linear regression of pre-hedge income, n , on change in futures price, *f. Note that, under this S assumption, following the minimum variance policy would not only reduce uncertainty of earnings in the coming period, but also reduce volatility of earnings over time. 2.1. Measuring hedging effectiveness: A refinement A problem with the approach outlined above is that it ignores the predictable variability of earnings due to factors such as the seasonal nature of airline demand as well as the upward trend in airline earnings. It seems desirable to measure the impact of hedging on the volatility of income after factoring out all predictable variation in the expected level of income. Accordingly, the measure of hedging effectiveness used in this study is calculated as follows: 1. The residuals from the regression of n on the followS ing explanatory variables is estimated: ¹IME, a trend variable that takes the value 1 in the first quarter of the sample period and is incremented by a unit every subsequent quarter; dummy variables, Q , Q , and Q , representing calendar quarters 2, 3 and 4, respectively, and income during the previous quarter. n "a #a ¹IME #a Q #a Q S R R R R #a Q #a n #e . (6) R S R\ R The dummy variables help account for seasonal variation in airline demand. The trend variable may be interpreted as allowing for the growth of the airline. Lagged income is included to allow for the possibility that shocks to airline earnings may dissipate only gradually. The residuals from this regression may be viewed as representing the unpredictable component of income. 2. Next, these residuals are regressed on change in futures price: e "b #b *f #u . R R R
(7)
As explained later, not including a lagged dependent variable in the model results in autocorrelation among the residuals.
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V.K. Rao / Journal of Air Transport Management 5 (1999) 39—44
The R of this regression is the percentage decrease in the unpredictable variability of income from following a minimum variance hedging strategy, and is therefore an appropriate measure of hedging effectiveness. Further, the minimum variance hedging quantity is given by !b , the negative of the coefficient of *f in Eq. (7). This approach to measuring hedging effectiveness is superior to one based on a simple regression of income on futures price change in that, unlike the latter, it allows the conditional mean of income to change over time. However, the approach has the following drawbacks: (a) It assumes that the conditional variances of income and futures price changes are constant over time; (b) it imposes the requirement that the quantity of futures contracts bought each quarter should be the same; and (c) the optimal hedge determined by this method could not have been implemented by an airline as the estimation is based on data pertaining to the entire sample period. While these objections have merit, it should be noted that the objective of this study is to obtain a first pass estimate of the potential effectiveness of fuel price risk hedging, rather than to present airline managers with a recipe for effective hedging. 2.2. Data and hedging strategies Data about the spot price of jet fuel as at the end of each month over 1988—97 were gathered from various issues of the Monthly Energy Review (published by the Energy Information Administration, US Dept. of Energy). Quarterly airline data, gathered from various issues of ¹he Airline Monitor (published by ESG Aviation Services), consist of total operating revenues, total operating costs, pretax income, cost per gallon of fuel consumed, and total number of gallons of fuel consumed in each quarter for the period 1988—97 for 10 of the largest US airline companies, namely, Alaska Air Group, America West, AMR Corp., Continental Airlines, Delta Air Lines, NWA Inc., Southwest Airlines, Trans World Airlines, UAL Corp., and US Airways Inc. The operating and financial statistics of the ‘‘average’’ airline are constructed as a weighted average of the statistics pertaining to these 10 companies with the weights based on the quantity of fuel consumed by an airline in each quarter. As mentioned earlier, the study focuses on pretax income rather than net income. The main reason for this is to avoid the complications associated with determining an appropriate tax rate for calculating after-tax profits/losses on futures positions for this fictional average airline. Table 1 contains sample statistics, namely the sample mean and standard deviation, pertaining to the average airline’s quarterly pretax income, operating revenues, operating costs, and per gallon fuel costs. The standard
Table 1 Summary statistics for the average airline, quarterly data, 1988—97 Op. revenues Op. costs Pretax Fuel cost (000,000s of $) (000,000s of $) income per gallon (000,000s of $) (cents) Mean 2443.02 Std dev 452.46
2358.99 382.93
38.03 177.06
61.80 9.88
deviation of per gallon cost of fuel shows that fluctuations of as much as 10 cents from one-quarter to the next are not uncommon. The hedging strategy is based on heating oil futures traded on the New York Mercantile Exchange (NYMEX). Data on futures prices were obtained from a CD-ROM titled ‘‘Historical data’’ sold on a commercial basis by the firm ¹urtle ¹rader. A description of the hedging strategy is as follows. The airline is assumed to hedge for one quarter at a time. Two alternative heating oil futures contracts are considered for the purpose of implementing the hedge: (a) the contract expiring in the month immediately following the quarter being hedged (hereafter referred to as Contract A) and (b) that expiring in the first month of the quarter being hedged (hereafter referred to as Contract B). The study examines a total of three hedging plans: two based on Contract A and one on Contract B. Plan 1 consists of taking a position in the heating oil futures Contract A at the end of the previous quarter and entering into an offsetting contract at the end of the quarter being hedged. In other words, Plan 1 consists of entering into an anticipatory hedge at the end of the previous quarter using Contract A. For example, under Plan 1, an airline whose income is negatively correlated with futures price changes and is seeking to hedge for the quarter January 1987 to March 1987 would buy the futures contract maturing in April 1987 in end-December 1986 and sell the contract in end-March 1987. Plan 2 consists of entering into an anticipatory hedge using Contract A three months prior to the quarter being hedged and offsetting the position at the beginning of the quarter. Plan 3 is identical to Plan 2 except that Contract B is used instead of Contract A.
3. Results Table 2 contains the results from regressing each airline’s per gallon cost of fuel for a quarter on each of four independent variables, namely (i) the average spot price of jet fuel in that quarter (an average of the spot prices that prevailed on the last day of each month during the quarter), (ii) the futures price of Contract A as at the end of the quarter, (iii) the futures price of Contract A as at
V.K. Rao / Journal of Air Transport Management 5 (1999) 39—44
Table 3 Empirical regression models to explain variation in pretax income, op. rev. and op. costs
Table 2 R of regressions Dependent variable: Quarterly fuel cost per gallon Independent variables
Independent variables
Spot price Futures price of jet fuel of Contract A as of end of quarter
Futures price Futures price of Contract A as of Contract B as of beg. of quarter of beg. of quarter
97.49%
87.94%
28.58%
43
74.59%
Intercept TIME
Note: All regressions are significant at the 1% level. Quarter 2
the beginning of the quarter and (iv) the futures price of Contract B as at the beginning of the quarter. Observe that the strong correlation between the spot price of jet fuel and the average airline’s cost of fuel confirms anecdotal evidence regarding the lack of hedging activity on the part of most US airlines. Further, note that (ii) is the price at which an airline implementing an anticipatory long hedge would execute the offsetting transaction (of selling the futures contract) as per Plan 1. Similarly, (iii) is the selling futures price according to Plan 2, and (iv) the selling futures price according to Plan 3. The higher the degree of correlation of either (ii), (iii) or (iv) with the airline’s cost of fuel, more effectively can the airline lock in its cost of fuel in advance by implementing the corresponding plan. The results suggest that Plans 2 and 3 are likely to perform better than Plan 1. However, hedging effectiveness ultimately depends on the relationship not between spot and futures prices but between income and futures price change, and this is examined next. Table 3 contains regression results of simple models to estimate the unpredictable component of the average airline’s income, operating revenues, and operating costs for the sample period 1988—97. The results show that all the dependent variables exhibit seasonality, and that pretax income and operating revenues also exhibit a statistically significant upward trend. An analysis of the residuals using the Breusch—Godfrey test does not reveal any autocorrelation patterns among the residuals. Further, the R’s of the models are also quite high. Thus, the models provide a good fit to the data. For example, the model for quarterly income explains over 75% of the variation in the variable. The balance may be interpreted as random or unpredictable variability. Table 4 contains results showing the effectiveness of each of the three hedging plans. Hedging effectiveness, as For all the three dependent variables, the Durbin—Watson statistic indicates the presence of autocorrelation among the residuals if a lagged value is not included as an explanatory variable. However, if a lagged value is included, then the Breusch—Godfrey test statistic is consistent with the hypothesis of no autocorrelation of up to the fourth-order among the residuals. Note that the Durbin—Watson statistic cannot be used in lagged dependent variable models, and hence the use of the Breusch—Godfrey test. See Thomas, 1997 pp. 304—306 for a discussion of relevant issues and details of the test.
Quarter 3 Quarter 4 Lagged dep. var. R of Regression Breusch—Godfrey
Dependent variables: (in millions of $) Pretax income
Op. rev.
Op. costs
!5.25 (0.905) 2.49 (0.077) 94.33 (0.029) 29.56 (0.537) !252.68 (0.000) 0.74 (0.000)
727.62 (0.003) 16.73 (0.004) 152.55 (0.000) 143.43 (0.000) !108.37 (0.012) 0.55 (0.001)
174.73 (0.170) 2.22 (0.364) 72.41 (0.009) 92.62 (0.001) 61.26 (0.025) 0.89 (0.000)
76.85% 5.76
98.44% 3.66
98.00% 2.79
Notes: (a) P-values in parentheses. (b) The Breusch-Godfrey test statistic follows a Chi-square distribution with 4 degrees of freedom under the null hypothesis of no autocorrelation of up to the fourth order. The critical values at the 10% and 5% level of significance are, respectively, 7.779 and 9.488.
Table 4 Regression results: estimating hedging effectiveness Independent variables
Intercept Change in futures price (in cents) R of regression Durbin—Watson
Dependent variable (in millions of $) Unpredicatable component of pretax income Plan 1
Plan 2
Plan 3
!0.93 (0.947) 0.41 (0.692)
4.72 (0.697) !4.09 (0.002)
5.63 (0.658) !2.60 (0.009)
0.42% 2.18
23.21% 2.13
16.81% 1.91
Notes: (a) P-values in parenthesis. (b) The critical lower and upper values for the Durbin—Watson statistic at the 5% level of significance are respectively 1.44 and 1.54. The results are consistent with the null hypothesis of no autocorrelation.
described in the previous section, is measured by the R in the regression of the unpredictable component of pretax income (the residuals from the pretax income regression reported in Table 3) on futures price change. In the case of Plan 1, there is no significant relationship between futures price change and income. However, in the case of Plan 2, the results indicate that hedging reduces the random variation of pretax income by over 23%. Further, the low p-value of the slope coefficient is strong evidence in favor of hedging effectiveness. The results for Plan 3 are similar though weaker; hedging
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V.K. Rao / Journal of Air Transport Management 5 (1999) 39—44
according to this plan reduces the random variation of income by about 17%.
4. Conclusion Volatile jet fuel prices and the sensitivity of airline earnings to fuel prices make the issue of fuel price risk hedging an important one. The main objective of this study is to investigate the effectiveness of hedging fuel price risk using heating oil futures contracts in dampening the volatility of the average airline’s pretax income. To this end, an average airline is constructed by combining the operating and financial statistics of a sample of 10 large US airlines, and regression analysis is performed using quarterly revenue, cost, income and fuel price data over the period 1988—97. The study examines 3 hedging plans with the difference between the plans based on the timing of the hedge as well as on using heating oil futures contracts expiring at different times in relation to the quarter being hedged. The results indicate that an ongoing policy of hedging according to one of the plans reduces the unexplained volatility of quarterly income by over 23%. Thus, the results indicate that hedging fuel price risk is not necessarily a strategy whose usefulness is restricted to weaker airlines which cannot withstand fuel price increases. While it is of course true that a hedging airline incurs opportunity costs if fuel prices go down rather than up, the results demonstrate that, over the long haul, the benefits in terms of more stable earnings can be substantial. Another contribution of this study is that it highlights the importance of selecting an appropriate futures contract for the purpose of implementing the hedge. In the case of the fictional average airline used in this study, it is seen that using the futures contract maturing immediately after the quarter being hedged (Contract A) is more effective than using the contract maturing at the beginning of the quarter being hedged (Contract B). Further, it
is also important to time the hedging transactions correctly. In the case of this study, it is seen that initiating the hedge three months prior to the quarter being hedged and closing the position at the start of the quarter being hedged (Plan B) is highly effective; while initiating the hedge at the start of the quarter being hedged and closing the position at the end of the quarter being hedged (Plan A) is found to be quite ineffective. While the results appear to strongly testify to the usefulness of hedging, a possible objection is that the results pertain to a fictional ‘‘average’’ airline. The income of this fictional airline is likely to be less noisy as random fluctuations across airlines are likely to offset one another. As a result, the relationship between this airline’s earnings and futures price changes is likely to be stronger, thereby potentially overstating the benefits from hedging. The point has merit, and underlines the need for each airline to carefully examine the relationship between its earnings and futures price changes before deciding on an appropriate strategy. However, the results of this study strongly point to the likelihood of the existence of substantial benefits from an ongoing hedging policy.
References Adams, J., 1997. Airlines struggle with fuel price turbulence. Corporate Finance 147, 25—26. Duffie, D., 1989. Futures Markets. Prentice-Hall, Englewood Cliffs, NJ. Ederington, H.L., 1979. The hedging performance of the new futures markets. The Journal of Finance 34, 157—170. Koppenhaver, G.D., 1985. Bank funding risks, risk aversion, and the choice of futures hedging instrument. The Journal of Finance XL, 241—255. Nikkhah, S., 1987. How end users hedge fuel costs in energy markets, Futures, 66—67. Quinn, L., 1996. Balancing act. Airfinance Journal. 18—21. Thomas, R.L., 1997. Modern Econometrics: An Introduction. AddisonWesley, Essex, England. Ubhi, H., 1996/97. Jet fuel price risk management. Air Finance Annual 60—62.