Jet Fuel Hedging, Operational Efficiency Improvement and Carbon Tax

Transcription

1 Jet Fuel Hedging, Operational Effiieny Improvement and Carbon Tax Rong Hu a, Yibin Xiao a, Changmin Jiang b, * a Shool of Mathematial Sienes, University of Eletroni Siene and Tehnology of China, Chengdu, China b Asper Shool of Business, University of Manitoba, Winnipeg, MB R3T 2N2, Canada Transport Institute, University of Manitoba, Winnipeg, MB R3T 2N2, Canada *Corresponding author (junior researher) hangmin.jiang@umanitoba.a 1. Introdution Aviation has a major impat on the limate system and aounts for up to 9 perent of the total limate hange impat of human ativity. Moreover, at a time when we urgently need to redue this impat, greenhouse gas (GHG) emissions from aviation ontinue to grow. Sine 1990, GHG emissions from international aviation have inreased 83 per ent. Airraft engine emissions are diretly related to fuel burn. Eah kilogram of fuel saved redues arbon dioxide (CO2) emissions by 3.16 kg. So the key for airlines to minimize their environmental impat is to use fuel more effiiently (IATA, 2015). Between 1968 and 2014 the average fuel burn of new airraft fell approximately 45%, or a ompound annual redution rate of 1.3%. Despite this progress, the industry ontinues to lag United Nations fuel effiieny goals. On average, industry is about 12 years behind the 2020 and 2030 fuel effiieny goals established by ICAO, the UN ageny that oversees international aviation (Kharina and Rutherford, 2015). The reality is that fuel effiieny improvements ahieved by legay arriers have oinided with rising fuel pries (Firestine and Guarino, 2012). Kwan and Rutherford (2014) find that domesti US aviation saw zero net improvement in its effiieny in 2013, when the global oil prie was low. In other words, airlines move towards higher fuel effiieny is almost purely driven by eonomi onsideration, as the aviation industry is haraterized by a onstant struggle with skyroketing and flutuating fuel osts. In 2015, fuel aounted for 27% of airlines average operating osts, and the overall fuel bill amounted to 180 billion U.S. dollars (IATA, 2015). Although substantial, these numbers are in fat already muh lower than the historial highs in 2013 (33% and 231 1

2 billion). However, even with the threat of high fuel prie, operational improvement may not neessarily be the only solution for the airlines. To manage the enormous risk from high fuel prie and improve profit margin, airlines an also use finanial hedge, a finanial investment to redue the risk of future high fuel prie, mainly through derivative produts suh as future ontrats, options and swaps (Smith and Stulz, 1985). In fat, finanial hedge has been a popular strategy among airlines in managing fuel prie (e.g., Rao, 1999; Berghöfer and Luey, 2014; Lim and Hong, 2014; Treanor et al., 2014a; Turner and Lim, 2015). Due to this potential substitutability between fuel effiieny improvement and finanial hedge, airlines operational improvement is at times referred to as operational hedge, a onept that has been studied in a variety of fields (e.g., operations management, finane, strategy and international business) but rarely given onsistent framework and definition (Boyabatli and Toktay, 2004). Some empirial studies investigate operational hedge for airline jet fuel prie without stritly defining it (Morrell and Swan, 2006; Weiss and Maher, 2009; Naumann et al., 2012; Treanor, 2008, 2012; Treanor et al., 2014b). Roughly speaking, in the ase of airline jet fuel, operational hedge is a group of strategies fousing on improving operational effiieny, inluding fleet fuel-effiieny, optimized fleet assignment and fueleffetive praties suh as flying slower or less into the wind (Ramos and Veiga, 2014). In other words, to investigate the airlines inentive in meeting the fuel effiieny goals of IATA and ICAO, it is rather important to take into aount this substitution between fuel operational effiieny improvement and fuel finanial hedge, whih is never speifially studied in literature as far as we know. More importantly, another long-ignored aspet of the issue is the relationship between airline s fuel strategies and environmental poliies suh as arbon tax. From a soial perspetive, operational effiieny improvement should be enouraged more, as finanial hedging does not generate muh real positive impat on airraft emission. If finanial hedging against high jet fuel is very suessful, it atually imposes an environmental ost on the soiety, as this suess would enourage airlines to ontinue using finanial tools to ombat high jet fuel pries instead of ommitting to the development of alternative fuel and new airraft tehnologies that an redue fossil fuel onsumption and hene greenhouse gas emission. This is a type of the urse of suess, whih is rarely mentioned. Under suh onsideration, when poliy makers are evaluating emission poliies suh as arbon tax or ap-and-trade (e.g., Sgouridis et al., 2011), it may also be helpful to take into aount the effets of suh poliies on the airlines hoies of fuel hedging 2

3 strategies. If these poliies an make operational improvement more attrative while finanial hedging less benefiial, then other than the diret impat on reduing emission, these poliies an also bring indiret benefits of promoting the adoption of new tehnologies, laying a more solid foundation for their implementation. On the other hand, if we prove the opposite, then suh poliies should be used with more aution. 2. Model Setting There are two stages for airlines deisions. In the first stage, there is no operation, and the airlines determine their fuel strategies without knowing the exat fuel prie in the seond stage when operations happen. The airlines only have information about the possible distribution of the fuel prie based on historial data. For simpliity, we assume that the per flight fuel prie follows a uniform distribution, i.e., ~U(, ). To simplify the analysis, we assume away the heterogeneities in the size of the airrafts, the load fator and the flight distane, so that every passenger served aounts for one unit of jet fuel. Three options are available: no move, finanial hedge and operational improvement. It should be noted that for simpliity we only allow the airline(s) to hoose one strategy, but we are well aware of the fat that in reality airlines normally adopt a mix of strategies at the same time, whih in itself is a way of hedging. To fous on the omparison between pure strategies, we are essentially investigating whih strategy is likely to be preferred and hene oupy a larger perentage in airlines fuel strategy portfolio. If no move is hosen by an airline, it doesn t inur any fixed investment but will fae the market fuel prie as it is realized in the seond stage. With finanial hedge, the airline invests a ost, f F, to fix the fuel prie at a ertain level. Without loss of generality, we assume that the finanial hedge is very effiient that it an fixate the fuel ost at, the lower bound of the fuel prie distribution. With operational improvement, the airline inurs an investment, f O, to improve the operation effiieny of fuel onsumption, in de fato giving a disount, r, to the market fuel prie (with 0 < r < 1). For the sake of omparison, we assume that f F = f O = f. Here we impliitly assume away the relationship between the investment ost of the strategies and the amount of fuel onsumed in the seond stage. In reality it is likely that there is a positive orrelation between these two fators, i.e., the larger the fuel purhase/onsumption involved, the more expensive the hedge would be. However, this relationship is also not linear or even ontinuous in reality, making an aurate modeling hard to ahieve. Therefore, in this paper we hoose the simplest setting for the ease of analysis. Moreover, 3

4 the parameter r gives the setting a ertain level of flexibility, so the impliations should not be affeted as long as the analytial results are arefully interpreted. In the seond stage, the market fuel prie will be realized, and the airlines will ompete in quantities (traffi) with the fuel ost determined by their fuel strategies in the first stage. Let s first onsider the situation when there is only one airline. Assume that we have a simple linear inverse demand funtion: P = a bq (1) When the airline adopts no move in the first stage, its profit funtion is: π 1 = (P )q C F = (a bq )q C F (2) where C F measures the fixed ost of operations. When the airline adopts finanial hedge, its profit funtion is: π 2 = (P )q C F f = (a bq )q C F f (3) Similarly, the profit funtion of the airline when it hooses operational improvement is: π 3 = (P r)q C F f = (a bq r)q C F f (4) Before we move into the analysis, it should be noted that due to the limited apaity of theoretial analysis, the setting of this paper is rather restritive and does not represent the real praties of the airlines very well. With these defiienies in mind, we realize the importane to resist the overinterpretation of our analytial results. Some of the poliy suggestions should also be taken with extra aution. However, the paper serves as the first theoretial work on this topi and hopefully opens up the window for further and more elaborated studies. 3. Main results We find that finanial hedge is more effiient in reduing the volatility of profits and risk exposure, while operational improvement is more likely to generate a higher expeted profit level ompared with finanial hedge when its effetiveness is suffiiently high. With market ompetition, operational improvement will beome less prevalent. A positive shok to the fuel prie (i.e., arbon tax) makes finanial hedge less attrative and operational improvement more attrative. 4

5 Referene Berghöfer, B., & Luey, B. (2014). Fuel hedging, operational improvement and risk exposure Evidene from the global airline industry. International Review of Finanial Analysis, 34, Boyabatli, O., & Toktay, L. B. (2004). Operational improvement: A review with disussion. Working paper. Firestine, T., & Guarino, J. (2012). A deade of hange in fuel pries and us domesti passenger aviation operations. teh. rep., U.S. Department of Transportation Researh and Innovative Tehnology Administration, Marh IATA (2015). Fat sheet: Fuel. [Online] available from: (Aessed 26/04/2017) Kharina, A., & Rutherford, D. (2015). Fuel effiieny trends for new ommerial jet airraft: 1960 to International Counil on Clean Transportation (ICCT) report. Kwan, I., & Rutherford, D. (2014). US domesti airline fuel effiieny ranking, White Paper, The International Counil on Clean Transportation. Lim, S. H., & Hong, Y. (2014). Fuel hedging and airline operating osts. Journal of Air Transport Management, 36, Morrell, P., & Swan, W. (2006). Airline jet fuel hedging: Theory and pratie. Transport Reviews, 26(6), Naumann, M., Suhl, L., & Friedemann, M. (2012). A stohasti programming model for integrated planning of re-fleeting and finanial hedging under fuel prie and demand unertainty. Proedia- Soial and Behavioral Sienes, 54, Ramos, S., & Veiga, H. (Eds.). (2014). The Interrelationship Between Finanial and Energy Markets (Vol. 54). Springer. Rao, V. K. (1999). Fuel prie risk management using futures. Journal of Air Transport Management, 5(1), Sgouridis, S., Bonnefoy, P. A., & Hansman, R. J. (2011). Air transportation in a arbon onstrained world: Long-term dynamis of poliies and strategies for mitigating the arbon footprint of ommerial aviation. Transportation Researh Part A: Poliy and Pratie, 45(10), Smith, C. W., & Stulz, R. M. (1985). The determinants of firms' hedging poliies. Journal of Finanial and Quantitative Analysis, 20(04), Treanor, S. D. (2008). The effetiveness of the operational and finanial hedge: Evidene from the airline industry (Proquest Dissertations And Theses). 5

6 Treanor, S. D. (2012). The flexibility and benefits of operating a diverse fleet: An analysis using real options. Management Researh Review, 35(6), Treanor, S. D., Rogers, D. A., Carter, D. A., & Simkins, B. J. (2014a). Exposure, hedging, and value: New evidene from the US airline industry. International Review of Finanial Analysis, 34, Treanor, S. D., Simkins, B. J., Rogers, D. A., & Carter, D. A. (2014b). Does operational and finanial hedging redue exposure? Evidene from the US airline industry. Finanial Review, 49(1), Turner, P. A., & Lim, S. H. (2015). Hedging jet fuel prie risk: The ase of US passenger airlines. Journal of Air Transport Management, 44, Weiss, D., & Maher, M. W. (2009). Operational improvement against adverse irumstanes. Journal of Operations Management, 27(5),

7 Jet Fuel Hedging, Operational Effiieny Improvement and Carbon Tax Rong Hu a, Yibin Xiao a, Changmin Jiang b, * a Shool of Mathematial Sienes, University of Eletroni Siene and Tehnology of China, Chengdu, China b Asper Shool of Business, University of Manitoba, Winnipeg, MB R3T 2N2, Canada Transport Institute, University of Manitoba, Winnipeg, MB R3T 2N2, Canada November 2017 *Corresponding author (junior researher) hangmin.jiang@umanitoba.a Abstrat: To investigate airlines inentives in fuel effiieny improvement, it might be important to onsider finanial hedge as its substitute. In this paper, we build a simple theoretial model to ompare the impliations of fuel finanial hedge and operational effiieny improvement on airlines expeted profitability. We find that finanial hedge is more effiient in reduing airlines profit volatility and risk exposure, while operational improvement will generate a higher expeted profit level when its effetiveness is suffiiently high. With market ompetition, operational improvement will be less prevalent. Furthermore, a fuel/arbon tax makes finanial hedge less attrative and operational improvement more attrative. Keywords: Operational improvement, Finanial hedge, Fuel, Carbon tax Aknowledgments This paper is intended to ompete for the Best Paper by a Junior Researher Prize. 7

8 4. Introdution Aviation has a major impat on the limate system and aounts for up to 9 perent of the total limate hange impat of human ativity. Moreover, at a time when we urgently need to redue this impat, greenhouse gas (GHG) emissions from aviation ontinue to grow. Sine 1990, GHG emissions from international aviation have inreased 83 per ent. Airraft engine emissions are diretly related to fuel burn. Eah kilogram of fuel saved redues arbon dioxide (CO2) emissions by 3.16 kg. So the key for airlines to minimize their environmental impat is to use fuel more effiiently (IATA, 2015). Between 1968 and 2014 the average fuel burn of new airraft fell approximately 45%, or a ompound annual redution rate of 1.3%. Despite this progress, the industry ontinues to lag United Nations fuel effiieny goals. On average, industry is about 12 years behind the 2020 and 2030 fuel effiieny goals established by ICAO, the UN ageny that oversees international aviation (Kharina and Rutherford, 2015). The reality is that fuel effiieny improvements ahieved by legay arriers have oinided with rising fuel pries (Firestine and Guarino, 2012). Kwan and Rutherford (2014) find that domesti US aviation saw zero net improvement in its effiieny in 2013, when the global oil prie was low. In other words, airlines move towards higher fuel effiieny is almost purely driven by eonomi onsideration, as the aviation industry is haraterized by a onstant struggle with skyroketing and flutuating fuel osts. In 2015, fuel aounted for 27% of airlines average operating osts, and the overall fuel bill amounted to 180 billion U.S. dollars (IATA, 2015). Although substantial, these numbers are in fat already muh lower than the historial highs in 2013 (33% and 231 billion). However, even with the threat of high fuel prie, operational improvement may not neessarily be the only solution for the airlines. To manage the enormous risk from high fuel prie and improve profit margin, airlines an also use finanial hedge, a finanial investment to redue the risk of future high fuel prie, mainly through derivative produts suh as future ontrats, options and swaps (Smith and Stulz, 1985). 1 In fat, finanial hedge has been a popular strategy among airlines in managing fuel prie (e.g., Rao, 1999; Berghöfer and Luey, 2014; Lim and Hong, 2014; Treanor 1 There exist other less onventional measures. For example, Delta Air Lines announed its intention to aquire an oil refinery in We ignore these measures in our analysis due to their relative insignifiane. 8

9 et al., 2014a; Turner and Lim, 2015). 2 Due to this potential substitutability between fuel effiieny improvement and finanial hedge, airlines operational improvement is at times referred to as operational hedge, a onept that has been studied in a variety of fields (e.g., operations management, finane, strategy and international business) but rarely given onsistent framework and definition (Boyabatli and Toktay, 2004). Some empirial studies investigate operational hedge for airline jet fuel prie without stritly defining it (Morrell and Swan, 2006; Weiss and Maher, 2009; Naumann et al., 2012; Treanor, 2008, 2012; Treanor et al., 2014b). Roughly speaking, in the ase of airline jet fuel, operational hedge is a group of strategies fousing on improving operational effiieny, inluding fleet fuel-effiieny 3, optimized fleet assignment 4 and fueleffetive praties suh as flying slower or less into the wind (Ramos and Veiga, 2014). In other words, to investigate the airlines inentive in meeting the fuel effiieny goals of IATA and ICAO, it is rather important to take into aount this substitution between fuel operational effiieny improvement and fuel finanial hedge, whih is never speifially studied in literature as far as we know. More importantly, another long-ignored aspet of the issue is the relationship between airline s fuel strategies and environmental poliies suh as arbon tax. From a soial perspetive, operational effiieny improvement should be enouraged more, as finanial hedging does not generate muh real positive impat on airraft emission. If finanial hedging against high jet fuel is very suessful, it atually imposes an environmental ost on the soiety, as this suess would enourage airlines to ontinue using finanial tools to ombat high jet fuel pries instead of ommitting to the development of alternative fuel and new airraft tehnologies that an redue fossil fuel onsumption and hene greenhouse gas emission. This is a type of the urse of suess, whih is rarely mentioned. Under suh onsideration, when poliy makers are evaluating emission poliies suh as arbon tax or ap-and-trade (e.g., Sgouridis et al., 2011), it may also be 2 A reent example for the popularity of jet fuel finanial hedging among airlines is that in early 2017, in spite of the low oil prie, Singapore Airlines extended some of its fuel-hedging ontrats to as long as five years, betting on an upswing in rude oil pries amid OPEC prodution uts and renewed tensions between the U.S. and Iran. Airlines utilize finanial hedge at a very extensive manner. Other than fuel, they re also involved in hedgings for exhange rate (e.g., Belghitar et al., 2008), airraft aquisition (e.g., Hu and Zhang, 2015) and airport apaity utilization (e.g., Xiao et al., 2017). 3 A reverse an also happen when fuel prie is low. For example, United Airlines took delivery of two used Boeing s in 2015, due in part to their more favorable eonomis thanks to fuel pries of around $50 per barrel, about 50% lower than six months ago. 4 For example, Ryerson and Kim (2014) find that two major US airline mergers in the late 2000s - early 2010s ahieved fuel savings ranging from 25 to 28 perent by eliminating network redundany, i.e., reorganizing and onsolidating hub networks and operations. 9

10 helpful to take into aount the effets of suh poliies on the airlines hoies of fuel hedging strategies. If these poliies an make operational improvement more attrative while finanial hedging less benefiial, then other than the diret impat on reduing emission, these poliies an also bring indiret benefits of promoting the adoption of new tehnologies, laying a more solid foundation for their implementation. On the other hand, if we prove the opposite, then suh poliies should be used with more aution. 5 In this paper, we first build a simple model to ompare the impliations of finanial hedge and operational effiieny improvement on airlines profitability in the ontext of a monopoly airline, figuring out the orresponding onditions for eah of these possible strategies to be optimal. We then extend our analysis to inorporate airline ompetition. We also study the impats of a fuel/arbon tax that moves the whole support of jet fuel prie to the right to see the indiret impat of this poliy when the substitutability between fuel effiieny improvement and finanial hedge is taken into aount. We find that finanial hedge seems to be more effiient in reduing the volatility of airlines profits and risk exposure, while operational improvement is more likely to generate a higher expeted profit level when its effetiveness is suffiiently high. With market ompetition, operational improvement will beome less prevalent. A positive shok to the fuel prie makes finanial hedge less attrative and operational improvement more attrative. The paper is organized as follows. Setion 2 provides relevant literature review while Setion 3 sets up the base model. Setion 4 analyzes the impats of fuel finanial hedging and operational effiieny improvement on airlines risk exposure. Setion 5 presents the impliations of the two strategies on a monopoly airline s expeted profit. Setion 6 extends the analysis to a duopoly airline market and finds out the Nash equilibrium regarding fuel hedging strategies and their orresponding onditions. Setion 7 disusses the impliations of an external shok to the fuel prie suh as arbon tax. Setion 8 ontains onluding remarks. 5. Literature Review Two streams of literature are partiularly relevant to this paper. First, there are a few empirial studies investigating airlines finanial and operational improvements together. Carter et al. (2006) 5 Some earlier studies inluding D Alfonso et al. (2015; 2016) have suggested that assessing the environmental impats of transportation poliies is usually more intriate than we thought. 10

11 as well as Treanor (2008) ome to the same onlusion: While the airline industry is exposed to high fuel pries, operational and finanial hedges an redue this exposure. Treanor et al. (2014b) look at the relationship between the real options of fleet diversity and airraft age and risk exposure, suggesting that for the same time period, both operational and finanial hedging redues airlines' risk exposure, but operational improvement tends to be more effetive in reduing risk exposure than finanial hedging. Berghöfer and Luey (2014) extend the study to over Asian and European airlines. They find that finanial hedging doesn t derease risk exposure. Meanwhile, although operational improvement does derease risk exposure, it is not very signifiant. Seond, an even larger number of studies have been dediated to investigate the potential impats of emission harges on the aviation industry. Bruekner and Zhang (2010) use a duopoly model to explore the effet of airline emissions harges on airfares, airline servie quality, airraft design features, and network struture. They show that emission harges will raise fares, redue flight frequeny, inrease load fators, and raise airraft fuel effiieny, while having no effet on airraft size. Hofer et al. (2010) investigate how air traffi emissions taxes may impat arbon emissions in the US, taking into aount the air-automobile substitution effet. They show that potentially sizeable inreases in automobile traffi and related emissions may substantially redue the environmental benefits of air travel arbon emissions taxes. In some instanes, arbon emissions may even inrease in short-haul markets. Yuen and Zhang (2011) investigate the effets of unilateral measures to ontrol greenhouse gas emitted by the aviation industry. They find that unilateral efforts might lead to an inrease in global greenhouse gas emissions, and emissions taxes ould lead to larger negative impats on home than on foreign airlines, possibly resulting in ompetitive issues. Chao (2014) alulates arbon emissions in individual phases of flight during air argo transportation, investigates resultant arbon footprints by airraft type and flight route, and estimates inreases in transportation osts for airlines due to arbon taxes imposed by the EU ETS. Fukui and Miyoshi (2017) examine the effet of an inrease in aviation fuel tax on redutions in fuel onsumption and arbon emissions using data from the US airline industry. The results suggest that the amount of the redution of fuel onsumption and CO2 emissions would be smaller in the longer term. Among these studies, Bruekner and Zhang (2010) is the most relevant to this paper, as a similar setting (duopoly ompetition) is onsidered in both. Bruekner and Zhang (2010) offer a holisti view about the effets of airline emissions harges, while we supplement their results by onsidering one element they left out, i.e., the trade-off between finanial hedge 11

12 and operational improvement. The ontribution of this paper is multi-fold. Other than being the first paper to investigate the impat of finanial hedging tools on airlines implementation of fuel effiieny improvements, and the impliations of fuel/arbon tax in this strategy substitution, it also fills a few gaps in existing literature. First, there is no theoretial study dediated to omparing finanial hedge and operational improvement in the ontext of the aviation industry. Seond, empirial studies fous mainly on the impats of these strategies on airlines' risk exposure instead of their profitability. Admittedly, reduing risk exposure is the major objetive for any hedging strategy, but hedging also has a non-negligible impliation on an airline s bottom line. This is even more substantial when we onsider finanial hedge as a substitute of operational effiieny improvement. Furthermore, when market ompetition is in plae, profitability beomes even more important Model Setting There are two stages for airlines deisions. In the first stage, there is no operation, and the airlines determine their fuel strategies without knowing the exat fuel prie in the seond stage when operations happen. The airlines only have information about the possible distribution of the fuel prie based on historial data. For simpliity, we assume that the per flight fuel prie follows a uniform distribution, i.e., ~U(, ). 7 To simplify the analysis, we assume away the heterogeneities in the size of the airrafts, the load fator and the flight distane, so that every passenger served aounts for one unit of jet fuel. Three options are available: no move, finanial hedge and operational improvement. It should be noted that for simpliity we only allow the airline(s) to hoose one strategy, but we are well aware of the fat that in reality airlines normally adopt a mix of strategies at the same time, whih in itself is a way of hedging. To fous on the 6 For example, in 2014 when rude pries dereased sharply, some major U.S. airlines inluding Delta and Southwest saw part of the benefits from heap fuel eaten away by hedging osts, leaving them with billions of dollars in losses. The situation was worsen onsidering their ompetitors suh as Amerian Airlines didn t have any hedge ontrats at that point and were set to see a greater boost to their bottom lines. In fat, Amerian Airlines reognized a net gain of $330M from its fuel-hedging program in 2013, but it stopped hedging against future fuel purhases in 2014, beause the ost of hedging was too high (Cook and Billig, 2017). Instead the airline favors long-term operational improvements, i.e., upgrading its fleet to one that is more fuel-effiient. These different attitudes seem to be driven by the impliations of hedging on airlines profitability instead of risk exposure. 7 This way to model unertainty is very ommon in transportation literature (e.g., Xiao et al., 2013; 2015; 2016; 2017), mainly due to its tratability. 12

13 omparison between pure strategies, we are essentially investigating whih strategy is likely to be preferred and hene oupy a larger perentage in airlines fuel strategy portfolio. If no move is hosen by an airline, it doesn t inur any fixed investment but will fae the market fuel prie as it is realized in the seond stage. With finanial hedge, the airline invests a ost, f F, to fix the fuel prie at a ertain level. 8 Without loss of generality, we assume that the finanial hedge is very effiient that it an fixate the fuel ost at, the lower bound of the fuel prie distribution. 9 With operational improvement, the airline inurs an investment, f O, to improve the operation effiieny of fuel onsumption 10, in de fato giving a disount, r, to the market fuel prie (with 0 < r < 1). For the sake of omparison, we assume that f F = f O = f. 11 Here we impliitly assume away the relationship between the investment ost of the strategies and the amount of fuel onsumed in the seond stage. In reality it is likely that there is a positive orrelation between these two fators, i.e., the larger the fuel purhase/onsumption involved, the more expensive the hedge would be. However, this relationship is also not linear or even ontinuous in reality, making an aurate modeling hard to ahieve. Therefore, in this paper we hoose the simplest setting for the ease of analysis. Moreover, the parameter r gives the setting a ertain level of flexibility, so the impliations should not be affeted as long as the analytial results are arefully interpreted. In the seond stage, the market fuel prie will be realized, and the airlines will ompete in quantities (traffi) with the fuel ost determined by their fuel strategies in the first stage. Let s first onsider the situation when there is only one airline. Assume that we have a simple linear inverse 8 Rao (1999) estimates the ost of hedging to be 1% of an airline's fuel bill. 9 Aording to Berghöfer and Luey (2014) and Turner and Lim (2015), on the organized exhange-traded futures market aviation fuel is usually not traded, so airlines typially use a ross hedge, where the hedging ontrats have ommodities that are highly orrelated with jet fuel, the most widely used being West Texas Intermediate Sweet Crude (WTI), Brent North Sea oil (Brent), heating oil and gasoil. The finanial hedging strategies of some airlines are at an even higher level of omplexity. For example, Air New Zealand hedged 48% of its estimated fuel expenditure for the first quarter of the 2012/13 fisal year, making provision for 910,000 barrels. Most of this was ahieved through all options on 740,000 barrels at a WTI strike prie of $ But a further 170,000 barrels are loked into a eiling prie of $ and a floor prie of $ So the arrier's hedges are positioned defensively against higher pries while retaining some exposure to lower pries. Here for the sake of analytial simpliity, we abstrat away all these ompliations. 10 For example, the airline an invest in new airraft that utilizes jet fuel more effiiently. This setting is onsistent with Treanor (2008), who suggests that the fuel-effiieny of the fleet is a hedge against the airline s risk to jet fuel pries. Aording to Treanor (2008), an airline s exposure to fuel ost is roughly defined as the hange in the airline s value to a hange in the prie of fuel. A newer airraft provides the same level of servie as an older airraft but at a lower fuel ost. This implies that a hange in fuel pries is less signifiant for a newer airraft than for an older airraft. 11 Sine r is flexible, this setting is equal to saying that the amount of investment that an seure the fuel prie at an help to improve the operational effiieny and to redue the usage of the fuel to 1 r of the original level. 13

14 demand funtion: P = a bq (1) When the airline adopts no move in the first stage, its profit funtion is: π 1 = (P )q C F = (a bq )q C F (2) where C F measures the fixed ost of operations. When the airline adopts finanial hedge, its profit funtion is: π 2 = (P )q C F f = (a bq )q C F f (3) Similarly, the profit funtion of the airline when it hooses operational improvement is: π 3 = (P r)q C F f = (a bq r)q C F f (4) Before we move into the analysis, it should be noted that due to the limited apaity of theoretial analysis, the setting of this paper is rather restritive and does not represent the real praties of the airlines very well. We offer a thorough disussion regarding these shortomings in our setting in the onluding setion (Setion 6). With these defiienies in mind, we realize the importane to resist the over-interpretation of our analytial results. Some of the poliy suggestions should also be taken with extra aution. However, the paper serves as the first theoretial work on this topi and hopefully opens up the window for further and more elaborated studies. 7. Impats on Airline Risk Exposure We an easily find the market equilibrium quantity under eah senario, and the orresponding expeted profit: Eπ 1 = π 1 f()d = a2 4b a 1 ( + ) + 4b 12b ( ) C F (5) Eπ 2 = π 2 f()d = (a )2 4b C F f (6) 14

15 Eπ 3 = π 3 f()d = a2 4b ar r2 ( + ) + 4b 12b ( ) C F f (7) While the varianes of the profits under the three senarios are: Var(π 1 ) = (π 1 Eπ 1 ) 2 f()d (8) = ( )2 720b 2 [15a2 15a( + ) + ( )] Var(π 2 ) = (π 2 Eπ 2 ) 2 f()d = 0 (9) Var(π 3 ) = (π 3 Eπ 3 ) 2 f()d (10) = ( )2 r 2 720b 2 [15a 2 15a( + )r + ( )r 2 ] Other than the varianes, we an also measure risk exposure as the expeted loss, i.e., the probability that the airline will get into negative profit multiplied by the orresponding loss. In the ase of no move, as long as > a 4bC F, the airline will get into negative profit. So risk exposure in this ase is: (a )2 1 RE(π 1 ) = [ C 4b F ] d (11) (a 4bC F ) For finanial hedge, sine the airline has full information about the profit it will end up with, it will not implement this hedging strategy if negative profit is going to exist, so the risk exposure is given by: RE(π 2 ) = 0 (12) For operational improvement, as long as > (a 4b(C F + f))/r, the airline will get into negative profit, thus risk exposure is: 15

16 (a r)2 1 RE(π 3 ) = [ C 4b F f] d (13) (a 4b(C F +f))/r From equations (8)-(13), we an easily ompare the impats of different fuel hedging strategies on the risk exposure of the airlines. Proposition 1: Finanial hedge is more effiient than operational effiieny improvement in reduing the volatility of profits and risk exposure. The proof of Proposition 1 is straightforward from omparing equations (9) and (10), as well as equations (12) and (13). Proposition 1 needs to be arefully interpreted, as it relies on a few key assumptions in our setting. In partiular, we abstrat away the influene of both strategies in the longer term. Operational effiieny improvement is a long-term investment, whih will help airlines to maintain a lower level of fuel onsumption in a long period of time. Finanial hedge, on the other hand, an only play a role in a muh shorter term. Moreover, if fuel prie has been high, the ontinuation of finanial hedge likely means higher investment ost, making it more and more expensive. But this short-term nature of finanial hedge also gives it a higher level of flexibility ompared with operational improvement, espeially in the environment of onsistent low oil prie. Fatoring in all these onsiderations, the onlusion from Proposition 1 might not be so straightforward anymore. But one also annot deny the fat that finanial hedge is likely to be a more natural hoie for the airlines to onsider when reduing volatility and risk exposure is the key objetive. 8. Expeted Profit of a Monopoly Airline Next we shift our analysis to the fous of this paper: the impats of different hedging strategies on the expeted profits of airlines adopting them. We first study the ase of a monopoly airline. Comparing the equations (5)-(7) pairwise, we an find that E(π 1 ) E(π 2 ) when f b + a( ) 4b (14) And E(π 3 ) E(π 1 ) when 16

17 f a 1 r2 ( + )(1 r) 4b 12b ( ) (15) While E(π 2 ) E(π 3 ) when t F,O r < 1, where 3a( + ) 9a 2 ( + ) 2 12( )(2a ) t F,O = 2( ) (16) The managerial impliations of inequalities (8)-(10) are straightforward, as they tell that if the investment ost for finanial hedge (operational improvement) is suffiiently high, this strategy will be dominated by the no move or operational improvement (finanial hedge). With a summary we an also onlude that no move will be the optimal strategy when f max { a 1 ( ) + 4b 12b (22 2 a(1 r) ), ( + ) 4b (1 r2 ) ( )} 12b (17) While finanial hedge will be the optimal strategy when { f a 1 ( ) + 4b 12b (22 2 ) t F,O r < 1 (18) And operational improvement will be the optimal strategy when { f a 1 ( + )(1 r) 4b 12b ( )(1 r 2 ) (19) 0 < r t F,O We an use Figures 1 to summarize the ranges of f and r in whih the three strategies are optimal to the airline. Insert Figure 1 about here Figure 1 is very intuitive. We an see that when f is suffiiently large (meaning that the hedging strategies are ostly to implement), no move will be the best option for the monopoly airline, as the benefits of fuel hedging and effiieny improvement annot justify their osts. Another straightforward result is that when r is not suffiiently small (meaning that operational improvement is not very effetive), finanial hedge will be the best option for the airline. An 17

18 observation omes from the interation between r and f, as the effetiveness of the operational improvement has an exponential impat on the upper bound of its ost that is aeptable. Proposition 2: Operational improvement will generate a higher expeted profit level ompared with finanial hedge when its effetiveness is suffiiently high. Proposition 2 an be obtained straight from Figure 1. Although mathematially straightforward, this proposition has some important poliy impliations. In partiular, if the operational improvement is not substantial in helping fuel effiieny, airlines may hoose to forgo this option and instead rely on finanial tools to management fuel ost. This effiieny improvement will be even less desirable if it is with a hefty prie tag. Unfortunately, the advanements in airraft tehnologies and airline operational best praties are notoriously slow and inremental, while new airrafts are also very expensive. Adding together, these elements an help partially explain why Bombardier s CSeries failed to attrat airline ustomers despite being the most fuel-effiient airraft for its size. In other words, the unimpressive performane of operational effiieny improvement in the industry, together with the availability of finanial hedge as an alternative, might be the reason why airlines fell short of the fuel effiieny goals set by IATA and ICAO. We an also show that when the airline is a soial welfare maximize instead (e.g., a publi airport), the ranges hange but the qualitative features of the ranges are onsistent with the profit maximizing ase The Impat of Market Competition Next we extend our analysis by inorporating market ompetition. Assume that we have two symmetri airlines, A and B. The per passenger fuel prie of both airlines follows the same uniform distribution ~U(, ). The demand funtion is linear as P = a b(q A + q B ). In this paper we will only analyze the Nash equilibrium of the game, whih is straightforward but might also have some downsides, whih we will disuss in the onlusion setion. When the airline adopts no move in the first stage, its profit funtion is: π i1 = P(q A, q B )q i q i C F (20) 12 Sine there is not muh new insight, we omit the analysis from this paper. But it is available upon request. 18

19 When the airline adopts finanial hedge, its profit funtion is: π i2 = P(q A, q B )q i q i C F f (21) Similarly, the profit funtion of the airline when it hooses operational improvement is: π i3 = P(q A, q B )q i rq i C F f (22) where i = A, B. Sine eah of the two ompanies has three hedging strategies, there are nine possible pairs of expeted payoffs, as illustrated in Table 1. Insert Table 1 about here For any pair of hedging strategies to be Nash equilibrium, both airlines need to have no inentive to unilaterally deviate. In other words, one airline will only end up with a lower expeted profit to hange its strategy given that the other airline is not hanging. In mathematial terms, for the pair of strategies (k A, k B ), with k i {1,2,3}, to be Nash equilibrium, we require Eπ AkA k B Eπ AlA k B, Eπ AkA k B Eπ AmA k B, Eπ BkA k B Eπ BkA l B and Eπ BkA k B Eπ BkA m B, with l i, m i {1,2,3} while k i l i m i to hold simultaneously. Summarizing the orresponding onditions to ensure these four inequalities gives rise to Figure 2. Insert Figure 2 about here One observation from Figure 2 is the existene of asymmetri equilibrium. From a tehnial point of view, these asymmetri equilibria exist beause we onsider Nash equilibrium in our analysis, whih means that although a arrier may earn less ompared with its ompetitor in ertain irumstanes, it doesn t have inentive to unilaterally hange its hedging strategy, as that would move it to an even undesirable situation. In partiular, when finanial hedge and operational improvement are not overly expensive and the effetiveness of operational improvement is in the middle, an airline has the inentive to use a different strategy ompared with its ompetitor. Despite the fat that the result is related to the equilibrium onept we adopt (and might go away if refinements are used), it in fat fits reality very well. Random observations from aviation markets give many examples of suh asymmetry. For instane, United Airlines and Amerian Airlines, two of the big three in the U.S., adopt very different hedging strategies for most of the time. More poliy impliations ome from Figure 3, whih is a omparison between Figures 1 and 2 19

20 (i.e., monopoly vs. duopoly). The most important observation from Figure 3 is about the hange in the overage of the fuel strategies. In partiular, Proposition 3 an be summarized as follows. Insert Figure 3 about here Proposition 3: Competition will redue the possibility that airlines adopt operational effiieny improvement. The proof of Proposition 3 is straightforward from Figure 3. It is easy to see that in the area where the monopoly airline will adopt operational effiieny improvement, the outome is a lot more diverse under duopoly ompetition. In partiular, either one airline or both airlines might deviate from operational improvement. In fat, the onditions under whih both airlines will adopt operational improvement are muh more stringent with ompetition. From a welfare perspetive, this phenomenon might not be desirable, as it might suggest that with ompetition it is in fat muh harder to have all the players ommitted to effiieny improvements. Admittedly, this omparison is partially driven by our model and thus not ompletely aurate, as our setting ignores the relationship between the ost of improvement investment and the amount of fuel onsumed. In other words, sine ompetition redues operation for any one airline, to pay the same level of investment in order to ahieve operational improvement, it is natural to see a derease of inentive for the strategy. However, the same logi also applies to finanial hedge, while its attrativeness relative to operational improvement still appear to grow with ompetition. In fat, dereasing eonomies of sale might indeed be a real onern for airlines to adopt operational improvement in reality, even if it is not as signifiant as our model predits. First, all tehnologial advanements and operational improvements exhibit ertain levels of eonomies of sale, whih means that airlines with larger market power will be able to utilize them more effiiently thus might have a higher inentive to get onboard. Seond, fiere ompetition might hurt the airlines apaity to plan for the long term so that they prefer shorter-term solution that might be heaper temporarily, whih is not rare in the history of ommerial aviation. Of ourse, we are not hampioning less ompetition, as a lot of the benefits from ompetition are not onsidered in our model. These results only serve the purpose of pointing out one potential drawbak of stronger ompetition that has been negleted by the literature, whih might have its value as a building blok for a more holisti view of the impats of market fores in the aviation industry. 20

21 10. The Impat of Fuel/Carbon Tax After omparing fuel finanial hedge and operational effiieny improvement in the ontexts of a monopoly airline and with ompetition, it may be more interesting to investigate the impat of external shoks on the omparative attrativeness of these strategies. In this setion, we onsider a possible external shok that will inrease the real prie of fuel. The most ommon example for this type of shok is a fuel tax or a arbon tax, whih is (roughly speaking) added on top of the market fuel prie. With the harge of a new fuel (arbon) tax, Δ, the whole distribution of the fuel prie will be moved to the right by a magnitude of Δ. In other words, the fuel prie distribution beomes ~U( + Δ, + Δ). In this ase, we an re-examine the ut-off values of f and r in Figures 1 and 2 and see the omparative attrativeness of the three fuel options. In the ase of a monopoly airline, equation (14) now beomes: f a 1 ( ) + 4b 12b [2( + )2 ( + )( + ) ( + ) 2 ] = a 1 ( ) + 4b 12b (22 2 ) ( ) 4b (23) By omparing inequalities (14) and (23), we an find that, with the tax, it is easier for no move to outperform finanial hedge. Besides, inequality (16) beomes: t F,O r < 1 with t F,O 1 = 2[ 2 [3a( ) ( + + )] (24) 9a 2 ( ) 2 12( + )[ ( + + )](2a )] So whena > ( + + ), we havet F,O > t F,O,whih means that it is easier for operational improvement to outperform finanial hedge. Furthermore, inequality (15) beomes: 21

22 f a ( )(1 r) 4b 1 12b [( + )2 + ( + )( + ) + ( + ) 2 ] (1 r 2 ) = a 1 ( + )(1 r) 4b 12b ( )(1 r 2 ) + (1 r) [2a 4b (25) ( + + )(1 + r)] Comparing inequalities (15) and (25), we an onlude that when 2a > ( + + )(1 + r), it is easier for operational improvement to outperform no move. These results an be summarized in Figure 4. Insert Figure 4 about here The ase of duopoly airlines is more ompliated but an also be niely summarized with a figure (Figure 5). We leave the detailed analysis to the Appendix. Proposition 4 an be derived from both Figures 4 and 5. Insert Figure 5 about here Proposition 4: A positive shok to the fuel prie makes finanial hedge less attrative and operational improvement more attrative. Proposition 4 suggests that a positive shok to the fuel prie would likely weaken the attrativeness of finanial hedge, and strengthen the attrativeness of operational improvement. This is beause when fuel prie beomes more expensive, the benefit of finanial hedge (the differene between potential fuel ost saving and the hedge ost) dereases as the equilibrium onsumption of jet fuel would derease. However, although the equilibrium onsumption of jet fuel should also derease with operational improvement in plae, the benefit of this hedge will still be larger, as given the same level of fuel effiieny improvement, the higher the fuel prie, the larger the saving to implement this improvement. Proposition 4 has some important poliy impliations. Almost all studies on emission tax neglet its impat on airlines fuel strategies. Sine operational improvement is a better option for the environment, this proposition points to the fat that emission tax will give airlines more inentive to adopt a fuel strategy that is superior to other strategies in terms of environmental impat. In other words, it shows that previous studies on the funtions of emission tax may in fat underestimate its positive outome. Having this in mind, poliy makers might want to work harder 22

23 to impose emission tax, as it brings in more benefit to the soiety by induing airlines to adopt more environmentally friendly fuel strategy. 11. Conlusion In this paper, we use a theoretial model to ompare the impliations of fuel finanial hedge and operational effiieny improvement on airlines profitability in the ontext of a monopoly airline, figuring out the orresponding onditions for eah of the three possible strategies: no move, finanial hedge and operational improvement to be optimal. We then extend our analysis to inorporate airline ompetition. We also study the impats of a shok that moves the whole support of jet fuel prie to the right, whih an be interpreted as the imposition of a fuel/arbon tax. We find that finanial hedge is more effiient in reduing the volatility of profits and risk exposure, while operational improvement is more likely to generate a higher expeted profit level ompared with finanial hedge when its effetiveness is suffiiently high. With market ompetition, operational improvement will beome less prevalent. A positive shok to the fuel prie makes finanial hedge less attrative and operational improvement more attrative. There are potentially some poliy impliations from this investigation. First, fuel finanial hedge as an alternative for operational improvement does seem to be attrative to impede the adoption of real effiieny improvement. Finanial hedge is superior to operational improvement in terms of reduing profit volatility and risk exposure, and it might also be better in terms of expeted profit if the operational improvement is not suffiiently effetive. This might partially explain why airlines have fallen short of the fuel effiieny goals set by IATA and ICAO, and should be taken into onsideration by the poliy makers when mehanisms to inentivize airlines the ahieve these goals in the future. Seond, despite its merit in many areas, ompetition seems to be less favorable in induing real effiieny improvement. In other words, (exessive) ompetition might not be desirable if we also onsider the inentive of airlines to make long-term investment in improving fuel effiieny. Third, fuel or arbon tax might be even more effetive in reduing emission if we take into aount its impat on airlines fuel strategy, as it tends to enourage airlines to adopt operational improvement and disourage them to use finanial hedge, whih is good for the environment. In this sense, it should be further supported by poliies and regulations. There are a few limitations, mainly due to the simplifiations of our model. First, in ontrast to our 23