Fine-Tuning a Corporate Hedging Portfolio: the Case of an Airline

JOURNAL OF APPLIED CORPORATE FINANCE VOLUME 25 | NUMBER 4 | FALL 2013

Journal of APPLIED CORPORATE FINANCE

Journal of Applied Corporate Finance c/o Wiley-Blackwell 350 Main Street Malden, MA 02148-5018

In This Issue: Risk Management

Risk Management Navigating the Changing Landscape of Finance 8 James Gorman, Chairman and CEO, Morgan Stanley

Reforming Banks Without Destroying Their Productivity and Value 14 Charles W. Calomiris, Columbia University

How Companies Can Use Hedging to Create Shareholder Value 21 René Stulz, Ohio State University

Do Trading and Power Operations Mix? 30 John E. Parsons, MIT Sloan School of Management

Aligning Incentives at Systemically Important Financial Institutions: 37 The Squam Lake Group A Proposal by the Squam Lake Group

Managing Pension Risks: A Corporate Finance Perspective 41 Gabriel Kimyagarov, Citigroup Global Markets, and Anil Shivdasani, University of North Carolina at Chapel Hill

Synthetic Floating-Rate Debt: An Example of an Asset-Driven Liability Structure 50 James Adams, J.P. Morgan Securities, and Donald J. Smith, Boston University

Hedge Fund Involvement in Convertible Securities 60 Stephen J. Brown, New York University; Bruce D. Grundy Uni-

VOLUME 25 versity of Melbourne; Craig M. Lewis, Vanderbilt University; and Patrick Verwijmeren, Erasmus University Rotterdam

Fine-Tuning a Corporate Hedging Portfolio: The Case of an Airline 74 Mathias Gerner, European Business School and Ehud I. Ronn, University of Texas at Austin | NUMBER 4

A Primer on the Economics of Shale Gas Production 87 Larry W. Lake, University of Texas; John Martin, Baylor The Simon Business School is ranked #7 in the world Just How Cheap is Shale Gas? University; J. Douglas Ramsey, EXCO Resources, Inc.; and for finance and #8 for accounting by the Financial Times. Sheridan Titman, University of Texas In addition to the flagship two-year MBA program and several | one-year master’s degree programs at its main campus FALL 2013 Evidence from German Companies of Effects of Corporate 97 Julita M. Bock, Otto von Guericke University in Rochester, New York, Simon offers one-year, part-time Risk Management on Capital Structure Decisions master’s degree programs in finance and management at its New York City location. Designed for working professionals, with alternate weekend classes in midtown Manhattan and residency weeks to further complement the classroom instruction, these programs feature senior Simon faculty, small class sizes, and personalized program support. For additional details, please visit www.simon.rochester.edu. Fine-Tuning a Corporate Hedging Portfolio: The Case of an Airline by Mathias Gerner, European Business School* and Ehud I. Ronn, University of Texas at Austin*

here is now a large body of academic research The Airline’s Hedging Strategy that attempts to explain why companies hedge Airlines are heavily exposed to fluctuations in jet fuel prices. T the risks arising from volatility in commodity Moreover, there are several factors that complicate strategies prices, foreign exchange, interest rates, and other for hedging such exposures. Although major commodity such “financial prices.” In recent years, there has also been a exchanges such as ICE and NYMEX have listed futures and number of academic papers on how companies should hedge, options on crude oil and various refined products, these do including discussions of optimal corporate hedging practices not include futures on jet fuel. As a result, many airlines, involving the use of linear futures-like contracts as well as including the one in this case study, use derivatives based nonlinear option-like contracts. But because actual corporate on crude oil or heating oil.4 There may also be a discrepancy hedging practices are typically confidential, these theoretical between a firm’s desired hedging horizon and the maturi- studies have generally been of limited use to practitioners.1 ties available for standardized derivative contracts. Finally, Studies of airline industry hedging activities, for example, exchanges require hedgers to post cash-variation margin for have been forced to rely on information from publicly avail- futures and short options positions, and this requirement can able sources, such as 10-K reports. And most academic studies be onerous for cash-strapped airlines. of corporate hedging have focused primarily on the question For all those reasons, airlines often find over-the-counter of whether there is a discernible relationship between the (“OTC”) derivatives offered by financial institutions prefer- firm’s hedging activities and its value.2 able to standard exchange-traded contracts. The high degree In this paper, we provide a case study involving in-depth of flexibility inherent in OTC derivatives—especially those analysis of an international air carrier’s actual jet-fuel price that provide payoffs based on average prices during a specific hedging strategy and compare it with an optimized mix delivery month—allows airlines to match their financing of derivatives. We also explain how the airline’s financial requirements and hedging objectives. strength, fuel price-and-quantity correlations, and risk We found that four major considerations influence the profile relate to that optimal mix of derivatives. With this airline’s hedging decision: air carrier’s specific objectives in mind, we recommend a 1. The firm’s financial strength and current credit rating; hedging strategy that proposes the use of a specific custom- 2. The correlations between the volumes of fuel it ized derivative: annually-settled Asian options. We show consumes and the prices it pays; how this derivative can be used to protect the airline against 3. Its fixed and variable transaction costs; and jet-fuel price fluctuations at reasonable cost while also 4. Its internal risk profile. preserving the corporate liquidity that can be jeopardized While these four considerations cannot easily be trans- by some hedging instruments.3 lated into quantitatively measurable rules, the overall hedging

* The authors acknowledge with thanks the financial support of the European Busi- conclude jet-fuel hedging is positively related to market values. Results show U.S. air- ness School Endowed Chair of Corporate Finance and Capital Markets for its support of lines engaging in hedging activities increase their firm value by roughly 14%. See “Fuel Mathias’ doctoral studies. They also thank the Department of Finance at the McCombs Hedging in the Airline Industry: The Case Study of Southwest Airlines,” Working Paper, School of Business, University of Texas at Austin for support of a summer visiting re- Oklahoma State University and Portland State University, 2004; “Does Hedging Affect search assistantship extended to Mathias. Previous drafts of this paper were presented Firm Value: Evidence from the U.S. Airline Industry,” in Financial Management, 35(1), at the March 2012 22nd Annual Derivatives Securities and Risk Management Confer- 53–86, 2006; and “Hedging and value in the U.S. Airline Industry” in this Journal of ence, Case Western Reserve University, Tulane University and the University of Alberta. Applied Corporate Finance, 18(4), 21–33, 2006. The comments and feedback of Ulrich Hommel, the executives of the airline whose jet- 3. Our analysis and recommendations are consistent with, and serve to confirm, the fuel hedging portfolio is examined here and the editors of this Journal are readily ac- theoretical findings of a 2001 study by University of North Carolina professor Greg knowledged. The authors are solely responsible for any errors in the paper. Brown and Goldman Sachs’ Klaus Toft that demonstrated how non-financial companies 1. For example of such papers, see “On the Optimal Mix of Corporate Hedging Instru- can optimize their hedging portfolios by using customized options. See Gregory Brown ments: Linear Versus Nonlinear Derivatives,” by Gerald Gay, Jouahn Nam and Marian and Klaus Toft, “How Firms Should Hedge,” Review of Financial Studies, 15(4), 1283- Turac in the Journal of Futures Markets, 23(3), 217–239, 2003; and “Managing Long 1324; 2001. and Short Price-and-Quantity Exposure at the Corporate Level,” a Working Paper at the 4. Jet-fuel is a kerosene-like middle distillate. The prices of crude oil, home heating University of Texas at Austin by Sergey Kolos and Ehud Ronn. oil and jet-kerosene are highly correlated as the latter two are derived physically from the 2. The balance of evidence suggests that hedging does create value. Most notable are former in the refining process. papers by David Carter and Betty Simkins of Oklahoma State and Daniel Rogers of Port- land State. Studying the hedging behavior of U.S. airlines between 1992 and 2003, they

74 Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 Figure 1 Continuous Hedging Approach (Expressed as a Percentage of the Expected Crude Oil Consumption at Time t)

100%

80%

60%

40% Hedging Ratio

20%

0% t-1 t-5 t-9 t-13 t-17 t-21 Time strategy recognizes these factors. And since management does time and cash flow to make the necessary operating changes. not have a specific quantitative optimization framework, it Such a gradual approach, which is illustrated in Figure relies instead on experience and rules of thumb. 1, begins with the airline hedging volumes equal to 5% An airline’s credit rating heavily influences the kinds of of its expected fuel consumption 24 months in the future. hedges it can obtain in the OTC market as well as the cost of With each passing month, the airline hedges another 5% those hedges. A high credit rating allows the firm to choose of expected volumes until the hedged position amounts to from a broad range of hedging instruments,5 some of which— approximately 85%-90% of the total six months prior to for example, a “collar” involving the purchase of a call and the actual consumption. This 24-month time horizon corre- sale of a put—are likely to involve the financial institution sponds to the airline’s confidence in its ability to forecast accepting some credit exposure to the airline. flight schedules for the next two years with a reasonable Airlines also have to contend with a somewhat uncertain degree of certainty. To minimize the risk of overhedging, relationship between fuel prices and the quantities of fuel it limits hedges to 85%-90% of the expected jet fuel they will consume at those different prices. During strong consumption. economic conditions, both the demand for flights and the This figure shows the layered hedging approach employed prices for jet fuel tend to increase, while the reverse typically by the airline in relative terms. The firm starts trading holds during a recession. While both the passenger and the derivative contracts with a volume of 5% of the expected cargo sectors face similar fluctuations of prices and quanti- consumption 24 months before the actual date of usage and ties, it is generally easier to pass fuel price increases on to then continually adds another 5% per month. the mostly industrial cargo customers than to the more Demand varies seasonally, especially within the passenger price-sensitive passengers. As a consequence, the cargo and sector, with peak consumption during June, July and August. passenger business segments may require substantially differ- Hedge volumes are adjusted to reflect such expected varia- ent hedge ratios. tion. Figure 2 projects the seasonal pattern of expected fuel The firm’s fixed and variable transaction costs, for reasons consumption and hedging volumes (in barrels of crude oil) for that are fairly self-evident, also influence the airline’s choices the two-year period (2007 - 2008) as perceived by manage- of jet fuel price hedging tools. ment at the end of 2006 (see also Table 1). As can be seen in Finally, the fourth major consideration is the airline’s the figure, the hedge ratio projected for the first six months internal “risk profile.” This factor reflects the firm’s airfare (from January to July 2007) stays at 85-90% of the expected ticket sales strategy, and its desire for flexibility in adjusting consumption, but then drops off in an almost linear fashion to changes in market conditions. The airline we studied seeks thereafter, finishing at a level of 5% by the end of 2008. to make gradual adjustments to changes in fuel costs, particu- This figure shows the layered hedging approach employed larly to increases in such costs, thereby giving it sufficient by the airline in absolute terms. The graph accentuates the

5. The airline in question has an investment grade with A-3 from S&P, and currently Ba1 from Moody’s.

Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 75 Figure 2 Hedging Volume (in Barrels of Crude Oil) for Each Month Between January 1, 2007 and December 31, 2008 as of December 31, 2006)6

4000

3500

3000

2500

2000

1500

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500 Barrels of crude oil (in thousand)

0 Jan-07 Apr-07 Jul-07 Oct 07 Jan-08 Apr-08 Jul-08 Oct 08

Expected Consumption Hedged Volume

Figure 3 Payoff Structure and Total Costs of the Firm’s Standard Hedging Strategy (Premium Collar)

Total Collar Structure Cost

Physical Short 80% 110% Position

Total Cost

Spot Price (at tie t) Long Call

Short Put Futures Price (at time t observed at time 0)

seasonal variations in hedging volume, as measured in barrels investment grade rating, the OTC market would be either of crude oil. For example, note the signifi cantly higher hedge inaccessible or available only at substantial credit costs. volume for Jul-07 relative to Jan-07. Moreover, instead of using “linear” instruments such as futures, forwards or swap contracts, our airline used only The Firm’s Use of Derivatives options (“non-linear”)—and of a type known to industry To benefi t from customized terms and less onerous margin participants as “Asian” options. The payoffs from Asian requirements, all of our airline’s hedges are fi nancial contracts options depend on the monthly-averaged crude oil price that are traded over the counter (OTC) with major invest- instead of the price at the end of the month or other settlement banks as counterparties. Th e airline’s ability to trade ment date. Th is is attractive to airlines because they purchase OTC, as noted, depends on its credit rating: without an fuel ratably (at the same rate each day) over the month.

6. The results shown for the “Expected Consumption” are estimates based on the hedge ratio presented in Figure 1: I.e., the expected consumption in July 2007 is the product of the total amount hedged during this month multiplied by 1/hedge ratio. The ratio is in this case at roughly 90% at t-7 (July 2007) for time t (December 2006).

76 Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 Additionally, the averaging feature of the option dampens not wish to find itself locked into higher prices in the event the volatility of the underlying asset, thereby reducing the of a 2008-style oil-price crash.8 premiums hedgers must pay for Asian options. The airline’s preference for option-like rather than This figure shows the Premium Collar structure most futures-like hedging tools is a fundamental strategic issue. commonly applied by the firm. The costs of an unhedged Its willingness to pay a net premium to be long further OTM physical short position (dashed black line) is compared with puts reflects its strategic preference to cap its exposure to the airline gross exposure (solid gray line) trading a long call fuel price increases while enjoying a proportionately greater and a short put option. upside from price decrease. (By preserving this upside, our The airline’s standard hedge, which is shown graphically airline may “protect itself” against any windfall experienced in Figure 3, consists of a long call and short put. Because the by financially weaker or less sophisticated competitors in strike of the call purchased is closer “to-the-money” than the the event of a precipitous drop in fuel prices.) The variabil- put sold, the hedge requires the airline to pay cash “up-front.” ity of, and resulting uncertainty about, the correlations For that reason it is referred to as a “premium collar” (as between the price the airline pays for fuel and the quanti- distinct from a “zero cost collar”).7 The net premium paid for ties it consumes also encourages use of option-type hedging the lower call option strike effectively provides higher pay-offs tools. And since the airline thus has a non-linear exposure for the airline if and when oil prices rise. to fuel prices, the non-linear option pay-offs are likely to be In a commonly used structure, the firm’s collar consists more attractive than the linear payoffs of futures, forwards of an out-of-the-money (OTM) call struck at 110% of the and swaps. relevant futures price together with a short position in an OTM put struck at 80% of the relevant futures prices. This Annual Asian Options derivative structure has the effect of limiting the airline’s net Asian options are settled according to the arithmetic mean exposure (as reflected in the solid gray line in Figure 3) to (or average) of the underlying price. These options are more increases in jet fuel prices while also allowing the airline to difficult to value than standard stock options, however,9 and benefit to some extent from falling fuel prices. the academic literature provides three different ways of pric- But the airline does not simply follow this strategy every ing them.10 (For details of our derivation of annual-average month in a mechanical fashion. Sometimes it alters its hedges option values using observable futures and listed-options based on its own price expectations. Depending upon those data, see Appendix A.) expectations and the prices for fuel options, it might, for example, sell another Asian call struck at 125% of the relevant Fine-Tuning the Hedge futures price, or purchase another OTM put option with a As noted in the earlier study by Brown and Toft, in cases strike price lower than 80% of the relevant futures price. where the “correlation between price and quantity is posi- In the case of the 125% call, this would provide cash to tive, exotic derivatives offer additional gains over forwards the airline if prices rose above 110% of the initial futures or options alone,” and the size of such gains increases with price but stop paying out if prices averaged more than 125% quantity risk but falls with price risk. of strike. By selling a higher strike option, the airline would To see this, consider the airline’s hedging portfolio as of reduce the net premium it would have to pay the option December 31, 2007 for the next 12 months—that is, from dealer up-front. The potential problem is that it would be January to December 2008. For simplicity, we assume all exposed to massive increases in fuel prices (i.e. of more option contracts are acquired on December 31, 2007 (in than 25%). Similarly, the purchase of the lower strike puts fact, they were acquired gradually each month, as mentioned increases the net premium required of the airline but permits earlier) and also assume constant crude oil consumption for it to benefit if prices drop precipitously. This latter effect can each month in 2008 (of 3.5 million barrels). be quite important in a market where certain airlines cannot We assume the airline uses the same premium collar afford to hedge, and thus benefit if oil prices drop sharply. hedge of buying a monthly Asian OTM call with a strike A financially strong airline can afford to hedge, but would at 110% of the crude oil futures price for month t, while

7. A zero-cost collar represents the combination of long call and short put strikes an changes depends on the sum of LogNormal distributed random variables, which is not option dealer would sell for no net premium up-front. itself LogNormal. Hence, we must rely on approximate solutions rather than closed-form 8. The airline’s decision to sell more OTM options can also be affected by the so- ones. called volatility “smiles” characteristic of OTM options. The “smiles” in question are 10. The first approach uses numerical procedures to estimate option values. The graphic representations of option implied volatilities shown over a wide range of strikes second approach uses Monte-Carlo simulations with variance reduction techniques. See from OTM puts to OTM calls. If the price of the OTM call seems high (or price of the OTM “A pricing method for options based on average asset values“ by Angelien Kemna and put seems low) to the airline, it will be more inclined to sell that call (or buy the OTM Ton Vorst in the Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, put). The hedger’s view of the optimal collar structure, therefore, strongly depends on the March, 1990. The third, which we prefer, uses approximations of the density distribution effective transaction costs associated with putting on the hedge, and to a lesser extent, of the arithmetic average which then allows the application of a closed-form solution. on future price expectations. This third approach was developed by Stuart Turnbull and Lee Wakeman in 1991. See 9. The classic closed-form Black-Scholes option formula assumes the distribution of “A Quick Algorithm for Pricing European Average Options” in the Journal of Financial and underlying price changes is LogNormal. However, the arithmetic mean of a series of price Quantitative Analysis, 26(3), 377-389, 1991.

Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 77 Table 1 Estimated Strike Prices of Monthly Asian Call and Put Options Based on Futures Prices at 31st of December 2007

Brent Oil—Futures Price Curve and Option Strikes (in $) Data are shown as of 31/12/2007 Month Futures Price - F Call Strike - KCall Put Strike -KPut t t t (100%) (110%) (80%) January 2008 $ 93.95 $ 103.35 $ 75.16 February 2008 $ 93.66 $ 103.03 $ 74.93 March 2008 $ 93.48 $ 102.83 $ 74.78 April 2008 $ 93.22 $ 102.54 $ 74.58 May 2008 $ 92.91 $ 102.20 $ 74.33 June 2008 $ 92.58 $ 101.84 $ 74.06 July 2008 $ 92.25 $ 101.48 $ 73.80 August 2008 $ 91.92 $ 101.11 $ 73.54 September 2008 $ 91.62 $ 100.78 $ 73.30 October 2008 $ 91.28 $ 100.41 $ 73.02 November 2008 $ 90.95 $ 100.05 $ 72.76 December 2008 $ 90.65 $ 99.72 $ 72.52 at the same time selling a monthly Asian OTM put with a (dotted blue line) compared to an unhedged position (solid strike price of 80% of the oil futures price. To value both the line) assuming twenty different oil price scenarios in 2008 “monthly Asian option” and “annual Asian option,” we use (x-axis). publicly available data on futures prices and implied volatili- Figure 4 shows the airlines costs with a “Benchmark ties for Brent crude oil contracts maturing on a monthly basis Portfolio” structure under each of the oil price scenarios from January 2008 to December 2008. (x-axis), including option premium costs.11 This figure shows Table 1 shows the futures price curve and the calculated how the premium collar portfolio (“S”-curve) compares with strike prices for the monthly call and put options. The prices a completely unhedged position where the airline buys all its for the strip of annually settled call and put options can now 2008 consumption on the spot market (the 45-degree line). easily be calculated applying the standard Black framework In what follows, the benchmark “S”-curve serves as our with the following information: (1) futures prices on Brent baseline when assessing alternative hedging portfolios. That is, crude oil (Ft), (2) strike prices for the call and put options we take the firm’s own “S”-curve depiction of risk and return, Call Put (K t ), (K t ), (3) an interest rate of 3% p.a., and (4) the which uses the implicit assumption of a specific variable price “blended volatility” ∑T , calculated based on Appendix A’s (from $10 to $200) throughout the year. Taking this objective equation (2) using the implied volatilities for plain vanilla function as a given, we then aim to optimize and fine-tune the options. These prices are reported in Table 2. combinations of derivatives to achieve better expected results We can see that for calendar-year 2008, the airline spends (measured in dollars per barrel of Brent oil) for each and every roughly $85 million on call option premiums and receives oil price scenario from $10 up to $200 in 2008. about $20 million from sales of OTM put options. The net premiums of $65 million per year mean that the firm spends Incorporating Annual Asian Options approximately $2.02 on variable hedging costs for each barrel Replacing the monthly settled options with annual ones of oil consumed (see Table 3). requires an estimate of annual volatility. Using Appendix A’s To evaluate the airline’s hedge portfolio, we consider a Equation (6) to calculate average annual crude oil volatility range of oil price outcomes over calendar year 2008. There for 2008, we derive an annual averaged volatility of 14.07% are 20 different scenarios, with average annual prices ranging (see Table 3), which is significantly lower than the individual from $10 to $200 per barrel of oil. monthly averages (compare Table 2). This figure shows the airline crude oil exposure—in $ per The other inputs needed to estimate the annual Asian barrel of oil consumed—applying the “Benchmark Portfolio” option values are publicly available: (1) the annual averaged

11. The firm’s annual exposure for each oil price scenario considering the standard amount of 9,843,110 barrels. Consequently, the amount fully exposed to the spot price collar position is calculated as follows: The airline’s total consumption in 2008 sums up depends on the oil price scenario considered—with spot prices ranging from $10 to to 42,000,000 barrels. The firm hedges 32,156,890 barrels with its option structure. $200. Hence, the airline total exposure is the payoff of the hedge portfolio plus the unhedged

78 Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 Table 2 Implied Vanilla Volatilities and Option Prices with Last-month-averaged Options for 2008

Volatilities and Option Prices (as of 12/31/2007) Volatilities (in %) Option Prices (in $) Implied Plain Vanilla Asian Plain Vanilla Call Asian Plain Vanilla Put Asian Volatility Call Put Jan 2008 32.72% 18.90% $ 0.76 $ 0.66 $ 0.02 $ 0.01 Feb 2008 31.43% 25.66% $ 1.66 $ 1.40 $ 0.17 $ 0.12 Mar 2008 28.96% 25.54% $ 2.12 $ 1.87 $ 0.32 $ 0.23 Apr 2008 26.89% 24.55% $ 2.47 $ 2.22 $ 0.43 $ 0.34 May 2008 25.67% 23.90% $ 2.79 $ 2.49 $ 0.60 $ 0.44 Jun 2008 25.19% 23.75% $ 3.18 $ 2.73 $ 0.73 $ 0.54 Jul 2008 24.69% 23.48% $ 3.50 $ 3.00 $ 0.88 $ 0.66 Aug 2008 24.31% 23.28% $ 3.81 $ 3.30 $ 1.04 $ 0.80 Sep 2008 24.04% 23.13% $ 4.11 $ 3.60 $ 1.20 $ 0.94 Oct 2008 23.70% 22.89% $ 4.36 $ 3.88 $ 1.34 $ 1.09 Nov 2008 23.08% 22.37% $ 4.48 $ 4.13 $ 1.42 $ 1.23 Dec 2008 21.61% 21.00% $ 4.29 $ 4.09 $ 1.32 $ 1.35

Figure 4 Firm’s Exposure Applying the “Benchmark Portfolio” (Premium Collar)

$200

$180

$160

$140

$120

$100

$80

$60 First-order stochastic dominance $40

Average Purchasing Price (in $) $20

$0 $10 $30 $50 $70 $90 $110 $130 $150 $170 $190 Oil Price Scenario (in $) Spot Purchase Hedged Portfolio

Table 3 Input Values for the Black (1976) Framework to Calculate the Annual Call and Put Option Prices

Input Values for Annual Asian Option

Futures Price (100%) Call Strike (110%) Put Strike (80%) Arithmetic Volatility

$ 92.37 $ 101.76 $ 74.01 14.07% futures price (mean of the twelve contracts from January to Asian options with annually-settled options on the 1,807,000 December 2008) is $92.37, and (2) the strikes are 110% of barrels common across all months. This gradually shifts the the underlying for the calls and 80% for the puts, $101.76 hedge portfolio from monthly-settled to annually-settled over and $74.01 respectively. The firm’s seasonally-adjusted hedge calendar year 2008. The resulting “Alternative Portfolio” then volume is 1,807,000 barrels of oil (see Table B.1) for December includes a mix of both monthly and annual Asian call and 2008. So, month-by-month, we replace the monthly-settled put options (see Figure 5).

Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 79 Figure 5 Volume Hedged with Monthly and Annual Asian Option Contracts on a Monthly Basis Applying the “Alternative Portfolio”

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0 Jan-08 Apr-08 Jul-08 Oct 08 Annual Asian Monthly Asian Spot Purchases Hedged Hedged (Unhedged)

Figure 6 The Superiority of the “Alternative Portfolio” to the “Benchmark” for Each Oil Price Scenario in 2008

$0.35

$0.30

$0.25

$0.20

$0.15

$0.10

Cost savings per barrel of oil $0.05

$0.00 $10 $30 $50 $70 $90 $110 $130 $150 $170 $190 Oil Price Scenarios

This figure shows the mix of derivative instru- Th is fi gure shows the cost savings (in $ per barrel of ments in each month in 2008 applying the “Alternative oil consumed by the airline) from applying the “Alterna- Portfolio” measured in barrels of crude oil (y-axis). Two tive Portfolio” in comparison to the currently established diff erent options are considered: a constant layer of annual “Benchmark” considering twenty diff erent [$10, $200] oil Asian options (dark blue area) and a variable layer of price scenarios in 2008 (x-axis). monthly Asian option (blue area). Th e remaining unhedged We can also see the fi rm’s gross exposure under diff erent volume (light blue area) is assumed to be purchased at the oil price scenarios and whether it is better off under each oil spot market. price between $10 and $200. Figure 6 shows the incremen- We can now compare the “Alternative Portfolio” struc- tal advantage provided by the Alternative Portfolio on a per ture to the “Benchmark Portfolio” in terms of option barrel basis. Consequently, reduced hedging costs are realized premium costs during 2008. Table B.2 presents the under all oil price scenarios in 2008. hedging amount and the actual costs or benefi ts of each short and long position on an aggregated basis. Using annual Option Strike Optimization Asian options saves 30 cents per barrel of oil hedged. And Next, we see whether the airline can further improve its as a result, the fi rm now needs to spend only $1.72 per hedged results by changing the strike prices (i.e. 110% and barrel on option premiums, roughly a 15% savings over the 80% of underlying futures). benchmark. We begin the optimization process by varying the call

80 Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 option strike between $.01 and $200.00 while keeping the for the airline is not to sell puts at all. The benefits to airline strike of the put at the previous $73.94 price level. Alterna- of being able to buy fuel when prices fall below 74.01 (the tively, we vary the put strike while holding the call strike initial strike price of the annual put option) are greater than fixed at $101.67. This allows us to define the following two the roughly 6 million it would receive from put sales (see optimization problems to find the optimal strike prices:12 Table B.3 for comparison of the capital inflow due to the sold put options). The overall spending on option premiums 20 opt bench min [Mi max{0,K Mi} + max{0,Mi K P } ] in 2008 is then roughly 61 million for average hedging costs K opt i=1 C C of 1.91, representing a reduction of 5.5% relative to the firm’s opt bench +PC (K ) PP (K P ) (8) currently-utilized Benchmark Portfolio. C Despite the significantly higher net option premiums it must pay, the airline is better off under both the “Optimized M max{0,K opt M } + max{0,M K bench}] i C i i P Call Portfolio” and the “Optimized Put Portfolio.” The opt slightly lower call strike price provides an additional average +PC (K ) s.t. C profit of 0.87 per barrel of oil consumed in 2008 under all the M max{0,K bench M } + max{0,M K bench} ] scenarios between 110 and 200 a barrel. For those scenarios i C i i P bench when prices are below 110, the results are the same as for +PC (K ) C benchmark case (see Figure 2). Not selling any annual Asian put options, however, allows the airline to benefit signifi-

Mi represents the oil price scenarios ranging from $10 cantly under oil-price scenarios of 74.01 and lower. This is opt bench (i=1) to $200 (i=20), KC and KC are the strike prices of the especially important strategically because competing airlines, optimized and the benchmark call options, respectively, and particularly the financially weak ones who had been unable

PC and PP are the premiums for the Annual Asian options. to deal in options, would be reaping significant benefits of Note that the following restrictions apply to the optimized prices below 74.01. call strike portfolio: This analysis demonstrates, first of all, that the airline could be better off than it is now by switching from monthly- bench Kp = $73.94, (9) settled to annually-settled options when establishing its collars. Second, it shows that the airline could improve its opt $0.01 ≤ Kc ≤ $200.00. (10) situation even more by purchasing more expensive, lower- strike calls or not selling any puts. When developing the optimized put strike portfolio, the restrictions (9) and (10) are replaced with: Cash Management and Corporate Hedging The interaction between a firm’s cash management, its lever- bench Kp = $101.67, (11) age and its hedging activities is critical. A number of academic studies have found that companies with lower returns on opt $0.01 ≤ Kp ≤ $200.00. (12) assets and high borrowing costs typically hold more liquid assets,14 as do both small companies and firms with volatile Our optimal strikes will be the ones that give us better and risky cash flows.15 A study on hedging in the U.S. airline expected outcomes under each scenario.13 industry found that “the most active hedgers of fuel costs The results are perhaps a bit surprising. We find, first of among airlines are the larger firms with the least debt and all, that the optimal call strike for the firm is 99.93, lower highest credit ratings.” Clearly, there is a trade-off between than the previously used 101.76. The lower strike does mean financing and commodity price risk management.16 the airline has to pay higher premiums for the calls. The The airline needs to maintain a certain cash position (or “Optimized Call Portfolio” requires an additional 2.02 per have credit lines) to buy physical jet-fuel. While an annually- barrel of oil hedged, or 9,507,620 more in total. settled option won’t pay off until the end of the year, owning In the second optimization, the optimal put strike turns such an option would make the airline more creditworthy out to be 0.01 (the lowest value possible in our optimiza- to its lenders. tion framework), which means that the optimal decision The simulations above that showed the advantage of the

12. We used Microsoft’s “Excel Solver” to apply the “Generalized Reduced Gradient” Soo Kim, David C. Mauer, and Ann E. Sherman in the Journal of Financial and Quantita- (GRG2) algorithm for optimizing nonlinear problems described by Leon Lasdon, Allan tive Analysis 33, 335–359; 1968. Waren, Arvind Jain, and Margery Ratner in “Design and Testing of a Generalized Re- 15. See “The Determinants and Implications of Cash Holdings” by Timothy Opler, Lee duced Gradient Code for Nonlinear Programming,” ACM Transactions on Mathematical Pinkowitz, and Rene Stulz in the Journal of Financial and Quantitative Analysis 33, Software, Vol. 4, No. 1, pp. 34-50; March 1978. 335–359; 1998. 13. Technically, this is known as first-order stochastic dominance. 16. See “Dynamic Risk Management,” 2012 SSRN Working Paper, by Adriano 14. See “The Determinants of Corporate Liquidity: Theory and Evidence” by Chang- Rampini, Amir Sufi, and S. Viswanathan.

Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 81 Figure 7 Development of the Spot Brent Price in 2008

$160 Brent Spot (in $ per barrel)

$140

$120

$100

$80

$60

$40

$20 Jan/ 08 Mar/ 08 May/ 08 Jul/ 08 Sep/ 08 Nov/ 08

Table 4 Cash Position of the Airline Ccomparing the “Benchmark Portfolio” and the “Alternative Portfolio”

Cash Position and Expenditures for Jet-Fuel 12/31/2007 06/30/2008 12/31/2008 (million $) (million $) (million $) BENCHMARK PORTFOLIO Options Premiums $67 $67 $67 Expenses Hedged Volume $1,777 $3,041 Annually hedged $0 $0 Monthly hedged $1,777 $3,041 Expenses Unhedged Position $337 $822 Liquidity Cushion due to Monthly Options -$236 $0 TOTAL $1,945 $3,929 ALTERNATIVE PORTFOLIO Options Premiums $57 $57 $57 Expenses Hedged Volume $1,883 $3,128 Annually hedged $1,184 $2,100 Monthly hedged $699 $1,028 Expenses Unhedged Position $337 $822 Liquidity Cushion due to Annual and Monthly -$526 $0 Options TOTAL $ 1,750 $4,006

Alternative Portfolio were based upon a very wide range of the beginning (December 31, 2007); (2) the midpoint (June oil prices. Of course, one should not draw strong conclu- 30, 2008), and (3) the end (December 31, 2008). sions about the soundness of a hedging strategy in just one Table 4 shows how the firm’s financial condition would year, but it is reasonable to ponder how the two portfolios have changed over 2008 under the “Benchmark Portfolio” would have performed under the specific circumstances that and the “Alternative Portfolio.” The Benchmark Portfolio unfolded in 2008. cost $67 million while the Alternative Portfolio cost only In that particular case, it turns out the existing Bench- $57 million. It is true that under the “Benchmark Portfo- mark strategy would have come out ahead. The situation in lio,” the airline receives cash from its monthly-settled options 2008 was particularly unusual as oil prices peaked around throughout the year; but the annual option also increases the Fourth of July, almost exactly mid-year, and then fell in mark-to-market value even if it does not pay out until precipitously during the next six months. We evaluate the year’s end. Given the Brent mid-year average spot price on firm’s hedging and cash position at three points in time: (1) June 30, 2008 of $109.75, the average of the six outstanding

82 Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 futures prices of $141.43, and assuming unchanged implied calculation that can lead a firm to an optimal hedging strat- volatilities, the annual Asian option would have increased in egy, but the four factors this firm used to guide its strategy value by approximately $468 million. This would have signifi- would seem pretty universally applicable: (1) the firm’s finan- cantly increased the airline’s borrowing capacity. Because of cial strength and credit rating, (2) the relationship between the mark-to-market gain, the “Alternative Portfolio” on June fuel prices and volumes consumed, (3) the fixed and variable 2008 is more valuable than the Benchmark. Under the Alter- costs of hedging, and (4) the firm’s internal risk profile. Given native Portfolio, total fuel purchase costs mid-year 2008 were all those considerations, we also believe that annually-settled $1.75 billion versus $1.95 billion for the Benchmark Portfolio. Asian options offer great economic benefits to corporate risk However, the performance of the two portfolios changes management programs. during the latter half of 2008. Because the average price for 2008 was $96.94, the annual Asian call options expired out of the money (their strike price was $101.67). This meant that Dr. Mathias Gerner obtained his doctoral degree in 2011 from the airline simply purchased fuel at the spot price throughout the European Business School in Germany with a focus on Energy Risk the year and enjoyed no payout from options it owned. It Management and Commodity Price Modeling. After completing his benefited from the collapse in prices at the end of the year, doctoral studies he gained professional experience in the energy trad- but this was not enough for the Alternative strategy to win ing environment as a Senior Energy Analyst at a major European utility in 2008. With the Benchmark portfolio, the airline spent firm. Since 2013 he works at Deloitte Consulting within the service line roughly $80 million less ($3.929 billion versus $4.006 billion) Strategy | Energy & Resources—focusing on energy companies in the than it would have under the Alternative. electricity, oil, and gas sector. The airline recognizes the importance of its liquidity in its annual reports. It holds liquid assets of $5 billion, mentions Ehud I. Ronn is a professor of Finance at the McCombs School of its good corporate credit rating, and notes that it has short- Business, University of Texas at Austin. Dr. Ronn received his Ph.D. term credit lines totaling $2.5 billion. This matters in the from Stanford University in 1983. During 1991–‘93, Dr. Ronn served hedging context because liquidity enables the airline to use as Vice President, Trading Research Group at Merrill Lynch & Co., and more economic annually-settled Asian options rather than from January 2010 to February 2011 as Commodity Market Model- monthly-settled. As long as the firm owns valuable annual ing practice area manager at Morgan Stanley & Co. Dr. Ronn was options, it should be able to draw on its bank credit lines to the founding director of the University of Texas Center for Energy satisfy any intra-year need for cash. Finance 1997–2009. Dr. Ronn’s research, teaching and consult- This case study of a real airline shows how a major ing have focused primarily on energy finance issues since 1997. corporate hedging program actually works. There is no one

Appendix A—Monthly Settled Average Rate Options 2 (2) We then compute the effective “blended variance,” ΣT To value the annually settled Asian options we recommend, which combines the variance of the non-averaging period and it is first necessary to understand the more commonly used the variance during the averaged period (with T≡ (T – t) + t)): monthly-settled options, in which the averaging takes place 2 2 2 ()T− tδTA + t δ only in the final month prior to expiration. ΣT = T We calculate the average volatility (ΣT) in a two-step 2 process using the implied volatilities (dT) of the plain vanilla the standard deviation of which is: options on Brent crude of the Intercontinental Exchange (ICE) in London. 2 2 2 ()T− tδTA + t δ (1) We first calculate the volatility, dA , during the option’s ΣT = (2) last month, which is lower than the implied plain vanilla one, T 2 dT, due to the “volatility-dampening” effect of averaging: where T represents the length of the non-averaging period d2 2 and t the averaging period. By using T the “blended volatil- 1 2eδTt (12 t ) 2 2 − +δT (1) ity” ΣT, we are able to value a monthly-settled option applying δ A = ln( 4 2 ) tδT t the standard Black formula for European style options on futures contracts:17

17. See “Modeling the Correlation Function in the Crude-Oil Futures Market” in En- ergy Risk, 2009, by Ehud I. Ronn.

Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 83 −r Τ and the corresponding implied volatilities of the plain vanilla Call OAML =e[()() FN d − KN d −ΣT Τ ] options (d1 , d2, …, d12), all of which are publicly available. −r Τ Applying Equation (2) and using d , t, and T, the first PutLMAO =e[()() KN ΣT Τ − d − FN − d ] AT two moments can be calculated as following: where F denotes the current price of the futures contract, N(.) stands for the cumulative normal distribution function, 1 N M = F r denotes the risk free rate of interest, T is the time to option 1 ∑ T (3) N T=1 Σ expiration, T represents the “blended standard deviation,” 2 Σ N T ρ ΣΣ min(T , t ) and 1 2 1 ( Tt t T ) M = F e 12 + F F e 12 F 2 2 ∑T 2 ∑∑ tT (4) log() N T=1 N ≠TtT d ≡K +1 Σ T 2 T ΣT T We computed the requisite correlations ρTt between the The “Annual Asian Option” twelve futures contracts using the following formula:18 While we like Asian options for the same reasons many hedg- a ers already do, we think companies should consider using −( ) tmin annually settled instead of monthly settled Asian options. ρ(Δt , tmin ) = A + (1 − A ) e (5) An annual settlement would involve a 12-month long averaging period, further dampening the measured volatility where and therefore requiring even lower option premia from the hedgers. Additionally, the standard time period in terms of A = e –b|Δ| financial or accounting purposes commonly also involves 12 months—the firm’s financial year. So, using a finan- a,b = two positive coefficients cial hedging instrument that averages price effects over the Δt = time span between two futures contracts (in years) whole financial year would seem quite practical. Therefore, tmin = time to maturity of the earlier of the two contracts we recommend using annually settled options in place of the commonly used strip of twelve successive, monthly-settled Finally, the one-year-averaged option volatility, denoted options. Σ, is then obtained from the two moments M1 and M2 using To illustrate annually settled option pricing, let us τ = 1: consider one with a maturity of one year (T = 1). We have 12 successive crude oil futures prices to observe, but we need to 1 M2 Σ = ()2 estimate the volatility of the annual average. τ M1 We do have the implied volatilities of plain-vanilla (6) options (dT) listed on the ICE. These implied volatilities could be converted into their last-month-averaged counterparts, ΣT . With the futures price sequence and the estimated As we do so, recall the computation of dA in Equation (1). We average volatility, we can now apply the Black commodity now add the subscript T to dA to denote the averaged volatil- futures option model to value the Annual Asian Option. For ity for month T, dAT, which can differ across the months due a given strike price K, and an interest rate r, the option can be to dt ≠ dt for t ≠ τ. Hence, the only required inputs are the valued with (1) the futures price F set to M1, (2) the time to sequence of twelve monthly futures prices (F1, F2, …, F12) expiration set to τ = 1, and (3) the volatility set to Σ.

18. This cost reduction is computed relative to the “Benchmark Portfolio” (in %).

84 Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 Appendix B

Table B.1 Volume of Barrels Oil Hedged Under “Alternative Portfolio”

Expected consumption & amount hedged per month (in thousands of barrels) (as of 31/12/2007) Year 2008 Expected consumption Monthly Asian Hedged Unhedged Spot Purchases Jan 3,500 1,807 594 Feb 3,500 1,807 745 Mar 3,500 1,807 480 Apr 3,500 1,807 411 May 3,500 1,807 435 Jun 3,500 1,807 477 Jul 3,500 1,807 483 Aug 3,500 1,807 818 Sep 3,500 1,807 988 Oct 3,500 1,807 1,134 Nov 3,500 1,807 1,579 Dec 3,500 1,807 1,692

Table B.2 Volume of Barrels Oil Hedged Under “Alternative Portfolio”

Expected consumption & amount hedged per month (in thousands of barrels) (as of 31/12/2007) Year 2008 Expected consumption Annual Asian Hedged Monthly Asian Hedged Unhedged Spot Purchases Jan 3,500 1,807 1,097 594 Feb 3,500 1,807 946 745 Mar 3,500 1,807 1,212 480 Apr 3,500 1,807 1,280 411 May 3,500 1,807 1,257 435 Jun 3,500 1,807 1,215 477 Jul 3,500 1,807 1,208 483 Aug 3,500 1,807 873 818 Sep 3,500 1,807 704 988 Oct 3,500 1,807 558 1,134 Nov 3,500 1,807 112 1,579 Dec 3,500 1,807 0 1,692

Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 85 Table B.3 Aggregated Hedging Costs in Terms of Option Premiums and Gross Exposure Per Barrel of Oil Consumed

Benchmark Portfolio Alternative Portfolio Optimized Call Portfolio Optimized Put Portfolio Hedging Instruments Aggregated Volume Aggregated Volume Aggregated Volume Aggregated Volume Premiums Hedged Premiums Hedged Premiums Hedged Premiums Hedged (in Mil. $) (Mil. barrels) (in Mil. $) (Mil. barrels) (in Mil. $) (Mil. barrels) (in Mil. $) (Mil. barrels) Monthly Call (long) $ 84.549 32.156 $ 24.640 10.469 $ 24.640 10.469 $24.640 10.469 Monthly Put (short) - $19.502 32.156 -$ 5.125 10.469 -$ 5.125 10.469 -$5.125 10.469 Annual Call (long) - - $ 41.817 21.687 $51.229 21.687 $41.817 21.687 Annual Put (short) - - -$ 6.025 21.687 -$6.025 21.687 - - Total cost $65.047 $55.307 $64.719 $61.332 Gross Exposure /barrel $ 2,02 $ 1,72 $ 2,01 $ 1,91 consumed Cost reduction19 - 14.9 % ~ 0 % 5.4 % Table B.3 shows the aggregated option premiums of the “Benchmark Portfolio” currently established by the airline and the three alternative portfolio including annual Asian options. The gross exposure (total cost) in $ per barrel of oil consumed is shown based on the derivatives’ payoff traded and the remaining spot market purchases.

19. This cost reduction is computed relative to the “Benchmark Portfolio” (in %).

86 Journal of Applied Corporate Finance • Volume 25 Number 4 Fall 2013 ADVISORY BOARD EDITORIAL

Yakov Amihud Robert Eccles Martin Leibowitz Charles Smithson Editor-in-Chief New York University Harvard Business School Morgan Stanley Rutter Associates Donald H. Chew, Jr.

Mary Barth Carl Ferenbach Donald Lessard Joel M. Stern Associate Editor Stanford University Berkshire Partners Massachusetts Institute of Stern Stewart & Co. John L. McCormack Technology Amar Bhidé Kenneth French G. Bennett Stewart Design and Production Tufts University Dartmouth College Robert Merton EVA Dimensions Mary McBride Massachusetts Institute of Michael Bradley Stuart L. Gillan Technology René Stulz Duke University University of Georgia The Ohio State University Stewart Myers Richard Brealey Richard Greco Massachusetts Institute of Alex Triantis London Business School Filangieri Capital Partners Technology University of Maryland

Michael Brennan Trevor Harris Richard Ruback Laura D’Andrea Tyson University of California, Columbia University Harvard Business School University of California, Los Angeles Berkeley Glenn Hubbard G. William Schwert Robert Bruner Columbia University University of Rochester Ross Watts University of Virginia Massachusetts Institute Michael Jensen Alan Shapiro of Technology Christopher Culp Harvard University University of Southern University of Chicago California Jerold Zimmerman Steven Kaplan University of Rochester Howard Davies University of Chicago Clifford Smith, Jr. Institut d’Études Politiques University of Rochester de Paris David Larcker Stanford University

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