Southwest Airlines- Fuel Hedging Case Analysis

1.
Southwest
Airlines:
Fuel
Hedging
Analysis
October
13,
2013
BA
618:
Advanced
Corporate
Finance
Vishal Prabhakar | Ajay Gnanasekaran
Embry-Riddle Aeronautical University

2. Table of Contents
Sl.No
1.
2.
3.
4.
5.
6.
7.
8.
9.
Contents
Southwest Airlines -Introduction
Fuel Hedging- A Win-Win
To Hedge or not to Hedge
Case Background
Hedging Strategies and Analysis
@Risk Analysis
Conclusion
Current Outlook-Hedging
References
2

3. SOUTHWEST AIRLINES – INTRODUCTION
In order to stay airborne, a commercial airline has to consistently keep generating
profits. Profits in an airline industry come from passenger revenue, hence all stratagems
must be customer centric. In this current scenario with all the mergers and acquisitions,
airlines competing with each other, one way of attracting passengers is to keep the cost
of flying low. Southwest’s business model is the best low cost model yielding
considerable profit, while providing value for money. The main expenses for an airline
are the operating and fuel cost, expenses must be tightly controlled to reach and stay at
the lowest possible level. Certain expenses are unavoidable; however, one variable that
can be kept low through decisive planning and foresight is the cost of fuel. Fuel prices
are extremely volatile. A good way to achieve this is by hedging fuel, which is a
complex, but rewarding process as Southwest Airlines proves beyond doubt.
Southwest Airlines, is the third largest airline in the world as well as in America in terms
of passenger aircraft among all of the world's commercial airlines. It operates more than
540 Boeing 737 aircraft today between 67 cities in the U.S.A. Today, Southwest
operates approximately 3,300 flights daily and boasts of being the only major airline to
post profits every year for the last thirty-six years. It justifiably claims to be United
States’ most successful low-fare, high frequency, point-to-point carrier.
It would be worthwhile examining Southwest’s modus operandi and strategies employed
to stay profitable every year, though it did suffer a minor hiccup when it’s profit dived
under the waterline in two quarters in 2008. Southwest keeps its aircraft in flight for
more than twelve hours a day. It carefully selects optimized destinations that could be
called secondary airfields, which facilitate fast turnaround averaging less than fifteen
minutes and charge low administrative fees. Using the same logic, they use only one
aircraft type. This helps them to reduce the fleet maintenance cost. The Boeing 737 has a
reasonable passenger capacity of around one hundred and twenty five to one hundred
and fifty. These are fitted with the most fuel-efficient engines and aerodynamically have
the lowest drag wet-wings available.
3

4. FUEL HEDGING – A WIN-WIN
Jet fuel represents a critical expense category for any airline that bears its own fuel costs
and most airlines bear at least 80% of its fuel costs. Fuel has consistently been one of the
largest expense categories for domestic airlines. During 2003, fuel costs represented, on
average, over 16% of the total operating expenses for all U.S. domestic airlines.
Moreover, airlines are generally unable to increase fares to offset any significant
increase in fuel costs. From 2001 to2003, these same airlines experienced a 25.9%
compound annual increase in jet fuel costs while average airline pricing decreased by
0.1%, as measured by revenue per available seat mile. Jet fuel costs have gone up over
the past several years laying a constant pressure on airlines to maintain a profitable
operation. Savings in the lines of operation and fuel cost turn out to be the profit earned.
In a fuel driven industry like Commercial Aviation, sudden hikes and fluctuations in
fuel prices can have an immense effect on the business plan, not to mention adding to
the difficult task of budgeting of Future fuel expenditures. If fuel costs are not actively
managed, they can lead a company into losses. Airlines can mitigate their exposure to
volatility and sudden hike in fuel costs, as well as natural gas and electricity costs,
through hedging. Hedging allows the fuel market participants to fix prices in advance,
while reducing the potential impact of volatile fuel prices.
‘Hedging’ items is a standard practice in almost every field that involves finance,
including Market players in precious metals like Gold, Silver and Platinum. While fuel
costs may be hedged, there is no perfect hedge available in either over-the-counter or
exchange traded derivatives markets. Over-the-counter derivatives on jet fuel are very
illiquid which makes them rather expensive and not available in quantities sufficient to
hedge all of an airlines’ jet fuel consumption. Exchange-traded derivatives are not
available in the United States for jet fuel, so airlines must use futures contracts on
commodities that are highly correlated with jet fuel, such as crude and heating oil. As
such, airlines employ a variety of strategies ranging from not hedging to fully hedging
using a combination of products. Domestic airlines have a variety of hedging strategies
available to them. These include using both over-the-counter and exchange-traded
derivatives or remaining unhedged.
Options, including collars and swaps are the
4

5. primary derivatives used by airlines. Many airlines, including southwest, stated that they
prefer over-the-counter derivatives (OTC) to exchange traded futures because they were
more customizable. OTC derivatives are traded directly between the airlines and
investment Banks, and as such have counterparty risk that must be considered.
Therefore, airlines like Southwest prefer to trade with three or four different banks to
diversify this risk and also to get the best pricing possible (ibid). Southwest Airlines
evidently kept their ears close to the ground by going in for very high levels of futures
before Iraq and Desert Storm drove oil prices upwards. The Airline went in for even
more hedging in 2004, 2005 and early 2006 in anticipation of oil Prices surging to
unprecedented levels.
TO HEDGE OR NOT TO HEDGE
Being unhedged is the ultimate short position; this infers we are constantly expecting the
fuel prices to go down which is an ultimate utopian scenario. Although airlines
sometimes lose money hedging, overall those that hedge have a 5% to 10% better
financial performance than those that don’t. Hedged airlines can make investments in
their operations and equipment; make other important decisions that positively affect
their firm's overall value. Hedging is about having an insurance policy against prices
rising. A position that is not hedged i.e., the holder of a naked position has taken no step
to reduce the risk inherent to the position.
The risk offsetting investments in a hedging strategy will not experience price changes
in entirely equal proportions. This imperfect correlation between the two investments
creates the potential for excess gains or losses in a hedging strategy, thus adding risk to
the position. This is known as basis risk. Basis in a hedging situation is defined as the
difference between the spot price of the asset being hedged and the futures price of the
contract used. The basis risk arises from the hedger’s uncertainty associated to the basis
at the expiration of the hedge.
Price risk is the biggest risk faced by all investors. Although price risk specific to a stock
can be minimized through diversification, market risk cannot be diversified away. Price
risk, while unavoidable, can be mitigated through the use of hedging techniques. Price
5

6. risk also depends on the volatility of the securities held within a portfolio. For example,
an investor who only holds a handful of junior mining companies in his or her portfolio
may be exposed to a greater degree of price risk than an investor with a well-diversified
portfolio of blue-chip stocks. Investors can use a number of tools and techniques to
hedge price risk, ranging from relatively conservative decisions such as buying put
options, to more aggressive strategies including short-selling and inverse ETFs.
SFAS 133, the standard for financial reporting of derivatives and hedging transactions,
was adopted in 1998 by the Financial Accounting Standards Board to resolve
inconsistent previous reporting standards and practices. It went into effect at most U.S.
companies at the beginning of 2001. It was issued to make a company’s exposure to its
derivative positions more apparent. It requires changes in derivatives’ fair value to be
recorded in the income statement or in a component of equity known as other
comprehensive income. The FAS 133 requirement in order to make the hedge more
effective has to consider both historical performance and anticipated future performance.
It has given broad guidelines regarding the “80-125” rule or the dollar-offset method and
the correlation method.
In the “80-125” rule, a hedge is deemed effective if the ratio of the change in the value
of the derivative to the change in the value of the hedged item falls between 80% and
125%. In the correlation method, a hedge is deemed effective if correlation between the
value of the hedged item and the derivative is high; the R-squared of the regression of
this relation is around 80% and the slope of the regression line should be close to 1.
Contango and Normal Backwardation
Patterns over time have established that a futures market is normal if futures prices are
higher at longer maturities and inverted if futures prices are lower at distant maturities.
•
As we approach contract maturity (we might be long or short on the futures
contract), the futures price must converge toward the spot price. The difference is
called the basis. That's because, on the maturity date, the futures price must equal
the spot price. If they don't converge on maturity, anybody could make free
money with an easy arbitrage.
6

7. •
The most rational futures price is the expected future spot price. For example, if
you and your counterparty both foresee that the spot price in crude oil would be
$80 in one year, you would rationally settle on an $80 futures price. Anything
above or below would represent a loss for one of you!
Now we can define contango and normal backwardation. Suppose we entered into a
December 2013 futures contract, today, for $100. One month later the same December
2013 future contract could still be $100, but it might also increase to $110 (this implies
normal
•
backwardation)
or
it
might
decrease
to
$90
(implies
contango).
Contango is when the futures price is above the expected future spot price.
Because the futures price must converge on the expected future spot price,
contango implies that futures prices are falling over time as new information
brings them into line with the expected future spot price.
•
Normal backwardation is when the futures price is below the expected future
spot price. This is desirable for speculators who are "net long" in their positions:
they want the futures price to increase. So, normal backwardation is when the
futures prices are increasing.
Let’s consider a near month futures contract for light sweet crude oil as the August
2013 contract, which settled on July 18 at $108.22 per barrel. But looking out 11 months
into the future to the July 2014 contract, we find that it closed at just $95.56. That is a
huge difference, and it says that oil futures traders are not willing to bet on the current
month's high price continuing into the future. In other words, it is a temporary anomaly.
Such anomalies can contain important information. This week's chart looks at the raw
price spread between the near month contract and the contract that is 11 months out.
When the near month contract is priced lower than the out months, that condition is
known as "contango". In commodities like gold and silver, contango is the norm since
the available supply consists of not just the mining production but also all of the bullion
sitting in warehouses and safes around the world.
But because oil is so much more expensive to store than gold is, there is not the same
sort of standing inventory available to remediate temporary supply-demand disruptions.
7

8. So oil prices can move to very large conditions of contango, or to the opposite condition
known as "backwardation" like we are seeing right now.
CASE BACKGROUND
Scott Topping, the Director of Corporate Finance for Southwest Airlines was concerned
about the cost of fuel for Southwest. High jet fuel prices over the past 18 months had
caused havoc in the airline industry. Scott knew that since the industry was deregulated
in 1978, airline profitability and survival depended on controlling costs.
After labor, jet fuel was the second largest operating expense for airlines. If airlines
could control the cost of fuel, they can more accurately estimate budgets and forecast
earnings. It was Scott’s job to hedge fuel costs, however, he knew that jet fuel prices are
largely unpredictable. As shown in Figure 1, jet fuel spot prices (Gulf Coast) have been
on an overall upward trend since reaching a low of 28.50 cents per gallon on December
21, 1998. On September 11, 2000, the Gulf Coast jet fuel spot price was 101.25
cents/gallon – a whopping increase of 255 % in the spot price since the low in 1998. The
prior day’s (June 11, 2001) spot price for Gulf Coast jet fuel closed at a price of 79.45
cents/gallon. While this price was lower than the highest level, Scott knew that future jet
fuel prices would be uncertain.
Senior management asked Scott to propose Southwest’s hedging strategy for the next
one to three years. Because of the current high price of jet fuel, Scott was unsure of the
best hedging strategy to employ. Because Southwest adopted SFAS 133 in 2001, Scott
needed to consider this in his hedging strategy.
Southwest’s average fuel cost per gallon in 2000 was $0.7869, which was the highest
annual average fuel cost per gallon experienced by the company since 1984. As
discussed previously, fuel and oil expense per ASM increased 44.1 percent in 2000,
primarily due to the 49.3 percent increase in the average jet fuel cost per gallon. (Refer
to Table 1: The average price per gallon of jet fuel in 2000 was $0.7869 compared to
$0.5271 in 1999.)
8

9. Although Scott thought the price of jet fuel would decrease over the next year, he cannot
be sure energy prices are notoriously hard to predict. Scott knew that: “Predicting is very
difficult, especially as it concerns the future” (Chinese Proverb). Any political instability
in the Middle East could cause energy prices to rise dramatically without much warning.
If the cost of jet fuel continued to rise, the cost of fuel for Southwest would rise
accordingly without hedging. On the other hand, if the cost of jet fuel declines, the cost
of fuel would drop if Southwest were un-hedged.
To deal with these risks, Scott identified the following 5 alternatives. Scott estimated
Southwest’s jet fuel usage to be approximately 1,100 million gallons for next year.
1. Do nothing.
2. Hedge using a plain vanilla jet fuel or heating oil swap.
3. Hedging using options.
4. Hedge using a zero-cost collar strategy.
5. Hedge using a crude oil or heating oil futures contract.
SOUTH WEST AIRLINES FUEL HEDGING ANALYSIS
Table 1 gives the Fuel Cost per Gallon for the past 7 years. The fuel price rise in year
1999 & 2000 wreaked havoc and had increased the total fuel costs to the airline by a
considerable amount. The airline has no control over the volatility of fuel prices and
hence makes it difficult to control fuel costs and total costs.
Year
Fuel Cost per Gallon in $
2000
0.7869
1999
0.53
1998
0.4567
1997
0.6246
1996
0.6547
1995
0.5522
1994
0.5392
Table 1
9

10. In order to offset fuel price rise and control fuel costs, keeping it constant to a level
acceptable, Southwest Airlines have to choose the best option among the following
alternatives based on two possible scenarios: 1) Fuel price decline and 2) Fuel price rise.
Table 2 below gives the list of variables and prices considered or assumed in each
scenario and for the hedging strategies.
NOTE: All Fuel and Total costs are indicated in $ millions.
Scenario 1
Scenario 2
Jet fuel spot price=
Heating oil spot price=
Crude oil spot price=
Hedging %=
6/11/01 spot price(Jet Fuel)=
Fixed Rate(Jet Fuel Swap)
Call Option Premium
Jet Fuel Swap Contract Size
6/11/01 spot price(Heating Oil)=
Fixed Rate(Heating Oil Swap)
Heating oil Contract Size
0.393
0.388
14.10
50%
0.7945
0.7600
1.8000
1.00
0.7002
0.73
0.042
6/11/01 Futures Price (Crude Oil)
$/gallon
$/gallon
$/barrel
1.1960 $/gallon
1.1860 $/gallon
40.00 $/barrel
$/gallon
$/gallon
$/contract
MM gal
$/gallon
$/gallon
MM gal
26.39 $/barrel
# Contracts
Contract Size
Fuel usage(Jet Fuel)=
0.001 MM barrel
1,100 MM gal
1,100
100% Hedging(Jet Fuel)=
50% Hedging(Jet Fuel)=
1,100 MM gal
550 MM gal
1,100
550
Fuel usage(Crude)=
26.1905 MM Barrel
26,190.48
100% Hedging(Crude)=
50% Hedging(Crude)=
Fuel usage(HO)=
100% Hedging(HO)=
50% Hedging(HO)=
26.1905
13.0952
1,100
1,100
550
26,190.48
13,095.24
26,190.48
26,190.48
13,095.24
MM
MM
MM
MM
MM
Barrel
Barrel
gal
gal
gal
Table 2
1)
Hedging Using a Plain Vanilla Jet Fuel Swap- This alternative is simple and a
basic form of swap. A certain amount of floating price is exchanged for a fixed
price over a certain period of time. The airline pays a fixed price and receives a
floating price both indexed to expected jet fuel use during each monthly settlement
period. The volume of fuel hedged is negotiated because this is a customized
contract arranged in the OTC market. Jet Fuel is not a liquid enough market to
warrant exchange-traded contracts unlike the Crude Oil and Heating oil, which have
active liquid markets (NYMEX and IPE). The contract size in this case is 1 million
gallons.
10

11. During the life of the contract, the airline buys jet fuel from the market as usual but
the swap contract makes up for the difference when fuel prices rise and removes
differences when fuel prices decline. This would result for the airline to maintain a
fixed fuel expense for the period covered. The fixed rate payment is set based on
the market conditions when the swap contract was initiated. In this case, the fixed
rate is $0.76 per gallon of Jet Fuel. The floating price is commonly based on Platt’s
New York Harbor jet fuel price and is calculated monthly using daily prices for the
month. However in this case, we will calculate the monthly floating rate based on
the beginning Spot Price of Jet fuel and the estimated spot price at end of year.
Based on the amount of fuel hedged, and the possible scenario, the airline can either
make a profit from the swap or a loss from its swap. The two fuel hedging ratios
analyzed in this case are the full hedge and 50% fuel hedge. The airline fuel usage
is estimated to be 1100 million gallons. Refer to Table 3A and 3B–Scenario 1 and
Scenario 2.
Hedge using a plain vanilla jet fuel swap-Full
Scenario 1-JET FUEL
Monthly Settlements
100% Hedge
50% Hedge
Gain(Loss)
Gain(Loss)
0.0955
0.0477
(2.9715)
(1.4858)
(6.0385)
(3.0193)
(9.1056)
(4.5528)
(12.1726)
(6.0863)
(15.2396)
(7.6198)
(18.3066)
(9.1533)
(21.3736)
(10.6868)
Sl. No
1
2
3
4
5
6
7
8
Date
Jul-01
Aug-01
Sep-01
Oct-01
Nov-01
Dec-01
Jan-02
Feb-02
Fixed Pmt
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
Floating Pmt
0.7610
0.7276
0.6941
0.6607
0.6272
0.5938
0.5603
0.5268
9
Mar-02
0.76
0.4934
(24.4406)
(12.2203)
10
11
Apr-02
May-02
0.76
0.76
0.4599
0.4265
(27.5076)
(30.5747)
(13.7538)
(15.2873)
12
Jun-02
0.76
0.3930
(33.6417)
(16.8208)
Total Gain(Loss)-100% Hedge
(201.2771)
Total Gain(Loss)-50% Hedge
(100.6385)
Table 3A-Fuel price decline: Jet Fuel Swap
11

12. Hedge using a plain vanilla jet fuel swap-Full
Scenario 2-JET FUEL
Sl. No
1
2
3
4
5
6
7
8
Date
Jul-01
Aug-01
Sep-01
Oct-01
Nov-01
Dec-01
Jan-02
Feb-02
Fixed Pmt
0.7600
0.7600
0.7600
0.7600
0.7600
0.7600
0.7600
0.7600
Floating Pmt
0.8280
0.8614
0.8949
0.9283
0.9618
0.9953
1.0287
1.0622
Monthly Settlements
100%
Hedge
50% Hedge
Gain(Loss) Gain(Loss)
6.2295
3.1148
9.2965
4.6483
12.3635
6.1818
15.4306
7.7153
18.4976
9.2488
21.5646
10.7823
24.6316
12.3158
27.6986
13.8493
9
Mar-02
0.7600
1.0956
30.7656
15.3828
10
11
Apr-02
May-02
0.7600
0.7600
1.1291
1.1625
33.8326
36.8997
16.9163
18.4498
12
Jun-02
0.7600
1.1960
39.9667
19.9833
Total Gain(Loss)-100% Hedge
277.1771
Total Gain(Loss)-50% Hedge
138.5885
Table 3B-Fuel price rise: Jet Fuel Swap
The jet fuel spot price on June 11th, 2001 was $0.7945 per gallon and the estimated
spot price (June 2002), for scenario 1 is $ 0.393 per gallon. The estimated spot price
(June 2002), for scenario 2 is $ 1.196 per gallon.
2) Hedging Using a Plain Vanilla Heating Oil Swap- This is similar to the jet fuel
swap in its operation, but this option is used with the NYMEX New York Heating
Oil Calendar Swap. The swap contract is 42000 gallons, the same size as the
NYMEX heating oil futures contract. The swap is in Heating Oil futures prices and
the rise or decline of these prices would act as an offset to the Fuel price volatility
since the correlation between Jet fuel prices and heating oil prices are high, as both
are byproducts of crude oil and assuming the basis has not changed. The loss or gain
in the futures contract will be offset by the lower cash price of jet fuel or by higher
cash price of jet fuel respectively. As a result, the airline effectively pays a fixed
price for jet fuel.
The fixed rate payment is set based on the market conditions when the swap contract
was initiated. In this case, the fixed rate is $0.73 per gallon of Heating Oil. The
12

13. floating price is commonly based on monthly heating oil Futures prices. However in
this case, we will calculate the monthly floating rate based on the beginning Spot
Price of Heating Oil and the estimated spot price at end of year. The heating oil
future price on June 11th, 2001 was $0.7002 per gallon and the estimated spot price
(June 2002), for scenario 1 is $ 0.388 per gallon. The estimated spot price (June
2002), for scenario 2 is $ 1.186 per gallon.
Based on the amount of fuel hedged, and the possible scenario, the airline can either
make a profit from the swap or a loss from the swap. The two fuel hedging ratios
analyzed in this case are the full hedge and 50% fuel hedge. The airline fuel usage is
estimated to be 1100 million gallons. Refer to Table 3C and 3D–Scenario 1 and
Scenario 2.
Hedge using a plain vanilla heating oil swap-Full
Scenario 1-Heating Oil
Monthly Settlements
100% Hedge
Sl. No
1
2
3
4
5
6
7
8
9
10
11
12
Date
Jul-01
Aug-01
Sep-01
Oct-01
Nov-01
Dec-01
Jan-02
Feb-02
Mar-02
Apr-02
May-02
Jun-02
Fixed Pmt
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
0.73
Total Gain(Loss)-100% Hedge
Total Gain(Loss)-50% Hedge
Floating Pmt
0.6742
0.6482
0.6222
0.5961
0.5701
0.5441
0.5181
0.4921
0.4661
0.4400
0.4140
0.3880
50% Hedge
Gain(Loss)
(5.1165)
(7.5014)
(9.8863)
(12.2711)
(14.6560)
(17.0408)
(19.4257)
(21.8106)
(24.1954)
(26.5803)
(28.9651)
(31.3500)
Gain(Loss)
(2.5583)
(3.7507)
(4.9431)
(6.1356)
(7.3280)
(8.5204)
(9.7128)
(10.9053)
(12.0977)
(13.2901)
(14.4826)
(15.6750)
(218.7992)
(109.3996)
Table 3C-Heating Oil Price decline: Heating Oil Swap
13

14. Hedge using a plain vanilla heating oil swap-Full
Scenario 2-Heating Oil
Sl. No
1
2
3
4
5
6
7
8
9
10
11
12
Date
Jul-01
Aug-01
Sep-01
Oct-01
Nov-01
Dec-01
Jan-02
Feb-02
Mar-02
Apr-02
May-02
Jun-02
Fixed Pmt
0.7300
0.7300
0.7300
0.7300
0.7300
0.7300
0.7300
0.7300
0.7300
0.7300
0.7300
0.7300
Total Gain(Loss)-100% Hedge
Total Gain(Loss)-50% Hedge
Monthly Settlements
100%
Hedge
50% Hedge
Floating Pmt
0.7407
0.7812
0.8217
0.8621
0.9026
0.9431
0.9836
1.0241
1.0646
1.1050
1.1455
1.1860
Gain(Loss) Gain(Loss)
0.9793
0.4897
4.6903
2.3451
8.4013
4.2006
12.1122
6.0561
15.8232
7.9116
19.5342
9.7671
23.2451
11.6226
26.9561
13.4781
30.6671
15.3335
34.3781
17.1890
38.0890
19.0445
41.8000
20.9000
256.6758
128.3379
Table 3D-Heating Oil Price rise: Heating Oil Swap
3) Hedging using a Crude Oil Call option- The call option gives the right to buy a
particular asset at a predetermined fixed price (strike price) at a time up until the
maturity date. In case of price rise, the call option can be exercised and the option
would make a profit, and would offset the loss from the actual price rise of the
commodity. In the case of a price decline, the call option may not be exercised,
giving it an advantage over other hedging strategies and hence would benefit
considerably from the price decline. However, the call option requires a premium to
be paid up front. This would sometimes act as a disadvantage to the airlines that
need to pay the cash upfront unlike other strategies.
In this alternative, the call option on crude oil futures is chosen. The profits or losses
made by this strategy would depend on the price volatility of crude oil in the market.
The call option with a premium of $1.80 per contract, and a strike price of $28 is
bought. The future price for crude oil (June 2001) is $26.39. The expected spot price
as per scenario 1 and scenario 2 is assumed to be $14.10 and $40. The contract size
for Crude Oil futures is 1000 barrels and the fuel usage in terms of barrel is 26.19
million barrels, where 1 barrel is 42 gallons of oil. Based on the amount of fuel
hedged, and the possible scenario, the airline can either make a profit or a loss from
14

15. its options. The two fuel hedging ratios analyzed in this case are the full hedge and
50% fuel hedge.
The profits or losses made by this strategy will offset the profit or loss made by the
jet fuel price. An important issue to consider here is the Basis Risk associated with
Crude Oil. Crude Oil has a higher basis risk than Heating Oil. After refining crude
oil, the products obtained are Heating Oil, Diesel Fuel, Jet Kerosene or Fuel. Refer
to Table 4A and 4B–Scenario 1 and Scenario 2.
Scenario 1- OPTION 3--Crude Oil
Call Strike Price(Jun 02)
Premium
Spot Price
Call Option Not exercised
Payoff
Profit(Loss)-100% Hedge
$
$
$
28.00
1.80
14.10
$
$
-47.14
Payoff
Profit(Loss)-50% Hedge
$
$
-23.57
Table 4A-Crude Oil Price decline: Crude Call Option
Scenario 2-OPTION 3--Crude Oil
Strike Price(Jun 02)
Premium
Spot Price
$
$
$
28.00
1.80
40.00
Payoff
Profit(Loss)-100% Hedge
$
$
314.29
267.14
Payoff
Profit(Loss)-50% Hedge
$
$
157.14
133.57
Table 4B-Crude Oil Price rise: Crude Call Option
4) Hedging using Zero Cost Crude Oil Collar- This is a combination of a call option
and a put option. The airline will buy the call option and sell the put option. It is a
zero cost collar because the premiums of both the options are the same. The
15

16. premium received from the put option will be used to pay the premium of the call
option. This is beneficial to those that cannot pay high upfront costs. In this case, the
options on crude oil futures are chosen.
In this alternative, the call option with a premium of $1.80 per contract, and a strike
price of $28 is bought. A put option with the same premium of $1.80 per contract
and a strike price of $22.50 is sold. The future price for crude oil (June 2001) is
$26.39. The expected spot price as per scenario 1 and scenario 2 is assumed to be
$14.10 and $40. The contract size for Crude Oil futures is 1000 barrels and the fuel
usage in terms of barrel is 26.19 million barrels, where 1 barrel is 42 gallons of oil.
The two fuel hedging ratios analyzed in this case are the full hedge and 50% fuel
hedge. In scenario 1, when the crude oil price declines, the call option will not be
exercised by the airline but the buyer of the put option will exercise the put option
and the airline would pay the buyer of the put option the difference of the strike price
and the spot price at year end. In scenario 2, when the crude oil price rises, the
airline would exercise the call option and would benefit from the difference of the
spot price at year-end and the strike price. The buyer will not exercise the put option.
The profits or losses made by this strategy will offset the profit or loss made by the
jet fuel price. Like in the previous strategy, the basis risk is pretty high with Crude
Oil Futures.
Scenario 1- OPTION 4-Crude Oil Collar
Call Strike Price
Put Strike Price
Premium(Call&Put)
Crude Spot Price
Payoff
Profit (Loss)-Full Hedge
Payoff
Profit (Loss)-50% Hedge
$
$
$
$
28.00
22.50
1.80
14.10
(220.0000)
(220.0000)
(110.0000)
(110.0000)
Buyer of Put option exercises the Put option
and SWA (buyerof call) will not exercise the
call option
Table 5A-Crude Oil Price decline: Crude Zero Cost Collar Option
16

17. Sce na rio 2- OPTION 4-Crude Oil Colla r
Ca ll Strike Price
Put Strike Price
Premium(Call&Put)
Crude Spot Price
Payoff
Profit (Loss)-Full Hedge
Payoff
Profit (Loss)-50% Hedge
$
$
$
$
28.00
22.50
1.80
40.00
314.2857
314.2857
157.1429
157.1429
Buye r of Put option doe s not e x e rcise
the Put option a nd SW A (buye r of ca ll)
w ill e x e rcise the ca ll option
Table 5B-Crude Oil Price rise: Crude Zero Cost Collar Option
5) Hedging using a Heating Oil Futures contract- A futures contract is an agreement
to buy or sell a specified quantity and quality of a commodity for a certain price at a
designated time in the future. The airline, which is the buyer, has a long position to
offset against the fuel price rise. There is a daily settlement to minimize the chance
of default. In this case, in order to hedge, the airline buys heating oil futures contract
from the NYMEX. The heating oil Future Price on June 11th, 2001 was $0.7002 per
gallon and the estimated spot price (June 2002), for scenario 1 is $ 0.388 per gallon.
The estimated spot price (June 2002), for scenario 2 is $ 1.186 per gallon. In
scenario 1, due to the price decline in Heating Oil, the loss from the hedge is the
difference between the future price and the spot price of $ 0.388 per gallon. In
scenario 2, due to the price rise in Heating Oil, the profit from the hedge is the
difference between the future price and the spot price of $ 1.186 per gallon. The
contract size is 42000 gallons and the amount of fuel used is 1100 million gallons.
The two fuel hedging ratios analyzed in this case are the full hedge and 50% fuel
hedge. The profits or losses made by this strategy will offset the profit or loss made
by the jet fuel price. In scenario 1, the basis loss is 8.93 cents/gallon and in scenario
2, there is a basis loss of 8 cents per gallon.
17

18. Scenario 1-Hedge using a heating oil futures contract
Basis Risk
Future Price(6/11/01)
$
0.7002
Jun-01
0.0943
Spot Price
$
0.388
Jun-02
0.0050
0.0893
Gain(Loss)-100% Hedge $
(343.42)
Gain(Loss)-50% Hedge $
(171.71)
Table 6A-Heating Oil Price decline: Heating Oil Futures Contract
Scenario 2-Hedge using a heating oil futures contract
Basis Risk
Future Price(6/11/01)
$
0.7002
Jun-01
Spot Price
$
1.186
Jun-02
Gain(Loss)-100% Hedge $
Gain(Loss)-50% Hedge $
0.0943
0.0100
0.08
534.38
267.19
Table 6B-Heating Oil Price rise: Heating Oil Futures Contract
6) Hedging using a Crude Oil Futures contract- This is similar to the Heating Oil
Futures Contract. The Crude Oil futures contract traded from NYMEX is a long
position for the airline. The Crude oil Future Price on June 11th, 2001 was $26.39 per
gallon and the estimated spot price (June 2002), for scenario 1 is $ 14.10 per gallon.
The estimated spot price (June 2002), for scenario 2 is $ 40 per gallon. In scenario 1,
due to the price decline in Crude Oil, the loss from the hedge is the difference
between the future price and the spot price of $ 14.10 per gallon. In scenario 2, due
to the price rise in Crude Oil, the profit from the hedge is the difference between the
future price and the spot price of $ 40 per gallon. The contract size is 1000 barrels
and the amount of fuel used is 26.19 million barrels. The two fuel hedging ratios
analyzed in this case are the full hedge and 50% fuel hedge. The profits or losses
made by this strategy will offset the profit or loss made by the jet fuel price. In
18

19. scenario 1, the basis gain is $11.89 per gallon and in scenario 2, there is a basis loss
of $13.21 per gallon.
Scenario 1-Hedge using a crude oil futures contract
Future Price(6/11/01)
$
26.39
Basis Risk
Gain(Loss)Spot Price
$
14.100 100% Hedge $ (321.8810) June-01 -25.60
Gain(Loss)50% Hedge
$ (160.940) Jun-02 -13.71
-11.89
Table 7A-Crude Oil Price decline: Crude Oil Futures Contract
Scenario 2-Hedge using a crude oil futures contract
Future Price(6/11/01)
26.39
Basis Risk
Gain(Loss)Spot Price $ 40.000 100% Hedge $ 356.45 June-01 $ (25.596)
Gain(Loss)50% Hedge
$ 178.2 June-02 $ (38.804)
$ 13.21
Table 7B-Crude Oil Price rise: Crude Oil Futures Contract
Overall Analysis:
Coming to the overall analysis of the Hedging strategies, Table 8 gives a comprehensive
list of all the Fuel Costs, Hedging Costs and Net Fuel Costs or Total Fuel Costs incurred
by the airline when all the discussed strategies are employed. The costs are shown in $
millions. The two main objectives of Southwest Airlines in fuel hedging are to
maintain fuel expenses at a constant level or minimum variance and to minimize the
fuel costs.
In order to achieve its objectives, the airline considers the probability of each scenario to
occur exactly the same i.e., 50%. Hence the minimum fuel costs are computed based on
19

20. the average of the fuel costs in Scenario 1 and Scenario 2. The minimum fuel costs are
shown in the column highlighted by green.
It is important to note that when no hedging takes place, there is no offset of risk or
protection against fuel rise. In this case, the fuel costs is the total fuel cost incurred by
the airline. In scenario 1, the total fuel cost is $432.3 million and $1315.6 million in
scenario 2. The average of these two costs ($873.95 million) is used as benchmark to
compute the variance of the fuel costs in each strategy. The column titled Var1
computes the difference of Total Fuel Costs in scenario 1 and the benchmark cost of
$873.95 million. The column titled Var2 computes the difference of Total Fuel Costs in
scenario 2 and the benchmark cost of $873.95 million. The Variance of Fuel costs as
shown in the column highlighted by red, are the average of Var1 and Var2 as there is an
equal probability of either scenario to occur.
Description
Option
1 Do nothing
2a-100% Hedge using a plain vanil a jet fuel swap-Full
2a-50% Hedge using a plain vanil a jet fuel swap-50%
2b-100% Hedge using a plain vanil a heating oil swap-Full
2b-50% Hedge using a plain vanil a heating oil swap-50%
3-100% Hedging using options-Full
3-50% Hedging using options-50%
4-100% Hedge using a zero-cost collar strategy-Full
4-50% Hedge using a zero-cost collar strategy-50%
5a-100% Hedge using a crude oil futures contract-Full
5a-50% Hedge using a crude oil futures contract-50%
5b-100% Hedge using a heating oil futures contract-Full
5b-50% Heade using a heating oil futures contract-50%
Scenario 1
Scenario 2
1
Fuel Hedge Costs Total Fuel Fuel Hedge Costs Total Fuel Average Fuel
Costs (Profit) Costs Costs (Profit) Costs
Costs
432.3
0.0
432.3 1315.6
0.0 1315.6 873.95
432.3 201.3
633.6 1315.6 (277.2) 1038.4 836.00
432.3 100.6
532.9 1315.6 (138.6) 1177.0 854.98
432.3 218.8
651.1 1315.6 (256.7) 1058.9 855.01
432.3 109.4
541.7 1315.6 (128.3) 1187.3 864.48
432.3
47.1
479.4 1315.6 (267.1) 1048.5 763.95
432.3
23.6
455.9 1315.6 (133.6) 1182.0 818.95
432.3 220.0
652.3 1315.6 (314.3) 1001.3 826.81
432.3 110.0
542.3 1315.6 (157.1) 1158.5 850.38
432.3 321.9
754.2 1315.6 (356.5) 959.1 856.66
432.3 160.9
593.2 1315.6 (178.2) 1137.4 865.31
432.3 343.4
775.7 1315.6 (534.4) 781.2 778.47
432.3 171.7
604.0 1315.6 (267.2) 1048.4 826.21
2
Var1
441.65
240.37
341.01
222.85
332.25
394.51
418.08
221.65
331.65
119.77
280.71
98.23
269.94
3
4
Var2 Variance
441.65 441.65
164.47 202.42
303.06 322.04
184.97 203.91
313.31 322.78
174.51 284.51
308.08 363.08
127.36 174.51
284.51 308.08
85.20 102.48
263.42 272.07
92.73
95.48
174.46 222.20
Table 8
20

21. Southwest Airlines has to choose the best hedging strategy that would have minimum
fuel variance and minimum fuel costs. As per basic analysis from Table 8, it appears
that the minimum fuel cost of $763.95 million is achieved from the Full Hedge –Call
Option strategy based on the annual fuel consumption of $1100 million gallons and the
minimum variance of $95.48 million is achieved from the Full Hedge- Heating Oil
Futures contract.
The below Figure 1 shows the Total costs incurred by the airline in scenario 1. It shows
the costs incurred by the Hedge strategies and the actual fuel costs. In this scenario, all
the hedge strategies have made a loss since, the price declines. Hence in this scenario,
the un-hedged strategy has the minimum fuel cost of $432.3 million.
Figure 2 shows the Total costs incurred by the airline in scenario 2. It shows the costs
incurred by the Hedge strategies and the actual fuel costs. In this scenario, all the hedge
strategies have made a profit since, the price rises. In this scenario, the 100% hedging
strategy of heating oil futures has the minimum fuel cost of $781.2 million.
Total Costs Scenario 1
900
800
700
($MM)
600
500
Hedge Costs (Profit)
400
Fuel Costs
300
200
100
0
Figure 1
21

22. Total Costs Scenario 2
1500
1000
($MM)
500
Fuel Costs
Hedge Costs (Profit)
0
-500
-1000
Figure 2
Figures 3 shows the Total Fuel costs of each strategy in Scenario 1. The purple bars
show the total costs when hedged fully and the maroon bars show the total costs when
50% hedging takes place. As discussed earlier, the un-hedged strategy (1st purple bar)
has the minimum fuel cost.
Total Costs - Scenario 1
1400
1200
Costs ($MM)
1000
800
Full Hedge
600
50% Hedge
400
200
0
1
2
3
4
5
6
7
Figure 3
22

23. Figures 4 shows the Total Fuel costs of each strategy in Scenario 2. The purple bars
show the total costs when hedged fully and the maroon bars show the total costs when
50% hedging takes place. As discussed earlier, the 100% hedged strategy with Heating
Oil Futures contract has the minimum fuel cost.
Total Costs - Scenario 2
1400
Costs ($MM)
1200
1000
800
Full Hedge
600
50% Hedge
400
200
0
1
2
3
4
5
6
7
Figure 4
Figure 5 combines Scenario 1 and 2 in one chart and shows the Net Cost or Total Fuel
costs incurred by the airline.
Net Cost of Jet Fuel
Costs ($MM)
1400
1200
1000
800
600
400
200
0
Do
Hedge Hedge Hedging Hedge Hedge Hedge
Nothing using a using a using using a using a using a
plain
plain options- zero- crude oil heating
vanilla vanilla
Full
cost
futures
oil
jet fuel heating
collar contract- futures
swap- oil swapstrategy- Full contractFull Scenario 2 Full Hedge Full
Full
Full
Scenario 1 Full Hedge
Scenario 1 50% Hedge
Scenario 2 50% Hedge
Figure 5
23

24. Scenario Costs Variance
0
Costs ($MM)
-100
-200
-300
Hedge using a Hedge using a Hedging using Hedge using a Hedge using a Hedge using a
plain vanilla jet plain vanilla
options-Full zero-cost collar
crude oil
heating oil
fuel swap-Full heating oil
strategy-Full
futures
futures
swap-Full
contract-Full contract-Full
-400
-500
-600
-700
-800
Scenario 1 - Scen 2
Scenario 1 - Scen 2
Figure 6
Figure 6 shows the Scenario variance of Fuel costs (Scenario 1 – Scenario 2) for all the
hedging strategies. The yellow bars are for the 100% hedged strategies. The purple bars
are for the 50% hedged strategies. This chart shows the variance between the fuel costs
in each scenario.
In order to consider a more comprehensive and effective analysis, the minimum fuel
costs and minimum variance considering equal probability of each scenario are
computed. Figure 7 shows the Average Fuel costs considering equal occurrence of
scenario 1 and 2. As stated earlier, the 100% hedging using call options have the
minimum fuel cost followed by the 100% hedge of heating oil futures.
24

25. Average
Fuel
Costs
900.00
880.00
860.00
840.00
820.00
800.00
780.00
760.00
740.00
720.00
700.00
Average
Fuel
Costs
Figure 7
Figure 8 shows the variance of fuel costs, considering equal occurrence of each
scenario. It can be seen that the minimum variance of $95.48 million is achieved by
using the 100% hedge –Heating oil futures contract. The maximum variance is by the
un-hedged or Do nothing option, as the fuel costs are not offset by any risk of price rise
or fall.
25

26. 500.00
450.00
400.00
350.00
300.00
250.00
200.00
150.00
100.00
50.00
0.00
Variance
Variance
Figure 8
As per basic analysis, the minimum fuel cost of $763.95 million is achieved from the
Full Hedge –Call Option strategy based on the annual fuel consumption of $1100
million gallons and the minimum variance of $95.48 million is achieved from the
Full Hedge- Heating Oil Futures contract. Introduction of sensitivity analysis will
further strengthen and make the analysis and decision for Southwest Airlines more
effective and complete.
@Risk Sensitivity Analysis
Each of the hedging strategies and the un-hedged strategy was evaluated using the
@Risk software to find the various output scenarios and probabilities for a range of key
input drivers. For the purpose of this project, the following key drivers were considered
for the analysis (Refer Table 9):
26

27. • Fuel Usage (Jet Fuel): This is an important input for the analysis, as the fuel
consumption plays an important role in determining the total fuel costs incurred by
the Airline. The fuel consumption of an airline increases yearly as the airline keeps
growing and adds more aircraft to its fleet. Based on the past fuel consumption data
available for Southwest Airlines, the fuel consumption range for the year 2001-2002
was decided. The values for the Max. , Median (most likely) and Min. are 1100,1150
and 1200 million gallons respectively.
• Jet Fuel Spot Price (2001): Since the expected future spot price of Jet fuel is
factored in the analysis in each scenario (price rise and decline). The variance of the
current spot price will vary the expected future spot price of Jet Fuel. The spot price
of Jet fuel has been varied by 15%. The values for the Max., Median (most likely)
and Min. are 0.68, 0.7962 and 0.9140 dollars per gallon respectively.
• Heating Oil Spot Price (2001): Similarly, since the expected future spot price of
heating oil is factored in the analysis in each scenario (price rise and decline). The
variance of the current spot price will vary the expected future spot price of Heating
Oil. The spot price of Heating Oil has been varied by 15%. The values for the Max. ,
Median (most likely) and Min. are 0.5952, 0.7018 and 0.81 dollars per gallon
respectively.
• Crude Oil Spot Price (2001): Similarly, since the expected future spot price of
crude oil is factored in the analysis in each scenario (price rise and decline). The
variance of the current spot price will vary the expected future spot price of Crude
Oil. The spot price of Crude Oil has been varied by 15%. The values for the Max. ,
Median (most likely) and Min. are 22.4315, 26.39 and 30.3485 dollars per gallon
respectively.
• Call option premium: This input would have an impact on the hedging strategy
using Crude Call options. If spot price is less than the strike price, then the airline
will not exercise the call option but will pay the premium. If the spot price is greater
than the strike price then the airline will exercise the call option but will pay the
premium as a cost. The value of the premium cost can be a factor in the analysis
where hedging options are considered. The values for the Max. , Median (most
likely) and Min. are 1.0, 1.83 and 2.7 dollars per contract respectively.
27

28. Table 9-@ Risk Model Inputs
Model Output -@Risk Analysis
In this analysis, there are 26 outputs considered. 13 outputs corresponding to the
Average Fuel costs of each hedging strategy and 13 outputs corresponding to the
Variance of each hedging strategy. Each output will consider an equal occurrence of
Scenario 1 and Scenario 2.
Average Fuel Outputs:
•
Do-Nothing or Un-hedged-Average Fuel Cost
•
Full Hedge using a Plain Vanilla Jet-fuel Swap-Average Fuel Cost
•
50% Hedge using a Plain Vanilla Jet-fuel Swap-Average Fuel Cost
•
Full Hedge using a Plain Vanilla Heating Oil Swap-Average Fuel Cost
•
50% Hedge using a Plain Vanilla Heating Oil Swap-Average Fuel Cost
•
Full Hedge using a Call option on Crude Futures -Average Fuel Cost
28

29. •
50% Hedge using a Call option on Crude Futures -Average Fuel Cost
•
Full Hedge using a Zero cost collar option on Crude Futures -Average Fuel Cost.
•
50% Hedge using a Zero cost collar option on Crude Futures -Average Fuel
Cost.
•
Full Hedge using a Crude Oil Futures Contract-Average Fuel Cost.
•
50% Hedge using a Crude Oil Futures Contract-Average Fuel Cost.
•
Full Hedge using a Heating Oil Futures Contract-Average Fuel Cost.
•
50% Hedge using a Heating Oil Futures Contract-Average Fuel Cost.
Variance Outputs
•
Do-Nothing or Un-hedged-Variance.
•
Full Hedge using a Plain Vanilla Jet-fuel Swap- Variance.
•
50% Hedge using a Plain Vanilla Jet-fuel Swap- Variance.
•
Full Hedge using a Plain Vanilla Heating Oil Swap- Variance.
•
50% Hedge using a Plain Vanilla Heating Oil Swap- Variance.
•
Full Hedge using a Call option on Crude Futures –Variance.
•
50% Hedge using a Call option on Crude Futures – Variance.
•
Full Hedge using a Zero cost collar option on Crude Futures – Variance.
•
50% Hedge using a Zero cost collar option on Crude Futures – Variance.
•
Full Hedge using a Crude Oil Futures Contract- Variance.
•
50% Hedge using a Crude Oil Futures Contract- Variance.
•
Full Hedge using a Heating Oil Futures Contract- Variance.
•
50% Hedge using a Heating Oil Futures Contract- Variance.
29

30. Target Level 1
118.7024149
Target-Fuel Cost Variance (SWA)-2002
Estimated-Fuel Cost per Gallon (SWA)-2002
Target-Total Fuel Cost (SWA)-2002
Target Level 2
129.4935436
$
0.76
$836.00
Table 10-Target Values for Fuel hedging
The target levels (Table 10) for the fuel cost and variance to be achieved by each of the
strategies is decided based on the past fuel cost data mentioned in Table 1. Based on the
annual fuel consumption data of 1100 million gallons and estimated jet fuel price of
$0.76 per gallon, the target average fuel cost is set at $836 million. Therefore any
strategy having the highest amount of probability below the target value of $836 million
is a good strategy for the airline.
The 1st target level for variance is set at a price of $118.70 million based on the standard
deviation of previous annual fuel prices (Table 1) and fuel consumption of 1100 million
gallons. The 2nd target level for variance is set at a price of $129.49 million based on the
standard deviation of previous annual fuel prices (Table 1) and fuel consumption of
1200 million gallons. Therefore any strategy having the highest amount of variance
probability below Target level 2 is considered very good. If probability of strategy is
below Target level 1, then the strategy is considered extremely good in terms of keeping
the fuel constant.
Southwest Airlines would require a hedging strategy that has a very high amount of
probability indicating minimum variance and minimum fuel.
The following outputs- Average fuel costs show the density probability distribution
diagram and the key inputs with the regression coefficients that impact the output the
most.
30

31. 1.
Do-Nothing or Un-hedged-Average Fuel Cost
Figure 9
Figure 9 shows that there is a probability of only 9% that the average fuel cost would
reach below the target level of $836 million.
2.
Full Hedge using a Plain Vanilla Jet-fuel Swap-Average Fuel Cost
Figure 10
31

32. Figure 10 shows that there is 0% probability that the average fuel cost would reach
below the target level of $836 million. Figure 11 shows that the only input, which
impacts in the Average Fuel price, is the fuel usage or fuel consumption. It has a very
high positive correlation of 1.00.
Figure 11
Regression
and
Rank
Information
for
Hedge
using
a
plain
vanilla
jet
fuel
swap-­‐
Full
/
Average
Fuel
Costs
Rank
Name
Regr
Corr
1
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
1.000
1.000
-­‐0.004017771
2
6/11/01
spot
price
(Jet
Fuel)=
/
0.000
Scenario
1
Figure 12
32

33. 3.
50% Hedge using a Plain Vanilla Jet-fuel Swap-Average Fuel Cost
Figure 13
Figure 13 shows that there is only about 2% probability that the average fuel cost would
reach below the target level of $836 million. Figure 14 displays that the Spot price of Jet
fuel and the fuel usage input impacts the output considerably. The jet fuel spot price and
fuel usage input has a very high positive correlation of 0.86 and 0.48 respectively.
Figure 14
33

34. Regression
and
Rank
Information
for
Hedge
using
a
plain
vanilla
jet
fuel
swap-­‐50%
/
Average
Fuel
Costs
Rank
1
Name
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
Regr
0.867
Corr
0.862
2
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
0.501
0.477
Figure 15
4.
Full Hedge using a Plain Vanilla Heating Oil Swap-Average Fuel Cost
Figure 16
34

35. Figure 16 shows that there is about 23% probability that the average fuel cost would
reach below the target level of $836 million. Figure 17 displays that the Spot price of
Jet fuel, spot price of Heating oil and the fuel usage input impacts the output. The jet
fuel spot price and fuel usage input has a positive correlation of 0.71 and 0.2
respectively, where as the spot price of Heating oil has a negative correlation of 0.64.
The jet fuel increases the actual fuel costs whereas the heating oil makes a profit from
the hedge costs, thereby having a negative correlation with the output.
Figure 17
Regression
and
Rank
Information
for
Hedge
using
a
plain
vanilla
heating
oil
swap-­‐Full
/
Average
Fuel
Costs
Rank
1
2
3
Name
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
6/11/01
spot
price
(Heating
Oil)=
/
Scenario
1
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
Regr
0.723
-­‐0.664
0.209
Corr
0.707
-­‐0.644
0.196
Figure 18
35

36. 5. 50% Hedge using a Plain Vanilla Heating Oil Swap-Average Fuel Cost
Figure 19
Figure 19 shows that there is about 14% probability that the average fuel cost would
reach below the target level of $836 million. Figure 20 displays that the Spot price of
Jet fuel, spot price of Heating oil and the fuel usage input impacts the output.
The jet fuel spot price and fuel usage input has a positive correlation of 0.88 and 0.24
respectively, where as the spot price of Heating oil has a negative correlation of 0.37.
The jet fuel increases the actual fuel costs whereas the heating oil makes a profit from
the hedge costs, thereby having a negative correlation with the output.
36

37. Figure 20
Regression
and
Rank
Information
for
Hedge
using
a
plain
vanilla
heating
oil
swap-­‐50%
/
Average
Fuel
Costs
Rank
1
Name
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
Regr
0.881
Corr
0.876
2
3
6/11/01
spot
price
(Heating
Oil)=
/
Scenario
1
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
-­‐0.404
0.257
-­‐0.378
0.240
Figure 21
37

38. 6. Full Hedge using a Call option on Crude Futures -Average Fuel Cost
Figure 22
Figure 22 shows that there is about 70% probability that the average fuel cost would
reach below the target level of $836 million. This is a very good indication that the
strategy would ensure minimum fuel costs. Figure 23 displays that the Spot price of Jet
fuel, future spot price of crude oil, fuel usage and the call option premium impact the
output.
The jet fuel spot price, fuel usage input and call option premium has a positive
correlation of 0.88, 0.22 and 0.14 respectively, where as the futures spot price of Crude
oil has a negative correlation of 0.34. The jet fuel increases the actual fuel costs whereas
the crude oil makes a profit from the hedge costs, thereby having a negative correlation
with the output. The fuel usage and call option add to the total costs of the output.
38

39. Figure 23
Regression
and
Rank
Information
for
Hedging
using
options-­‐Full
/
Average
Fuel
Costs
Rank
1
Name
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
Regr
0.894
Corr
0.888
2
6/11/01
Futures
Price
(Crude
Oil)
/
Scenario
1
-­‐0.360
-­‐0.335
3
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
0.232
0.217
4
Call
Option
Premium
/
Scenario
1
0.155
0.138
Figure 24
39

40. 7.
50% Hedge using a Call option on Crude Futures -Average Fuel Cost
Figure 25
Figure 25 shows that there is about 35% probability that the average fuel cost would
reach below the target level of $836 million. Figure 26 displays that the Spot price of
Jet fuel, future spot price of crude oil, fuel usage and the call option premium impact the
output.
Figure 26
40

41. The jet fuel spot price, fuel usage input and call option premium has a positive
correlation of 0.94, 0.24 and 0.067 respectively, where as the futures spot price of Crude
oil has a negative correlation of 0.172. The jet fuel increases the actual fuel costs
whereas the crude oil makes a profit from the hedge costs, thereby having a negative
correlation with the output. The call option has a very negligible impact to the total
costs.
Regression
and
Rank
Information
for
Hedging
using
options-­‐50%
/
Average
Fuel
Costs
Rank
Name
Regr
1
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
0.945
2
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
0.262
3
6/11/01
Futures
Price
(Crude
Oil)
/
Scenario
1
-­‐0.190
4
Call
Option
Premium
/
Scenario
1
0.082
Corr
0.942
0.244
-­‐0.172
0.067
Figure 27
8. Full Hedge using Zero-cost collar on Crude Futures -Average Fuel Cost.
Figure
28
41

42. Figure 28 shows that there is about 34% probability that the average fuel cost would
reach below the target level of $836 million. Figure 29 displays that the Spot price of
Jet fuel, future spot price of crude oil, and fuel usage impact the output.
Figure 29
The jet fuel spot price and fuel usage input has a positive correlation of 0.75 and 0.20
respectively, where as the futures spot price of Crude oil has a negative correlation of
0.592. The jet fuel increases the actual fuel costs whereas the crude oil makes a profit
from the hedge costs, thereby having a negative correlation with the output. The fuel
usage adds to the total costs of the output.
Regression
and
Rank
Information
for
Hedge
using
a
zero-­‐cost
collar
strategy-­‐Full
/
Average
Fuel
Costs
Rank
Name
Regr
Corr
1
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
0.763
0.751
2
6/11/01
Futures
Price
(Crude
Oil)
/
Scenario
1
-­‐0.615
-­‐0.592
3
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
0.214
0.202
Figure 30
42

43.
9.
50% Hedge using a Zero cost collar option on Crude Futures -Average Fuel
Cost.
Figure 31
Figure 31 shows that there is about 19% probability that the average fuel cost would
reach below the target level of $836 million. Figure 32 displays that the Spot price of
Jet fuel, future spot price of crude oil, and fuel usage impact the output.
Figure 32
The jet fuel spot price and fuel usage input has a positive correlation of 0.89 and 0.24
respectively, where as the futures spot price of Crude oil has a negative correlation of
0.336. The jet fuel increases the actual fuel costs whereas the crude oil makes a profit
43

44. from the hedge costs, thereby having a negative correlation with the output. The fuel
usage adds to the total costs of the output.
Regression
and
Rank
Information
for
Hedge
using
a
zero-­‐cost
collar
strategy-­‐50%
/
Average
Fuel
Costs
Rank
Name
Regr
Corr
1
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
0.899
0.894
2
6/11/01
Futures
Price
(Crude
Oil)
/
Scenario
1
-­‐0.362
-­‐0.336
3
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
0.259
0.243
Figure 33
10. Full Hedge using a Crude Oil Futures Contract-Average Fuel Cost.
Figure 34
44

45. Figure 34 shows that there is about 15% probability that the average fuel cost would
reach below the target level of $836 million. Figure 35 displays that the Spot price of
Jet fuel, and fuel usage impact the output.
Figure 35
Regression
and
Rank
Information
for
Hedge
using
a
crude
oil
futures
contract-­‐Full
/
Average
Fuel
Costs
Rank
Name
Regr
Corr
1
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
0.961
0.960
2
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
0.279
0.259
3
6/11/01
Futures
Price
(Crude
Oil)
/
Scenario
1
0.000
0.007182983
Figure 36
The jet fuel spot price and fuel usage input has a positive correlation of 0.96 and 0.259
respectively, where as the futures spot price of Crude oil has a very negligible impact.
The jet fuel spot price increases the actual fuel costs whereas the fuel usage adds to the
total costs of the output.
45

46. 11. 50% Hedge using a Crude Oil Futures Contract-Average Fuel Cost.
Figure 37
Figure 37 shows that there is about 11% probability that the average fuel cost would
reach below the target level of $836 million. Figure 38 displays that the Spot price of
Jet fuel, and fuel usage impact the output.
Figure 38
The jet fuel spot price and fuel usage input has a positive correlation of 0.96 and 0.261
respectively, where as the futures spot price of Crude oil has a very negligible impact.
46

47. The jet fuel spot price increases the actual fuel costs whereas the fuel usage adds to the
total costs of the output.
Regression
and
Rank
Information
for
Hedge
using
a
crude
oil
futures
contract-­‐50%
/
Average
Fuel
Costs
Rank
Name
Regr
Corr
1
2
3
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
6/11/01
Futures
Price
(Crude
Oil)
/
Scenario
1
0.961
0.281
0.000
0.959
0.261
0.007167339
Figure 39
12. Full Hedge using a Heating Oil Futures Contract-Average Fuel Cost.
Figure 40
47

48. Figure 40 shows that there is about 62% probability that the average fuel cost would
reach below the target level of $836 million. This is a very good indication of hedging
strategy to be used for minimum fuel costs. Figure 41 displays that the Spot price of Jet
fuel, Spot price of Heating Oil and fuel usage impact the output.
Figure 41
The jet fuel spot price, heating oil spot price and fuel usage input have a positive
correlation of 0.88,0.391 and 0.217 respectively. The jet fuel spot price and the heating
oil spot price increases the actual fuel costs whereas the fuel usage adds to the total costs
of the output.
Regression
and
Rank
Information
for
Hedge
using
a
heating
oil
futures
contract-­‐Full
/
Average
Fuel
Costs
Rank
Name
Regr
Corr
1
2
3
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
6/11/01
spot
price
(Heating
Oil)=
/
Scenario
1
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
0.882
0.405
0.233
0.883
0.391
0.217
Figure 42
48

49. 13. 50% Hedge using a Heating Oil Futures Contract-Average Fuel Cost.
Figure 43
Figure 43 shows that there is about 31% probability that the average fuel cost would
reach below the target level of $836 million. Figure 44 displays that the Spot price of
Jet fuel, Spot price of Heating oil and fuel usage impact the output.
Figure 44
49

50. The jet fuel spot price, heating oil spot price and fuel usage input has a positive
correlation of 0.94,0.208 and 0.244 respectively. The jet fuel spot price and the heating
oil spot price increases the actual fuel costs whereas the fuel usage adds to the total costs
of the output.
Regression
and
Rank
Information
for
Hedge
using
a
heating
oil
futures
contract-­‐50%
/
Average
Fuel
Costs
Rank
Name
Regr
Corr
1
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
0.940
0.940
2
3
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
6/11/01
spot
price
(Heating
Oil)=
/
Scenario
1
0.263
0.216
0.244
0.208
Figure 45
Variance –Outputs: With the variance, most of the outputs have a probability of zero in
reaching Target Level 1 or Target Level 2. Hence only those outputs having a
probability of reaching the Target levels will be discussed below:
1. Full Hedge using a Crude Oil Futures Contract- Variance.
Figure 46
50

51. Figure 46 shows that there is 100% probability that this hedging strategy would reach
the target level 1 and level 2 of variance. Hence this strategy is very effective in
maintaining fuel costs constant or with minimum variance. Figure 47 shows that the
fuel usage has the biggest impact on the variance of the output as indicated by the
correlation of 1, whereas the other inputs such as spot price of Jet fuel and spot price of
Crude oil futures have a negligible effect.
Figure 47
Regression
and
Rank
Information
for
Full
Hedge-­‐Crude
Oil
Futures-­‐Variance
Rank
Name
Regr
Corr
1
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
1.000
1.000
2
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
0.000
-­‐0.004017771
3
6/11/01
Futures
Price
(Crude
Oil)
/
Scenario
1
0.000
-­‐0.001101022
Figure 48
51

52. 2. Full Hedge using a Heating Oil Futures Contract- Variance.
Figure 49
Figure 49 shows that there is 87% and 76% probability that this hedging strategy would
reach the target level 2 and level 1 of variance. Hence this strategy is very effective in
maintaining fuel costs constant or with minimum variance. Figure 50 shows that the
spot price of Heating Oil futures has the biggest impact on the variance of the output as
indicated by the negative correlation of 0.997, whereas the other input i.e., Usage of jet
fuel has a negligible effect with a correlation of 0.068. The negative correlation of the
Heating oil spot price show that this input helps in limiting variance.
Figure 50
52

53. Regression
and
Rank
Information
for
Full
Hedge-­‐Heating
Oil
Futures-­‐Variance
Rank
Name
Regr
1
6/11/01
spot
price
(Heating
Oil)=
/
Scenario
1
-­‐0.996
2
Fuel
usage
(Jet
Fuel)=
/
Scenario
1
0.070
3
6/11/01
spot
price
(Jet
Fuel)=
/
Scenario
1
0.000
Corr
-­‐0.997
0.068
-­‐0.00762999
Figure 51
Summary of @Risk analysis.
•
As per the analysis of the Outputs -Average Fuel Costs and Outputs- Variance, it
is clear that in order to achieve the objectives of Southwest Airlines, it is
necessary to have a strategy, which has a combination of both the minimum fuel
cost and minimum variance.
•
The minimum fuel cost objective is achieved by having a strategy that has the
highest probability to reach below the target level of $836 million. There are two
strategies that have achieved this target with the highest amount of probability
than the others. They are the Full Hedge using a Call option on Crude Futures
and the Full Hedge using a Heating Oil Futures Contract.
•
The minimum variance objective is achieved by having a strategy that has the
highest probability to reach below the target level 1 of $118.7 million and target
level 2 of 129.4 million. There are two strategies that have achieved this target
with the highest amount of probability than the others. They are the Full Hedge
using a Crude Oil Futures and the Full Hedge using a Heating Oil Futures
Contract.
•
Since, the Full Hedge using a Heating Oil Futures contract strategy has a very
high amount of probability in achieving the Target levels of the objectives, it is
the preferred hedging strategy to achieve Southwest’s objectives.
53

54. Conclusion
After carefully considering all the hedging strategies, in the primary and the sensitivity
analysis, it can be recommended that the best strategy, which can be used to maintain
constant and minimum fuel costs, is the Full Hedge Heating Oil Futures Contract. This
strategy also has a very low basis risk compared to the other strategies using Crude Oil.
It is therefore advised that Scott Topping utilizes this strategy for Southwest Airlines.
Current Outlook
Most of the major airlines are hedging fuel using jet fuel, gas oil and crude derivatives.
Few cover more than 12 months’ expected consumption, and it is rare to find more than
80% of future needs hedged beyond three months ahead. Crude oil provides more
liquidity and flexibility for hedging, but the spread between crude and jet aviation fuel
had tended to widen at times of market instability. Not many airlines report gains and
losses from fuel hedging activity, but many are now required to report the market value
of unexpired contracts on their balance sheets. There seems to be no reason to contradict
the economic fundamentals of hedging. A policy of permanent hedging of fuel costs
should leave expected long-run profits unchanged. If it damps out profit volatility, it
should do so in a way that the market would not value. Data suggests it may not damp
out volatility, after all. Oil prices and air travel demand cycles are correlated when oil
supply reductions drive GDP declines. But oil and travel are negatively correlated when
GDP demand surges drive oil price increases. So oil prices can be observed to either
increase or decrease airline profit cycles, depending on the time period sampled.
A fuel price hedge would create exceptional value is when an airline is on the edge of
bankruptcy. However, when on the verge of bankruptcy, an airline does not have the
liquidity to buy oil futures. On the other hand, foreign exchange hedges probably did
make sense, when airlines were state-supported. And variable levels of hedging can be
useful in transferring profits from one quarter to another. Finally, hedging may be a
zero-cost signal to investors that management is technically alert. Perhaps this is the
most compelling argument for airline hedging. However, it lies more in the realm of the
psychology of markets than the mathematics of economics.
54

55.
Average Brent Crude Oil
price per barrel
$80
$90
Current Market (1)
$110
$120
Period
Southwest
Airlines
Co.
Fuel
Derivative
Contracts
As
of
April
22,
2013
Estimated economic jet fuel price per gallon,
including taxes
2Q 2013 (2)
Second Half of 2013 (2)
$2.95 - $3.00
$2.90 - $2.95
$2.95 - $3.00
$2.95 - $3.00
$3.00 - $3.05
$3.00 - $3.05
$3.10 - $3.15
$3.20 - $3.25
$3.15 - $3.20
$3.30 - $3.35
Average percent of estimated fuel consumption covered
by fuel derivative contracts at varying WTI/Brent
crude oil-equivalent price levels
2014
Approx. 60%
2015
Approx. 35%
2016
Approx. 30%
2017
Approx. 50%
(1) Brent crude oil average market prices as of April 22, 2013 were approximately $101
and $99 per barrel for second quarter and second half 2013, respectively.
(2) The Company has approximately 95 percent of its second quarter and second half 2013
estimated fuel consumption covered by fuel derivative contracts with approximately 75
percent at varying Gulf Coast jet fuel-equivalent prices and the remainder at varying Brent
crude oil-equivalent prices. The economic fuel price per gallon sensitivities provided above
assume the relationship between Brent crude oil and refined products based on market
prices as of April 22, 2013.
Table
11-­‐Southwest
Fuel
Derivative
Data
Airline
Jet fuel as a %
of Operating
Expenses
Years Jet
Fuel
Hedged
Average %
of Next Year
Hedged
Std. Dev of
Next year
Hedged
Fuel Passthrough
Agreement
Charter
Operations
AirTran
Alaska Air
American
Continental
Delta Air
Frontier
Airlines
JetBlue
Airlines
Southwest
Airlines
United
Airlines
US Airways
Average
18.84%
13.92%
11.97%
15.14%
12.20%
15.58%
2000-2008
2001-2008
2000-2008
2000-2008
2000-2008
2002-2008
29%
36%
23%
13%
37%
17%
8
16
12
13
23
15
0
0
0
0
0
0
0
0
0
0
0
0
16.07%
2002-2008
22%
17
0
0
14.51%
2000-2008
69%
28
0
0
12.30%
2000-2008
10%
12
0
0
9.69%
14.02%
2000-2008
23%
28%
17
0
0
Table
12-­‐U.S.
Airline
Industry
Hedging
Data
by
FASB
55

56. REFERENCES
Raghavan, S. (2010). Advanced case studies in corporate finance with application to
aviation & aerospace industries. (5th ed.). New York: Linus Publications,Inc.
Retrieved October 12, 2013 from http://www.financialsense.com
Retrieved October 12, 2013 from http://www.finance.yahoo.com
Retrieved October 12, 2013 from http://www.cnbc.com
Retrieved October 12, 2013 from http://www.longviewfunds.com
Retrieved October 12, 2013 from http://www.investopedia.com/articles/07/contango
56