dynamic optimality of fuel cost hedging for us...

Dynamic Optimality of Fuel Cost Hedgingfor US Airlines

Liuren Wujoint with Xiaolu Hu and Malick Sy

Baruch College

October 4, 2019

Hu, Sy, Wu (RMIT & Baruch) Dynamic Optimality of Fuel Cost Hedging October 4, 2019 1 / 26

Does hedging enhance firm value?

Several channels have been proposed for hedging to be value accretive:(Stulz; Smith & Stulz; Froot, Scharfstein, &Stein; Bessembinder)

Reduce tax, distress risk, underinvestment, ...

Various tests have been designed to test the value benefit of hedging

Positive: Allayannis & Weston (2001, FX); Perez-Gonzalez & Yun(2013, weather); Cornaggia (2013, agriculture); Gilje & Taillard (2017,oil producers); Carter, Rogers, & Simkins (2006, airlines)

Negative: Jin & Jorion (2006, oil producers)

Hedging is small: Guay & Kothari (2003)

Our view in this paper:

Hedging is value beneficial only when it is done right.

It is not always easy to get it right.

The projected notional exposure can differ from actual exposure.Net exposure can differ from notional exposure.


Fuel cost hedging for airline companies

Appropriate fuel cost hedging should be highly beneficial for airlines:

Airlines have high financial/operational leverage, thin profit margin.Jet fuel prices are very volatileEvidence: Carter, Rogers, & Simkins (2006) for US airlines (1992-2003)

An airline’s net oil exposure can be quite different from its notional exposureand can vary strongly over time.

Oil can be driven by both supply shocks and demand shocks.

Supply-driven price hikes (a) increase fuel cost and (b) negativelyimpact travel demand via negative impact on the economy— Net exposure can be larger than notional exposure. Definitely hedge!

Demand-driven price hikes (a) increase fuel cost but (b) can also beaccompanied by higher travel demand /revenue— Net exposure can be small relative to notional exposure.

Sy & Wu (2019): The composition varies strongly over time

Optimal fuel cost hedging depends crucially on timely and accurateidentification of the time-varying supply-demand shock decomposition of oilprice movements — This is not that easy (nor too complicated) to get right.


The practical background

90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 19 200

50

100

150

WT

I F

ront-

month

futu

res

price

Airlines started to actively pursue jet fuel cost hedging in the late 90s

Most hedges worked great with the oil price shot through the roof

Oil price went down after the 2008-2009 financial crises, and have beenstaying down for a variety of reasons (e.g., shale in the US)

Some airlines’ hedging practices incurred huge losses

Some stopped hedging, some were asking for guidance

Will the oil price stay down?Hu, Sy, Wu (RMIT & Baruch) Dynamic Optimality of Fuel Cost Hedging October 4, 2019 4 / 26

What we do in this paper

Set up a simple theoretical structure to derive the optimal fuel cost hedgingratio (in percentage of notional) as a function of

market hedging demand: variance contribution of demand shocksversus supply shocks to oil price movementsfirm-specific exposure: revenue sensitivity to market demandversus jet fuel cost exposure to total revenue

Use WTI return to proxy oil shock, SPX return to proxy demand shock,rolling regression to construct a time-varying market hedging demand index.

Supply shocks dominate oil price variation before 2008, demand shocksbecome larger after that — Hedging demand is higher before 2008 ...

Test value benefit of hedging under different market conditions

Value benefit is significant only when market hedging demand is high.

Estimate the dynamic optimality of each airline’s hedging practice

Among 33 US airlines: 1/3 do not hedge at all, 1/3 move against thehedging demand variation (“anti-optimal”?).

Hedging is value accretive only when the policy is somewhat optimal.

“Anti-optimal” hedging reduces value, worse than not hedging at all!


Time-varying supply and demand oil shocks

Decompose oil price movements into demand & supply shocks:

dOt/Ot = ηdt

√vdt dW

dt − ηst

√v st dW

st . (1)

Use SPX to proxy demand shock:

dDt/Dt =

√vdt dW

dt . (2)

Treat “supply” shock as projection residual: E[dW dt dW

st ] = 0.

We don’t intend to “hedge” via directional speculation— omit drift specifications all together

Identification:

Sy & Wu (2019): Identify (vdt , η

dt , v

ot ) in real time using options on

SPX and WTI futures.Captures more timely, forward-looking variation

In this paper, we perform a quarterly rolling-window regression of WTIfutures daily returns on SPX daily returns.

Simpler to discuss, longer time series


Airline revenue & cost exposures

Decompose an airline company’s operating income (It,i ) into twocomponents: revenue (Rt,i ) and operating expense (Ct,i ),

It = Rt,i − Ct,i . (3)

Project revenue variation to market demand (SPX):

dRt,i

Rt,i= βr

t,i

dDt

Dt+ (idiosyncratic) (4)

Idiosyncratic movements do not matter (much) for optimal hedging decision

Attribute expense variation to oil price movement:

dCt,i

Rt,i= ϕt,i

dOt

Ot+ (variation in other costs) (5)

ϕct,i = fuel cost exposure as a fraction of total revenue by assuming:

(i) perfect correlation between jet fuel price and hedging instrument.(ii) variations in other costs are not correlated with oil price or market

Or simply treat this as a projection of cost variation on oil variation


To hedge or not to hedge?

It depends on what moves.

Profit margin exposures and dynamics

Unhedged:

dIUt,iRt,i

= (βrt,i − ϕc

t,iηdt )

√vdt dW

dt + ϕc

t,iηst

√v st dW

st + σzdZ (6)

100%-notional hedged:

dIHtRt

= βrt,i

√vdt dW

dt + σzdZ . (7)

Hedge or no-hedge depends on oil demand shock contribution ηdt

Purely supply shock: ηdt = 0 (or even negative), hedging definitelyreduces risk.

When demand shock ηdt is large, (βrt,i − ϕc

t,iηdt ) can be small or even

zero. No hedging can lead to smaller variation than hedging.


The optimal hedging ratio

Choose the hedging ratio ht,i to minimize profit margin variation

The profit margin dynamics as a function of the hedging ratio ht,i

dI (ht,i )

Rt,i= (βr

t,i−(1−ht,i )ϕct,iη

dt )

√vdt dW

dt +(1−ht,i )ϕc

t,iηst

√v st dW

st +...σzdZ .

The time-t conditional variance for the profit margin as a function of ht,i

V (ht,i ) =(βrt,i − ϕc

t,i (1− ht,i )ηdt

)2vdt +

(ϕct,i

)2(1−ht,i )

2 (ηst )2 v st +σ2

z . (8)

We can derive the optimal hedging ratio from the first-order condition:

h∗t,i = 1 −

βrt,i

ϕct,i

ηdt vdt

vot

. (9)

The optimal hedging ratio depends crucially on market conditions

Hedge 100% notional when demand shock loading is zero (ηdt = 0).

Lower hedging ratio when demand shock variance contribution (ηdt vdt )

is large relative to total oil return variance vot .


Separate firm-specific exposure fromtime-varying market conditions

Define an airline’s firm-specific exposure γt,i as the revenue sensitivity tofuel cost exposure ratio

γt,i = βrt,i/ϕ

ct,i . (10)

Construct a market hedging demand index Ht to capture the time variationin aggregate demand for fuel cost hedging

Ht = 1 − ηdt vdt

vot

. (11)

An airline’s optimal hedging ratio is a weighted average of the two:

h∗t,i = (1 − γt,i ) + γt,iHt . (12)

Ht is a measure of the market condition, determined by the timelyvariance decomposition of the oil price dynamics

γi captures firm-specific exposures as a function of the airline’sbusiness construct.

Some operational “hedging” practices such as pass-throughs,surcharges can alter the exposure structures...


Testable hypotheses

1 The value benefit of jet fuel cost hedging for airline companies is moresignificant when the market hedging demand index is high, and less so whenthe market hedging demand index is low.

2 The value benefit of an airline’s fuel cost hedging practice increases with thedynamic optimality of its hedging policy

1 One can measure the dynamic optimality of an airline’s hedging policyvia the time-series correlation ρi = corr(ht,i ,Ht) between its hedgingratio variation and the variation of the market hedging demand index.

2 With robust estimates on firm-specific exposures γi , one can alsomeasure the policy’s distance to optimality (δi = βh

i − γi ).

βhi denotes the statistical loading of an airline’s hedging ratio ht,i on

the market hedging demand indeHt ,

γi denotes its optimal loading based on its revenue/cost exposures


Summary stats across airlines

Name Ticker Hedging ratio Log Tobin’s Q SampleMean Stdev Min Max Mean Stdev Min Max Start End Years

Ccair CCAR 0.00 0.00 0.00 0.00 0.22 0.51 -0.37 1.09 1992 1998 7Comair COMR 0.00 0.00 0.00 0.00 0.53 0.36 0.04 1.03 1992 1998 7Expressjet XJT 0.00 0.00 0.00 0.00 -0.50 1.18 -2.37 0.77 2002 2009 8...United UAL 0.18 0.19 0.00 0.75 -0.64 0.64 -2.12 0.08 1992 2016 25Airtran AAI 0.19 0.17 0.00 0.52 0.19 0.40 -0.32 1.38 1994 2010 17Jetblue JBLU 0.20 0.13 0.05 0.40 -0.07 0.34 -0.53 0.53 2002 2016 15American AAL 0.22 0.15 0.00 0.48 -0.41 0.27 -0.94 0.25 1992 2016 25Delta DAL 0.33 0.32 0.00 1.05 -0.42 0.27 -0.98 0.05 1992 2016 25Alaska ALK 0.35 0.17 0.00 0.50 -0.38 0.36 -0.85 0.51 1992 2016 25Southwest LUV 0.43 0.34 0.00 0.95 0.18 0.41 -0.56 1.00 1992 2016 25

Out of 33 airlines, 11 have never hedged (but only one is still alive).

Large time-series variations for ones with largest avg. hedging ratios

No positive relation between avg hedging ratio and avg log Q: −7.5%


Summary stats across time

Year Hedging ratio Log Tobin’s Q No. ofMean Stdev Min Max Mean Stdev Min Max Companies

1992 0.06 0.11 0.00 0.28 0.00 0.38 -0.43 0.86 121994 0.04 0.12 0.00 0.50 -0.25 0.29 -0.70 0.42 181996 0.02 0.05 0.00 0.22 -0.09 0.36 -0.44 0.62 231997 0.03 0.07 0.00 0.23 0.04 0.38 -0.43 0.85 241998 0.11 0.21 0.00 0.80 0.11 0.55 -0.88 1.12 241999 0.16 0.29 0.00 0.85 -0.10 0.41 -0.61 0.70 212004 0.15 0.23 0.00 0.85 -0.43 0.76 -1.92 0.89 212007 0.12 0.17 0.00 0.70 -0.46 0.42 -1.28 0.44 192008 0.15 0.17 0.00 0.50 -0.45 0.61 -2.37 0.80 172009 0.18 0.20 0.00 0.50 -0.45 0.49 -1.72 0.52 162011 0.15 0.17 0.00 0.50 -0.49 0.36 -0.94 0.32 142015 0.18 0.21 0.00 0.63 0.11 0.40 -0.64 0.92 122016 0.17 0.25 0.00 0.63 0.18 0.30 -0.26 0.73 10

Number of airlines reached the maximum (24) in 1997, but has beendeclining since then, with a slew of corporate actions

A staggering number of chapter 11 filings ...Hu, Sy, Wu (RMIT & Baruch) Dynamic Optimality of Fuel Cost Hedging October 4, 2019 13 / 26

Fuel cost exposures and revenue sensitivities

Statistics Mean Median Stdev Min Max NobsPanel A. Fuel cost as percentages of total revenue

Pooled 19.05 16.26 9.48 0.69 46.81 423LCC 22.46 19.73 9.49 8.28 46.81 134FSC 17.47 14.87 9.07 0.69 44.46 289

Panel B. Revenue sensitivity to market demand (SPX return)Intercept, % βr ,% R2,%

Pooled 9.50 ( 1.26 ) 17.24 ( 6.21 ) 1.87LCC 18.17 ( 2.22 ) 10.38 ( 10.82 ) 7.55FSC 5.73 ( 1.46 ) 19.42 ( 7.27 ) 7.55

Fuel cost averages 19.05% of total revenue (21.30% of total expense).

Revenue growth has an average 17.24% exposure to SPX return, leading toa grand average estimate of firm exposure γ = 0.9.

Ht captures the average hedging demand well.

LCCs have a higher percentage spent on fuel cost, and a lower revenuesensitivity to market demand, hence a lower exposure γ = 0.46 compared toγ = 1.11 for FSCs.


The time-varying market hedging demand index

The market hedging demand index Ht represents the optimal hedging demand foran airline with a unit firm-specific exposure γ = 1.

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 201640

60

80

100

120

140

Mark

et hedgin

g d

em

and, %

40 50 60 70 80 90 100 110 120 130 140

Market hedging demand, %

0

0.5

1

1.5

2

2.5

3

3.5

4

Density

Broad shift: ∼ 100% before 2008, much lower (∼ 70%) since then, due toincreased demand shock contribution to oil price movement

2008-2009 financial crises; low rate environment; shale revolution

Large intertemporal movements in addition to the broad shift


Value benefit hedging under different market conditions

lnQt,i = ht,i + Xt,i + e

Models 1. Sub-sample 2. Full-sample 3. High demand 4. Low demandVariables 1992-2003 1992-2016 Ht ≥ 1 Ht < 1

h 0.3947 0.1914 0.3096 -0.1382(0.1475) (0.1017) (0.1561) (0.1327)

...R2 0.4982 0.4851 0.4388 0.4907Nobs 239 438 240 198

1 Replication: Results similar to Carter, Rogers, Simkins (2006)

2 Full sample: lower benefit (about half)

3 Conditional on High hedging demand: Strong positive value benefit

4 Conditional on low hedging demand: Negative and insignificant

Value benefit of fuel cost hedging is strongly positive only when market hedgingdemand is high.


The control variables

lnQt,i = ht,i + Xt,i + e

Models 1. 2. 3. 4.

ln(Assets) -0.15 -0.10 -0.15 -0.04(0.03) (0.02) (0.03) (0.03)

Dividend Indicator 0.21 0.13 0.20 0.12(0.06) (0.05) (0.07) (0.07)

LT Debt-to-Assets 0.58 0.71 0.82 0.52(0.19) (0.15) (0.18) (0.24)

Cap Exp to Sales 0.39 0.32 0.30 0.64(0.22) (0.16) (0.22) (0.23)

Z-score 0.17 0.16 0.15 0.28(0.04) (0.03) (0.03) (0.05)

Advertising-to-Sales 13.31 12.01 13.18 11.43(2.95) (3.01) (3.51) (5.99)

Fuel Pass-through Indicator -0.16 -0.17 -0.24 -0.18(0.07) (0.06) (0.08) (0.09)

Negative: Asset level, pass-through agreements

Positive: Dividend, Leverage, Cap expenditure, Z-score, advertising


Value maximization at optimal hedging ratio

Perform nonparametric conditional regression of lnQ on h, conditional onHt = 100% (solid) and Ht = 70% (dashed), respectively.

0 10 20 30 40 50 60 70 80 90 100

Hedging ratio, %

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Tobin

Q

High Demand

Low Demand

Presence of hump shape proves(?) existence of optimality.

At Ht = 100%, h∗ = (1− γ) + γHt = 100%, regardless of firm exposure γ.

At Ht = 70%, h∗ = 68% implies an average firm exposure of γ = 1.07.

With very low hedging ratios, valuation variation driven by other factors.Hu, Sy, Wu (RMIT & Baruch) Dynamic Optimality of Fuel Cost Hedging October 4, 2019 18 / 26

Dynamic optimality of hedging and value accretion

We measure dynamic optimality ρi by time-series correlation betweenhedging ratio ht,i and market hedging demand Ht .

The measure does not depend (much) on firm-specific exposure.

Out of 33 airlines, 11 companies do not hedge at all;9 have positive correlation; 12 have negative correlations

Dynamic optimality is a highly unfulfilled task.

Of those who hedge, over half vary against hedging demand —“anti-optimal”?

Firm value increases strongly with dynamic optimality

The 9 airlines with positive optimality has an average lnQ of −0.0678.

The 11 with negative optimality has an average lnQ of −0.2933. Thedifference is highly significant (t = 3.82).

The 10 that do not hedge at all average at lnQ = −0.1969

Hedging with negative optimality is worse than not hedging at all.


Dynamic optimality of hedging and value accretion

-60 -40 -20 0 20 40

Dynamic fuel cost hedging optimality , %

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Ave

rag

e ln

Q

ALK AALDALHA

LUV

UAL

lnQi,t = a + b ρi + ei,t−0.157 0.371 R2 = 5.33%(0.031) (0.089)

Diamond represents the average of airlines that do not hedge.


Deviation from optimal exposure

Measure statistical dependence (βhi ) on hedging demand by regressing ht,i

on Ht for each airline.

Compare to the average firm exposure γi to define distance to optimalityδi = βh

i − γiγ = 0.46 for LCCs and 1.11 for FSCs.

Firm level sensitivity estimates become unstable

Findings:

All airlines’ hedging ratios are under-exposed to market hedgingdemand.

The smaller the distance to optimality, the higher the firm valuation.


Deviation from optimal exposure and value accretion

-1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0

Deviation from optimal market demand exposure

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Ave

rag

e ln

Q

ALK AALDALHA

LUV

UAL

lnQi,t = a + b δi + ei,t0.293 0.493 R2 = 15.45%

(0.061) (0.055)

The more aligned a hedging policy is with the market hedging demand variation,the more value accretive it becomes.


The source of value accretion

Model Optimality Intercept Slope R2,% NobsPanel A. Mean profit margin, %

1. ρ 6.253 ( 0.253 ) 7.427 ( 0.722 ) 25.50 3102. δ 8.389 ( 0.629 ) 3.409 ( 0.570 ) 7.58 4373. δ 7.081 ( 0.761 ) 2.812 ( 0.655 ) 5.80 300

Panel B. Standard deviation of profit margin, %1. ρ 7.283 ( 0.181 ) -3.544 ( 0.517 ) 13.18 3102. δ 7.380 ( 0.429 ) -0.274 ( 0.389 ) 0.11 4373. δ 6.977 ( 0.362 ) -0.701 ( 0.311 ) 1.67 300

Panel C. Mean-standard deviation ratio of profit margin1. ρ 1.094 ( 0.053 ) 1.666 ( 0.153 ) 27.78 3102. δ 1.789 ( 0.114 ) 0.884 ( 0.103 ) 14.41 4373. δ 1.734 ( 0.121 ) 0.981 ( 0.104 ) 22.88 300

Dynamically optimal hedging both increases average profit margin andreduces risk.

Hedging is costly, more so when done right.


The source of value accretion

-80 -60 -40 -20 0 20 40 60

Dynamic fuel cost hedging optimality , %

2

4

6

8

10

12

14

16

Pro

fit

ma

rgin

, %

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

Info

rma

tio

n r

atio

Mean

Stdev

IR

-180 -160 -140 -120 -100 -80 -60 -40 -20 0

Deviation from optimal market demand exposure , %

2

4

6

8

10

12

14

16

Pro

fit

ma

rgin

, %

0

0.5

1

1.5

2

2.5

3

Info

rma

tio

n r

atio

Mean

Stdev

IR

Dynamically optimal hedging both increases average profit margin andreduces risk.

The closer the hedging strategy is to dynamic optimality, the stronger is thevalue benefit.

When the policy changes from no hedge to 40% correlated with themarket hedging demand index, the average profit margin doubles from6% to 12% while risk declines from 7% to 6%.


A tale of two airlines

Similar hedging ratio mean/std stats, but very different dynamics and results

Hedging dynamic optimality Financial performance

LUV 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 0

20

40

60

80

100

120

Hedgin

g r

atio

, %

0

20

40

60

80

100

120

Mark

et hedgin

g d

em

and, %

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 0

4

8

12

16

20

24

Re

ve

nu

e,

$b

n

0

0.4

0.8

1.2

1.6

2

2.4

Ne

t in

co

me

, $

bn

DAL 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 0

20

40

60

80

100

120

Hedgin

g r

atio

, %

0

20

40

60

80

100

120

Mark

et hedgin

g d

em

and, %

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 5

10

15

20

25

30

35

40

45

50

Re

ve

nu

e,

$b

n

-8

-6

-4

-2

0

2

4

6

8

10

Ne

t in

co

me

, $

bn

LUV has managed to be profitable for 44 consecutive years, with one of themost successful hedging programs, closely following the Ht variation.

DAL’s profitability is as haphazard as its hedging policy.Hu, Sy, Wu (RMIT & Baruch) Dynamic Optimality of Fuel Cost Hedging October 4, 2019 25 / 26

Concluding remarks

Hedging can be highly value accretive, but not always easy to get right.

Net exposure can differ from notional exposure

Need to understand time-varying dynamics and exposures

Fuel cost hedging for airlines is one such example

Many airlines do not hedge.

Among those who do, over half have done it so wrong that they arebetter off not doing it at all.

When done (nearly) right, fuel cost hedging can be highly beneficial,with both higher average profit margin and lower risk.

There is a lot potential for value creation ...

Bottom line

Directional forecasts are obviously very valuable, but difficult to do.

Better variance decompositions and variance/covariance forecasts canalso create a lot of value.


dynamic optimality of fuel cost hedging for us...

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