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MakingSenseofDieselPrices 1 SpiderFinancialCorp,2013

MakingSenseofDieselPrices

Inthiscasestudy,weexaminecloselythehighwayretailprice($/Gallon)forNo.2UltraLowSulfur(0

15ppm)DieselintheEIAnine(9)PADDregions.Wecarryonprincipalcomponentanalysisinan

attempttofindaminimalsubsetoftheprincipalcomponentsthatcapture(orexplains)thevariationin

pricesbetweenregionswithaminimallossofinformation.

Next,wewillusetheweeklyaveragehighwayretailprice($/Gallon)forNo.2UltraLowSulfur(015

ppm)DieselintheEIAnine(9)PADDregions.ThesampledatastartonFebruary5th,2007andendon

May6th,2013(327observations). Eachobservationrepresentstheweeklyaveragepricesinnine

regions:

1. EastCoast2. NewEngland3. CentralAtlantic(PADD1B)4. LowerAtlantic(PADD1C)5. Midwest6. GulfCoast7. RockyMountain8. WestCoast9. California

Theweeklypricesacrossthedifferentregionsarehighlycorrelated:

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Inthistutorial,wellinvestigatethedriversbehindthepricevariationamongthedifferentregions,and

attempttoimplythephysicalrepresentationofthosecomponentsusingtheeachregionsprice

loadings.

ProcessNowwearereadytoconductourprincipalcomponentanalysis. First,selectanemptycellinyour

worksheetwhereyouwishtheoutputtobegenerated,thenlocateandclickontheprincipal

component(PCA) iconintheNumXLtab(ortoolbar).

Theprincipalcomponentanalysiswizardappears.

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Selectthecellsrangeforthefiveinputvariablevalues.

Notes:1. Leaveoutthelastthreeobservations,soourinputdataendsonApril15th,2013.Theremaining

threepointswillbeusedforcomparingtheforecastvalueslateron.

2. LeavetheVariablesMaskfieldblankfornow.Wewillrevisitthisfieldinlaterentries.Next,selecttheOptionstab.

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MakingSenseofDieselPrices 4 SpiderFinancialCorp,2013

Initially,thetabissettothefollowingvalues:

StandardizeInputsischecked.Leavethisoptionchecked. PrincipalComponentOutputischecked. Leaveitchecked. Thesignificancelevel(aka. )issetto5%. Underprincipalcomponent,checktheValuesoption,sothegeneratedoutputtables

includetheprincipalcomponentvaluesfordifferentdates.

InputVariablesisunchecked.Leaveitunchecked.Now,clicktheMissingValuestab.

Inthistab,youcanselectanapproachtohandlemissingvaluesinthedataset(X).Bydefault,any

missingvaluefoundinanyobservationwouldexcludetheobservationfromtheanalysis.

Thistreatmentisagoodapproachforouranalysis,soletsleaveitunchanged.

Now,clickOKtogeneratetheoutputtables.

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MakingSenseofDieselPrices 5 SpiderFinancialCorp,2013

Analysis1. Statistics

Inthetableabove,weshowthevarianceofeachprincipalcomponentandtheproportionoftheinput

(standardized)datasetstotalvariancevariablethatitaccountsfor. Examiningthetablecloser,the1st

twocomponentscapture99.8%ofthedatasetvariation.

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2. LoadingsIntheloadingstable,weoutlinetheweightsoftheprincipalcomponentineachinputvariable:

.

Examiningtheinputvariables(i.e.regionprice)loadingsforthefirstcomponentshowsauniform

loadingforallvariables.Thiscanbeinterpretedasthelevelfactor(pricethatislocaleneutral).

Forthesecondfactor,thepictureisabitdifferent:

ForallPADDregionsintheeast,theloadingisnegative. ForPADDregionsinthewest,theloadingispositive. Gulfcoastsloadingisslightlynegative. Midwestloadingisslightlypositive.

Thisfactorsloadingcanbeviewedasproximityto(oravailabilityof)refinerycapacityorimportports

(example: NewYorkharbor). Thesecondfactorreflectsthecostoftransportationandtaxofthefuel.

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MakingSenseofDieselPrices 7 SpiderFinancialCorp,2013

Note:Theloadingsoftheinputvariablesforthe1stcomponentareverycomparable,so,ineffect,thesecondcomponent(factor)iswhatdrivesthepricedifferentialbetweenthedifferentPADDregions.

3. PrincipalComponentValuesLets

examine

the

values

of

the

first

two

principal

components.

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Thetwotimeseriesexhibitsomeseasonality,althoughitismoreapparentinthesecondfactor.

Furthermore,thefirstprincipalcomponentexhibitsapatternclosetocrudeoilprices.

NOTE:ThelackofanexactmatchmaybeattributedtoothercostsincurredinthemakingofNo.2Ultra

LowSulfurDiesel: labor,energyprices,rawmaterial,etc.Furthermore,refineriesbuildupinventoryof

products(e.g.diesel)inanticipationoftheseasonaldemandpeaks,sotheremaybealag.

4. AddingWTISpotPricesAsalastthoughtontheWTIspotprice,wewillincludetheWTIspotpriceinourinputdatasetandre

examinethe

input

loadings.

Intuitively,

adding

an

input

variable

for

raw

material

price

(i.e.

crude

oil)

withthefinishedproductspricesinthesamedatasetwilllikelyrevealanotherdriver:costof

production.

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Now,wedneedthreedriverstoaccountfor99.8%ofthepricevariation.

IMPORTANT:Theprincipalcomponentsofthenewdatasetarenotnecessarilythesameastheoneswecomputedearlierwithonlythedieselprices.

Letslookattheinputvariablesloadingsineachprincipalcomponent(i.e.driver):

Notes:

1. Theloadingsforthefirstcomponentaresimilartooneswecalculatedearlierwithonlythediesel

prices.

Note

that

the

WTI

loadings

are

slightly

lower

than

their

diesel

counterparts.

Again,

welldesignatethisfactorasthegeneralpricelevel(regionneutral).

2. Theloadingsforthesecondfactorareverydifferentnow,andtheloadingforWTIisnegative(%94.5)whilealltherestarepositive.Wecandesignatethisfactorasthecostofcrackingdiesel

ofcrude.

3. Theloadingforthe3rdfactorisverysimilartotheloadingofthesecondcomponentintheearlierdatasets.Again,theloadingvariesbasedonthelocation(eastvs.west).TheWTI,Gulf

Coast,andMidwestarealmostneutral.

Letsnowplotthefactorstimeseries.

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Ingeneralterms,thefirstandthethirdcomponentareverysimilartothefirsttwocomponentswe

calculatedearlier(w/oWTIinthedataset).

Forthesecondcomponent,wehypothesizethisoneastheproxyofthedieselcrackingcost.

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ConclusionInthistutorial,weexaminedanontrivialapplicationforPCA.Weattemptedtoexplaintheprice

variationamongdifferentPADDregionsbyuncoveringthedrivingforcesbehindtheprices.

Whatsnext?Wementionedearlierthatrefineriesbuildupinventoryofproducts(e.g.diesel)inanticipationofthe

seasonaldemandpeaks,sotheremaybealag.Howdowecapturethisvariable?Futures:wecan

includethefuturepricesofthedieselandcrudeoil.

Why?Intuitively,futurespricesreflectmarketanticipationof(1)futuredemand(2)futurestoragecost,and

possiblyapremiumforsupplyscarcity.

Thisapplication

is

intended

to

give

you

asample

of

how

to

apply

PCA

and

time

series,

as

well

as

how

to

useorinterpretthevariablesloadingsinderivingapracticalproxyforthem.

Insum,PCAisamathematicalprocedurethatNumXLcanhelpyouexecute.Makingsenseofand

interpretingtheresultsiswhereyourexpertiseandintuitionareindispensable.