on stock market index methodology

7/30/2019 On Stock Market Index Methodology

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OnStockMarketIndexMethodology:

UsingPrincipalComponentAnalysisas

BasketSelectionCriterion

JericC.Briones

MelloneyDayeF.AwitEJRannelChristianD.Manalang

Inpartialfulfillmentforthedegree

MasterofAppliedMathematicsmajorinMathematicalFinance

March2013

MathematicsDepartmentAteneodeManilaUniversity


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Nopartofthispapermaybereproducedwithoutpermissionfromthe

authorsand/ortheAteneodeManilaMathematicsDepartment.


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Awit, Briones, Manalang i

M AMF 2012-2013 On Stock Market Index Methodology

ABSTRACT

Currently,thePhilippineStockExchangehaseightindices.However,theseindicesdonot

capturemuchinformationregardingthestockmarketandthelistedstocks.Also,mostoftheselectioncriteriacurrentlyuseddonothavestatisticalbasis.Inlightoftheneedtohavean index or an index methodology that is more objective, while encapsulating moreinformation regarding the market, a review of related literature points out to usingprincipalcomponentanalysis.Thispaperexaminesanindexmethodologywithprincipalcomponentanalysisasthebasic

basketselectioncriterionforthePhilippinestockmarket.Newindicesthatwouldprovidemore information to the investors will also be suggested using financial measures.Specifically,betacoefficients,sustainablegrowthrate,D/EandP/Eratios,andROEwouldbeusedasadditionalselectioncriteriatocapturemoreinformationaboutthestocks.Basedontheresultsoftheanalysis,thispaperconcludesthat,whiletheindicesareeasiertounderstand,abletocapturemoreinformationregardingthemarketandthestock,andofferhigherlogreturns,theyarerelativelymorevolatilecomparedtothecurrentindices.


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Awit, Briones, Manalang ii


TABLEOFCONTENTS

ABSTRACT IINDEXOFFIGURESANDTABLES IV

ACKNOWLEDGEMENT V1.INTRODUCTION 1STOCKMARKETINDICES 1

PHILIPPINESTOCKEXCHANGEINDEX(PSEI) 1ALLSHARESINDEX 1SECTORINDICES 2INDEXCALCULATION 2

BASKETSELECTIONCRITERIA 2

SIGNIFICANCEANDOBJECTIVES 3

PRINCIPALCOMPONENTANALYSISASSELECTIONCRITERION 3OBJECTIVES 4SCOPEANDLIMITATIONS 52.STATISTICALMETHODS,FINANCIALMEASURESANDSPECIALIZEDINDICES 6PRINCIPALCOMPONENTANALYSIS 6

INTRODUCTION 6DEFINITIONOFPRINCIPALCOMPONENTS(PCS) 6DERIVATIONOFTHEPRINCIPALCOMPONENTS(PCS) 7THESINGULARVALUEDECOMPOSITION(SVD)THEOREM 8IMPORTANCEOFSVDTOPCA 9

FINANCIALMEASURES 10

BETACOEFFICIENT 10DEBTEQUITY(D/E)RATIO 10RETURNONEQUITY(ROE) 10PRICEEARNINGS(P/E)RATIO 11SUSTAINABLEGROWTHRATE(G) 11

SPECIALIZEDINDICES 11

FTSEDEFENSIVEINDEXSERIES 11RUSSELLGROWTHANDVALUEINDICES 12

3.METHODOLOGY 13INDEXMETHODOLOGY 13

FINANCIALMEASURECRITERIA 14BACKTESTING 15DATATRANSFORMATION 15FACTORLOADINGS 16BASKETCOMPOSITION 17

INDEXLEVELCOMPUTATION 18


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Awit, Briones, Manalang iii


4.RESULTSANDANALYSIS 19INDEXBASKETS 19

MARKETINDEX 19DEFENSIVEINDEX 21EQUITYINDEX 22GROWTHINDEX 23BASKETCOMPOSITION 23CLASSIFICATIONPERSECTOR 23CLASSIFICATIONPERMARKETCAPITALIZATION 24

INDEXPERFORMANCE 25

INDEXLEVEL 25LOGRETURNS 28INDEXBASKETVOLATILITY 29

FORECASTINGTHEBASKETCOMPOSITION 30

5.CONCLUSION 31SUMMARY 31

RECOMMENDATIONS

32

REFERENCES 33APPENDIXA:RCODEPCAFORLOGRETURNS AAPPENDIXB:RCODEPCAFORVOLUMETURNOVER CAPPENDIXC:RCODEBETAESTIMATION EAPPENDIXD:BASKETCOMPOSITION:SECTOR F

APPENDIXE:

BASKET

COMPOSITION:

MARKET

CAPITALIZATION

G


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Awit, Briones, Manalang iv


INDEXOFFIGURESANDTABLES

Figure1IndexPerformance.....................................................................................................................................................................26Figure2DefensiveIndexLevel........................................................................................................................................................ .......26Figure3EquityIndexLevel......................................................................................................................................................................27Figure4GrowthIndexLevel....................................................................................................................................................................27

Table1DateRangeforPCA......................................................................................................................................................................16Table2ProportionofVarianceofPC1................................................................................................................................................17Table3PCACriteriaRanking...................................................................................................................................................................17Table4MarketIndex...................................................................................................................................................................................17Table5DefensiveIndex.............................................................................................................................................................................18Table6EquityIndex....................................................................................................................................................................................18Table7GrowthIndex..................................................................................................................................................................................18Table8IndexLevels....................................................................................................................................................................................18Table9MarketIndex...................................................................................................................................................................................19Table10MarketIndexVSPSEi...............................................................................................................................................................20Table11TELMarketIndexRanking....................................................................................................................................................20Table12DefensiveIndex..........................................................................................................................................................................21Table13EquityIndex.................................................................................................................................................................................22Table14GrowthIndex...............................................................................................................................................................................23

Table15AverageBasketCompositionPerSector.........................................................................................................................24Table16MarketCapitalizationClassifications................................................................................................................................24Table17AverageBasketCompositionsperMarketCapitalization.......................................................................................25Table18GrowthRate..................................................................................................................................................................................27Table19KeyStatisticsoftheLogReturnsoftheIndices...........................................................................................................28Table20IndexBasketVolatilityMeasure..........................................................................................................................................29Table21ForecastedBasketsforMarch2013..................................................................................................................................30Table22BasketCompositions................................................................................................................................................................30Table23BasketDrivers.............................................................................................................................................................................30


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Awit, Briones, Manalang v


ACKNOWLEDGEMENT

Withoutthehelpofcertainindividuals,thegroupwouldnothavebeenabletoconductandfinishthisstudy.Assuch,thegroupwouldliketoacknowledgethesepeople,asatokenoftheirappreciationfortheirhelpandassistance.WithouttheguidanceofMr.AntonyR.Zosa,Dr.EmmanuelA.Cabral,andDr.ElviraP.deLaraTuprio,thegroupwouldnothavebeenabletofindtherightdirectionneededforthisstudy.Without thementoringofMs.MicaEllaN.Cu andMr.MarkFrederickV. Visda, the groupwouldnothaveironedoutthedetailsofthepaper.Becauseoftheircontinuouseffortstocheckeventhesmallestdetails,thegroupwasabletoaddmorevaluetothestudy.

WithouttheperseveranceofMs.ReginaGeorgiaR.Crisostomo,thegroupwouldnothavehadthedataneededtoconductthestudy.Withoutherprovidingallthedatathegroupasked,thisstudywouldnothavepushedthrough.WithouttheguidanceofMr.RamilT.Bataller,thegroupwouldnothavebeenabletofullygraspandunderstandthestatisticalmethodsemployedinthisstudy.Becauseofthegenerosityofthesepeople,thegroupwasabletofinishthisstudy.Becauseoftheirguidance,

thegroupwasabletoconductastudythatwouldhopefullycontributemoretotheunderstandingofstockmarketindexmethodology.


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Awit, Briones, Manalang 1


1.INTRODUCTION

StockMarketIndices

Stockmarket indicesprovide amore efficientwayofmeasuringaparticularsectionof the associated

stockmarket.Whilethere are indicesspecificto aparticular collection ofstocks thatsatisfysomesetcriteria,therearealsoindicesthatmeasurethegeneralmovementofthemarket.Theseindicesarecalledbroadbasedindices.ForthePhilippineStockExchange,thesolebroadbasedindexusedisthePhilippineStockExchangeIndex(PSEi).Nowreachingbreakthroughlevelsbeyondthe6000pointmark,thePSEihasbeenheraldedasthesecondbestperformingindexinAsiaPacific.Asidefromthemainindex,theStockExchangehas severalotherindices. Dependingonwhat the informationthe investorsneed, thePhilippineStockExchangehaseightindicestooffer.PhilippineStockExchangeIndex(PSEi)

BeingthemainindexofthePhilippineStockExchange(PSE),thePSEiiscomposedofafixedbasketof30companies,whoseselectionisbasedonaspecificsetofcriteria.Itmeasurestherelativechangeinthefreefloat1adjustedmarketcapitalizationofthe30largestandmostactivecommonstockslistedatthePSE,basedontheExchangesbasketselectioncriteria.Bygaugingchangesinthestockpricesofselectedlistedcompanies,thePSEiprovidesasnapshotofthemarketsoverallcondition.ThebaselevelofthePSEiwaspeggedat1,022.045points.ThiswasreckonedaccordingtothecloseoftheindexonFebruary28,1990,whichisthePSEisbasedate.TheExchangeadoptedthenamePSEiinApril2006.Inthepast,variouslabelswereusedtorefertotheExchangesmainindex,suchasthePhisixandthePSECompositeIndex.2

AllSharesIndex

Asidefromthemainindex,theStockExchangehasabroaderindex,theAllSharesIndex,whichincludesinitsbasketalllistedcommonstocksoftheExchange,excludingthoseintheSmallandMediumEnterprise (SME)Board. Instead of free floatadjustedmarket capitalization, this indexmeasures therelativechangeinfullmarketcapitalization.Giventhesequalitiesoftheindex,AllSharesIndexcoversmoreinformationaboutthemarket.Assuch,investorswhowishtoknowmoreaboutthemarket,andnotjustthestateofthebluechipcompanies,canlookatthisindex.

1Freefloat,alsoknownaspublicfloat,referstotheportionoftheoutstandingsharesthatarefreelyavailableandtradableinthemarket,orthoseshareholdings,whicharenonstrategicinnature.2SeeThePhilippineStockExchange,Inc.RevisedPolicyonIndexManagement(MemorandumNo.20110181)


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SectorIndices

Uponenlistment intheExchange, each company isassigned tooneofthesixsectorsof theExchange.Eachsectorhasanassociatedindex,whichtracksthesectorsperformance.Thesixindicesarethe(1)FinancialsIndex;(2)IndustrialIndex;(3)HoldingFirmsIndex;(4)PropertyIndex;(5)ServicesIndex;

and(6)Mining&OilIndex.Giventhenatureoftheseindices,sectorindicescovermorespecializedinformationaboutits respective sector.Hence, investors interested ina specific sectorcan lookatitssectorindextoknowmoreaboutitscondition.IndexCalculation

Foranytradingday,theindexiscomputedbyderivingthechangeintheindexcomponentscurrenttotalfreefloatadjustedmarketcapitalizationfromthebasetotalfreefloatadjustedmarketcapitalization,andmultiplyingthischangewiththepreviousdaysclosingindexlevel.Mathematically,thisisgivenby

Index

, Indexwhere=numberof constituentsoftheindex,=lasttradedpriceofcompanyatday,and=numberoffreefloatsharesofcompanyatday3.However,morethantheactual valueof the index,investorsaregenerallymoreinterestedonthereturnsoftheindex.BasketSelectionCriteria

OnlycompanieswithcommonstockslistedinthemainboardofthePSEforatleastsixmonthsduringthereviewperiodareeligibleforinclusioninthePSEi.Thecurrentcriteriaforlistedcompaniestobeeligible

forthePSEi,asstatedinPSEsrevisedpolicyonindexmanagement,areasfollows:1. FreeFloat.Acompanysfreefloatsharesmustbe12%ofitsoutstandingsharesattheendofthe12monthperiodinreview.

2. Liquidity.Thestocksofthecompanymustrankamongthetop25%intermsofmediandailytradingvaluepermonth4innineoutofthetwelvemonthperiodinreview.

3. Full Market Capitalization. Companies that pass the free float and liquidity eligibilityrequirementarerankedfromhighesttolowestaccordingtotheirfullmarketcapitalization,insteadoffloatmarketcapitalization.Therankingdoesnotconsiderthesectorrepresentationofcompanies,andtreatseligiblecompaniesequally.

3Thiscanalsobecalculatedbymultiplyingthenumberofoutstandingsharesofcompanyatdaywiththefreefloatfactorofcompanytobeappliedtoeachsecurity,expressedasanumberbetween0and1,where1represents100%freefloat.ForAllSharesIndex,insteadoffreefloat, isequaltothefullmarketcapitalization.4Thisiscomputedbyrankingeachdailytradingvalueintheregularboardofacompanysstockandselectingthemiddlevalue


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The30largestcompaniesbasedonfullmarketcapitalizationaretobeincludedinthePSEibasket.Thenext five companies shall form the reserve list. On the other hand, the sector indices have a fewerselectioncriteria5,andhasnolimitonthenumberofmembersofbasketoftheirrespectiveindices.

Significanceand

Objectives

GiventhecurrentindicesoftheExchange,aswellastheinformationtheycarry,thereisaneedtohaveotherindicesthatwillcovermoreinformationaboutthemarket.Alternatively,giventhecurrentbasketselectioncriteria,theremayalsobeaneedtoaddmorecriteriaintheselectionprocesstohavetheindexcovermore information.Assuch, inlinewith the PSEsgoalofattracting investor interest, this studydelves into the creation of possible indices which may be of relevance to various investor types.Alongsidethis,modificationstomakethestockindexmethodologymoreobjectivearealsointroduced.Thisisimportantasthecurrentselectioncriteriaarerathersubjectivesincethenumbersusedinthecriteriadonothavestatisticalbasis.PrincipalComponentAnalysisasSelectionCriterion

Themotivationfortheutilizationoftheprincipalcomponentanalysis(PCA)inthisstudyisnotforeigntopreviousmethodologiesdirectedtowardsthedevelopmentof"optimal"stockindices.AstudyconductedbyFeeneyandHester(1964), Stock Market Indices:A Principal ComponentAnalysis,ontheDowJonesIndustrial Average (DJI)contrasted against three indices constructedbasedondata generated by theperformanceofPCAdelvedintotheefficacyofthesaidindicesindeliveringinformationasrelevanttoinvestors.Workingundertherationalethatstockmarketindicesareeffectiveonlyinsofarastheyrelate

informationaboutthemarket(uponwhichinvestorscomparetheirrespectiveportfolios),PCAiscapableofcapturing the desired informationbyreducing the dimensionalityof themovement ofstockpricesand/or stock price returns while allowing for the retention of the variability of the said elements.Whereasweightedindicesgenerallyassumeanapriorisetofweightsforstocks,intheutilizationofPCAatthearrivalofamarketreflectiveindex,weightsareperceivedasinternallydeterminedastheyaredrivenbystockpricevolatility,andarethusdynamic.PCA,therefore,allowsforaneliminationofstatic,arbitraryandexternallydrivenassumptionsthatareusuallyusedinthecraftingofmarketindices.Similarly,Amenc,Chan,Goltz,Martellini(2010)presentedintheirpaper EfficientEquityIndices:Towardsa New Paradigmanindexmethodologythatisriskefficient.Incorporatingestimatesofriskinindexmethodologyisimportantsoanestimateofthecovariancematrixisrequired.However,computingthecovariancematrixusingpastreturnobservationsoftenleadstoestimationerror,resultinginpooroutofsampleperformance.Thisismainlyattributedtothelargenumberofparameterstoestimateinthe

5Sectorindicesonlyhavetwoselectioncriteria:liquidityandtradability.


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covariancematrix,andthepresenceofnoiseinherentindata.Thisproblembecomesseverewhendealingwithalargenumberofassets,sincemostfinancialportfoliosconsistofmultipleassetsandtheirreturnsdependconcurrentlyonmanyeconomicandfinancialvariables.Hence,itisimportanttocomeupwithamodelthatwillreducethedimensionalityoftheestimationproblemwhilegettingridofthe

noiseintheprocess.Inpractice,observedreturnseriesoftenexhibitsimilarcharacteristicswhichmightbedrivenbysomecommonsources,oftenreferredtoascommonfactors.Whilefactormodelscanbeusedtodescribethereturnsthroughitsexposurestocommonriskfactors(e.g.,macroeconomicvariables),one alternative istoavoid taking aviewonwhich factorsmatter, and torelyon statisticalfactoranalysistoextractfactorsfromthedata.Principalcomponentanalysisisastatisticalmethodwhichgeneratesfactorsaslinearcombinationsofconstituentstocksreturns.Technically,thesecomponentshavetheadvantageofsummarizingthemaximumamountofinformationcontainedinthedata,withalownumberofuncorrelatedfactors.Sincetheprincipalcomponentsarelinearcombinations,theycanalsobeinterpretedasreturnstoportfoliosofconstituentstocks.Typically,thefirstprincipalcomponent

closely resembles the average return of constituents since it is a roughly equally weighted linearcombinationofthestockreturns.Hence,thiscomponentmightrepresentthegeneralmovementofthestockmarketandcanbeinterpretedasamarketcomponent.Objectives

BasedonthefindingsofFeeneyandHester(1964)andAmenc,Chan,Goltz,Martellini(2010),thispapershalldiscussusingprincipalcomponentanalysis(PCA)asabasketselectioncriterioninthePhilippinestockmarketsetting.GiventhenatureofPCA,theresultsofthesaidanalysiswillleadtotheidentification

ofmarketdrivers.Thiscreatesforamorestringentandobjectivecriteria,shiftingoutthearbitrarinessoftheexistingrulesforbasketselection.For the creation of indices containing specialized information, the paper looks into other financialmeasuressuchasbeta,anddebtandequityratios,amongothers.Thecreationofalternativeindiceswhichmeasureotherareasofthemarketthatarecurrentlyunaccountedforisrelevantnotonlyintherealizationofthegoalofattractinginvestors,butalsointhecreationofamorecompetitivemarketrelativetootherstockexchangeswhichhavelongdevelopedindicesthatcatertodifferentareasofinterest.Afterwhich,thenewindiceswouldbeevaluatedtodeterminehowwelltheywouldperformin

termsoftheirgrowthrateandlogreturns.Whilethemainobjectiveofthispaperistocreatenewindices,havingindicesthatwouldoutperformthecurrentsetwouldbebeneficialforthisstudy,astheseindiceswouldbeconsideredbetternotonlyintermsofmethodologyemployed,butalsointermsofreturns.Withthisobjective,therestofthepaperwillbedividedasfollows:Section2discussesprincipalcomponentanalysis, including the derivationand selection of the principal components, the different


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financialmeasuresthatwouldbeusedasselectioncriteria,andthemethodologyofcomparableandrelevantspecializedindicesfromotherexchanges;Section3detailsthebasketselectionmethodologyfortheproposedindices;Section4analyzesthemethodologypresentedintheprevioussection,aswellastheperformanceoftheirassociatedindexlevels;andSection5summarizesthispaper,aswellasprovide

somerecommendationsforimprovingtheproposedmethodology.ScopeandLimitations

Giventheobjectivesofthispaper,severallimitationshavetobeconsidered.First,thisstudyperformsprincipalcomponentanalysisoncommonstocksonly.Othertypesofsecuritiessuchaspreferredstocks,warrants,andPhilippineDepositReceipts(PDRs)areomittedfromthedataset,asthesesecuritiesarenotasliquidasthecommonstocks.Second,thispaperisfocusedoncreatingnewindexmethodologiesthatarebasedprimarilyonprincipalcomponentanalysis.Assuch,allothercriteriaofthecurrentbasketselectionwillnotbeusedforthemethodologyunderstudy,unlessotherwisestated.Furthermore,establishingthecredibilityofprincipalcomponentanalysisasbasketselectioncriterionwillnotbediscussed indetail. Third, this paper shallbe limited to introducing four new indices. Otherpossiblevariations,asidefromthefour,willnotbediscussed.Otherlimitationsincludetheconstraintsbroughtaboutbydataavailabilityandaccessibility,suchasthecollectionofhistoricalbetasandstandardizedratios.Likewise,incasesoffinancialmeasuresnotreadilyavailable,thenthesemeasureswouldbecomputedusingstandardformulasandavailablemarketdata.Hence,somecomputedmeasuresmaybedifferentfromthosereportedbyfinancialinstitutionssuchasBloombergandReuters.Lastly,sincetherecomposition dates and the date range of the data set subjected tothe analysis do notmatch, it is

assumedthattheresultswouldholdoneffectivedatesofthebasketrecomposition.Thisassumptionisgroundedonthefactthatstocksaremartingales.Assuch,theexpectedvalueofastock,conditionaloninformationknownuptotoday,isthepriceofthestocktoday.Asthemarketdatausedinthispaperwereobtainedduringabullstockmarket,interpretationsandanalysisshouldbeseeninlightofthesaidmarketcondition.Sincethereisnodatasetthatcouldrepresentabearmarketcondition,comparingtheresultsduringabullmarketwiththeresultsduringabearmarketisnotpossible;thatis,itwouldnotbepossibletoseetheperformanceoftheproposedindicesduringabearstockmarket.


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2.STATISTICALMETHODS,FINANCIALMEASURESAND

SPECIALIZEDINDICES

PrincipalComponentAnalysis

Introduction

Thecentralideaofprincipalcomponentanalysis(PCA)istoreducethedimensionalityofadatasetconsistingofalargenumberofinterrelatedvariables,whileretainingasmuchvariationpresentinthedatasetaspossible.Thisisachievedbytransformingthecurrentvariablestoanewsetofvariables,theprincipalcomponents(PCs),whichareuncorrelated,andwhichareorderedsothatthefirstfewretainmostofthevariationpresentinalloftheoriginalvariables.Inmathematicalterms,itsbasicaimistodescribethevariationinasetofcorrelatedrandomvariables,

, , , ,intermsofanewsetofuncorrelatedvariables,, , , ,where1 ,eachofwhichis a linear combination of the variables. The new variables are derived in decreasing order ofimportance.Thismeansthataccountsforasmuchasthevariationintheoriginaldataamongstalllinearcombinationsof, , , .Thenischosentoaccountforasmuchastheremainingvariation,subjecttobeinguncorrelatedwith, and soon. In this process, thenew set ofvariables called theprincipal components, , , , , are derived such that the following properties hold: var var varand, , , areuncorrelated.DefinitionofPrincipalComponents(PCs)

Let , , , bea 1vectorofrandomvariables.Assumethatallsecondmomentsofexist.Let cov.Assumeforsimplicitythat 0.Thefirstprincipalcomponent,,isdefinedby

where , , , ,suchthatvar ismaximum.Thesecondprincipalcomponent,,istherandomvariabledefinedby

where , , , ,suchthatandareuncorrelatedandvar ismaximum.


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Ingeneral,theprincipalcomponent,istherandomvariablesuchthat1. where , , , 2. , , , areuncorrelated3. var ismaximum

DerivationofthePrincipalComponents(PCs)

First Principal Component. Consider the first principal component, suchthatvar ismaximum.Notethatthemaximumwillnotbeachievedforfinite soanormalizationconstraintisneeded.Theconstraintthatwillbeusedinthederivationis 1, thatis,thesumofsquaresofelementsofequals1.Otherconstraints,suchasmax 1,maybeusedhowever itleadsto amoredifficult optimizationproblem,anditwillproduce aset ofderivedvariables differentfromthePCs.

Tomaximizevar subjecttotheconstraint 1, the usual approach is to use thetechniqueofLagrangemultipliers.Maximize

1whereisaLagrangemultiplier.Differentiatingwithrespecttogives

2 2

where is the identity matrix. Hence, is an eigenvalue of andisthecorrespondingeigenvector.Todecidewhichoftheeigenvectorsgiveswithmaximum variance, note that thequantitytobemaximizedis

since 1.Somustbeaslargeaspossible.Thus,var var ,whereisthelargesteigenvalueof,andisitscorrespondingeigenvector.SecondPrincipalComponent.Now,considerthesecondprincipalcomponentdefinedby suchthatvar ismaximum,and and areuncorrelatedwhichisequivalentto

cov, cov

,

0.Notethatcov,


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Ifisthelargesteigenvalueandisitsassociatedeigenvector,then 0.Tospecifyzerocorrelationbetweenand,anyofthefollowingequationscouldbeused:

0 0

0 0Using 0asconstraintforzerocorrelationand 1asnormalizationconstraint,thequantitytobemaximizedis

1 whereandareLagrangemultipliers.Differentiatingwithrespecttogives

2 2

2

andmultiplyingthisequationby gives

2

Since 0and 1,theequationgives 0.Therefore,

Soisaneigenvalueofand isthecorrespondingeigenvector.Again, ,so is tobeas

largeaspossible.Notethattheeigenvaluesof

areunique.If not, implyingthat ,whichviolatestheconstraint 0. Hence, var var , whereisthesecondlargesteigenvalueof,andisitscorrespondingeigenvectorof.

Principal Component.Ingeneral,theprincipalcomponentofis andvar var , where is thelargesteigenvalueof,and is the correspondingeigenvector.TheSingularValueDecomposition(SVD)Theorem

Theorem. Letbe an matrix measured about theirmeans i.e., 0.TheSingularValueDecompositiontheoremstatesthatcanbewrittenas

where

isan matrixandisan matrixsuchthat and


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isan diagonalmatrixistherankof

ImportanceofSVDtoPCA

TheimportanceoftheSVDistwofold.First,itprovidesacomputationallyefficientmethodoffindingthePCs.Itisclearthatifthereexist,,andsatisfying ,thenandwillgivetheeigenvectorsandthesquarerootsoftheeigenvaluesof,andhencethecoefficientsandstandarddeviationsof theprincipalcomponentsforthesamplecovariancematrix.Inaddition,italsoyields,thestandardizedversionofPCscores.Toshowthis,multiply ontherightby toget ,since .Butisan matrixwhosecolumnconsistsofthePCscores forthePC.ThePCscoresarethereforegivenby

for 1,2, , , 1,2, , .Inmatrixform, ,or

.Thevarianceofthescoresforthe

PCis , 1,2, , .Notethatheredenotesthe eigenvalueof ,sotheeigenvalueofis

.Therefore,thescoresgivenbyaresimplythosegivenby,butscaledtohavevariance

.Second,itprovidesadditionalinsightintowhataPCAactuallydoes,anditgivesusefulmeans,bothgraphicalandalgebraic,ofrepresentingtheresultsofaPCA.Notethateachelementofcanbeexpressedas

where ,arethe, ,, elementsof,,respectively,and isthediagonalelementof.Thuscanbesplitintoparts

for 1,2,,,correspondingtoeachofthefirstPCs.IfonlythefirstPCsareretained,then

providesanapproximationto .Infact,givesthebestpossiblerankapproximationto ,inthesenseofminimizing

whereisanyrankapproximationto.


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FinancialMeasures

BetaCoefficientBetacoefficientisametricthatshowstheextenttowhichagivenstocksreturnsmoveupanddownwiththe stock market. In other words, betameasures a stocks volatility the degree to which its price

fluctuatesinrelationtotheoverallmarket.Itgivesasenseofthestocksmarketriskcomparedtothegreatermarket.Thismeasureiscalculatedusingregressionanalysis.Dependingonthevalueofbeta,thefollowinginterpretationscanbemade:

1. Negative beta. Companies having beta less than 0, which is possible but highly unlikely,indicateaninverserelationtothemarket.

2. Beta of 0.Regardlessofwhichwaythemarketmoves,companieswithbetaof0remainunaffected.

3. Beta between 0 and 1

.Companieswithvolatilitieslowerthanthemarkethaveabetabetween0and1.4. Betaof1.Abetaof1representsthevolatilityofthegivenindexusedtorepresenttheoverall

market,againstwhichotherstocksandtheirbetasaremeasured.Ifastockhasabetaofone,itwillmovethesameamountanddirectionastheindex.

5. Betagreaterthan1.Stocksthathaveabetagreaterthan1havegreaterpricevolatilitythantheoverallmarket,andaremorerisky.

DebtEquity(D/E)Ratio

D/Eratio TotaldebtCommonequityDebttoequityratioisameasureofacompanysfinancialleveragecalculatedbydividingitstotaldebtbycommonequity.Itindicateswhatproportionofdebtandequitythecompanyisusingtofinanceitsassets.AhighD/Eratiogenerallymeansthatacompanyhasbeenaggressiveinfinancingitsgrowthwithdebt.Thiscanleadtovolatileearningsduetoadditionalinterestexpense.ReturnonEquity(ROE)

ROE Netincome

Commonequity

Returnon equitymeasuresa firmsprofitability bycalculatinghowmuchprofita companygenerateswiththemoneyshareholdershaveinvested.Ahighreturnonequityoftenreflectsthefirmsacceptanceofstronginvestmentopportunitiesandeffectiveexpensemanagement.However,if thefirmhaschosentoemploya levelofdebt that ishighbyindustrystandards, ahighROEmightsimplybetheresultofassumingexcessivefinancialrisk.


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PriceEarnings(P/E)Ratio

P E ratio PricepershareEarningspershare Pricepershare

NetincomeCommonsharesoutstanding

Thepriceearningsratioshowshowmuchinvestorsarewillingtopayperpesoofreportedprofits.This

ratiocanalsobeseenasareflectionofthemarketsoptimismconcerningafirmsgrowthprospects.Generally, a high P/E means that investors are anticipating higher earnings growth in the futurecomparedtocompanieswithalowerP/E.SustainableGrowthRate(g)

g ROE 1DividendpayoutratioSustainablegrowthrateisthemaximumgrowthratethatafirmcansustainwithouthavingtoincreasefinancialleverage.It isthemostrealisticestimateofthegrowthrateofa companysearnings,assuming

thatthecompanydoesnotalteritscapitalstructure.SpecializedIndices

FTSEDefensiveIndexSeries

The FTSE Defensive Index Series is designed to be relatively insensitive to the economic cycle. Itsmethodologymakesuseof theIndustryClassificationBenchmark(ICB)subsectors,whichclassifiesthesubsectorsasDefensive,CyclicalorNeutral,basedonanintuitiveeconomicrationale.DefensiveIndexcalculatedoverthefirstyear(basedontheclassificationatthebeginningofthefirstyear)arereferredtoasthe'Ideal'index.Atsubsequentannualreviews,thesubsectorclassificationisreviewedandthesubsectorscomprisingeach'Ideal'indexareupdated.AsubsectorpreviouslyclassifiedaseitherCyclicalorNeutralthathasacorrelationwiththe'Ideal'DefensiveIndexthatisgreaterthan0.5,andamarketbetalower than0.5, and a volatility less than 90%of the volatilityof the 'Ideal'DefensiveIndex,willbereclassifiedasDefensiveattheannualreview.Ontheotherhand,ifasubsectorthatisclassifiedasDefensivehasabetaabove1,anegativecorrelationwiththe'Ideal'DefensiveIndex,andvolatilitygreaterthan110%ofthevolatilityofthe'Ideal'DefensiveIndex,itisremovedfromtheDefensiveIndex.Iflessthan10subsectorsarerepresentedintheDefensiveindex,eachneutralsubsectorisrankedbybetaandvolatilityindescendingorder,andcorrelationwiththe'Ideal'Defensiveindexinascendingorder.The

compositerankofeachneutralsubsectorisdefinedasthesumofthethreerankings.SubsectorswiththehighestcompositerankareaddedtotheDefensiveindexsuchthataminimumof10subsectorsarealwayspresentintheDefensiveindex.


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RussellGrowthandValueIndices

TheRussellGrowthIndexisconstructedtoprovideacomprehensive,unbiased,andstablebarometerofthemarket.Itiscompletelyreconstitutedannuallytoensurenewandgrowingequitiesareincludedandthattherepresentedcompaniescontinuetoreflectgrowthcharacteristics.

Last2011reconstitution,Russellstartedusingthreevariablesinthedeterminationofgrowthandvalue.Onthevalueside,adjustedbooktoprice(B/P)ratioisused,whileon thegrowthside,theInstitutionalBrokers' Estimate System (I/B/E/S) forecast mediumterm growth (2 years) and sales per sharehistoricalgrowth(5years)areutilized.Foreachbaseindex,stocksarerankedbytheaforementionedfinancial measures. These rankings are converted to standardized units, where the value variablerepresents50%ofthescoreandthetwogrowthvariablesrepresenttheremaining50%.Thesearethencombinedtoproducea compositevalue score(CVS).Stocksare thenrankedby theirCVS,andanonlinearprobabilityalgorithmisappliedtotheCVSdistributiontoassigngrowthandvalueweightstoeachstock.Ingeneral,astockwithalowerCVSisconsideredgrowth,astockwithahigherCVSisconsideredvalueandastockwithaCVSinthemiddlerangeisconsideredtohavebothgrowthandvaluecharacteristics,andisweightedproportionatelyinthegrowthandvalueindex.Stocksarealwaysfullyrepresentedbythecombinationoftheirgrowthandvalueweights.Forinstance,astockthatisgivena20%weightinaRussellvalueindexwillhavean80%weightinthecorrespondingRussellgrowthindex.


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3.METHODOLOGY

Inusingtheprincipalcomponentanalysis(PCA)asbasisforbasketselectioncriterion,anewindexmethodologywillbepresentedfirst.Afterwhich,theproposedmethodologyshallundergobacktesting.Usinghistoricaldata,theproposedmethodologywillbeimplemented,andtheresultingbasketofeachindexwillbecomparedtotheactualbasketforthegivenperiodofacomparableindex.Lastly,theindexleveloftheresultingbasketforeachofthenewindicesformedshallbecomputed,comparedwhenpossible,andanalyzed.

IndexMethodology

Inusingtheprincipalcomponentanalysis(PCA),theproposedindexmethodologywillhavethreephases.Thefirstphaseinvolvescarryingouttwoprincipalcomponentanalyses:aprincipalcomponentanalysisonthereturnsof all listed stocks intheExchange,anda principalcomponent analysison the volume

turnoverofallstocks.Thisshallserveasthefirsttwocriteriaforthebasketselection.Tocaptureasmuchmarketinformationasavailable,alltradedstocksduringrecompositionperiodshallbeincludedintheanalysis,includingthosethatweredelistedorenlistedinthemiddleoftheconsideredperiod.6Anindexbasedonlyontheresultofthefirstphasewillbecreated,andthiswillbecalled MarketIndexasthisindexismarketdriven.After which, additional criteria that will define the index will be considered in the second phase.Dependingonthedesirednatureoftheindex,differentcriteriamaybeaddedinthisphase.Forthisstudy,threenewindiceswillbeproposed.Toquantifythecharacteristicsofthesethreeproposedindices,financialmeasureswillbeusedascriteria.

1. DefensiveIndex:Anindexmeasuringtheperformanceofdefensivestocks.Thisindexprovidesanoverviewofhowstocksthatprovidestableearningsregardlessofthestateoftheoverallstockmarketperform.

2. EquityIndex:Anindexmeasuringtheperformanceofcompaniesthathaveequityheavycapitalstructure,andwhichprovidehighreturnsforitsshareholders.

3. GrowthIndex.Anindexmeasuringtheperformanceofcompanieswithhighpotentialgrowth,asmeasuredbytheirsustainablegrowthrate.

Lastly,thethirdphaseinvolvesassigningaranktoeachstockbasedonallthecriteriaconsidered.Eachstockwillberankedpercriterion,with1beingassignedtothestockthatbestmeetsthecriterion.After

6Incaseofdelistment,thestockpriceshallbezeroafterdelistment.Incaseofenlistment,thestockpriceshallbezeropriortoenlistment.


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which,astocksrankinthebasketwillbebasedonarithmeticsumofitsranks.Thetop30stockswouldmakeupthebasket.Someadjustmentswillbemadewhenmakingupthebasket:

1. Stocksdelistedinthemiddleoftherecompositionperiodwillnotbeincludedinthebasket.2. IfastockhasanAandB,andoneofthementeredthebasket,thentheothershallenteras

well.However,theywillbecountedasone,eventhoughtheyaretreatedindividually.3. Incasesoftiedstocks,theirperformanceinthesecondphaseshallbeusedtobreakties.Thatis,for each tied stocks, their respective rank per criteria in the second phase are totaled. Thestock/swiththelowestsum/senter/sthebasket.

FinancialMeasureCriteria

DefensiveIndex.Foranindextobedefensive,itsbasketshouldhavedefensivestocks.Recallthatthekey characteristics to identifydefensive stocks are typically low priceearnings (P/E) ratiosand betavalueslessthan1.0.Thus,thethirdandfourthcriterionforthisindexshallbethebetasandP/Eratiosofthestocks,wherelowerbetaandlowerP/Eratioaremoredesirable.However,negativeP/Eratios,indicativeofnegativenetincomeandthusunattractive,arepossible.Similarly,stocksmovingagainstthemarket,asindicatedbynegativebetaswouldnotprovidestableearnings.Hence,stockswithnegativeP/Eratiosand/ornegativebetastockswouldnotbeconsideredinthethirdphase.EquityIndex.Recallthatacompanythathasalowdebtequity(D/E)ratiohasacapitalstructurethatisgenerallyequityoriented.IfthethirdcriterionwouldbelowD/Eratio,thentheresultingindexwouldbethedesiredEquityIndex.Toensurethathavinganequityheavycapitalstructureistotheadvantageof

theinvestors,afourthcriterion,returnonequity(ROE),isadded.Ontheotherhand,itisimportanttoalsoconsider somedebtheavycompanieswhichmayhave incurreddebt toideallyincreasetheir netincomeinthenearfuturethroughexpansion,andasaconsequence,increasethereturnsoftheirshareholders. ComparedwithothercompanieswithhigherD/E ratiobuthavenoplansof expansion,these companies are more attractive for investors. Adding the ROE criterion would make thesecompaniesseekingexpansionthroughdebtbetteroffintheranking.Thus,lowerD/EratioandhigherROEarethedesirablecriteriaforthisindex.Inusingthesefinancialmeasures,notethatanegativeD/Eratioindicatesanegativeequity 7.Assuch,

stockswiththisratiowillbedisregardedinthethirdphasesincethegoalofthisindexistodeterminetheperformanceofstockswithequityheavycapitalstructure.Ontheotherhand,havinganegativeROEisallowablesincethisindexwishestomaximizeROE,hencehavinganegativeratiowouldjustputthestockbelowthelist.

7Assetsarelessthandebt.Hence,equityshouldbenegativetomaintaintheAsset=Debt+Equityrelationship.


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GrowthIndex.Companieswithhighpotentialgrowtharethosethathavehighsustainablegrowthrate.Assuch,thisindexhashighergrowthrateas itssolecriterion.However,itispossibletohaveapositivegrowthratedespitehavingnegativeROE8.Assuch,stockswithnegativeROEandnegativeretentionratio

wouldnotbeconsidered,todisregardcompaniesthatdonotactuallyhavepotentialgrowth.BackTesting

Totesttheeffectivenessofthenewmethodology,historicaldatafrom2008onwardsshallbeusedwhenimplementingtheproposedmethodology.Thebasketshallberecomposedusingthesaidmethodologyonthefollowingpreviousrecompositiondates:May4,2009,November3,2009,May11,2010,November8,2010,May9,2011,September12,2011,March12,2012,andSeptember10,2012,foratotalofeightbasketrecompositions.DataTransformation

Inperforming principalcomponent analysis, dailydata onthepriceand the volume turnoverofeachlisted stock in the Exchange from January 2, 2008 to December 28, 2012 will be used,with severaltransformationsappliedonthedata.Log Return.Fortheanalysisonreturns,eachstockreturnisobtainedbyapplyingalogdifferencetransformationonthedailyclosingpricesofeachstock.Thereturnonstockisdefinedas

ln ln,

whereistheclosingpriceofstockontradingday,and,istheclosingpriceofthesaidstockontheprevioustradingday.Logdifferencetransformationisdonetoremoveanydependenceontheactualvalueofthestock,sinceapplyingtheanalysisdirectlyonthestockpricewillbebiasedtowardsstocksthathavehigherprices.Stockswithhigherpricestendtohavehigherabsolutereturnscomparedtostockswithlowerprice,eventhoughtheirrelativereturnsmaybeotherwise.Also, adjusted stock prices were used so that stock returns are market driven. Doing so effectivelyremoveschangescausedbymanagementdecisions,suchasissuanceofstockdividendstostockholders,changeinparvalue,quasireorganization,stockrightsoffering,etc.

8Iftheretentionratiowerelessthanzero,thengivenanegativeROE,theestimatedgrowthratewouldbepositive.


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Volume Turnover. For the analysisonvolume turnover,eachvolume turnovershallbe expressed aspercentageofitsoutstandingsharesperday.Thevolumeturnoveronstockisgivenby

whereistheactualtradedvolumeofstockontradingday,andisitsoutstandingsharesonthesametradingday.Similartoreturns,thisisdonetoremoveanybiastowardsstocksthathavehighoutstandingsharestobeginwith.

MeanCorrected.Beforeperformingtheanalysis,eachdatasetmustfirstbedemeaned,i.e.,observationsmustbemeasuredabouttheirmeans.ThisisimportantsincetheprincipalcomponentanalysiswillbeutilizingtheSingularValueDecompositionTheorem,whichassumesthatgivenadatamatrix, .FactorLoadings

Inperformingtheprincipalcomponentanalysis,the SingularValue

Decomposition

Theoremshallbeusedtoderivethefactorloadings.Moreover,inapplyingthetheorem,thedatawillnotbestandardized,i.e.,

divide by their respective standard deviations. Standardizing the data will not be necessary as allobservationsareexpressedinthesameunits.Principal component analysis is performed on a specific range of observations based on therecompositiondateconsidered(seeTable1).Sincetheindexmethodologyisonlyinterestedinthefirstfactorloading(orPC1),onlytheproportionofvarianceofthefirstprincipalcomponent,ortheamountofinformationthatcanbeexplainedbythePC1,willbetakenintoconsideration(seeTable2).

Table1DateRangeforPCA

RecompositionDate DateRange

May4,2009 Jan.1,2008 Dec24,2008Nov.3,2009 July1,2008 June30,2009May11,2010 Jan.5,2009 Dec29,2009Nov.8,2010 July1,2009 June29,2010May9,2011 Jan.4,2010 Dec30, 2010

Sept.12,2011 July1,2010 June30,2011March12,2012 Jan.3,2011 Dec29,2011Sept.10,2012 July1,2011 June29,2012


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Table2ProportionofVarianceofPC1

RecompositionDate Returns VolumeTurnover

May4,2009 37.1962% 24.4861%Nov.3,2009 40.0785% 38.3235%May11,2010 37.1590% 32.6911%Nov.8,2010 32.1995% 30.7006%May9,2011 29.4224% 36.6394%Sept.12,2011 81.9857% 59.4350%

March12,2012 73.3162% 40.3616%Sept.10,2012 23.0652% 31.9962%

BasketComposition

Afterperformingtheprincipalcomponentanalysis,eachstockisrankedbasedontheabsolutevalueofitsfactorloading:thehighertheabsolutefactorloadingofastock,thehigheritsrank.AsamplerankingbasedonthefirsttwocriteriafortheMay2011recompositionforthefirsttenstocksisgivenasanexample(seeTable3).

Table3PCACriteriaRanking

Stock Returns VolumeTurnover

AbsolutePC1 Rank AbsolutePC1 Rank

2GO 0.000098 150 0.000037 127AAA 0.000120 143 0.000000 220AB 0.008111 15 0.000006 171

ABA 0.000028 195 0.001176 34ABB 0.009529 11 0.000000 212ABG 0.000000 237 0.000000 239ABS 0.000869 67 0.000034 130AC

0.057474 6 0.000036 128The rankof thestockforthesecondphasedependson thenatureoftheindex,asdescribedearlier.AsamplebasketrankingforthefirstfivestocksforMarch2012recompositionforeachofthefourindicesisalsogivenbelowasexample(seeTables4to7).

Table4MarketIndex

Stock Returns VolumeTurnover BasketRank

AbsolutePC1 Rank AbsolutePC1 Rank Total Rank

2GO 0.000029 87 0.000003 172 259 150AAA

0.000047 69 0.000080 94 163 41AB 0.000053 64 0.000001 211 275 166ABA 0.000001 207 0.000419 48 255 146ABG 0.000246 26 0.000075 97 123 19


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Table5DefensiveIndex

Stock Returns VolumeTurnover Beta Earnings BasketRank

AbsolutePC1 Rank AbsolutePC1 Rank Beta Rank P/E Ratio Rank Total Rank

2GO 0.000029 87 0.000003 172 AAA 0.000047 69 0.000080 94 0.000734 80 AB 0.000053 64 0.000001 211 9,145.68 182

ABA 0.000001 207 0.000419 48 0.000007 24 3.944689 12 291 14ABG 0.000246 26 0.000075 97 0.031382 150

Table6EquityIndex

Stock Returns VolumeTurnover CapitalStructure ROE BasketRank

AbsolutePC1 Rank AbsolutePC1 Rank D/E Ratio Rank ROE Rank Total Rank

2GO 0.000029 87 0.000003 172 2.684451 210 19.291837 222 691 222AAA 0.000047 69 0.000080 94 NSE AB 0.000053 64 0.000001 211 0.005014 5 0.659385 171 451 104

ABA 0.000001 207 0.000419 48 0.205360 63 15.793238 55 373 45ABG 0.000246 26 0.000075 97 0.045133 23 11.529555 217 363 39

Table7GrowthIndexStock Returns VolumeTurnover Growth Basket Rank

AbsolutePC1 Rank AbsolutePC1 Rank GrowthRate Rank Total Rank

2GO 0.000029 87 0.000003 172 19.291837 222 148 201AAA 0.000047 69 0.000080 94 AB 0.000053 64 0.000001 211 0.659385 158 434 171

ABA 0.000001 207 0.000419 48 15.793238 35 290 69ABG 0.000246 26 0.000075 97 11.529555 216 339 100

Afterthebasketranking,previouslydescribedadjustmentswillbemade.Afterwhich,thebasketis

composedonthebasisofitsbasketrankingandtheadjustmentsmade.IndexLevelComputation

Aftercomposingthebasketforeachrecompositiondate,theindexleveliscomputedforeachindex,usingthesamecomputationasthatoftheExchangeindex(PSEi).ThebaseindexvaluewouldbetheExchangeindexvalueonApril30,2008fortheMarketIndex,and1,000forthethreenewindices(seeTable8foryearend index levels). Each basket is effective from the date of announcement, until the nextannouncementdate.

Table8

Index

Levels

Year PSEi MarketIndex DefensiveIndex EquityIndex GrowthIndex

2009 3,052.68 3,815.68 2,179.74 2,230.97 13,039.252010 4,201.14 5,382.42 4,119.56 2,757.23 18,390.782011 4,371.96 5,400.16 4,162.21 2,860.37 18,743.642012 5,812.73 7,911.68 5,938.43 3,854.08 27,911.75


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4.RESULTSANDANALYSIS

IndexBaskets

MarketIndex

Basedontheproposedindexmethodology,thefollowingarethemembersofthebasketforeachrecompositiondatefortheproposedMarketIndex.

Table9MarketIndex

May2009 Nov2009 May2010 Nov2010 May2011 Sep2011 Mar2012 Sep2012

1 AC AGI AEV AEV AEV AEV ABG AGI2 AGI ALI AGI AGI AGI AGI AEV AP3 ALI AP ALI ALI AP ALI AGI AT4 AT AT AP AP AT AP ALI BDO5 BCOR BCOR AT AT BDO BDO AP BLOOM6 BPI BDO BDO BDO BPI BEL BEL BPI

7 BRN BPI BPI BPI CEB BPI CEB CAL8 DMC DMC CPM CPM DMC CEB CMT CHI9 EDC EDC EDC DMC EDC CMT CYBR COL10 GEO FGEN FGEN EDC FGEN DMC DFNN DIZ11 ICT FPH ICT FGEN FPH GERI DMC DMC12 ISM ICT ISM FLI ICT HLCM GERI ICT13 JFC JGS JFC ICT ISM ICT ICT JGS14 LPZ LPZ LIB ISM JGS ISM LIHC LMG15 MARC MARC MBT JFC LPZ LIHC LR MBT16 MBT MBT MEG LIB MARC LR MARC MIC17 MEG MEG MER LPZ MBT MARC MBT MWC18 MER MER MIC MARC MEG MBT MER NI19 MWC OM MPI MBT MPI MER MIC OM

20 OM PAX MWC MEG NI MPI MPI PCOR21 PCOR PCEV NI MER ORE ORE NI PNB22 PX PNB PAX MPI PNB PCOR ORE PXP23 RLC PX PCEV PAX PX PNB PCOR RCB24 SM RLC PNB PX RLC PX PNB RLC25 SMB SCC PX RLC SCC RLC RCB SECB26 SMCB SM RLC SECB SECB SECB RLC SM27 SMPH SMPH SECB SM SM SMB SM SMDC28 URC UBP SPH SMPH SMPH SMC SMC SMPH29 VLL VLL URC URC URC SMPH SMDC UBP30 WEB WEB WEB WEB WEB URC SMPH URC


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CompatibilitywithHistorical Basket.CompatibilityoftheMarketIndexwiththehistoricalbasketofPSEiwasalsoevaluated,i.e.,howmanymembersoftheMarketIndexbasketwereactuallyinthePSEibasketduringthegivenrecompositiondate(seeTable10).

Table

10

Market

Index

VS

PSEi

RecompositionDate Match

May2009 60%Nov 2009 57%May 2010 60%Nov 2010 70%May 2011 67%Sept 2011 60%Mar 2012 53%Sept 2012 50%

Despitehavingahighcompatibilitywiththehistoricalbasketof PSEi,TEL,themostpopularPhilippine

stockandthelargestintheExchangesroster,didnotappearinanyoftheMarketIndexbaskets.Basedfromitsfactorloadings,TELconsistentlyhadoneofthehighestPCforthefirstanalysis.However,italsohadoneofthelowestfactorloadingsinthesecondPCA.Assuch,eventhoughTELwasamarketmoverintermsoflogreturns,itwasnotconsideredassuchintermsofvolumeturnover.ThiscouldbeexplainedbythefactthatTELisoneofthemostexpensivestockinthemarket.Hence,someinvestorswouldratherholdontoit,ratherthantradeitactivelyonadailybasis.Thisattitudewouldthencausethestocktohavealowfactorloadinginthevolumeturnovercriterion.

Table11TELMarketIndexRanking

RecompositionDate Returns VolumeTurnover Final

May2009 1 145 45Nov2009 1 157 55May2010 1 138 39Nov2010 2 166 54May2011 1 196 72Sept2011 5 164 51Mar2012 2 179 55Sept2012 2 174 50


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DefensiveIndex

Basedontheproposedindexmethodology,thefollowingarethemembersofthebasketforeachrecompositiondatefortheproposedDefensiveIndex.

Table

12

Defensive

Index


1 ABA ABA ABA AEV AEV AGI ABA AGI2 AEV AEV AEV AGI AGI AP AEV AP3 AGI AGI AGI AP ALHI APO ANI AT4 AP AP AP BDO AP BCBCB AP

BCBCB

5 APO BHI APO BPI BDO BSC APO BSC6 BKD BRN BHI CMT CEB CMT BSC EEI7 BRN CMT CMT COAT DGTL CPG DMC EW8 CMT COAT DMC DGTL EDC EEI EEI FGEN9 COAT DMC EDC DMC EEI FLI ELI FJP

FJPB10 DMC EEI EEI EDC FGEN IP FDC FLI11 EVER EVER EVER EEI FLI KPM FLI IPO12 FLI FLI FLI FDC FPH LFM IRC IRC13 FOOD LPZ FOOD FGEN GMA7 LOTO ISM JGS14 GMA7 MEG JGS FLI HI MAMAB LPZ LPZ15 KPM OM LPZ FOOD JGS MAKE MAKE MARC16 LPZ PCEV MEG FPH LOTO MEG MARC MBT17 LR PECPECB MPI HI LPZ

OPMOPMB MPI MEG

18 MEG PHA MWC LPZ MAKE ORE NIKL MWC19 MWC PIP OM MEG MEG OV OPM

OPMBORE

20 OPMOPMB PNB PAX MWC MHC PCOR ORE PAX21 PCEV PNX PCEV PNB MWC RFM OV PHA22 PHA RFM PNB POPI OM RLC PCOR PNB23 PIP RLC POPI RCB OV SECB PHA RCB24 PX SMB RLC RLC PX SGI RCB RLC25 RLC SMCB SGI SECB RCB SHNG RLC ROX26 SMCSMCB SMDC SMB SGI RLC SMC SGI SECB27 SMPH SMPH SPH SMPH SECB SMPH SHNG SGI28 VLL UBP TA URC UBP UBP SMDC SOC29 WEB VLL URC V URC V SMPH TA

30 WPI WEB VLL WEB V VUL V UBP


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EquityIndex

Basedontheproposedindexmethodology,thefollowingarethemembersofthebasketforeachrecompositiondatefortheproposedEquityIndex.

Table

13

Equity

Index


1 ABA ABA ABA AEV AEV AEV AEV AP2 AGI AGI AEV AGI AGI AP AP AT3 ALI ALI AGI ALI ANS BCOR BCOR BCOR4 AP AP BCOR AP AP BMM BSC BLOOM5 ATNATNB BCOR

CACAB BCOR ATI BSC CEB BSC

6 BCOR CMT CMT CACAB BCOR CEB CMT CAL7 BKD COAT COAT CMT BMM CMT DMC CHI8 CMT COL COL COL CEB DMC FJP

FJPBCMT

9 COAT DMC CPM CPM CMT HLCM HLCM DMC10 FOOD FLI EDC DMC DMC ICT ICT FJPFJPB11 GMA7 GMA7 FOOD EDC FPH IP ISM GMA712 ISM ICT GMA7 FPH GMA7 ISM LIHC HLCM13 JFC ISM ISM GMA7 HLCM LFM LOTO ISM14 MAC JFC JFC ICT ICT LOTO MAC JGS15 MEG LPZ LOTO ISM ISM LR MARC LIHC16 MWC MAC LPZ JFC JGS MAMAB MIC LMG17 OM MEG MEG LPZ LPZ MWIDE NI MARC18 PCEV OM MWC MEG MAC NI NIKL MWC

19 PERC PCEV PCEV MWC MARC NIKL OPMOPMB NI20 PHA PHA PERC OV NI ORE ORE NIKL21 PIP PIP PHA PCEV OM OV OV ORE22 PSE PX PIP PSE OV PCOR PCOR OV23 PX RLC PX PX PSE PSE PECPECB PAX24 RLC SCC RLC RLC PX PX PHA PSE25 SCC SM SMCSMCB SMPH RLC RLC PSE PX26 SMB SMB SMPH SOC SCC SCC RLC RLC27 SMCSMCB

SMCSMCB SOC STR SMPH SMPH SMDC SCC

28 SMPH SMPH SPH URC SOC STR SMPH SMDC29 VLL VLL URC V URC URC V URC30 WEB WEB WEB WEB WEB WEB WEB WEB


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GrowthIndex

Basedontheproposedindexmethodology,thefollowingarethemembersofthebasketforeachrecompositiondatefortheproposedGrowthIndex.

Table

14

Growth

Index


1 ABA ABA AEV ABS AEV AEV AEV AEV2 AC AGI AGI AEV AGI AGI AGI AP3 AGI ALI ALI AGI ALHI ALHI ALI AT4 ALI AP AP ALI AP ALI AP BCOR5 AP BCOR BDO AP BDO AP CEB BDO6 AT CMT COL BDO CEB BCBCB CMT BPI7 ATNATNB COL DGTL BPI CMT BCOR DMC BSC8 BCOR DMC DMC COL DGTL CEB ICT CAL

9 DMC EEI EDC DGTL DMC CMT ISM DMC10 FOOD FGEN EEI DMC EDC DMC LOTO EEI11 GMA7 FPH FPH EDC EEI ICT MARC GTCAP12 ICT GMA7 ICT FGEN FGEN IP MBT IRC13 ISM ICT ISM FPH FPH ISM MEG ISM14 JFC JFC JFC ICT ICT LOTO MWIDE JGS15 LPZ LPZ JGS ISM ISM MAKE NIKL LPZ16 MBT MBT LPZ JGS JGS MBT ORE MARC17 MEG MEG MEG LPZ LPZ MWIDE PCOR MBT18 MER MER MER MBT MBT NIKL PGOLD MWC19 MWC MPI MWC MEG MWC ORE PNB MWIDE20 PCEV PCEV PAX MWC PNB PCOR PNX ORE21 PHA PNB PCEV PAX PX PNB PRC PAX

22 PX PX PHA PNB RCB PNX PTC PCOR23 RLC RLC PNB PX RLC PX RCB PNB24 SECB SECB PX RLC SCC RLC SCC RCB25 SM SM RLC SCC SECB SCC SECB RLC26 SMB SMCSMCB SECB SECB SMB SECB SM SECB27 SMCSMCB SMPH

SMCSMCB SM SMPH SMC SMB SM

28 SMPH UBP SMPH SMPH UBP SMPH SMC SMDC29 VLL VLL URC URC URC UBP SMDC SMPH30 WEB WEB WEB WEB WEB URC SMPH UBP

BasketComposition

ClassificationperSector

Whenthestocksmakingupthebasketswereclassifiedaccordingtotheirrespectivesectors,stocksfromtheIndustrialsectorgenerallydominatedalloftheindices.Ontheotherhand,MiningandOilwastheleastrepresentedsectorinbothMarketandGrowthIndices,whereasServicesandFinancialshadtheleastnumberofstocksintheDefensiveandEquityIndex,respectively.


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Table15AverageBasketCompositionPerSector

Sector PSEi Market Defensive Equity Growth

Financials 12.16% 15.42% 11.68% 4.79% 16.43%Industrial 27.58% 21.25% 24.99% 25.55% 24.86%HoldingFirms 20.05% 20.83% 22.25% 16.84% 18.35%Property 17.53% 15.83% 18.03% 11.99% 13.45%Services 14.17% 14.58% 11.21% 23.23% 18.74%Mining&Oil 8.52% 12.08% 11.83% 17.61% 8.17%

ComparedwiththeExchangeIndex,theMarketIndexwasmorerepresentativeofthemarket,i.e.,thedifferencebetweenthenumbersofstockspersectorwaslessfortheMarketIndex.Ontheotherhand,giventhatstocksfromIndustrialsectorsaremostlycompaniesthatprovideutilitiesandnecessitiestoindividuals,thenhavingaDefensiveIndexdominatedbystocksfromthissectorwasquiteexpected.

ClassificationperMarketCapitalization

Astocksmarketcapitalization9isclassifiedaccordingtotheconventionoftheMarketingServicesDepartmentoftheExchange.Companiesareclassifiedassmallcapwhentheirmarketcapitalizationislessthan$300M,asmidcapwhentheircapitalizationisbetween$300Mand$1B,andaslargecapwhenitgoesbeyond$1B.Sincethese are expressed inUSdollars,theaverageforeignexchange ratefor thedaterangeoftheobservationsusedintherecompositionwillbeused(seeTable16)toconvertthesetoPhilippinepesos.

Table16MarketCapitalization Classifications

RecompositionDate FOREX SmallCap MidCap LargeCap

May2009 PHP44.47 PHP44.475BNov2009 PHP47.39 PHP47.394BMay2010 PHP47.64 PHP47.637BNov2010 PHP46.61 PHP46.613BMay2011 PHP45.11 PHP45.11BSept2011 PHP43.99 PHP43.986BMar2012 PHP43.31 PHP43.313BSept2012 PHP43.01 PHP43.008B

When the stocks making up the baskets were classified according to their market capitalization,companieswithlargemarketcapitalizationgenerallydominatedmostoftheindices,exceptforthe

Defensive andEquity Indices,whichwereprimarily dominated bysmallcap companies. Onthe otherhand,theleastrepresentedmarketcapitalizationclassificationvariedperindex.

9Theaveragemarketcapitalizationofthestocksduringthedaterangeoftheobservationsusedintherecompositionwasused.


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Table17AverageBasketCompositionsperMarketCapitalization

MarketCapitalization PSEi Market Defensive Equity Growth

SmallCap 19.93% 32.50% 62.55% 44.90% 30.06%MidCap 26.59% 30.00% 21.41% 29.89% 31.42%LargeCap 53.48% 37.50% 16.04% 25.21% 38.52%

Sincesmallercompaniesarelesslikelytobeaffectedbythemarketconditions,thentheDefensiveIndexshouldlikelybedominatedbythesecompanies,whichwaswhathappenedwiththesaidindex.Ontheotherhand,similartowhathappenedwhenstockswereclassifiedpersector,theMarketIndexwasmorerepresentativethanthatofthePSEiwhenstockswereclassifiedaccordingtotheirmarketcapitalization.IndexPerformance

IndexLevel

MarketIndex.ThoughboththeMarket IndexandPSEi follow the sametrend, theMarketIndexgrewfaster(seeFigure1).ThisissupportedbythefactthattheMarketIndexlevelwasalwayshigherthanthePSEilevelfromSept2009onwards.Asidefromthat,performinglinearregressiononbothPSEiandMarketindex,theslopeoftheMarketIndexwashigherthanthatofPSEi(seeTable18).SincethesloperepresentsthegrowthrateoftheindexandtheMarketIndexhasahighergrowthrate,thenMarketIndexgrewfastercomparedtotheExchangeIndex.

Defensive Index.CheckingontheperformanceoftheDefensiveIndex,itsindexlevelhadapositivetrend(seeFigure2).Moreover,fittingastraightlinewouldgiveaslopeof4.791,whichwouldindicate

thattheindexhadarelativelyhighgrowthrate.Furthermore,defensivestocksperformedquitewellinthepreviousyears.Also,itsgrowth ratewas largerthanthatof PSEi,which isexpected,asthis indexmeasuresstockswhichprovidestableearningsregardlessofmarketconditions.

Equity Index.Ontheotherhand,theequityindex,whilehavingasimilarpositivetrend,grewslower(see Figure 3). By fitting a straight line, its growth rate is given as 2.578, which is relatively smallcomparedtotheotherthreeindices.Thisisexpected,asthisindexfocusedoncompanieswithcapitalstructureleaningtowardsequity.Sincesuchcompanieshavemoreequitythandebt,theyaregenerallylessrisky.Assuch,theirexpectedreturnwouldalsobelessthanthoseofriskycompanies.

GrowthIndex.Lastly,theGrowthIndexgrewfasterthananyotherindex(seeFigure4),withtheslopeofthefittedstraightlineequalto22.26.However,thiscouldbeattributedtoitsinitialgrowthratewhichisrelativelyveryhigh.Sincethisindexrepresentsthestockswithhighgrowthrate,thentheindexlevelaffirmsthisfactregardingthestocksincludedinthebasket.Sincethebasketiscomposedofstockswithhighpotentialgrowth,thenhighgrowthrateoftheindexlevelwasanaturalconsequence.


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Figure1IndexPerformance

Figure2DefensiveIndexLevel


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Figure3EquityIndexLevel

Figure4GrowthIndexLevel

Table18GrowthRate PSEi Market Defensive Equity Growth

Slope 3.431 4.973 4.791 2.578 22.26CAGR 31.37% 42.93% 62.31% 44.40% 146.01%


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CompoundedAnnualGrowthRate.Consideringthecompoundedannualgrowthrate(CAGR)10,ortherateofreturnshouldtheinstrumentbeinvestedinarisklessasset,allindiceshadthesameresultasthatoftheslopeofthefittedline,exceptfortheEquityIndex,whichhadahigherratethanthatoftheMarketIndexwhilehavingalowerslope.Ontheotherhand,consistentwithpriorresults,theMarketIndexhad

outperformedthePSEi.LogReturns

Taking theaverage log returnsofPSEiandtheMarket Index, the latterregisteredhigherreturns(seeTable19).ThoughtheMarketIndexmayhadthehigheraverageandmedianvaluesforitslogreturns,itwasmorevolatile,asithadahighermaximumreturnandalowerminimumreturn,andhadhigherstandarddeviation.Though,whenthecoefficientofvariationistakenintoaccount(standarddeviationpermeanreturn,i.e., ),theMarketIndexwaslessvolatilethanthePSEi.

Table19

Key

Statistics

of

the

Log

Returns

of

the

Indices

PSEi Market Defensive Equity Growth

Min 0.05267 0.05959 0.08949 0.06152 0.06307Median 0.00129 0.00152 0.00177 0.00120 0.00290

Max 0.04984 0.05061 0.07510 0.08021 0.06165Average 0.00112 0.00146 0.00198 0.00150 0.00368

StandardDeviation 0.01089 0.01232 0.01400 0.01424 0.01428CoefficientofVariation 9.76577 8.43925 7.07076 9.48121 3.88098

Despite having additional criteria, each index had the same, or at least relatively close, standarddeviations.SincetheseindiceshadthefactorloadingsofthefirstPCAasitsfirstcriterion,thentheywouldlikelyhavethesamevariationcapturedin thesaidprincipalcomponentanaylsis.However,theircoefficient of variations would no longer be approximately equal, as the said coefficients take intoaccounttheaveragelogreturn,whichvariedperindex.Similar tohowtheirrespectiveindex levels performed, the statisticsof the log returns ofmostof theother indices were consistent with their nature. The Defensive Index had the lower coefficient ofvariationofvariationwhilehavingahigheraveragelogreturnwhencomparedtotheMarketIndexandPSEi.Thisisaproofthatthisindexiscapableofprovingstable 11earnings,regardlessofthemarket

condition.Ontheotherhand,theGrowthIndexstillhadthehighestaveragelogreturns,whilehavingthelowestcoefficientofvariation.Theperformanceofitslogreturnsisarealizationofthehighpotential

10Thisisgivenby

1,whereisthenumberofinclusiveyearsconsidered.

11Theearningsaresaidtobestable,asitscoefficientofvariationwasrelativelylowerthanthatoftheMarketIndexandPSEi.


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growththeindexwassupposedtocapture.However,theEquityIndex,thoughhavinglogreturnsbetweenthatoftheMarketandDefensiveIndices,hadahighercoefficientofvariation.Thiswasbecausethe said indexhadagenerally low average returnwhilehaving asimilar standarddeviationwith theotherindices.Furthermore,sincedebtheavystocksareadmitted(aslongastheyhadhighROE),then

basketwouldhadmoreriskinit,thuscausingtheoverallrisklevelofthebaskettogoup.IndexBasketVolatility

Eventhoughastockindexisperformingwell,investorswouldgenerallywantalessvolatilebasket.Theywouldpreferthatchangestothebasketduringrecompositiondateswouldbeminimal.Todescribethevolatilityoftheproposedindex,thefollowingnumberswouldbeconsidered.

1. Retained Stocks. An index basket could be considered less volatile if most of the stockscurrentlyin thebasketwould beretainedin the next recomposition date.However,thisonlymeasureshowmanystockswereretained.Itdoesnottakeintoaccountforhowlongthosestockswouldberetained.Itmaybepossiblethat15stockswouldberetainedinarecompositiondate,andanother20forthenextrecomposition,butthetwosetsof15stockswerenotthesameas,atworst,completelydifferent.Whatisonlysureisthat20stockswereretained.

2. LengthinBasket.Anotherwaytodescribeindexbasketvolatilityisthroughthestocksinthebasket.Abasketisrelativelylessvolatileifthestockscomprisingitappearinthebasketoftenand consecutively. If the stocks length in basket is the number of times it is in a basketconsecutively,thenthelengthinbasketiscloseorapproximatelyequaltothenumberofrecompositionsconsidered,forittobeconsideredlessvolatile.

Takentogether,thetwoaforementionednumbersprovideanoverviewofthedynamicsofthebasket.Thehighertheaverageretainedstocksandaveragestockslengthinbasketisthelessvolatiletheindexis.Thisismainlybecause,asmorestocksareretainedperrecomposition,thelesserchancesofhavingadifferentsetofstocksbeingretainedinthenextrecomposition.Likewise,thelongertheaveragelengththe stockis ina basket consecutively is, the lesser chances ofotherstocksenteringthebasket duringrecomposition.

Table20IndexBasketVolatilityMeasure

PSEi Market Defensive Equity Growth

AverageRetainedStocks

29.43 20 17.86 21.86 22AverageLengthinBasket 5.58 2.87 2.15 2.69 2.96Giventhenumbers(seeTable20),thePSEiwaslessvolatilethananyofthecomposedindex.Similarly,allfour indices were generally volatile, as the number average number of retained stocks was justapproximately20,andtheaveragestockslengthinthebasketwastwobasketrecompositions.ThiscouldbeattributedtothefactthatthefourindiceswerebasedfromthePCAloadings.This,inturn,was


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dependentonthestocksmarketmovements.Thus,everyrecompositionwashighlydependentonthestocks performance, which would then explain why these indices are rather volatile, as theirperformanceis,initself,unpredictableandvolatile.

Forecastingthe

Basket

Composition

ImplementingtheindexmethodologyforobservationsfromJanuary2,2012toDecember28,2012willprovide a forecast for the basket composition on the March 2013 recomposition (see Table 21).Additional information regarding the forecasted basket are also provided, such as the basketscompositions(seeTable22), andwhichstocks aremore likely todrivetheirrespectivebasket, giventheirlargemarketcapitalizationasofDecember28,2012(seeTable23).

Table21ForecastedBasketsforMarch2013

Market Defensive Equity GrowthAEV EDC NIKL AEV EDC MPI ABG DMC PGOLD AEV EEI OREAGI EEI ORE AGI EEI MWC AEV FEU PRC AGI EW PAXALI ELI PGOLD AP EVER NIKL AGI GMA7 PSE AP FGEN PIPAP ICT PIP APO EW PAX AP LRI PX BPI FPH PRC

BLOOM IP PXP BPI FGEN PHA AT MARC RLC CAL ICT RCBBPI LRI RCB BSC FLI PNX BCOR NIKL SCC CHI JGS SECBCAL LTG RLC CAT FPH PRC BSC ORE STI CMT MARC SEVNCHI MEG STI CHI JGS RCB CAL OV URC CPG MEG UBPDIZ MPI UBP CMT LPZ UBP CHI PAX VVT DMC MWC VVTDMC MWC URC DMC MEG VVT CMT PEC

PECBWEB EDC MWIDE WEB

Table22BasketCompositions

Market Defensive Equity Growth

Sector

Financials 10% 13% 3% 17%Industrial 27% 33% 19% 33%HoldingFirms 13% 23% 13% 17%Property 17% 13% 6% 10%Services 20% 10% 29% 20%Mining&Oil 13% 7% 29% 3%MarketCapitalization

SmallCap 27% 30% 26% 27%MidCap 20% 37% 23% 33%LargeCap 53% 33% 52% 40%

Table23BasketDrivers

Market Defensive Equity Growth

SM 16.73% MBT 16.79% JGS 16.90% SM 17.60%BPI 11.79% JGS 12.82% URC 14.97% BPI 12.40%

AGI 11.78% AP 12.55% AEV 10.05%


38/47



5.CONCLUSION

Summary

Thispaperintroducedanindexmethodologythatwasbasedontheresultsofprincipalcomponent

analysis.Thebasicindexmethodologyiscomposedofthreesteps.First,aprincipalcomponentanalysisisappliedonthelogreturnsandvolumeturnoverofthestocks.StocksarethenrankedbasedontheirabsolutePC1loadings.Second,stocksarerankedbasedoncertainfinancialmeasures.Lastly,thestocksarerankedbasedontheirranksonallofthecriteriaused.Certainadjustmentsaremadetoaccountfordelistedstocks,orstockswhichhaveAandBshares.Also,incaseofties,financialmeasuresareusedtobreakthetie.Despitebeingsimple,theproposedmethodologywasmoreobjectiveandhadmorestatisticalbasiscomparedtothecurrentindexmethodology.Thebasisofthebasketwassimplyastocksmarket

movementandfinancialposition.Assuch,thecriteriafortheindiceswereeasiertounderstandandexplain. Themembers of an index basket were simply themarket movers and those that meet thefinancialqualificationsoftheindex,asmeasuredbycertainfinancialmeasures.Whatdifferentiatetheindicesfromeachotherwerethefinancialmeasuresusedasadditionalcriteria.Ofthefourindicescomposed,onlytheMarketIndexwascomparabletoanexistingindex.Thisisbecausethesaidindexattemptstomeasuretheoverallperformanceofthemarketusingthemostactivestocks,similartothenatureofPSEi.Computingfortheirrespectiveindexlevel,thereturnsoftheproposedindexwashigherthanthatofthecurrent.Thestatisticsofthelogreturns,aswellasthegrowthrateoftheindexleveloftheMarketIndexwerebothhigherthanthatofPSEi.Furthermore,whenthebasketcompositionwasanalyzed,theMarketIndexwasmorerepresentativeofthemarketsincethenumberofstockspersectorandpermarketcapitalizationwascloserthanthatoftheExchangeindex.Hence,theMarketIndexhadoutperformedthePSEi.Thethreeotherindiceswereincomparabletoanyotherexistingindex.Computingfortheirrespectivelevel,theirreturnswereconsistenttohowtheyweredefined.However,thiswasnoteasilyobservedintheEquityIndex.Despitehavingaslopeconsistentwithitsdefinition,theCAGRandthestatisticsofits

logreturnshadcontraryresults.WhereasEquityIndexwasexpectedtohavelowerreturnsandlesserrisks,thelogreturnshadahigheraveragethanthatoftheMarketandPSEi,andhadahighercoefficientofvariation,meaningitwasmorevolatile,thusmorerisky.ThiscouldbeattributedtothefactthatstocksincludedinthebasketeitherhavehighD/E,orlowD/EbuthighROE.


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Despiteoutperformingthecurrentindexandbeingmorerepresentativeofthemarketinformation,allfourindiceshadonemajordrawback:theyweremorevolatilethanthatofthecurrent.Thebasketsoftenchangedduringrecomposition.Whiletherewasnothingwrongwithsuch,mostinvestorswouldpreferalessvolatileindexbasket.ThevolatilenatureofthefourindicescanbeattributedtoPCA.SincePCAwas

basedontheirlogreturnsandvolumeturnover,whichisbynaturevolatile,thentheresultingbasketfromthismethodologywouldalsobevolatile.Recommendations

Asidefromthethreeindicesproposed,severalotherindicescouldbeexplored.Thiscanbedonebyconsideringotherfinancialmeasures,suchasdividendyield,returnoninvestment,etc.However,thechoiceoffinancialmeasureshouldbeabletodefinethenatureoftheindexbeingcreated.Also,theresultsoftheprincipalcomponentanalysisshouldstillbeincludedasthefirsttwocriteria.Sincethemethodologyisheavilybasedonprincipalcomponentanalysis,thenitisalsorecommendedtointroduce refinements in the first phase. Consider adding a nonnegativity constraint to the factorloadings,similartowhatwasdonebyAffleckGravesandMoney(1979).Thesaidauthorsusedquadraticprogramming to incorporate such constraint. The reason for the said constraint is that, for someinvestors,thenegativePC1loadingsdonotcarryanyinherentmeaning.Assuch,havingallpositiveloadingswouldmaketheresultsofthePCAacceptabletoawiderrangeofinvestors.Otherpossiblerefinement could be the inclusion of other PC loadings. Their inclusion, and the loadings possibleinterpretation,however,shouldbejustified.

Improvementsinthethirdphasecouldalsobedone.Recallthat,currently,theranksofthestockarejustadded,andthenthesesumsareusedasabasisfortherankinginthethirdphase,i.e.,eachcriteriausedareofequalweights.Thus,itissuggestedtointroducingadifferentrankingsystembasedonthedifferentcriteriaused,where the ranksin eachcriteriondo not haveequalweights. Tomaketheindicesmoreconsistentwithitsdefinition,emphasisshouldbegivenonthefinancialmeasurecriteria.Lastly, incomputing the indexlevel, the current formula ofthePSEiwasused.It isthensuggested toexploreotherwaystocomputeforanindex.Moreso,itisrecommendedtohaveanindexcomputation

thatcouldincorporatethefinancialmeasuresusedinthesecondphase,andnotjustrelyonthestockspricesandfreefloatmarketcapitalization.


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REFERENCES

AffleckGraves,J.,Troskie,C.,&Money,A.(1979),APrincipalComponentIndexSubjecttoConstraints,retrievedfromhttp://www.iassa.co.za/articles/014_sep1979_04.pdf

Amenc,N.,etal.(2010),EfficientEquityIndices:TowardsaNewParadigm,retrievedfromhttp://www.ftse.com/Indices/FTSE_EDHEC_Risk_Index_Series/FTSE_Edhec_Risk_Efficient_Whitepaper.pdf

Beta:Gaugingpricefluctuations.(2012,Nov25),retrievedfromhttp://www.investopedia.com/articles/01/102401.asp

Brigham,E.,&Houston,J.(2009),FundamentalsofFinancialManagementTwelfthEdition,USA:SouthWesternCengageLearning.

Drake,P.,Sustainablegrowth,retrievedfromhttp://educ.jmu.edu/~drakepp/FIN362/resources/sgr.pdf

Feeney,G.,&Hester,D.(1964),StockMarketIndices:APrincipalComponentAnalysis,Pittsburg,retrievedfromhttp://cowles.econ.yale.edu/P/cm/m19/m1905.pdfGroundRulesfortheManagementoftheFTSECyclicalandDefensiveIndexSeries.(2012Dec),retrieved

fromhttp://www.ftse.com/Indices/FTSE_Cyclical_and_Defensive_Index_Series/Downloads/FTSE_Cyclical_and_Defensive_Index_Series_Ground_Rules.pdf

Jolliffe,I.(2002),PrincipalComponentAnalysisSecondEdition,NewYork:Springer.PSE:Recordbreakingperformance,TheManilaTimes,retrievedfrom

http://www.manilatimes.net/index.php/business/topbusinessnews/32935pserecordbreaking

performanceRussellU.S.EquityIndexesConstructionandMethodology.(2012Aug),retrievedfrom http://www.russell.com/indexes/documents/Methodology.pdfTsay,R.(2005),AnalysisofFinancialTimeSeriesSecondEdition,NewJersey:JohnWiley&Sons,Inc.VanHorne,J.,&Wachowicz,J.(2008),FundamentalsofFinancialManagementThirteenthEdition,

England:PearsonEducationLimited.


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Awit, Briones, Manalang A


APPENDIXA:RCODEPCAFORLOGRETURNS

basket PCA = f uncti on( dat e, m, f i rs tDate) {dat e = toStr i ng( dat e)f i l eName = paste( "NewBasket PCA " , dat e, ". csv" , sep="" )

dat a = r ead. csv( f i l eName)

st ocks = c( )count = 1x = nrow( dat a)f or ( i i n 1: x) {

y = toStr i ng( dat a[ i , 2] )i f ( ! ( y %i n% st ocks) ) {

st ocks[ count ] = ycount = count + 1

}}

pri ces = c( )f or ( i i n 1: l engt h( st ocks) ) {

y = dat a[ dat a$Stock==st ocks[ i ] , ] [ , 3]z = dat a[ dat a$Stock==st ocks[ i ] , ] [ , 1]w = l engt h( y)i f ( w==m) {

Dat e = z}i f ( ! ( w==m) ) {

i f ( z[ 1] ==f i rs tDate) {y[ w+1: m] = 0

}el se{

y[ w: m] = yy[ 1: ( m- w) ] = 0

}}pri ces = cbi nd( pri ces, y)

}col names( pr i ces) = st ocks

pr i ces. l = l og( pri ces)pr i ces. d = di f f ( pri ces)

pri ces. demean = t ( t ( pr i ces .d) - col Means( pr i ces .d) )pr i cesPCA = prcomp(pr i ces. demean)

l oadi ngs = dat a. mat ri x(pri cesPCA$rotat i on)

numPC = ncol ( l oadi ngs)t otal SDev = sum( pr i cesPCA$sdev 2)prop=c( )cprop=c( )r esul t PCA = st ocksnamePCA = c( "St ock" )f or ( i i n 1: numPC) {

r esul t PCA = cbi nd( r esul t PCA, abs( l oadi ngs[ , i ] ) )namePCA[ i +1] = paste("PC" , i , sep="")

sum = 0f or (j i n 1: i ) {

sum = sum + pr i cesPCA$sdev[j ] 2}prop[ i ] = pri cesPCA$sdev[ i ] 2/ t otal SDevcprop[ i ] = sum/ t otal SDev

}r esul t PCA = cbi nd( r esul t PCA, st ocks)namePCA[ numPC+2] = "St ock" col names( r esul t PCA) = namePCA

t emp = t ( c( r ep( " " , numPC+2) ) )


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Awit, Briones, Manalang B


sdev = t ( c( "St d Dev", pr i cesPCA$sdev, "" ) )prop = t ( c( "Propor t i on" , prop, " " ) )cprop = t ( c( "Cumul at i ve" , cprop, "" ) )r esul t PCA = rbi nd( r esul t PCA, t emp, sdev, prop, cprop)

newFi l eResul t = paste( "PCA " , dat e, " Resul t . csv" , sep="")wri te. tabl e( r esul t PCA, f i l e=newFi l eResul t , sep=" , " , r ow. names=F)

}

basket Date = c( "2009 May" , "2009 Nov" , "2010 May" , "2010 Nov" , "2011 May" , "2011 Sep" , "2012Mar " , "2012 Sep" , "2013 Mar " )

m = c( 246, 245, 242, 241, 244, 249, 249 , 247, 244)f i rs tDate = c( "1/ 2/ 08" , "7/ 1/ 08" , "1/ 5/ 09" , "7/ 1/ 09" , "1/ 4/ 10" , "7/ 1/ 10" , "1/ 3/ 11" , "7/ 1/ 11" ,"1/ 2/ 12" )

f or ( i i n 8: 8) {basket PCA(basket Dat e[ i ] , m[ i ] , f i rs tDate[ i ] )

}


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Awit, Briones, Manalang C


APPENDIXB:RCODEPCAFORVOLUMETURNOVER

basket PCA = f uncti on( dat e, m, f i rs tDate) {dat e = toStr i ng( dat e)f i l eName = paste( "NewBasket PCA " , dat e, ". csv" , sep="" )


st ocks = c( )count = 1x = nrow( dat a)f or ( i i n 1: x) {

y = toStr i ng( dat a[ i , 2] )i f ( ! ( y %i n% st ocks) ) {

st ocks[ count ] = ycount = count + 1

}}

vol ume = c( )f or ( i i n 1: l engt h( st ocks) ) {

y = dat a[ dat a$Stock==st ocks[ i ] , ] [ , 3]z = dat a[ dat a$Stock==st ocks[ i ] , ] [ , 1]w = l engt h( y)i f ( w==m) {

Dat e = z}i f ( ! ( w==m) ) {

i f ( z[ 1] ==f i rs tDate) {y[ w+1: m] = 0

}el se{

y[ w: m] = yy[ 1: ( m- w) ] = 0

}}vol ume = cbi nd( vol ume, y)

}col names( vol ume) = st ocks

vol ume. demean = t ( t ( vol ume) - col Means(vol ume) )vol umePCA = prcomp(vol ume. demean)

l oadi ngs = dat a. mat ri x(vol umePCA$rotat i on)

numPC = ncol ( l oadi ngs)t otal SDev = sum( vol umePCA$sdev 2)prop=c( )cprop=c( )r esul t PCA = st ocksnamePCA = c( "St ock" )f or ( i i n 1: numPC) {

r esul t PCA = cbi nd( r esul t PCA, abs( l oadi ngs[ , i ] ) )namePCA[ i +1] = paste("PC" , i , sep="")

sum = 0f or (j i n 1: i ) {

sum = sum + vol umePCA$sdev[j ] 2}

prop[ i ] = vol umePCA$sdev[ i ] 2/ t otal SDevcprop[ i ] = sum/ t otal SDev

}r esul t PCA = cbi nd( r esul t PCA, st ocks)namePCA[ numPC+2] = "St ock" col names( r esul t PCA) = namePCA

t emp = t ( c( r ep( " " , numPC+2) ) )sdev = t ( c( "St d Dev", vol umePCA$sdev, "" ) )prop = t ( c( "Propor t i on" , prop, " " ) )


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Awit, Briones, Manalang D


cprop = t ( c( "Cumul at i ve" , cprop, "" ) )r esul t PCA = rbi nd( r esul t PCA, t emp, sdev, prop, cprop)

newFi l eResul t = paste( "PCA " , dat e, " Resul t . csv" , sep="")wri te. tabl e( r esul t PCA, f i l e=newFi l eResul t , sep=" , " , r ow. names=F)

}

basket Date = c( "2009 May" , "2009 Nov" , "2010 May" , "2010 Nov" , "2011 May" , "2011 Sep" , "2012

Mar " , "2012 Sep" , "2013 Mar " )

m = c( 246, 245, 242, 241, 244, 249, 249 , 247, 244)f i rs tDate = c( "1/ 2/ 08" , "7/ 1/ 08" , "1/ 5/ 09" , "7/ 1/ 09" , "1/ 4/ 10" , "7/ 1/ 10" , "1/ 3/ 11" , "7/ 1/ 11" ,"1/ 2/ 12" )

f or ( i i n 8: 9) {basket PCA(basket Dat e[ i ] , m[ i ] , f i rs tDate[ i ] )

}


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Awit, Briones, Manalang E


APPENDIXC:RCODEBETAESTIMATION

bet aRegr ess = f unct i on( dat e) {dat e = toStr i ng( dat e)f i l eName = paste( "StockPri ces " , dat e, " . csv" , sep="")


bet a = c( )nS = ncol ( dat a)pse = dat a[ , 1]st ocknames = names( dat a) [ - 1]

f or ( i i n 2: nS) {stock=c( )st ockA = dat a[ , i ]n = l engt h( st ockA)start = NAend = NAi f ( st ockA[ 1] ==0 | st ockA[ n] ==0) {

start = 1f or (j i n 1: n) {

i f (j ! =n) {i f ( st ockA[j ] ==0 && st ockA[j +1] ! =0) {

start =j +1

next }}i f ( st ockA[j ] ! =0) {

stock = c( stock, st ockA[j ] )}el se i f ( l engt h( st ock) ! =0) {

end =j - 1break

}end =j

}stock = st ockA[ start : end]psei = pse[ start : end]

}el se {

stock = st ockA

psei = pse}b = l m( stock~psei )bet a[ i - 1] = b$coef[ 2]

}

bet aLi st = cbi nd( st ocknames, bet a)newFi l eResul t = paste( "Bet a ", dat e, " Resul t . csv" , sep="")wri te. tabl e( bet aLi st , f i l e=newFi l eResul t , sep=", " , r ow. names=F)

}

basket Date = c( "2009 May" , "2009 Nov" , "2010 May" , "2010 Nov" , "2011 May" , "2011 Sep" , "2012Mar " , "2012 Sep" , "2013 Mar " )

f or ( i i n 1: 9) {bet aRegr ess( basket Date[ i ] )

}


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Awit, Briones, Manalang F


APPENDIXD:BASKETCOMPOSITION:SECTOR

Defensive

Index

May

2009

Nov

2009

May

2010

Nov

2010

May

2011

Sep

2011

Mar

2012

Sep

2012

Mar

2013

Financials 1 2 1 6 6 4 3 6 4

Industrial 8 9 10 10 7 8 4 6 10HoldingFirms 6 5 10 8 6 3 9 8 7Property 7 8 5 4 4 6 7 4 4Services 5 3 2 1 3 2 2 3 3Mining&Oil 3 3 1 0 3 9 6 5 2

EquityIndexMay

2009

Nov

2009

May

2010

Nov

2010

May

2011

Sep

2011

Mar

2012

Sep

2012

Mar

2013

Financials 2 1 1 3 1 1 2 1 1Industrial 10 8 13 9 6 8 4 6 6HoldingFirms 4 5 5 5 8 2 7 6 4Property 5 6 3 5 2 3 3 3 2Services 6 7 6 5 8 8 8 7 9Mining&Oil 4 3 3 3 5 9 8 8 9GrowthIndex

May

2009

Nov

2009

May

2010

Nov

2010

May

2011

Sep

2011

Mar

2012

Sep

2012

Mar

2013

Financials 2 5 4 6 6 5 5 7 5Industrial 8 9 10 6 9 7 7 5 10HoldingFirms 8 6 5 6 5 3 5 7 5Property 5 5 4 4 3 4 4 4 3Services 6 4 5 5 4 6 6 4 6Mining&Oil 2 1 1 2 2 6 3 3 1

Market

Index

May

2009

Nov

2009

May

2010

Nov

2010

May

2011

Sep

2011

Mar

2012

Sep

2012

Mar

2013Financials 2 5 5 4 5 5 3 8 3

Industrial 8 5 8 6 5 8 6 5 8HoldingFirms 6 6 4 7 8 6 8 5 4Property 6 5 3 5 3 5 7 4 5Services 4 4 5 5 4 4 4 3 6Mining&Oil 4 4 4 3 5 2 2 5 4

PSEiMay

2009

Nov

2009

May

2010

Nov

2010

May

2011

Sep

2011

Mar

2012

Sep

2012

Mar

2013

Financials 4 5 4 4 4 3 3 3 4Industrial 11 9 9 8 8 8 8 9 11HoldingFirms 4 5 5 7 7 7 7 7 4Property 5 5 5 5 5 6 6 6 5Services 5 5 6 4 4 4 4 3 5Mining&Oil 3 3 3 3 3 2 2 2 3


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APPENDIXE:BASKETCOMPOSITION:MARKET

CAPITALIZATION

Defensive

Index

May

2009

Nov

2009

May

2010

Nov

2010

May

2011

Sep

2011

Mar

2012

Sep

2012

Mar

2013

SmallCap 23 23 22 15 13 21 21 18 9MidCap 7 5 7 10 8 7 6 3 11LargeCap 2 3 1 5 9 5 4 11 10

EquityIndexMay

2009

Nov

2009

May

2010

Nov

2010

May

2011

Sep

2011

Mar

2012

Sep

2012

Mar

2013


GrowthIndexMay

2009

Nov

2009

May

2010

Nov

2010

May

2011

Sep

2011

Mar

2012

Sep

2012

Mar

2013


MarketIndexMay

2009

Nov

2009

May

2010

Nov

2010

May

2011

Sep

2011

Mar

2012

Sep

2012

Mar

2013


PSEiMay

2009

Nov

2009

May

2010

Nov

2010

May

2011

Sep

2011

Mar

2012

Sep

2012

Mar

2013


on stock market index methodology

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