FINAL THESIS OF THE BACHELOR’S DEGREE IN INTERNATIONAL ...

FINAL THESIS OF THE BACHELOR’S DEGREE IN

INTERNATIONAL BUSINESS AND MARKETING (ESCI-UPF)

PortfolioTheory:OptimalAssetAllocation AUTHOR: Albert Chumilla Pérez

NIA: 101054

DEGREE: International Business and Marketing

ACADEMIC YEAR: 2017-2018 DATE: 15/05/2018 DIRECTOR/S: Bernat Raventós Ruiz

INDEX

1.INTRODUCTION.........................................................................................................................................................12.ABSTRACT...................................................................................................................................................................13.OBJECTIVES................................................................................................................................................................23.1Mainobjective.................................................................................................................................................................................23.2Secondaryobjectives....................................................................................................................................................................2

4.ANALYSISOFTHESUBJECT...................................................................................................................................34.1Theoreticalframework...............................................................................................................................................................34.1.1EfficientMarketHypothesis(HME)......................................................................................................................3

4.1.1.1EMHtesting.Empiricalfindings..........................................................................................................................................44.1.1.2Marketanomalies.......................................................................................................................................................................4

4.1.2Valueinvestingcriterion...........................................................................................................................................54.1.2.1Resultsobtainedbysomevalueinvestors......................................................................................................................6

4.1.3Markowitz’smodel.......................................................................................................................................................64.1.3.1Modelhypothesis.......................................................................................................................................................................64.1.3.2Modelapproach..........................................................................................................................................................................74.1.3.3Efficientfrontier.........................................................................................................................................................................74.1.3.4Modelresolution.........................................................................................................................................................................84.1.3.5Correlationeffect........................................................................................................................................................................84.1.3.6CriticismtoMarkowitz’smodel...........................................................................................................................................8

4.1.4RelationshipbetweenvalueinvestingandMarkowitz’smodel...............................................................84.2Practicalapplication...................................................................................................................................................................94.2.1Previousconsiderations............................................................................................................................................9

4.2.1.1Timehorizon................................................................................................................................................................................94.2.1.2Originofdataandobservations...........................................................................................................................................94.2.1.3Benchmark.................................................................................................................................................................................10

4.2.2Assetselection..............................................................................................................................................................104.2.2.1Sectorcorrelations.................................................................................................................................................................104.2.2.2Selectedindicatorsandscoringsystem........................................................................................................................104.2.2.3Selectedassets..........................................................................................................................................................................11

4.2.3Markowitz’smodelresolution..............................................................................................................................114.2.3.1Calculationoftheexpectedreturnandvolatility......................................................................................................114.2.3.2Correlationmatrix..................................................................................................................................................................114.2.3.3Annualizedvariance-covariancematrix.......................................................................................................................124.2.3.4Expectedportfolioriskandreturn..................................................................................................................................134.2.3.5Efficientfrontiercalculation...............................................................................................................................................134.2.3.6Graphicalrepresentationoftheefficientfrontier.....................................................................................................15

4.2.4Backtesting....................................................................................................................................................................154.2.4.1Evolutionofcornerportfolios...........................................................................................................................................164.2.4.2Portfolioindicators.................................................................................................................................................................174.2.4.3Distributionofreturns..........................................................................................................................................................18

5.CONCLUSIONS.........................................................................................................................................................196.BIBLIOGRAPHY......................................................................................................................................................20ANNEXES.......................................................................................................................................................................21Annex1.EUROSTOXX50at31/03/2014................................................................................................................................21Annex2.Sectorscorrelationmatrix..........................................................................................................................................22Annex3.Selectedindicators.........................................................................................................................................................22Annex4.Scoringtable.....................................................................................................................................................................23Annex5:Cornerportfolios.............................................................................................................................................................24Annex6.Distributionofreturns..................................................................................................................................................26Annex7.Financialstatementsinformation...........................................................................................................................30Annex8.ExcelSolver’sworksheet..............................................................................................................................................31

1

1.INTRODUCTIONThe objective of this paper is to build a set of efficient portfolios to eventually beat the

EUROSTOXX50benchmark.Firstofall,fiveassetsbelongingtothisbenchmarkwillbeselected

usingthevalueinvestingcriterionand,subsequently,HarryMarkowitz’sportfoliooptimization

modelwillbeapplied.Oncetheefficientportfoliosareidentified,thegoalistoverifywhether

thisstrategyworksinordertoobtainahigherrateofreturnthanthemarketinthefuture.To

doso,thisstudywillbeginon31/03/14,fromwherefundamentalanalysiswillbecarriedout

andthenecessarydatawillbeextractedtoexecute theMarkowitz’smodel,exclusivelyusing

informationpriortotheaforementioneddate.Finally,backtestingwillbeperformedtoverify

whethertheimplementationofvalueinvestingcriterion,combinedwithMarkowitz'sportfolio

optimization model, can be implemented to obtain a higher return than the market in the

future. Finally, results and behaviour of portfolios will be analysed and the opportune

conclusionswillbeextracted.

2.ABSTRACT

Inthisproject,aseriesofcompanieswillbeanalysedusingthevalue investingcriterion,

withtheaimofidentifyingstocksthatquoteatalowerpricecomparedtotheirintrinsicvalue.

The term value investing is based on Benjamin Graham (1894 - 1976) and David Dodd’s

(1895 - 1988) ideas developed in Security Analysis, a book published in 1934where these

authorssetouttheirmethodologytoanalysefinancialstatements.Oneofthemostimportant

conceptsoftheirworkisthemarginofsafety,definedasthedifferencebetweentheintrinsic

valueofasecurityanditsmarketprice.Evenso,Graham'sbest-knownbookisTheIntelligent

Investor, published in 1949, to provide investors with little knowledge, a series of tools to

adoptandimplementanintelligentinvestmentpolicy.Inchaptereight,BenjaminGrahamuses

theMr.Marketallegory tohighlight theshort-term irrationalbehaviourof financialmarkets.

Author’s recommendation is to maintain an adamant emotional discipline and to make

decisionsbasedonthelongtermthroughfinancialstatementanalysis(fundamentalanalysis).

Nowadays,Graham'sphilosophyremainsoneofthemostimportantpillarsinsecurityanalysis

and it is difficult to thinkof someonewhohas substantially addedvalue to theseprinciples.

However, it shouldbementionedthatsomeofhisadviceshavebeenoutdatedtoday,buthis

thinkingessenceremainsveryvaluablefordecision-making.

2

In relation to efficient portfolio construction, the first person that presented a model of

diversificationthroughmathematicalformulationwasHarryMarkowitz.In1952hepublished

"PortfolioSelection" inThe JournalofFinancemagazine, the firstarticle referring tooptimal

portfolioselection.Itwasnotuntil1959,withthepublicationofthebook"PortfolioSelection:

EfficientDiversificationofInvestments"whenhistheorybegantogainweightintheworldof

activeportfoliomanagement.ItshouldbenotedthatMarkowitz'sstudydidnotfocusonasset

selectionbutonoptimumselectionofportfolios.Oncetheinvestorhasselectedtheassetsthat

bestfithisprofile,thisoptimizationprocessdisplaysthecombinationofassetsthatmaximizes

returngivena level of riskor, the combination thatminimizes riskwith a given return.The

graphicrepresentationofMarkowitz’smodelisknownastheMarkowitz’sefficientfrontier,

a curve where all those combinations of assets are considered to be optimal or efficient.

Curiously, thisportfolio selectionmethod ismorepopular today than in its firstyearsof life

mainlyduetoitstechnicalcomplexity,butnowadaysitalreadyexistssoftwarethateasesthe

resolution.

3.OBJECTIVES

3.1Mainobjective

Themaingoalofthisthesis istobuildasetof five-assetefficientportfoliosthatbeatthe

EUROSTOXX 50 benchmark, in order to provide the investor with several alternatives that

allowhimtominimizetheriskwithagivenreturn.

3.2Secondaryobjectives

PuttingintopracticeMarkowitz’smodeltogetherwithvalueinvestingcriterioninorderto

learnaboutsomeofthetypicalmethodologieswithinactiveportfoliomanagement.

Since historical results are known in advance, it is also intended to verify whether the

strategyofcombiningaportfoliomanagementmodelwith fundamentalanalysis isuseful for

achievingahigherrateofreturnthanthemarket,aswellasanalysingtheresults,behaviour

andcharacteristicsofeachportfolio.

3

4.ANALYSISOFTHESUBJECT

4.1Theoreticalframework

To understand this work, it is necessary to previously explain the theoretical basis on

which it is based. The first stepbefore defining a strategy is to know the rules of the game,

which translates into approximating the level of market efficiency. Subsequently, value

investingcriterionandMarkowitz’smodelwillbeexplained.

4.1.1EfficientMarketHypothesis(HME)

Theefficientmarkethypothesisisbasedontheassumptionthat,atanytime,thepriceofa

financialassetreflectsalltheinformationrelevanttoitsvalue(E.Fama,1970).

TheHMEisthecentrepieceoftheEfficientMarketTheoryanditisbasedontheRandom

WalkTheory initiallyproposedbyLouisBachelier in1900butpopularized in1973with the

publicationof"ARandomWalkDownWallStreet"byBurtonG.Malkiel.

The"EfficientCapitalMarkets:AReviewofTheoryandEmpiricalWork"papercollectsthe

historical evidence that demonstrates market efficiency by analysing price adjustments of

financialassets inrelationtothreesubsetsof information,whichwilleventuallydefinethree

variantsofthemainhypothesisinitiallyraisedbyHarryRobertsin1967:

• Weak form: thepriceofa financialasset fullyreflects thehistoricalmarket information

(prices, volumes and transactions). It implies that the historical data do not have

predictivecapacityandtheportfoliomanagercannotobtainahigherthanexpectedreturn

inrelationtotheriskassumed.

• Semi-strong form: the price of a financial asset fully reflects all available public

information (valuation ratios, company announcements, news, etc.). It implies that any

strategy based on decisions that are made since the information is public will not be

rewarded.

• Strong form:thepriceofafinancialassetfullyreflectspublicandprivateinformation.It

impliesthatnoindividualand/orgroupcangetahigherthanexpectedreturninrelation

totheriskassumedbyhavingaccesstoinsiderinformation.

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4.1.1.1EMHtesting.Empiricalfindings.

SinceFama’sarticlepublication,severalstudieshavebeencarriedoutwiththeaimtotest

eachofthevariantsoftheefficientmarkethypothesis.

Regardingtheweakform,ontheonehand,thereisevidencethatstrategiesbasedonthe

selection of assets that have outperformed the market in the past medium term, entail

significantreturnsduringsuccessiveperiodsofthreetotwelvemonths(JegadeeshandTitman,

1993).Ontheotherhand,therearestudiesthatshowthatreturnsmadeoverashortperiodof

timedonotgiveanyinformationaboutreturnsforafollowingperiod(CrackandLedoit,1996).

When it comes to the semi-strong form, evidence is stillmore contradictory, since the

amountofinformationtotestishigherandthereareagreatvarietyofexperiments.Referring

tovalueinvestingcriterion, it isdemonstratedthatcompanieswithalowerP/Eratiotendto

outperformothers(Basu,1977).Also, therearealsoresearchespointingout that themarket

reactiontonewinformationisvirtuallyinstantaneous(KeownandPinkerton,1981).

However,thestrongformofefficiencyisdeniedbyKeownandPinkerton’sresearchsince,

despite agreeing with the semi-strong form, they provide evidence that some market

participantsdobenefitfromoperatingonthebasisofinsiderinformation.

In conclusion, the weak form of efficiency is the one that has more general consensus

amongeconomistswhileinthesemi-strongformthereismorecontroversy.Thestrongformof

efficiencyisthehypothesisthatcanberejected.

4.1.1.2Marketanomalies

Market anomalies are irregularities that do not have any explanation according to the

EfficientMarketTheory.Theseirregularities,arisingfromthestudiesthathavetriedtotestthe

threehypothesesdescribedabove,aresogeneralizedthatcannotbeignored.Somehavebeen

mentionedintheprevioussection,buttherearemanymorethatwillnotbetreatedbecause

theyarenotpartoftheobjectofthispaper.Inanycase,fromtheinvestor’spointofview,there

are sufficient anomalies that justify an active portfolio management strategy by searching

undervaluedcompaniesinordertoobtainahigherthanexpectedreturn,therefore,thisstudy

putsintoquestiontheefficiencyoffinancialmarkets.

5

4.1.2Valueinvestingcriterion

Thiscriterionrejectsmarketefficiencyinstrongandsemi-strongformsintheshortterm,

because there is some information that is not incorporated in the price, specifically, public

financialinformation.

Investorswhoareinfavourofthiscriterionaredevotedtocarryoutexhaustiveresearch

in order to detect undervalued companies that are listed below their intrinsic value. The

differencebetweencurrentmarketpriceandintrinsicvalueisthemarginofsafety,whichwill

alwaysdependonthepricepaid.The larger it is, the less theprobabilityofmakingmistakes

(Graham,1949).

Although the essence of Graham's ideas remains intact, value investing criterion has

evolvedinrecentdecades.Graham'soutstandingstudent,WarrenBuffett,understandsthat"it

ismuch better to buy awonderful company at a fair price than to buy a fair company at a

wonderfulprice”.Hisapproachfocusesonidentifyingcompaniesthatsellauniqueproductor

serviceand, thus,holdacompetitiveadvantageoverthe longterm,whilemakingsurenotto

payanexcessivepriceforthem.

InchapterfourteenofTheIntelligentInvestor,Grahamdescribespracticalapplicationsof

theinvestmentpolicythataninvestormustfollowifhedoesnotwanttoassumeahighlevelof

risk,inordertomakesurethattheacquisitionpriceisnotunjustifiablyhigh.Itshouldbenoted

that,asbeingadefensive investor isassumed,requirementsareveryconservativeandthere

arereallyfewcompaniesthatmeetthem.Investmentrequirements,listedfrommajortominor

importanceare:1)largecompanies,2)2:1workingcapitalratio,3)stableprofits,4)dividends

inthelast20years,5)profitsgrowth,6)productofP/EratiomultipliedbyP/Bratiolessthan

22.5. These are dumping requirements because they are not only dependent on investor’s

profile but also on company’s operating sector, although companies that meet all of these

previouslymentionedrequirementsarelikelytobeagoodbuyingopportunity.

It isnecessarytorememberthatsincethemid-20thcenturyuntilnowadaystherehavebeen

sucha largenumberof investors thathaveachievedahigher rateof return than themarket

consistently, and there isnoonewhohasmanaged tobeat themarketusing someoneelse’s

methodology at one hundred per cent. Value investing criterion is clearly defined, but each

investormust find its own system,which shouldbe adapted tohisprofile, if hewants tobe

successful.

6

4.1.2.1Resultsobtainedbysomevalueinvestors

Within thegroupof investorswhohavebased theirmethodologyonBenjaminGraham’s

ideas, there are cases of real success, starting by himself. As indicated in the book, The

Intelligent Investor, all those who invested in the investment fund Graham-Newman

Corporation,between1936and1956,obtainedanannualized returnof14.7%, compared to

12.2%obtainedbythestockmarketasawhole.Itisanexcellentrecord.

When it comes to Warren Buffett, according to the letter that Berkshire-Hathaway

addressedtoitsinvestorsin2017,theannualizedreturnobtainedbetween1965untilletter’s

release datewas 20.9%versus 9.9%of the SP500, reaching one of the best records inWall

Street’shistory.

Within the Spanish framework, Francisco García Paramés, manager of Bestinfond from

1993 until nowadays, also represents a remarkable case of success. As indicated in fund’s

official website, from its beginnings the fund has obtained an annualized rate of return of

15.08%.

4.1.3Markowitz’smodel

The first assumptionof theMarkowitz’smodel is that the investorbehaves in a rational

mannerandhasanaversiontorisk,therefore,everyonewillseektomaximizetheirexpected

utilityfunctionbutbearinginmindthatalower-return/lower-riskportfoliowillbepreferred

toahigher-return/higher-riskportfolio.Asaresult,aportfoliowillbeefficientifitmaximizes

returngivenalevelofriskorminimizesriskgivenarateofreturn.

Thetwomainvariablesofthemodelarereturnandrisk,thefirst isdefinedastheprofit

that is obtained from an investment in relation to the price paid, and the second as the

probabilitythathasaninvestmenttosignificantlyloseitsvalue,alsocalledvolatility(standard

deviation)oftheinvestment.

4.1.3.1Modelhypothesis

TheMarkowitz’smodel isbasedonthe followingassumptionsaboutassetsandfinancial

markets:

• Itisaone-periodmodel:TheinvestmentsethasthesameperiodoftimeT;itmeansthat

allinvestmentsareconstitutedandsettledatthesametime.

• Financialassetsthatarepartoftheportfolioareknown.

• Therearenorisk-freeassets;varianceisgreaterthanzero.

7

• Randomreturnvariablesareknownandfollowanormaldistribution.

• Financialassetsareinfiniteandindivisible.

• Therearenotaxesorinflationintheeconomy.

• Financialmarketsareperfect.

• Shortsellingisnotpermitted.

4.1.3.2Modelapproach

Inordertosolvethemodelandtodeterminethesetofefficientportfoliositisnecessaryto

meetthefollowingconditions:

𝜎!!=Portfoliovariance

𝑋! =Weightofi

𝑋! =Weightofj

𝜎!" =Covariancei,j

𝐸! =Expectedportfolioreturn

𝜇! =Expectedreturnofi

4.1.3.3Efficientfrontier

The set of combinations [E! ,σ!! ] of all efficient portfolios is the so-called "efficient

frontier",asallthoseportfoliosprovidemaximumreturnataminimumrisk.

Allthoseportfoliosthatarelocatedabovetheefficientfrontierareunattainableandthose

thatarelocatedbelow,inefficient.

𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒: 𝜎!! =!! 𝑋!

!

!!!

· 𝑋!

!

!!!

· 𝜎!"

𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒: 𝐸! = !𝑋! · 𝜇!

!

!!!

𝑅𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑠: ! 𝑋!

!

!!!

= 1

∀𝑖 ∈ (1,2,… , 𝑛) 𝑋! > 0

8

4.1.3.4Modelresolution

Leaving aside the graphical resolution, it is necessary to solve the model using

mathematical optimization methods that are solved by programming. One way to solve it

would be to match the expected return to a given value in order to obtain the minimum

varianceandtorepeat theprocedureuntil theefficient frontier isbuilt.Giventhedifficulties

foritscalculation,theMicrosoftExcelSolverprogramhasbeenusedtobuildthesetofefficient

portfolios.

Once the set of efficient portfolios is defined, the investorwill choose the one that best

suitshimbasedonhisinvestor’sprofileandthelevelofriskaversionhehas.

4.1.3.5Correlationeffect

One of the most important conclusions reached by Markowitz is that the key for good

diversificationisnotlimitedtothenumberofassetsthatmakeupaportfolio,italsodepends

onthecorrelationamongassetreturns.

Bearinginmindthatcovariancedependsoncorrelation:

𝜎!" = 𝜌!" · 𝜎! · 𝜎!

Andportfoliovariancedependsoncovariance:

𝜎!! = 𝑋!

!

!!!

· 𝑋!

!

!!!

· 𝜎!"

Itcanbeobservedthattoreducetheportfoliovariance(risk),correlationamongdifferent

assetsmustbenegative.Intheeventthatitisnotpossible,itispreferabletoselectassetswith

correlationscloseto0onthosewithcorrelationscloseto1.

4.1.3.6CriticismtoMarkowitz’smodel

Currently, criticism to this model is focused on its previous assumptions. Some of the

initial premises are the non-consideration of taxes or transaction costs and the infinite

divisibilityofassets.Anotherrelevantcritiqueistosupposethatfinancialmarketsarerational

andperfectandthatthereisnoinsiderinformation.

4.1.4RelationshipbetweenvalueinvestingandMarkowitz’smodel

Valueinvestingcriterionpresupposesthatfinancialmarketsareefficientinthelongterm

but in the short term there are price inaccuracies generated by the margin of security

9

mentionedbefore.Markowitz, on the other hand, believes inmarket efficiency at its highest

level and considers that the best way to select assets is to seek for risk reduction through

correlation. In practice, it is very difficult to obtain a matrix of negative correlations for a

sufficient number of assets that allowdiversification, however, it is easier to find anomalies

thatjustifyassetselectionbasedonfundamentalanalysis.Themostimportantreasonofwhyit

hasbeendecidedtocombinebothmethodologiesisthatitisconsideredthatfinancialmarkets

arenotefficientintheshortterm,buttendtobeefficientinthelongterm.

4.2Practicalapplication

Oncetheapplicabletheoretical frameworkisknown,themethodologyforassetselection

andtheoptimalassetallocationcanbealreadydeveloped.

4.2.1Previousconsiderations

At the beginning, it is necessary to take into account a series of aspects that have been

criticalinstrategyimplementation.

4.2.1.1Timehorizon

The time horizon inwhich the study is carried out begins on 31/03/2014 and ends on

31/03/2018, the goal is to analyse the investment’s behaviour assuming that only previous

informationuntilthebeginningofthestudyisavailable.Thisstudyisinitiatedon31/03/2014

inordertobeabletoanalyseportfolioevolutionforasufficiently longperiodandalsoit isa

dateonwhichallthecompanieshadalreadypublishedtheirannualreports.

4.2.1.2Originofdataandobservations

In relation to asset selection, relevant information has been extracted from the

correspondingconsolidatedfinancialstatementsforthefiscalyear2013and,toalesserextent,

fromYahooFinancefortheperiod31/03/2012-31/03/2014.

FortheMarkowitz’smodelresolution,datawasextractedfromYahooFinanceandforthe

sameperiodmentionedabove,buttradingdaysthatwerenotcommonamongassetsandthe

benchmark,weredeletedinordertomakedailyreturnscorrelative.However,thepercentage

ofdeleteddaysinrelationtototaldaysisnotrelevant.

10

4.2.1.3Benchmark

EUROSTOXX 50 has been chosen as a benchmark because it is a well-known index in

Europe and includes companies fromdifferent countries and sectors (seeAnnex 1 formore

information).

4.2.2Assetselection

Thissectiondefinesthevalueinvestingrequirementsforassetselection.Onceestablished,

theselectedcompaniesareidentified.

4.2.2.1Sectorcorrelations

In order to take advantage of the correlation effect on portfolio risk, the four sectors

comprising EUROSTOXX 50 with the highest average correlation with respect to the others

have been discarded (see Annex 2 for correlationmatrix). Therefore, there are five sectors

availableandeachof theselectedcompaniesbelongs toadifferentsector inorder toreduce

riskthroughsectordiversification.Thesectorschosenare:ConsumerStaples,Energy,Health

Care,TechnologyandUtilities.

4.2.2.2Selectedindicatorsandscoringsystem

Oncethesectorshavebeenidentified,itmustbedefinedwhichrelevantindicatorsprovide

informationaboutpossiblesuperiorperformanceofanassetrelativetothosebelongingtothe

samesector.Theseindicatorsare:highestP/Eratio,lowestP/Bratio,WorkingCapitalratio>

1, Debt to Equity < 2.5, highest ROA, highest ROE, highest ROICC, ROA > Kd, ROE > Ke and

ROICC > WACC (see Annex 3 for more information). Companies with losses have been

discarded.

Given that there are a total of ten indicators, the weight of each one in the final score

should be 10%, but there are indicators that have been considered more important than

others. Themost relevant are the last two, since, on the one hand, return should always be

higher than the opportunity cost of investing in the company (Ke), on the other hand, the

return on invested capital (ROICC) must also be higher than the weighted average cost of

capital(WACC)inordertoguaranteelong-termsurvival.Asaresult,weighthasbeenreduced

forthefirsttwoindicatorsbecausetheyprovidesimilarinformation(P/EandP/Bratios)and

alsoforthenexttwoforthesamereason(seeAnnex4tocheckthescoringtableandresults).

11

4.2.2.3Selectedassets

Theselectedassetsthatwilltakepartofportfoliosare:Total(FP.PA),EssilorInternational

(EI.PA),Unilever(UNA.AS),SAP(SAP.DE)andEnel(ENEL.MI).

4.2.3Markowitz’smodelresolution

Sincethefivecompaniesthatwilltakepartoftheoptimalportfoliosareidentified,nowit

istimetocarryouttheportfoliooptimizationmodel.

4.2.3.1Calculationoftheexpectedreturnandvolatility

Tocalculatetheexpectedreturnforeachasset,averagedailyreturnbetween02/04/2012

and03/31/2014wascalculatedusingthesimplereturnformula.Subsequently,theresultwas

multipliedbythenumberofdaysthatastockisquotedforoneyear,whichistwohundredand

fifty. Ithasbeendecidedtoannualizereturninthiswayinordertobalancetheweightofall

dailyreturns.Ithadnotbeenmadethroughcompoundinterestbecause,inthiscase,themost

recentdailyreturnswouldhavemoreweightonthefinalresult,whichisnotaccuratebecause

itisanexpectedreturnandnotarealone.Itmustbementionedthatdividendshavenotbeen

takenintoaccountbecauseEUROSTOXX50doesnottakethemintoaccounteither.

Withregardtoexpectedvolatility,themostcommonwayofobtainingit isbycalculating

the standarddeviationofdaily returns.To annualize the averagedaily volatility, it hasbeen

multipliedbythesquarerootoftwohundredandfifty.

Thisisthesetofdataobtained:

TOTAL ESSILOR UNILEVER SAP ENEL

Annualizedreturn 12.65% 6.92% 9.03% 7.72% 25.18%

Annualizedvolatility 18.57% 21.86% 15.64% 19.85% 29.76%

Averagereturn 0.05% 0.03% 0.04% 0.031% 0.10%

Averagevolatility 1.17% 1.38% 0.99% 1.26% 1.88%

Source:ownwork,usingYahooFinancedata.

4.2.3.2Correlationmatrix

Thecorrelationmatrix shows inavisualwaywhatare theassets thataremost likely to

coexist within the same portfolio because they have a low correlation among the assets

themselves.Apriori,correlationwillberelativelyhighsimplybecausetheyarethesametype

ofassets(equities).

12

Thecorrelationmatrixofthefiveselectedassetsisasfollows:


TOTAL 1

ESSILOR 0.52 1

UNILEVER 0.51 0.53 1

SAP 0.49 0.46 0.44 1

ENEL 0.64 0.34 0.37 0.32 1


ItcanbeobservedthatEnelisthecompanywiththelowestcorrelationwithalltheothers,

however, since it has a higher expected return and volatility it may be difficult to see Enel

takingpresencewithinthelower-volatilityportfolios,althoughitmayhaveasignificantweight

in thehigher-returnandhigher-volatilityportfolios.Ontheotherhand,Total is thecompany

withthehighestcorrelationwithalltheothers,butthefactthatithasahighexpectedreturn

andalowexpectedvolatilitycouldleadtoasignificantpresenceinlower-volatilityportfolios,

despite the highest weighting in the least risky portfolios is likely to be taken by Unilever

becauseitistheassetwiththelowestexpectedrisk.

4.2.3.3Annualizedvariance-covariancematrix

Thelastvariablethat isneededtodevelopthemodel is thecovarianceamongtheassets

themselves. Itprovides informationsimilar to thatof thecorrelationcoefficientbutof lesser

quality,sinceitisnotaccurateinprovidinginformationaboutthedegreeoflinearrelationship

beyond the sign. In order to solve the model, it is necessary to annualize variances and

covariances as it has been done with the expected return and volatility. This time it is

multipliedbytwohundredandfifty.

Theannualizedvariance-covariancematrixisasfollows:


TOTAL 3.45% 2.09% 1.48% 1.81% 3.52%

ESSILOR 2.09% 4.78% 1.80% 1.99% 2.22%

UNILEVER 1.48% 1.80% 2.45% 1.38% 1.74%

SAP 1.81% 1.99% 1.38% 3.94% 1.88%

ENEL 3.52% 2.22% 1.74% 1.88% 8.86%


13

4.2.3.4Expectedportfolioriskandreturn

The expected portfolio return is very easy to calculate. The return of each asset is

multipliedbyitsweightingandthesumofallrepresentstheexpectedportfolioreturn.

Tocalculatetheportfoliorisk,itisnecessarytocalculatethevariancefirst,whichisamore

complicatedcalculation.Thegeneralexpressionis:

𝜎!! = 𝑋!

!

!!!

· 𝑋!

!

!!!

· 𝜎!"

Itisarelativelysimpleformulatocalculateifthevarianceofaportfoliocontainsbetween

twoandfiveassets,butasthenumberofassetsincreases,calculationismorecomplicatedand

increases the probability to make mistakes. The alternative is through a matrix calculation

where the variance-covariance matrix and the weighting matrix arise, but it has not been

carried out because in this particular case it is feasible to calculate the variance using the

standardformula.Oncethevarianceoftheportfolioisobtained,onlythesquarerootmustbe

appliedtoobtainthestandarddeviation,whichistheportfolioriskorvolatility.

4.2.3.5Efficientfrontiercalculation

NowthatallthenecessaryinformationtostartwiththeMarkowitz’smodelresolution,the

followingoptimizationproblemmustbesolved:

Tosolve it, theMicrosoftExcelSolverapplicationhasbeenusedbecause itgreatlyeases

theproceduretakingintoaccountthatuptofivedifferentassetsareinvolved.

𝑀𝑖𝑛𝑖𝑚𝑖𝑧𝑒: 𝜎!! =!! 𝑋!

!

!!!

· 𝑋!

!

!!!

· 𝜎!"

𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒: 𝐸! = !𝑋! · 𝜇!

!

!!!

𝑅𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑖𝑜𝑛𝑠: ! 𝑋!

!

!!!

= 1

∀𝑖 ∈ (1,2,… , 𝑛) 𝑋! > 0

14

First of all, the two ends of the border have been identified, which are the minimum

variance portfolio and the maximum return portfolio. To calculate the minimum variance

portfolio, theportfoliovariance cellhasbeensetas theobjective cell tominimize.Later, the

restrictionsof themodelhavebeenestablished, settingdefaultweightsof0.2 foreachasset.

Finally, the software has been executed and the minimum variance of the portfolio, the

associated weights and the expected return of the portfolio have been obtained. Next, to

calculatethemaximumreturnportfolio,theportfolioreturncellhasbeensetasthetargetcell

tomaximizeandthesamerestrictionshavebeenleft.Thesoftwarehasbeenexecutedandthe

maximumexpectedreturnoftheportfolio,theassociatedweightsandtheexpectedvarianceof

theportfoliohavebeenobtained.

Assoonastheendsoftheefficientfrontierhavebeenidentified,andthereforethefigures

forminimumandmaximumreturn,fourpointshavebeendefinedbetweenthesetwofigures

andtheminimumvarianceportfoliohasbeencalculated,aswellastheweightingsassociated

withthegivenreturn.Todoso,anewcellhasbeencreatedinordertoestablishagivenreturn

andtheconditionfortheequalizationoftheportfolio’sreturntothenewcellhasbeenadded.

Finally,theprocesshasbeenrepeatedthreemoretimesandanapproximationoftheefficient

frontierisobtained.

Sincethemainobjectiveof thispaper is tobuildandstudyasetofefficientportfolios, it

has been decided to select the so-called "corner portfolios". Corner portfolios are those in

which, either a new asset is about to enter the portfolio or an asset has already come out

completely, including theminimumvarianceportfolioand themaximumreturnportfolio.To

identify them, starting from the minimum variance portfolio, the given return has been

incrementeduntilthecornerportfoliosoftheefficientfrontierarefound.

Thecornerportfoliosare:

Portfolio Vol Er TOTAL ESSIL UNILEV SAP ENEL

1 14.15% 9.50% 22.17% 3.28% 54.81% 19.74% 0.00%

2 14.20% 10.00% 24.79% 1.03% 54.11% 18.02% 2.05%

3 14.30% 10.50% 24.41% 0.00% 53.48% 17.09% 5.02%

4 19.54% 17.50% 13.72% 0.00% 36.90% 0.00% 49.38%

5 25.90% 22.50% 0.00% 0.00% 16.59% 0.00% 83.41%

6 29.76% 25.18% 0.00% 0.00% 0.00% 0.00% 100.00%


15

4.2.3.6Graphicalrepresentationoftheefficientfrontier

Oncethecornerportfoliosareidentified,anapproximationoftheefficientfrontiercanbe

represented.Although fourmoreportfolioshavebeenadded togainaccuracy, the sixpoints

marked on the graph correspond to the corner portfolios and the green point represents a

portfoliothatreplicatestheEUROSTOXX50.

Source:ownwork,usingExcelSolverandYahooFinancedata.

Inthisgraph,astheEUROSTOXX50isbelowtheefficientfrontierithasbeenpossibleto

identify portfolios that offer a higher return for the same risk and/or portfolios that offer a

lowerriskforthesamereturnofferedbythebenchmark.Firstobjectiveofthethesisachieved.

4.2.4Backtesting

Subsequently, backtesting is performed to assess the behaviour of corner portfolios in

relationtoEUROSTOXX50from31/03/2014to31/03/2018.

EUROSTOXX50

0%

5%

10%

15%

20%

25%

30%

10% 15% 20% 25% 30% 35%

Return

Volatility

Ef\icientfrontier

16

4.2.4.1Evolutionofcornerportfolios

The best way to display the evolution of corner portfolios is through graphical

representation. It has been considered an initial investment of 10,000€ and it has been

weighted according to the weight of each asset in each corner portfolio. A portfolio that

replicatestheEUROSTOXX50hasbeenbuiltforcomparison.TheevolutionofPortfolio1isas

follows(seeAnnex5fortheremainingportfolios):


Interestingly,theminimumvarianceportfolio(Portfolio1) istheonethathasobtaineda

higherreturncomparedtotheothersandtoEUROSTOXX50.TheweightingofEssilorandSAP

decreasesas it advances toaportfoliowithahigherexpected return.AlthoughEssilorhasa

very small share, themaximumweightof3.28% inPortfolio1and the fact thatbothEssilor

and SAP have had a higher return than expected was key for being the best performing

portfolio.

ThelossofimportanceexperiencedbyEssilorandSAPcombinedwiththeshareincrease

ofEnel intheportfolioastheexpectedreturn is increased,explainswhyreturndecreasesas

Portfolio6approaches,sinceEnelhasobtainedalowerreturnthanexpected.

17

Although there are portfolios that performed better than others, all portfolios have

managed to beat the EUROSTOXX 50 as a benchmark, even when investing 100% in Enel.

Therefore, beyond the portfolio optimization model, the selection process through value

investinghasbeenrewarding.

4.2.4.2Portfolioindicators

Belowaresomeofthemostrelevantindicatorswhenevaluatingportfolioperformance:


Asmentioned in the previous section, Portfolio 1 is the one that has achieved a higher

returnand,inaddition,ithasthelowestvolatilityandthelowestBeta(β),soitisalsotheleast

riskyportfolio.Incontrast,Portfolio6hasbeentheonethathasobtainedalowerreturnandit

isthemostriskyone,takingintoaccounttheinformationprovidedbyvolatilityandBeta(β).

TheβshowsthedegreeofamplificationofeachportfoliowithrespecttotheEUROSTOXX50;

therefore,itiscloselylinkedtovolatilityandcorrelationoftheportfoliowiththebenchmark.

Other indicators such as Maximum Drawdown (MD) and Value at Risk (VaR) are very

usefulforanalysingthelevelofriskassumedbytheinvestor.

Regarding the MD, it shows the portfolio loss of value in the moment of minimum

quotationwithrespecttothepreviousmaximum,inotherwords,themaximumfallinrelative

value.Ontheotherhand,theVaRexposesinhowmanydaystheportfoliohaslostmorethan

Portfolio1 Portfolio2 Portfolio3 Portfolio4 Portfolio5 Portfolio6 EUROSTOXX50

Annualized

return8.62% 8.25% 8.12% 6.73% 6.04% 4.88% 1.54%

Annualized

volatility18.00% 18.38% 18.57% 20.39% 23.28% 25.80% 18.94%

µ 0.04% 0.04% 0.04% 0.03% 0.03% 0.03% 0.01%

σ 1.14% 1.16% 1.17% 1.29% 1.47% 1.63% 1.20%

σ 2 0.0130% 0.0135% 0.0138% 0.0166% 0.0217% 0.0266% 0.0143%

β 0.77 0.80 0.81 0.90 0.98 1.03 1.00

Sharpe 0.39 0.36 0.35 0.25 0.19 0.13 -0.001

Maximum

Drawdown-12.81% -13.64% -13.98% -16.85% -19.45% -23.88% -29.99%

VaR95% -1.88% -1.92% -1.94% -2.13% -2.43% -2.69% -1.98%

VaR99% -2.65% -2.71% -2.74% -3.00% -3.43% -3.80% -2.79%

α 0.071 0.067 0.066 0.052 0.045 0.033 0.000

18

therelativevaluewithrespecttotheinitialvalueshownineachcase,forexample,VaR95%at

Portfolio1reportsthatin5%oftotallisteddays,theportfoliohaslostmorethan1.88%ofits

initialvalue.

Inrelationtoportfolioperformance,theSharperatioshowsthereturnobtainedinexcess

ofthe1.57%riskfreerate(annualizedreturnofthe10-yearGermanbundasof31/03/2014)

for eachunit of risk (volatility). In the case of EUROSTOXX50, the ratio is negative because

returnhasbeenlowerthantherisk-freerate.

Withregard toAlpha(α), it isanotherrisk-adjustedmeasure that refers to theabilityof

theportfoliomanagertobeatthemarket.

4.2.4.3Distributionofreturns

Thissectionevaluates towhatextent thedistributionofdailyreturnsofEUROSTOXX50

fits into a normal distribution. (See Appendix 6 for the distribution of returns of corner

portfolios and additional information). It is an analysis that allows to approximate to what

extent indicators such as Value at Risk, Sharpe ratio, Alpha and everything that surrounds

CAPMmodelisadjustedtoreality,sincemanyindicatorsarebasedonanormaldistributionof

marketreturns.Therepresentationofthedistributionofdailyreturns(inred)andthenormal

distributionrelativetotheaveragevaluesofdailyreturnsandstandarddeviationsareshown

(inblue):


19

Itcanbeobservedthat,inthisparticularcase,thedistributionofdailyreturnsinfinancial

marketsdoesnotcompletelyfitintothenormaldistribution.Therearemoreoutliersofwhat

shouldbeaccordingtothenormaldistribution;therefore,itisanegativelyskewedleptokurtic

distributionwheretherearemoreatypicalobservationsconcentratedinthenegativesidebut

with less frequency than in the positive side. This distribution may vary depending on the

marketandperiodanalysedbuttherearestudiesthatalsosuggestthistypeofdistributionof

thedailyreturnsinfinancialmarkets(Egan,2007).

5.CONCLUSIONSFirstofall,wecanclearlyconcludethattheobjectivesofthisworkhavebeenachieved.A

setofefficientportfoliosthathavebeatentheEUROSTOXX50inefficiencyandreturnhasbeen

built, but it must be taken into account that Markowitz’s model is based on past data and,

therefore,hasnopredictivecapacity.

Theefficientfrontieronlygivesinformationaboutoptimalportfoliosthatcouldhavebeen

built,fromthemomentinwhichtheoldestdataiscollecteduntiltheexecutionofthemodel,in

ordertoobtainahigherreturn for thesame levelofriskofferedbythebenchmark.Evenso,

Markowitz’smodelcanalwaysserveasanorientationontheweightingsthateachassetmust

haveinaportfoliobasedonexpectedriskandreturn.

Therefore, much of themerit is attribuable to themethodology applied based on value

investingbecauseallthecornerportfolioshavebeenabletobeatEUROSTOXX50intheperiod

31/03/2014 - 31/03/2018. The indicators used to evaluate the financial statements of

companieshaveprovidedrelevantinformationinordertoselectfiveassetsthathaveachieved

asubsequentreturnbetterthantheoneofferedbythebenchmark,andthescoringsystemhas

allowedtopositivelydiscriminatethoseindicatorsthatwereconsideredthemostimportant.

Ithasalsobeenobservedthatthedistributionofreturnsinthefinancialmarketstendstobe

leptokurticandnegativelyskewed,anaspect thatmustbe taken intoaccountwhenapplying

modelsandinterpretingindicatorsthatarebasedonnormaldistribution.

Finally, note that backtesting results cannot be extrapolated beyond this particular

situation and, if this studywere repeated again using another samplewithin a distinct time

frame,probablydifferentandevennegativeresultswouldhavebeenobtained.Leavingaside

themethodologyusedtoselectassetsandtheimplementedmodeltobuildaseriesofefficient

portfolios,itwouldhavebeeninterestingtodeepenandanalysethedistributionofreturnsin

financialmarketsandtheirimplicationsfortheinvestor.

20

6.BIBLIOGRAPHY

Graham,B.andDodd,D.(1934).SecurityAnalysis.NewYork:McGraw-Hill.Graham,B.(1949).TheIntelligentInvestor.HarperBusiness.Fama,E.(1970).EfficientCapitalMarkets:AReviewofTheoryandEmpiricalWork.TheJournalofFinance,25(2),pp.383-416.Malkiel,B.(2016).ArandomwalkdownWallStreet.NewYork:W.W.Norton&Company.Crack,T.andLedoit,O.(1996).RobustStructureWithoutPredictability:The"CompassRose"PatternoftheStockMarket.TheJournalofFinance,51(2),pp.751-761.Jegadeesh,N.andTitman,S.(1993).ReturnstoBuyingWinnersandSellingLosers:ImplicationsforStockMarketEfficiency.TheJournalofFinance,48(1),pp.65-91.Basu,S.(1977).InvestmentPerformanceofCommonStocksinRelationtoTheirPrice-EarningsRatios:ATestoftheEfficientMarketHypothesis.TheJournalofFinance,32(3),pp.663-682.Keown,A.andPinkerton,J.(1981).MergerAnnouncementsandInsiderTradingActivity:AnEmpiricalInvestigation.TheJournalofFinance,36(4),pp.855-869.Markowitz,H.(1952).PORTFOLIOSELECTION*.TheJournalofFinance,7(1),pp.77-91.Stuart,A.andMarkowitz,H.(1959).PortfolioSelection:EfficientDiversificationofInvestments.Egan,W.(2007).TheDistributionofS&P500IndexReturns.SSRNElectronicJournal.

21

ANNEXES

Annex1.EUROSTOXX50at31/03/2014Company Code Sector Country PriceAIRLIQUIDE AI.PA BasicMaterials FR 95.77AIRBUS AIR.PA Industrial FR 51.99ALLIANZ ALV.DE Financials DE 122.70ANHEUSER-BUSCHINBEV ABI.BR ConsumerStaples BE 76.10ASMLHLDG ASML.AS Technology NL 67.23ASSICURAZIONIGENERALI G.MI Financials IT 16.18AXA CS.PA Financials FR 18.86BASF BAS.DE BasicMaterials DE 80.68BAYER BAYN.DE HealthCare DE 98.18BCOBILBAOVIZCAYAARGENTARIA BBVA.MC Financials ES 8.72BCOSANTANDER SAN.MC Financials ES 6.81BMW BMW.DE ConsumerDiscretionary DE 91.62BNPPARIBAS BNP.PA Financials FR 55.99CARREFOUR CA.PA ConsumerStaples FR 28.09CRH CRG.IR BasicMaterials IR 20.20DAIMLER DAI.DE ConsumerDiscretionary DE 68.59DANONE BN.PA ConsumerStaples FR 51.33DEUTSCHEBANK DBK.DE Financials DE 27.64DEUTSCHEPOST DPW.DE Industrial DE 26.97DEUTSCHETELEKOM DTE.DE Technology DE 11.73E.ON EOAN.DE Utilities DE 12.86ENEL ENEL.MI Utilities IT 4.11ENGIE ENGI.PA Utilities FR 19.86ENI ENI.MI Energy IT 18.21ESSILORINTERNATIONAL EI.PA HealthCare FR 73.20GRPSOCIETEGENERALE GLE.PA Financials FR 44.71IBERDROLA IBE.MC Utilities ES 5.08IndustriadeDiseñoTextilSA ITX.MC ConsumerDiscretionary ES 108.90INGGRP INGA.AS Financials NL 10.27INTESASANPAOLO ISP.MI Financials IT 2.46L'OREAL OR.PA ConsumerStaples FR 119.70LVMHMOETHENNESSY MC.PA ConsumerDiscretionary FR 131.95MUENCHENERRUECK MUV2.DE Financials DE 158.60ORANGE ORA.PA Technology FR 10.72PHILIPS PHIA.AS HealthCare NL 25.50REPSOL REP.MC Energy ES 18.52RWE RWE.DE Utilities DE 29.46SAINTGOBAIN SGO.PA ConsumerDiscretionary FR 43.85SANOFI SAN.PA HealthCare FR 75.68SAP SAP.DE Technology DE 58.76SCHNEIDERELECTRIC SU.PA Industrial FR 64.35SIEMENS SIE.DE Industrial DE 97.70TELEFONICA TEF.MC Technology ES 11.35TOTAL FP.PA Energy FR 47.60UNIBAIL-RODAMCO UL.AS Financials FR 188.50UNICREDIT UCG.MI Financials IT 33.22UNILEVERNV UNA.AS ConsumerStaples NL 29.83VINCI DG.PA Industrial FR 53.91VIVENDI VIV.PA Technology FR 20.22VOLKSWAGENPREF VOW3.DE ConsumerDiscretionary DE 188.10Source:OfficialpageofEUROSTOXX50,pricesextractedfromYahooFinanceandownwork.

22

Annex2.Sectorscorrelationmatrix

Source:portfoliovisualizer.comandownelaboration.

Annex3.SelectedindicatorsCompany β P/B P/E CA/CL D/E ROA ROE ROICC Ke Kd WACC

TOTAL 0.85 1.49 12.81 1.37 1.39 4.86% 11.62% 9.68% 11.29% 1.38% 5.53%

ENI 1.00 1.12 12.79 1.53 1.37 3.69% 8.74% 3.23% 13.00% 0.80% 5.95%

REPSOL 1.29 0.89 124.70 1.52 1.39 0.30% 0.72% 2.95% 16.31% 2.12% 8.05%

PHILIPS 0.76 2.10 20.06 1.35 1.37 4.41% 10.45% 9.27% 10.26% 4.20% 6.76%

BAYER 0.94 3.92 25.46 1.36 1.48 6.21% 15.39% 10.48% 12.31% 5.05% 7.98%

SANOFI 2.61 1.78 27.26 1.71 0.69 3.87% 6.53% 5.77% 31.40% 2.03% 19.42%

ESSILOR 0.70 4.15 26.30 1.49 1.03 7.78% 15.79% 13.55% 9.57% 1.89% 5.67%

L'OREAL 0.69 3.21 24.60 1.42 0.38 9.45% 13.07% 12.46% 9.46% 1.04% 7.13%

UNILEVERNV 0.50 6.08 18.01 0.70 2.17 10.64% 33.76% 21.60% 7.29% 2.78% 4.20%

DANONE 0.60 2.82 21.24 0.74 1.89 4.60% 13.30% 7.44% 8.43% 1.90% 4.15%

CARREFOUR 1.14 2.49 15.45 0.84 4.55 2.90% 16.10% 8.68% 14.60% 3.33% 5.36%

ANHEUSER-BUSCHINBEV 0.64 2.49 15.73 0.73 1.81 5.64% 15.85% 11.94% 8.89% 4.48% 6.04%

SAP 0.68 4.38 21.11 1.16 0.69 12.28% 20.74% 18.81% 9.34% 2.91% 6.72%

ASMLHLDG 0.73 4.21 24.41 2.45 0.66 10.37% 17.25% 17.29% 9.91% 1.48% 6.55%

TELEFONICA 1.13 2.42 11.18 1.00 4.61 3.86% 21.68% 9.86% 14.49% 4.61% 6.37%

ORANGE 1.00 1.16 15.04 0.61 2.53 2.18% 7.69% 5.54% 13.00% 2.81% 5.70%

DEUTSCHETELEKOM 0.71 2.15 55.12 0.98 3.95 0.79% 3.89% 3.22% 9.69% 1.92% 3.49%

VIVENDI 0.85 1.55 13.73 0.92 1.82 4.00% 11.27% - 11.29% 2.87% 5.85%

ENEL 1.23 1.08 11.95 1.04 3.57 1.97% 9.00% 5.40% 15.63% 4.51% 6.95%

IBERDROLA 1.17 0.93 12.53 0.94 1.66 2.80% 7.44% 1.90% 14.94% 2.91% 7.44%

E.ON 0.81 0.73 11.45 1.08 2.91 1.64% 6.40% 4.79% 10.83% 3.26% 5.20%

RWE 0.78 1.73 - 1.11 6.77 - - 8.12% 10.49% 4.42% 5.20%

ENGIE 0.86 0.98 - 1.07 2.33 - - - 11.40% 3.83% 6.10%

ForWACCcalculation,theannualizedreturnofEUROSTOXX50hasbeencalculatedbetween02/04/2012and

31/03/2014(13%)andtheannualizedreturnofthe10-yearGermanbundasof31/03/2014(1.57%).

TheBetaofeachcompanyhasbeencalculatedbasedontheprevioustwoyearsandwithrespecttoEUROSTOXX50.

Source:consolidatedfinancialstatementscorrespondingtoFY2013,YahooFinanceandownwork.

23

Annex4.Scoringtable

Weighting 0.5 0.5 0.5 0.5 1 1 1 1 2 2

LowestP

/E

LowestP

/B

CA/CL>1

Deb

ttoEq

uity

<2.5

Highe

stROA

Highe

stROE

Highe

stROICC

ROA>Kd

ROE>Ke

ROIC>W

ACC

SUM

TOTAL 0 0 1 1 1 1 1 1 1 1 9

ENI 1 0 1 1 0 0 0 1 0 0 2.5

REPSOL 0 1 1 1 0 0 0 1 0 0 2.5

PHILIPS 1 0 1 1 0 0 0 1 1 1 6.5

BAYER 0 0 1 1 0 0 0 1 1 1 6

SANOFI 0 1 1 1 0 0 0 1 0 0 2.5

ESSILOR 0 0 1 1 1 1 1 1 1 1 9

L'OREAL 0 0 1 1 0 0 0 1 1 1 6

UNILEVERNV 0 0 0 1 1 1 1 1 1 1 8.5

DANONE 0 0 0 1 0 0 0 1 1 1 5.5

CARREFOUR 1 1 1 0 0 0 0 0 1 1 5.5

ANHEUSER-

BUSCHINBEV 0 1 0 1 0 0 0 1 1 1 6

SAP 0 0 1 1 1 0 1 1 1 1 8

ASMLHLDG 0 0 1 1 0 0 0 1 1 1 6

TELEFONICA 1 0 1 0 0 1 0 0 1 1 6

ORANGE 0 1 0 0 0 0 0 0 0 0 0.5

DEUTSCHE

TELEKOM 0 0 0 0 0 0 0 0 0 0 0

VIVENDI 0 0 0 1 0 0 0 1 0 0 1.5

ENEL 0 0 1 0 0 1 1 0 0 0 2.5

IBERDROLA 0 0 0 1 1 0 0 0 0 0 1.5

E.ON 1 1 1 0 0 0 0 0 0 0 1.5

Source:ownwork.

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Annex5:Cornerportfolios



25



26


Annex6.Distributionofreturns


27



28



29


30

Annex7.Financialstatementsinformation

Source:correspondingFY2013consolidatedfinancialstatements.

31

Annex8.ExcelSolver’sworksheet


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