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
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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 ESSILOR UNILEVER SAP ENEL
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
Source:ownwork,usingYahooFinancedata.
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 ESSILOR UNILEVER SAP ENEL
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%
Source:ownwork,usingYahooFinancedata.
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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%
Source:ownwork,usingYahooFinancedata.
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):
Source:ownwork,usingYahooFinancedata.
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:
Source:ownwork,usingYahooFinancedata.
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):
Source:ownwork,usingYahooFinancedata.
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.
24
Annex5:Cornerportfolios
Source:ownwork,usingYahooFinancedata.
Source:ownwork,usingYahooFinancedata.
25
Source:ownwork,usingYahooFinancedata.
Source:ownwork,usingYahooFinancedata.
26
Source:ownwork,usingYahooFinancedata.
Annex6.Distributionofreturns
Source:ownwork,usingYahooFinancedata.
27
Source:ownwork,usingYahooFinancedata.
Source:ownwork,usingYahooFinancedata.
28
Source:ownwork,usingYahooFinancedata.
Source:ownwork,usingYahooFinancedata.
29
Source:ownwork,usingYahooFinancedata.
30
Annex7.Financialstatementsinformation
Source:correspondingFY2013consolidatedfinancialstatements.
31
Annex8.ExcelSolver’sworksheet
Source:ownwork,usingYahooFinancedata.