CorporatefinanceEighthEditionChapter8PortfoliotheoryandthecapitalassetpricingmodelRiskCompaniesfaceriskfromvariabilityinprojectcashflows.Investorsfaceriskfromvariabilityincapitalgainsanddividends.Rationalaimistominimiseriskforgivenlevelofreturn.Tocontrolriskitmustbeunderstoodandmeasured.ThemeasurementofriskRiskismeasuredbythestandarddeviationofthereturnsonashare,basedoneitherhistoricalreturnsorexpectedfuturereturns.Probability(left)/Historicdata(right)

Mean(top)/Standarddeviation(bottom)DistributionofreturnsonSandTTheconceptofdiversificationTotalriskcanbedividedintosystematicandunsystematicrisk.Systematicriskisduetosystematicfactorssuchaschangesininterestrates,businesscyclesandgovernmentpolicy.Unsystematicriskisspecifictoagivenshare.Unsystematicriskdecreasesasthenumberofinvestmentsinaportfolioincreases:thisiscalledportfoliodiversificationofrisk.DiversificationofriskTotalriskfallsasnumberofinvestmentsrisesThetwo-shareportfolioTheamountofriskdiversificationdependsoncorrelationbetweenreturnsandhenceonthevalueofthecorrelationcoefficient(CC).+1:nodiversificationofunsystematicrisk.–1:fulldiversificationofunsystematicrisk.0:nocorrelationbetweenreturnsandpartialdiversificationofunsystematicrisk.Thetwo-shareportfolio(continued)sp=

(Wx).(x)

+

(Wy).(y)

+

2

.Wx

.Wy.x.y.

x,y

222ssssr2ShareSMeanreturn:5.96%Standarddeviation:8.16%ShareTMeanreturn:9.10%Standarddeviation:13.39%Calculatedcorrelationcoefficient=–0.389.Thetwo-shareportfolio(continued)Portfoliowith80%Sand20%T:Return=(0.8×5.96)+(0.2×9.1)=6.59%Risk=((0.82×8.162)+(0.22×13.392)+ (2×0.8×0.2×8.16×13.39×–0.389))?=6.02%ThisgivespointAonnextslide.SeetextbookforpointsB,CandD.Thetwo-shareportfolio(continued)Thetwo-shareportfolio(continued)InvestorscanchooseportfoliosanywherealongthearcSABCDTinFigure8.3.TheriskoftheseportfoliosislessthanthatrepresentedbythestraightlineST.CombiningSandThasreducedtotalriskbydiversifyingunsystematicrisk.Asnumberofsharesintheportfolioincreases,the‘bat-wing’shapeinthenextdiagramarises.Thetwo-shareportfolio(continued)Four-shareportfolioRisk(standarddeviation)Return(%)0ABCDInvestorattitudestoriskInvestorattitudestorisk(continued)Investorsandtheirrisksaturationpoints

PortfoliotheoryRationalinvestorsinvestonlyontheefficientfrontier,therebymaximisingtheirutility.Ifrisk-freeassetsareavailable,investorswillcombinethemwiththemarketportfolio.Rationalinvestorsthenthereforeselecttheiroptimalportfolioonthecapitalmarketlineatapointoftangencywiththeirutilitycurves.Risk(standarddeviation)0Return(%)EFGHAIEnvelopecurve(riskyinvestments)Theenvelopecurve

Risk(standarddeviation)0Return(%)EFGHAIEfficientfrontierBTheefficientfrontier

ZRisk(standarddeviation)0

mRfReturn(%)MEFGHRmAIMarketportfolioCapitalmarketlineBThemarketportfolio

ZRisk(standarddeviation)0RfReturn(%)MEFGHNU0BAIOptimumpointifonlyriskyassetsareavailableNoriskfreeassetsavailable

ZRisk(standarddeviation)0RfReturn(%)MEFGHNU0U1U2PRp

pBAIRiskfreeassetsavailable

Portfoliotheoryisusedbymanyinstitutionalinvestors(e.g.insurancecompanies,pensionfunds)whohavelargediversifiedportfolios.Problemswithusingportfoliotheory:Borrowingattherisk-freerateIdentifyingthemarketportfolioConstructingthemarketportfolioChangingcompositionofmarketportfolioPortfoliotheory(continued)CAPM:anintroductionTheCAPMisamethodofsharevaluationdevelopedbyWilliamSharpein1964.Itisbasedonalinearrelationshipbetweenriskandreturn.Itisadevelopmentofportfoliotheory.Itconsidersthatsystematicriskistheonlyrelevantriskwhenvaluingshares.CAPMassumptionsInvestorsarerationalutilitymaximisers.Informationisfreelyavailable.Allinvestorshavesimilarexpectations.Investorscanborrowandlendattherisk-freerate.Investorsholddiversifiedportfolios,therebyeliminatingallunsystematicrisk.Capitalmarketsareperfect:NotaxesortransactioncostsFreeentryandexitManybuyersandsellersInformationiscostlessandfreelyavailableSingleperiodtransactionhorizon:returnsarecalculatedoverastandardperiod.usuallytakenas1year.CAPMassumptions(continued)Rj=Rf+βj(Rm–Rf)ThesecuritymarketlineCAPMcomponentsReturnofthemarket(Rm)Risk-freerateofreturn(Rf)Equityriskpremium(Rm–Rf)Betavalueofordinaryshares(βj)MeaningandcalculationofbetaBetaisseenasan‘indexofresponsiveness’ofchangesinasecurity’sreturnsrelativetochangesinreturnsonthemarket.Example:BP’sequitybeta=0.75Marketreturnincreasesby10%ReturnonBP’ssharesincreasesby7.5%Meaningandcalculationofbeta(continued)Betacanbefoundfrom:βj

=(σjxσmxρj,m)/σm2

where:σj=standarddeviationofreturnsonassetjσm=standarddeviationofmarketreturnsΡj,m=correlationcoefficientbetweenjandmσm2=varianceofreturnsonthemarketBetacanbefoundbyregressionanalysisofsecurityreturnsagainstmarketreturns.Betacanbefoundfromalineofbestfitofaplotofsecurityreturnsagainstmarketreturns.CompanybetavaluesarefoundintheBetaBookspublishedbytheLondonBusinessSchoolRiskMeasurementServiceandfromotherfinancialresourcessuchasDatastream.Meaningandcalculationofbeta(continued)Meaningandcalculationofbeta(continued)Security Beta WeightWeightedbetaBarclays 1.43 20% 0.286BP 1.49 35% 0.522Kingfisher 0.84 15% 0.126SevernTrent 0.53 20% 0.106Tesco 0.94 10% 0.094PortfolioBeta 1.134

Meaningandcalculationofbeta(continued)Returnofthemarket(Rm)ApproximatedbyusingstockexchangeindexsuchasFTSE100,forexample:Rm=[(FTSE1

–FTSE0)/FTSE0]+DividendYield.Calculatedonamovingaveragebasisfrommonthlyorannualdata.Equityriskpremiumcanbedeterminedoneithera‘geometric’oran‘a(chǎn)rithmetic’basis.Arithmeticriskpremiumoverestimatessogeometricriskpremiumisrecommended.Equityriskpremium(Rm–Rf)DimsonandBrealey(1978)found9%fortheperiod1918–77–nowseenastoohigh.Allanetal.(1986)found9.1%fortheperiod1919–84.Dimsonetal.(2002)gave4.5%fortheperiod1900–2001and7.2%for1951–2001.CreditSuisse(2018)foundERPintheUKfrom1968–2017tobe4.8%usingUKTreasurybills.Currentequityriskpremiumof3%to5%?Risk-freerate(Rf)Noassetsare

totallyrisk-free,butbondsissuedbygovernmentsofstablecountriesareseenasalmostrisk-free.Rfapproximatedbytheyieldtomaturityoftreasurybills(short-termgovernmentdebt).Shortmaturityasthesehavelowestrisk.ExampleofusingtheCAPMEquitybetaofBurberryGroupplc=1.14Risk-freerate(yieldonTreasurybills):1.0%Marketriskpremium(Rm–Rf):4.5%Rj=1%+(1.14×4.5%)=6.1%Thisrepresentsshareholders’requiredrateofreturnandhencethecostofequityofBurberryGroupplc.ImplicationsoftheCAPMInvestorswillrequirecompensationonlyforsystematicrisk,sinceunsystematicriskcanbeeradicatedbyportfoliodiversification.Securitieswithhighlevelsofsystematicriskshould,onaverage,yieldhighratesofreturn.Thereshouldbealinearrelationshipbetweensystematicriskandreturn.Correctlypricedsecuritiesshouldplotonthesecuritymarketline(SML).ImplicationsoftheCAPM(continued)EmpiricalevidenceEvidenceinyearsfollowingdevelopmentoftheCAPMwassupportive: SharpeandCooper(1972)foundportfolio betas(10ormoreshares)werestablewhile individualbetaswerenot. Jacob(1971)andBlack,Jen