risk return and cost of capital风险回报和资本成本.pptx
Return,Risk,andtheSecurityMarketLinenTypesofReturnsnExpectedReturnsandVariancesnPortfoliosnAnnouncements,Surprises,andExpectedReturnsnRisk:SystematicandUnsystematicnDiversificationandPortfolioRisknSystematicRiskandBetanTheSecurityMarketLinenTheSMLandtheCostofCapitalnSummaryandConclusionsTypesofReturnsnTotalMonetaryreturn=DividendIncome+CapitalGainuEganinvestmentof1000risesinvalueto1500providingacapitalgainof500.Overthesameperiodthedividendincomeis5%=50.Totalreturnisthen500+50=550.uTotalmonetaryreturnisanabsolutemeasureofreturns.Ittellsyouhowmuchmoneyyouhavemadeins.ItisoftenmoreusefultoknowthePercentageReturn.nThePercentageReturnisthetotalmonetaryreturndividedbytheamountofcapitalinvested.nPercentageReturn=Dividends+CapitalGainsamountinvestedOrRit=Dit+(PitPit-1)=Div.Yield+%capitalgainPit-1ExpectedReturnsandVariances:BasicIdeasnThequantificationofriskandreturnisacrucialaspectofmodernfinance.Itisnotpossibletomake“good”(i.e.,value-maximizing)financialdecisionsunlessoneunderstandstherelationshipbetweenriskandreturn.nRationalinvestorslikereturnsanddislikerisk.nConsiderthefollowingproxiesforreturnandrisk:Expectedreturn-weighted average of the distribution of possible returns in the future.Varianceofreturns-a measure of the dispersion of the distribution of possible returns in the future.Howdowecalculatethesemeasures?.CalculatingtheExpectedReturn.Example1sE(R)=(pixRi)i=1piRiProbabilityReturninipixRiStateofEconomyofstateistatei+1%changeinGNP.25-5%i=1-1.25%+2%changeinGNP.5015%i=27.5%+3%changeinGNP.2535%i=38.75%Expectedreturn=(-1.25+7.50+8.75)=15%CalculatingtheVariance(Example1ofCalculatingtheexpectedreturn)Var(R)i(RiE(R)2pix(RiE(R)2i=1(-0.05-0.15)2=0.04 0.25*0.04=0.01i=2(0.15-0.15)2=00.5*0=0i=3(0.35-0.15)2=0.040.25*0.04=0.01Var(R)=.02Whatisthestandarddeviation?ExpectedReturnsandVariancesExample2StateoftheProbabilityReturnonReturnoneconomyofstateassetAassetBBoom0.4030%-5%Bust0.60-10%25%1.00nA.ExpectedreturnsE(RA)=0.40 x(.30)+0.60 x(-.10)=.06=6%E(RB)=0.40 x(-.05)+0.60 x(.25)=.13=13%Example:ExpectedReturnsandVariances(concluded)nB.VariancesVar(RA)=0.40 x(.30-.06)2+0.60 x(-.10-.06)2=.0384Var(RB)=0.40 x(-.05-.13)2+0.60 x(.25-.13)2=.0216nC.StandarddeviationsSD(RA)=.0384=.196=19.6%SD(RB)=.0216=.147=14.7%CalculatingExpectedReturnsandVarianceinpracticenThemostcommonmethodistouseatimeseriesofreturnscalculatedfrompastpricesanddividends.dayBP pricediv.Ret.=Ret.Monday4300Tuesday4350(435-430)/4300.0116Wednesday4370(437-435)/4350.0046Thursday4410(441-437)/4370.0092Friday4350(435-441)/441-0.0136Monday4350(435-435)/4350.0000Tuesday4200(420-435)/435-0.0345CalculatingExpectedReturnsandVarianceinpractice(2)nE(Ri)isassumedtobeequaltothesampleaveragereturnn=(0.0116+0.0046+0.0092-0.0136+0-0.0345)/6n=-0.00378nTocalculatethevariancewecalculatethedeviationforeachdaysreturnfromtheexpectedreturn,squaretomakeitpositiveandthendividebyn-1.Inthiscasen=6.CalculatingExpectedReturnsandVarianceinpractice(3)Ret.Rit-E(Rit)(Rit-E(Rit)20.01160.01540.000240.00460.00840.000070.00920.01290.00017-0.0136-0.00980.000100.00000.00380.00001-0.0345-0.03070.00094-0.003780.00031MeasuringrisknIfweweretoplotthedailyreturnsonasecurityoveralongperiodthenitmightlooksomethinglikeanormaldistribution(picturenextslide)nWhatwewanttodoistosummarisethispictureassimplyaspossible.Themeanistheexpectedreturn,thespreadorvariationisthestandarddeviationorvariance.WearguethatthisspreadrepresentsrisktoinvestorsandhencethattheSt.Dev.orvarianceisameasureoftheriskofashare.nInfactreturndistributionsdontusuallylookexactlylikethis.Theytendtohaveatruncatedlefttailandalongerrighttail.Variancemaynotbethebestmeasureofrisk.DescribingadistributionPortfolioExpectedReturnsandVariancesnWhatwehavedonesofarisdescribetheriskandreturnofindividualsecurities.Wealsowanttobeabletodescribetheriskandreturnofportfoliosofsecurities.nWehavetwoequivalentalternativesopentous.uComponent-Wecandeterminethereturnandriskoftheportfoliobycombiningthereturnsandrisksofthesecuritiesthatmakeuptheportfolio.uSecurity-Wecantreattheportfolioasjustanothersecurityandcalculateitsreturnandriskaswehavebeendoing.nBothoftheseapproachesgivethesameanswerbutthefirstallowsustoseehowindividualsecuritiesaffectthereturnandriskofaportfolio.PortfolioExpectedReturnsandVariances(usingreturnsfromExample2)nPortfolioweights:put50%inAssetAand50%inAssetB:StateoftheProbabilityReturnReturnReturnoneconomyofstateonAonBportfolioBoom0.4030%-5%12.5%Bust0.60-10%25%7.5%1.00Example:PortfolioExpectedReturnsandVariances(continued)Calculateexpectedreturns:SecurityapproachE(RP)=0.40 x(.125)+0.60 x(.075)=.095=9.5%ComponentapproachE(RP)=.50 xE(RA)+.50 xE(RB)=9.5%Calculatevarianceofportfolio:SecurityapproachVar(RP)=0.40 x(.125-.095)2+0.60 x(.075-.095)2=.0006PortfolioapproachThesumofthevariancesisnotthevarianceoftheportfolioVar(RP).50 xVar(RA)+.50 xVar(RB)FtthisweeknOlympussagacontinuesresignationofPresident,openletterbymajorshareholder,questions(atlast!)byJapanesePressandGovernment.nEurozonethedealmoreofthesame,bigger(voluntary)haircuts,moreausteritybutthedebtorstrikesback(Greekreferendum).nMFGlobalcollapsebroker-dealersufferingfromeurozoneratingsdowngrades($6.3bnexposure).nManagementgreedhugeincreaseinseniormanagementpayoverlastyear.TheStorysofarnOuraimistorelatereturntorisk.Basicprincipleisthatinvestorsrequirearewardfortakingonrisk.Thelargertherisk,thelargerthereward.nButhowarewetomeasureriskandreturn?nManydifferenttypesofrisk.Weconcentrateonriskasperceivedbythecapitalmarkets.nThepriceofashareatanytimereflectseverythingthatisknownaboutthecompany.Suggeststhatwecanusepricechangestoprovideinformationaboutthecompany.nByexaminingthedistributionofpercentagepricechanges(returns)wecandeterminethelikelyorexpectedreturn,andthedispersionofreturnsthatmightoccur.Thestorysofar(2)nAnobviousmeasureofexpectedreturnisthearithmeticmean.Ameasureofdispersionisthevariance.Thisisusedasameasureoftheriskofashare.Thevarianceisareasonablemeasureifthedistributionofreturnsissymmetric.nMostcompaniesarenotheldinisolationbutareheldaspartofaportfolio.Weusetwoshareportfoliostodemonstratehowriskchanges.TheproportionofeachcompanyintheportfolioisknownastheportfolioWeight.nOurinterestisinhowonecompanyrelatestoanother.Weareconcernedaboutthejoint distribution of returns.JointDistributionofreturnsprobabilityReturnonSecurityXReturnonSecurityYCovarianceandCorrelationTheCovarianceisameasureofhowthetwosecuritiesarerelated.SimilartoVariancebutusescrossdeviations.Variance=E(RAtE(RAt)(RAtE(RAt)Covariance=average(deviationofreturnonAfromitsmean)*(deviationofreturnonBfromitsmean)CAB=E(RAtE(RAt)(RBtE(RBt)CorrelationisastandardisedCovariance.CorrelationbetweenAandBistheCovariancebetweenAandBdividedbythestandarddeviationofAtimesthestandarddeviationofB.AB=CovAB/A BCovarianceandCorrelationnTheriskofaportfolioiscomprisedoftheriskoftheindividualsecuritiesplusthecorrelationbetweenthem.nIftherearetwosecuritiesthentheriskoftheportfoliocanbecalculatedfromthevarianceofeachsecurityplusthecorrelationbetweenthem.nFortwosecuritieswehave:n p2=X12Var1+X22Var2+2X1X2Cov12Remember:Cov12=1 2 12 p2=X12 12+X22 22+2X1X2 1 2 12Cov12=E(R1t-E(R1t)(R2t-E(R2t)=E(R2t-E(R2t)(R1t-E(R1t)=Cov21TwosecurityPortfolioSelectionExampleRpt=X1R1t+X2R2tE(Rpt)=E(X1R1t+X2R2t)=X1E(R1t)+X2E(R2t)p2=E(Rpt-E(Rpt)2p2=EX1R1t+X2R2t-(X1E(R1t)+X2E(R2t)2p2=EX1(R1t-E(R1t)+X2(R2t-E(R2t)2Fromalgebraweknowthat(a+b)2=a2+b2+2abp2=X12E(R1t-E(R1t)2+X22E(R2t-E(R2t)2+2X1X2E(R1t-E(R1t)(R2t-E(R2t)=X1212+X2222+2X1X2Cov12HowCorrelationaffectsrisk(2securityexample)HowCorrelationaffectsrisk(2securityexample)HowCorrelationaffectsrisk(2securityexample)TheEffectofcorrelationonPortfolioVarianceStockAreturns0.050.040.030.020.010-0.01-0.02-0.03-0.04-0.050.050.040.030.020.010-0.01-0.02-0.03StockBreturns0.040.030.020.010-0.01-0.02-0.03Portfolioreturns:50%Aand50%BCovarianceandCorrelation:morethan2securitiesnOnewayofthinkingofthecovarianceofsecuritieswithinaportfolioistovisualiseamatrixofsecurities.Eachsecuritymustpairwitheachother.Ifthenumbersarethesameitisavariance,otherwiseacovariance.egiftherearefivesecuritieswecanthinkof:security1234511=1variance1,2correlation1,3correlation1,41,522,1correlation2,2variance2,32,42,533,13,23,3Variance3,43,544,14,24,34,4variance4,555,15,25,35,45,5varianceComponentsofPortfolioRiskVarianceCovarianceExpressionCovarianceandCorrelation(cont.)nImpactofcorrelation(covariance)SizeofportfolioNumberofvariancesNumberofdistinctcorrelations(covariances)22133355101010451001004950StandardDeviationsofAnnualPortfolioReturns(3)(2)RatioofPortfolio(1)AverageStandardStandardDeviationtoNumberofStocksDeviationofAnnualStandardDeviationinPortfolioPortfolioReturns(%)ofaSingleStock149.241.001023.930.495020.200.4110019.690.4030019.340.3950019.270.391,00019.210.39FiguresfromTable1inMeirStatman,“HowManyStocksMakeaDiversifiedPortfolio?”Journal of Financial and Quantitative Analysis 22(September1987),pp.35364,andderivedfromE.J.EltonandM.J.Gruber,“RiskReductionandPortfolioSize:AnAnalyticSolution,”Journal of Business50(October1977),pp.41537.PortfolioDiversificationAverageannualstandarddeviation(%)NumberofstocksinportfolioDiversifiableriskNondiversifiablerisk49.223.919.21102030401000Diversification:analyticalsolutionDiversification:analyticalsolution(2)Diversification:analyticalsolution(3)Ifweweretolookatthecasewherecovariancesarenotequaltozerowewouldfindthattheriskofalargeportfolioofstocksisapproximatelyequaltotheaveragecovariancebetweenallthestocks.P2 CovAVPeterBernsteinonRiskandDiversification“Bigrisksarescarywhenyoucannotdiversifythem,especiallywhentheyareexpensivetounload;eventhewealthiestfamilieshesitatebeforedecidingwhichhousetobuy.Bigrisksarenotscarytoinvestorswhocandiversifythem;bigrisksareinteresting.Nosinglelosswillmakeanyonegobroke.bymakingdiversificationeasyandinexpensive,financialmarketsenhancethelevelofrisk-takinginsociety.”PeterBernstein,inhisbook,CapitalIdeasHowcorrelationaffectsrisk:TheEfficientFrontierFTthisweeknOlympusadmitswrongdoing.nEurozonemanyinterestingarticleshighlightingthepowerofGreece,Germanroleandinterest,dangerstoItalyandothers.Focusononearticle:RobertJenkins,Insight(nov.8)-GreekrestructuringexitfromtheeurozonenGreekgovtdecidesonexit.uGreekcitizensandcompanieswithdraweurodepositswhilsttheyarestilleuros.Foreignlendersstoplendingandrecallloansasquicklyaspossible.uGovt.announcesanewdrachma.Capitalcontrolsareintroduced.Govtdebtisredenominatedindrachma.OlympussharepriceFTthisweek(cont)GreekrestructuringnValueofthedrachmaplunges,Greekinflationsoars.nDisputesoverprivatesectordebt.Aretheyindrachmaoreuros?Ifdrachmathenforeignbankshaveaproblemassetvalueshavefallen.IfineurosthenGreekborrowershaveaproblemnContagioncommences.Portugesecitizensthinkitmighthappentothemandmoveouteurosfromthebanks.Similarmovesinseveralothercountries.nEuropeanbanksindifficultiesbecauseofexposuretoeurodebtofvariouscountrieswithlikelydifficulties.Counterpartyriskmeansmarketinbankloansdriesup.Banklendinghalts!nBankscollapseunlessGovtrescuethem.TheStorytodatenTheriskofaportfoliodependsontheCovarianceorCorrelationbetweenassets.Varianceisimportantforanindividualassetbutbecomeslessandlessimportantasaportfolioincludesmoreandmorestocks.nTheriskofaportfoliodependsontheaveragecovariancebetweenstocks.nTherelationshipbetweenriskandreturncanberepresentedgraphicallybyaquadraticfrontier.ThebestcombinationsofriskandreturnareontheEfficientFrontier.Theshapeofthefrontierarisesfromthecovariancebetweenassets.HowCorrelationaffectsrisk:ariskfreeassetHowCorrelationaffectsrisk:ariskfreeasset(2)TobinsSeparationTheoremSimplifyingourRiskMeasurenOurmessagesofarhasbeenthatwhenweaddsecuritiestogetherriskisaffectedbythecorrelation(covariance)betweenthem.Becausesecuritiesarelessthanperfectlycorrelated,riskisreduced.nWhilstthisisusefulasaconceptitisoperationallyverydifficulttouse.Thenumberofcorrelationsthatweneedtoconsidertoconstructoptimalportfoliosusingthissortofapproachisverylarge.Weneedtofindsomeothermeasureofriskthatwillenableustosimplifytheproblem.Onesuchmeasureisthebetaofasecurityorportfolio.Thebetaofasecuritycanbethoughtofas:the(standardised)sumofthesecurityscovariancewithallsecuritiesnSinceall securities isjustanotherwayofsayingthe market,thebetaofasecurityis:the(standardised)covarianceofthesecuritywiththe marketEstimatingBetanBetaisusuallyestimatedusinglinearregression.BetaisanoutputfromtheMarketModel.Thisassumesthatthereisalinearrelationshipbetweenthereturnonthemarketandthereturnonashare.Returnsonashareareregressedagainstreturnsonamarketindex.Rit=ai+biRmtcitaiisthealphaofshareIbiisthebetaofshareIBetaCoefficientsforSelectedCompanies(Table10.7)BetaCompanyCoefficient(i)Alcatel-Lucent1.44LOreal0.45SAP0.56Siemens1.51Daimler1.25PhilipsElectron0.92Renault1.64Volkswagen0.40Source:Hillier,Ross,Westerfield,Jaffe,Jordan.CorporateFinance.PortfolioBetaCalculationsPortfolioBetahasaverydesirablecharacteristic.Itisthe(weighted)averageoftheindividualbetas.AmountPortfolioStockInvestedWeightsBeta(1)(2)(3)(4)(3)x(4)HaskellMfg.$6,00050%0.900.450Cleaver,Inc.4,00033%1.100.367RutherfordCo.2,00017%1.300.217Portfolio$12,000100%1.034Cash(risklessasset),PortfolioExpectedReturnsandBetasnAssumeyouwishtoholdaportfolioconsistingofariskyassetAandcash(arisklessasset).Giventhefollowinginformation,calculateportfolioexpectedreturnsandportfoliobetas,lettingtheproportionoffundsinvestedinassetArangefrom0to125%.AssetAhasabeta()of1.2andanexpectedreturnof18%.ThereturnoncashattheCentralBank(risk-freerate)is7%.AssetAweights:0%,25%,50%,75%,100%,and125%.Cash(risklessasset),PortfolioExpectedReturnsandBetasProportionProportionPortfolioInvestedinInvestedinExpectedPortfolioAssetA(%)Risk-freeAsset(%)Return(%)Beta01007.000.0025759.750.30505012.500.60752515.250.90100018.001.20125-2520.751.50Plotthisandmeasuretheslope-(.18-.07)/1.2=0.092.Thisistheriskpremiumperunitofsystematicrisk.Cash(risklessasset),PortfolioExpectedReturnsandBetasExpectedreturn18%7%01.2betaSlope=(.18-.07)/1.2=.092Return,Risk,andEquilibriumnKeyissues:uWhatistherelationshipbetweenriskandreturn?uWhatdoessecuritymarketequilibriumlooklike?Thefundamentalconclusionisthattheratiooftheriskpremiumtobetaisthesameforeveryasset.Inotherwords,thereward-to-riskratioisconstantandequalto E(Ri)-Rfslope=Reward/riskratio=iReturn,Risk,andEquilibrium(concluded)nExample:AssetAhasanexpectedreturnof12%andabetaof1.40.AssetBhasanexpectedreturnof8%andabetaof0.80.Aretheseassetsvaluedcorrectlyrelativetoeachotheriftherisk-freerateis5%?a.ForA,(.12-.05)/1.40=_b.ForB,(.08-.05)/0.80=_nWhatwouldtherisk-freeratehavetobefortheseassetstobecorrectlyvalued?(.12-Rf)/1.40=(.08-Rf)/0.80Rf=_TheCapitalAssetPricingModelnTheCapitalAssetPricingModel(CAPM)-anequilibriummodeloftherelationshipbetweenriskandreturn.Whatdeterminesanassetsexpectedreturn?uTherisk-freerate-thepuretimevalueofmoneyuThemarketriskpremium-therewardforbearingsystematicriskuThebetacoefficient-ameasureoftheamountofsystematicriskpresentinaparticularassetTheCAPM:E(Ri)=Rf+E(RM)-Rf xiCapitalAssetPricingModel(2)nExpectedreturnonassetiisalinearfunctionoftheriskfreerateandtheassetsmarginalrisk(beta)timestheexpectedriskpremiumonthemarket.E(Ri)=Rf+(E(Rm)-Rf)in iisthebetaofasecurity.Itisderivedfromthemarketmod
