risk return and cost of capital风险回报和资本成本.ppt

Return,Risk,andtheSecurityMarketLine,TypesofReturnsExpectedReturnsandVariancesPortfoliosAnnouncements,Surprises,andExpectedReturnsRisk:SystematicandUnsystematicDiversificationandPortfolioRiskSystematicRiskandBetaTheSecurityMarketLineTheSMLandtheCostofCapitalSummaryandConclusions,TypesofReturns,TotalMonetaryreturn=DividendIncome+CapitalGainEganinvestmentof1000risesinvalueto1500providingacapitalgainof500.Overthesameperiodthedividendincomeis5%=50.Totalreturnisthen500+50=550.Totalmonetaryreturnisanabsolutemeasureofreturns.Ittellsyouhowmuchmoneyyouhavemadeins.ItisoftenmoreusefultoknowthePercentageReturn.ThePercentageReturnisthetotalmonetaryreturndividedbytheamountofcapitalinvested.PercentageReturn=Dividends+CapitalGainsamountinvestedOrRit=Dit+(PitPit-1)=Div.Yield+%capitalgainPit-1,ExpectedReturnsandVariances:BasicIdeas,Thequantificationofriskandreturnisacrucialaspectofmodernfinance.Itisnotpossibletomake“good”(i.e.,value-maximizing)financialdecisionsunlessoneunderstandstherelationshipbetweenriskandreturn.Rationalinvestorslikereturnsanddislikerisk.Considerthefollowingproxiesforreturnandrisk:Expectedreturn-weightedaverageofthedistributionofpossiblereturnsinthefuture.Varianceofreturns-ameasureofthedispersionofthedistributionofpossiblereturnsinthefuture.Howdowecalculatethesemeasures?.,CalculatingtheExpectedReturn.Example1,sE(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=0.040.25*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?,ExpectedReturnsandVariancesExample2,StateoftheProbabilityReturnonReturnoneconomyofstateassetAassetBBoom0.4030%-5%Bust0.60-10%25%1.00A.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),B.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=.0216C.StandarddeviationsSD(RA)=.0384=.196=19.6%SD(RB)=.0216=.147=14.7%,CalculatingExpectedReturnsandVarianceinpractice,Themostcommonmethodistouseatimeseriesofreturnscalculatedfrompastpricesanddividends.,CalculatingExpectedReturnsandVarianceinpractice(2),E(Ri)isassumedtobeequaltothesampleaveragereturn=(0.0116+0.0046+0.0092-0.0136+0-0.0345)/6=-0.00378Tocalculatethevariancewecalculatethedeviationforeachdaysreturnfromtheexpectedreturn,squaretomakeitpositiveandthendividebyn-1.Inthiscasen=6.,CalculatingExpectedReturnsandVarianceinpractice(3),Measuringrisk,Ifweweretoplotthedailyreturnsonasecurityoveralongperiodthenitmightlooksomethinglikeanormaldistribution(picturenextslide)Whatwewanttodoistosummarisethispictureassimplyaspossible.Themeanistheexpectedreturn,thespreadorvariationisthestandarddeviationorvariance.WearguethatthisspreadrepresentsrisktoinvestorsandhencethattheSt.Dev.orvarianceisameasureoftheriskofashare.Infactreturndistributionsdontusuallylookexactlylikethis.Theytendtohaveatruncatedlefttailandalongerrighttail.Variancemaynotbethebestmeasureofrisk.,Describingadistribution,PortfolioExpectedReturnsandVariances,Whatwehavedonesofarisdescribetheriskandreturnofindividualsecurities.Wealsowanttobeabletodescribetheriskandreturnofportfoliosofsecurities.Wehavetwoequivalentalternativesopentous.Component-Wecandeterminethereturnandriskoftheportfoliobycombiningthereturnsandrisksofthesecuritiesthatmakeuptheportfolio.Security-Wecantreattheportfolioasjustanothersecurityandcalculateitsreturnandriskaswehavebeendoing.Bothoftheseapproachesgivethesameanswerbutthefirstallowsustoseehowindividualsecuritiesaffectthereturnandriskofaportfolio.,PortfolioExpectedReturnsandVariances(usingreturnsfromExample2),Portfolioweights:put50%inAssetAand50%inAssetB:StateoftheProbabilityReturnReturnReturnoneconomyofstateonAonBportfolioBoom0.4030%-5%12.5%Bust0.60-10%25%7.5%1.00,Example: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),Ftthisweek,OlympussagacontinuesresignationofPresident,openletterbymajorshareholder,questions(atlast!)byJapanesePressandGovernment.Eurozonethedealmoreofthesame,bigger(voluntary)haircuts,moreausteritybutthedebtorstrikesback(Greekreferendum).MFGlobalcollapsebroker-dealersufferingfromeurozoneratingsdowngrades($6.3bnexposure).Managementgreedhugeincreaseinseniormanagementpayoverlastyear.,TheStorysofar,Ouraimistorelatereturntorisk.Basicprincipleisthatinvestorsrequirearewardfortakingonrisk.Thelargertherisk,thelargerthereward.Buthowarewetomeasureriskandreturn?Manydifferenttypesofrisk.Weconcentrateonriskasperceivedbythecapitalmarkets.Thepriceofashareatanytimereflectseverythingthatisknownaboutthecompany.Suggeststhatwecanusepricechangestoprovideinformationaboutthecompany.Byexaminingthedistributionofpercentagepricechanges(returns)wecandeterminethelikelyorexpectedreturn,andthedispersionofreturnsthatmightoccur.,Thestorysofar(2),Anobviousmeasureofexpectedreturnisthearithmeticmean.Ameasureofdispersionisthevariance.Thisisusedasameasureoftheriskofashare.Thevarianceisareasonablemeasureifthedistributionofreturnsissymmetric.Mostcompaniesarenotheldinisolationbutareheldaspartofaportfolio.Weusetwoshareportfoliostodemonstratehowriskchanges.TheproportionofeachcompanyintheportfolioisknownastheportfolioWeight.Ourinterestisinhowonecompanyrelatestoanother.Weareconcernedaboutthejointdistributionofreturns.,JointDistributionofreturns,probabilityReturnonSecurityXReturnonSecurityY,CovarianceandCorrelation,TheCovarianceisameasureofhowthetwosecuritiesarerelated.SimilartoVariancebutusescrossdeviations.Variance=E(RAtE(RAt)(RAtE(RAt)Covariance=average(deviationofreturnonAfromitsmean)*(deviationofreturnonBfromitsmean)CAB=E(RAtE(RAt)(RBtE(RBt)CorrelationisastandardisedCovariance.CorrelationbetweenAandBistheCovariancebetweenAandBdividedbythestandarddeviationofAtimesthestandarddeviationofB.AB=CovAB/AB,CovarianceandCorrelation,Theriskofaportfolioiscomprisedoftheriskoftheindividualsecuritiesplusthecorrelationbetweenthem.Iftherearetwosecuritiesthentheriskoftheportfoliocanbecalculatedfromthevarianceofeachsecurityplusthecorrelationbetweenthem.Fortwosecuritieswehave:p2=X12Var1+X22Var2+2X1X2Cov12Remember:Cov12=1212p2=X1212+X2222+2X1X21212Cov12=E(R1t-E(R1t)(R2t-E(R2t)=E(R2t-E(R2t)(R1t-E(R1t)=Cov21,TwosecurityPortfolioSelectionExample,Rpt=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+2X1X2Cov12,HowCorrelationaffectsrisk(2securityexample),HowCorrelationaffectsrisk(2securityexample),HowCorrelationaffectsrisk(2securityexample),TheEffectofcorrelationonPortfolioVariance,StockAreturns,0.050.040.030.020.010-0.01-0.02-0.03-0.04-0.05,0.050.040.030.020.010-0.01-0.02-0.03,StockBreturns,0.040.030.020.010-0.01-0.02-0.03,Portfolioreturns:50%Aand50%B,CovarianceandCorrelation:morethan2securities,Onewayofthinkingofthecovarianceofsecuritieswithinaportfolioistovisualiseamatrixofsecurities.Eachsecuritymustpairwitheachother.Ifthenumbersarethesameitisavariance,otherwiseacovariance.egiftherearefivesecuritieswecanthinkof:,ComponentsofPortfolioRisk,VarianceCovarianceExpression,CovarianceandCorrelation(cont.),Impactofcorrelation(covariance),StandardDeviationsofAnnualPortfolioReturns,(3)(2)RatioofPortfolio(1)AverageStandardStandardDeviationtoNumberofStocksDeviationofAnnualStandardDeviationinPortfolioPortfolioReturns(%)ofaSingleStock149.241.001023.930.495020.200.4110019.690.4030019.340.3950019.270.391,00019.210.39FiguresfromTable1inMeirStatman,“HowManyStocksMakeaDiversifiedPortfolio?”JournalofFinancialandQuantitativeAnalysis22(September1987),pp.35364,andderivedfromE.J.EltonandM.J.Gruber,“RiskReductionandPortfolioSize:AnAnalyticSolution,”JournalofBusiness50(October1977),pp.41537.,PortfolioDiversification,Averageannualstandarddeviation(%),Numberofstocksinportfolio,Diversifiablerisk,Nondiversifiablerisk,49.2,23.9,19.2,1,10,20,30,40,1000,Diversification:analyticalsolution,Diversification:analyticalsolution(2),Diversification:analyticalsolution(3),Ifweweretolookatthecasewherecovariancesarenotequaltozerowewouldfindthattheriskofalargeportfolioofstocksisapproximatelyequaltotheaveragecovariancebetweenallthestocks.P2CovAV,PeterBernsteinonRiskandDiversification,“Bigrisksarescarywhenyoucannotdiversifythem,especiallywhentheyareexpensivetounload;eventhewealthiestfamilieshesitatebeforedecidingwhichhousetobuy.Bigrisksarenotscarytoinvestorswhocandiversifythem;bigrisksareinteresting.Nosinglelosswillmakeanyonegobroke.bymakingdiversificationeasyandinexpensive,financialmarketsenhancethelevelofrisk-takinginsociety.”PeterBernstein,inhisbook,CapitalIdeas,Howcorrelationaffectsrisk:TheEfficientFrontier,FTthisweek,Olympusadmitswrongdoing.EurozonemanyinterestingarticleshighlightingthepowerofGreece,Germanroleandinterest,dangerstoItalyandothers.Focusononearticle:RobertJenkins,Insight(nov.8)-GreekrestructuringexitfromtheeurozoneGreekgovtdecidesonexit.Greekcitizensandcompanieswithdraweurodepositswhilsttheyarestilleuros.Foreignlendersstoplendingandrecallloansasquicklyaspossible.Govt.announcesanewdrachma.Capitalcontrolsareintroduced.Govtdebtisredenominatedindrachma.,Olympusshareprice,FTthisweek(cont)Greekrestructuring,Valueofthedrachmaplunges,Greekinflationsoars.Disputesoverprivatesectordebt.Aretheyindrachmaoreuros?Ifdrachmathenforeignbankshaveaproblemassetvalueshavefallen.IfineurosthenGreekborrowershaveaproblemContagioncommences.Portugesecitizensthinkitmighthappentothemandmoveouteurosfromthebanks.Similarmovesinseveralothercountries.Europeanbanksindifficultiesbecauseofexposuretoeurodebtofvariouscountrieswithlikelydifficulties.Counterpartyriskmeansmarketinbankloansdriesup.Banklendinghalts!BankscollapseunlessGovtrescuethem.,TheStorytodate,TheriskofaportfoliodependsontheCovarianceorCorrelationbetweenassets.Varianceisimportantforanindividualassetbutbecomeslessandlessimportantasaportfolioincludesmoreandmorestocks.Theriskofaportfoliodependsontheaveragecovariancebetweenstocks.Therelationshipbetweenriskandreturncanberepresentedgraphicallybyaquadraticfrontier.ThebestcombinationsofriskandreturnareontheEfficientFrontier.Theshapeofthefrontierarisesfromthecovariancebetweenassets.,HowCorrelationaffectsrisk:ariskfreeasset,HowCorrelationaffectsrisk:ariskfreeasset(2),TobinsSeparationTheorem,SimplifyingourRiskMeasure,Ourmessagesofarhasbeenthatwhenweaddsecuritiestogetherriskisaffectedbythecorrelation(covariance)betweenthem.Becausesecuritiesarelessthanperfectlycorrelated,riskisreduced.Whilstthisisusefulasaconceptitisoperationallyverydifficulttouse.Thenumberofcorrelationsthatweneedtoconsidertoconstructoptimalportfoliosusingthissortofapproachisverylarge.Weneedtofindsomeothermeasureofriskthatwillenableustosimplifytheproblem.Onesuchmeasureisthebetaofasecurityorportfolio.Thebetaofasecuritycanbethoughtofas:the(standardised)sumofthesecurityscovariancewithallsecuritiesSinceallsecuritiesisjustanotherwayofsayingthemarket,thebetaofasecurityis:the(standardised)covarianceofthesecuritywiththemarket,EstimatingBeta,Betaisusuallyestimatedusinglinearregression.BetaisanoutputfromtheMarketModel.Thisassumesthatthereisalinearrelationshipbetweenthereturnonthemarketandthereturnonashare.Returnsonashareareregressedagainstreturnsonamarketindex.Rit=ai+biRmtcitaiisthealphaofshareIbiisthebetaofshareI,BetaCoefficientsforSelectedCompanies(Table10.7),BetaCompanyCoefficient(i)Alcatel-Lucent1.44LOreal0.45SAP0.56Siemens1.51Daimler1.25PhilipsElectron0.92Renault1.64Volkswagen0.40,Source:Hillier,Ross,Westerfield,Jaffe,Jordan.CorporateFinance.,PortfolioBetaCalculations,PortfolioBetahasaverydesirablecharacteristic.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%1.034,Cash(risklessasset),PortfolioExpectedReturnsandBetas,AssumeyouwishtoholdaportfolioconsistingofariskyassetAandcash(arisklessasset).Giventhefollowinginformation,calculateportfolioexpectedreturnsandportfoliobetas,lettingtheproportionoffundsinvestedinassetArangefrom0to125%.AssetAhasabeta()of1.2andanexpectedreturnof18%.ThereturnoncashattheCentralBank(risk-freerate)is7%.AssetAweights:0%,25%,50%,75%,100%,and125%.,Cash(risklessasset),PortfolioExpectedReturnsandBetas,ProportionProportionPortfolioInvestedinInvestedinExpectedPortfolioAssetA(%)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),PortfolioExpectedReturnsandBetas,Expectedreturn18%7%01.2betaSlope=(.18-.07)/1.2=.092,Return,Risk,andEquilibrium,Keyissues:Whatistherelationshipbetweenriskandreturn?Whatdoessecuritymarketequilibriumlooklike?Thefundamentalconclusionisthattheratiooftheriskpremiumtobetaisthesameforeveryasset.Inotherwords,thereward-to-riskratioisconstantandequaltoE(Ri)-Rfslope=Reward/riskratio=i,Return,Risk,andEquilibrium(concluded),Example:AssetAhasanexpectedreturnof12%andabetaof1.40.AssetBhasanexpectedreturnof8%andabetaof0.80.Aretheseassetsvaluedcorrectlyrelativetoeachotheriftherisk-freerateis5%?a.ForA,(.12-.05)/1.40=_b.ForB,(.08-.05)/0.80=_Whatwouldtherisk-freeratehavetobefortheseassetstobecorrectlyvalued?(.12-Rf)/1.40=(.08-Rf)/0.80Rf=_,TheCapitalAssetPricingModel,TheCapitalAssetPricingModel(CAPM)-anequilibriummodeloftherelationshipbetweenriskandreturn.Whatdeterminesanassetsexpectedreturn?Therisk-freerate-thepuretimevalueofmoneyThemarketriskpremium-therewardforbearingsystematicriskThebetacoefficient-ameasureoftheamountofsystematicriskpresentinaparticularassetTheCAPM:E(Ri)=Rf+E(RM)-Rfxi,CapitalAssetPricingModel(2),Expectedreturnonassetiisalinearfunctionoftheriskfreerateandtheassetsmarginalrisk(beta)timestheexpectedriskpremiumonthemarket.E(Ri)=Rf+(E(Rm)-Rf)iiisthebetaofasecurity.Itisderivedfromthemarketmodelandrepresentsthemarginalriskofanasset.Theinvestorisassumedtoberational.Assuchtheinvestorwillknowthatbyholdingadiversifiedportfolioofassetss/hecangetridofalltheunsystematicrisk.Theinvestorcanthowever,getridofthesystematicormarketrisk.Inconsequencetobearmarketrisktheinvestordemandscompensationrelatedtotheamountofmarketrisk.Allassetreturnsarerelatedtotheirrisk.InequilibriumallassetswillplotonthestraightlinegivenrepresentingtheCAPM.ThestraightlineisknownastheSecurityMarketLine.,TheCapitalAssetPricingModel:assumptions(3),InvestorsselectefficientportfoliosInvestorshavethesamedecisionhorizonandoverthisperiodmeansandvariancesexist.CapitalMarketsareperfect:Assetsinfinitelydivisible,notransactioncosts,informationiscostlessandavailabletoallNotaxesIndividualscanborrowasmuchoraslittleastheywishatthesameborrowingandlendingrateRfHomogeneousExpectationsandPortfolioOpportunities,TheSecurityMarketLine(SML),Assetexpectedreturn(E(Ri),Assetbeta(i),=E(RM)Rf,E(RM),Rf,M=1.0,TheCostofCapital:Issues,Keyissues:Whatdowemeanby“costofcapital”Howcanwecomeupwithanestimate?Preliminaries1.Vocabularythefollowingallmeanthesamething:a.Requiredreturnb.Appropriatediscountratec.Costofcapital(orcostofmoney)2.Thecostofcapitalisanopportunitycostitdependsonwherethemoneygoes,notwhereitcomesfrom.3.Fornow,assumethefirmscapitalstructure(mixofdebtandequity)isfixed.,TheWeightedAverageCostofCapital,Capitalstructureweights1.Let:E=themarketvalueoftheequity.D=themarketvalueofthedebt.Then:V=E+D,soE/V+D/V=100%2.SothefirmscapitalstructureweightsareE/VandD/V.3.Interestpaymentsondebtaretax-deductible,sotheaftertaxcostofdebtisthepretaxcostmultipliedby(1-corporatetaxrate).Aftertaxcostofdebt=RDx(_)4.ThustheweightedaveragecostofcapitalisWACC=(E/V)xRE+(D/V)xRDx(1-Tc),Example:EastmanChemicalsWACC,EastmanChemicalhas80millionsharesofcommonstockoutstanding.Thebookvalueis$19.10andthemarketpriceis$62.375pershare.T-billsyield5%,andthemarketriskpremiumisassumedtobe8.5%.Thestockbetais1.1.Thefirmhasthreedebtissuesoutstanding.CouponBookValueMarketValueYield-to-Maturity6.375%$499m$521m5.70%7.250%$495m$543m6.50%7.625%$200m$226m6.60%,Example:EastmanChemicalsWACC(concluded),Costofequity(SMLapproach):RE=.05+1.1x(.085)=.05+.0935=.143514.4%Costofdebt:Multiplytheproportionoftotaldebtrepresentedbyeachissuebyitsyieldtomaturity;theweightedaveragecostofdebt=6.2%Capitalstructureweights:Marketvalueofequity=80millionx$62.375=$4990mMarketvalueofdebt=$521m+$543m+$226m=$1290mV=$4990m+$1290m=$6280mD/V=$1.29/$6.28=.205421%E/V=$4.99/$6.28=.794679%WACC=(.79x.144)+(.21x.062x.65)=.122212.2%,Example:TheSMLApproach,AccordingtotheCAPM:RE=Rf+Ex(RM-Rf)1.Gettherisk-freeratefromfinancialpressmanyusethe1-yearTreasurybillrate,say6%.2.Getestimatesofmarketriskpremiumandsecuritybeta.a.Riskpremiumhistorical-_%b.Betahistorical(1)Investmentinformationservices-e.g.,Bloomberg(2)Estimatefromhistoricaldata3.Supposethebetais1.40,then,usingtheapproach:RE=Rf+Ex(RM-Rf)=0.06+1.40 x_=_%,CostsofDebt,Costofdebt1.Thecostofdebt,RD,istheinterestrateonnewborrowing.2.Thecostofdebtisobservable:a.Yieldoncurrentlyoutstandingdebt.b.Yieldsonnewly-issuedsimilarly-ratedbonds.3.Thehistoricdebtcostisirrelevant-why?Example:Wesolda20-year,12%bond10yearsagoatpar.Itiscurrentlypricedat86.Whatisourcostofdebt?Theyieldtomaturityis_%,sothisiswhatweuseasthecostofdebt,not12%.,SummaryofCapitalCostCalculations,TheWeightedAverageCostofCapitalA.TheWACCistherequiredreturnonthefirmasawhole.Itistheappropriatediscountrateforcashflowssimilarinrisktothefirm.B.T