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

Return,Risk,andtheSecurityMarketLineTypesofReturnsExpectedReturnsandVariancesPortfoliosAnnouncements,Surprises,andExpectedReturnsRisk:SystematicandUnsystematicDiversificationandPortfolioRiskSystematicRiskandBetaTheSecurityMarketLineTheSMLandtheCostofCapitalSummaryandConclusionsTypesofReturnsTotalMonetaryreturn=DividendIncome+CapitalGainEganinvestmentof£1000risesinvalueto£1500providingacapitalgainof£500.Overthesameperiodthedividendincomeis5%=£50.Totalreturnisthen£500+£50=£550.Totalmonetaryreturnisanabsolutemeasureofreturns.Ittellsyouhowmuchmoneyyouhavemadein£’s.ItisoftenmoreusefultoknowthePercentageReturn.ThePercentageReturnisthetotalmonetaryreturndividedbytheamountofcapitalinvested.PercentageReturn=Dividends+CapitalGainsamountinvestedOrRit=Dit+(Pit–Pit-1)=Div.Yield+%capitalgainPit-1ExpectedReturnsandVariances:BasicIdeasThequantificationofriskandreturnisacrucialaspectofmodernfinance.Itisnotpossibletomake“good”(i.e.,value-maximizing)financialdecisionsunlessoneunderstandstherelationshipbetweenriskandreturn.Rationalinvestorslikereturnsanddislikerisk.Considerthefollowingproxiesforreturnandrisk:Expectedreturn-weightedaverageofthedistributionofpossiblereturnsinthefuture.Varianceofreturns-ameasureofthedispersionofthedistributionofpossiblereturnsinthefuture.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(Ri–E(R))2pix(Ri–E(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?siiiiRERp122))((*ExpectedReturnsandVariancesExample2StateoftheProbabilityReturnonReturnoneconomyofstateassetAassetBBoom0.4030%-5%Bust0.60-10%25%1.00A.ExpectedreturnsE(RA)=0.40x(.30)+0.60x(-.10)=.06=6%E(RB)=0.40x(-.05)+0.60x(.25)=.13=13%Example:ExpectedReturnsandVariances(concluded)B.VariancesVar(RA)=0.40x(.30-.06)2+0.60x(-.10-.06)2=.0384Var(RB)=0.40x(-.05-.13)2+0.60x(.25-.13)2=.0216C.StandarddeviationsSD(RA)=.0384=.196=19.6%SD(RB)=.0216=.147=14.7%CalculatingExpectedReturnsandVarianceinpracticeThemostcommonmethodistouseatimeseriesofreturnscalculatedfrompastpricesanddividends.dayBPpricediv.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)E(Ri)isassumedtobeequaltothesampleaveragereturn=(0.0116+0.0046+0.0092-0.0136+0-0.0345)/6=-0.00378Tocalculatethevariancewecalculatethedeviationforeachday’sreturnfromtheexpectedreturn,squaretomakeitpositiveandthendividebyn-1.Inthiscasen=6.CalculatingExpectedReturnsandVarianceinpractice(3)Ret.Rit-E(Rit)(Rit-E(Rit))^20.01160.01540.000240.00460.00840.000070.00920.01290.00017-0.0136-0.00980.000100.00000.00380.00001-0.0345-0.03070.00094-0.003780.00031MeasuringriskIfweweretoplotthedailyreturnsonasecurityoveralongperiodthenitmightlooksomethinglikeanormaldistribution(picturenextslide)Whatwewanttodoistosummarisethispictureassimplyaspossible.Themeanistheexpectedreturn,thespreadorvariationisthestandarddeviationorvariance.WearguethatthisspreadrepresentsrisktoinvestorsandhencethattheSt.Dev.orvarianceisameasureoftheriskofashare.Infactreturndistributionsdon’tusuallylookexactlylikethis.Theytendtohaveatruncatedlefttailandalongerrighttail.Variancemaynotbethebestmeasureofrisk.DescribingadistributionPortfolioExpectedReturnsandVariances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%1.00Example:PortfolioExpectedReturnsandVariances(continued)Calculateexpectedreturns:SecurityapproachE(RP)=0.40x(.125)+0.60x(.075)=.095=9.5%ComponentapproachE(RP)=.50xE(RA)+.50xE(RB)=9.5%Calculatevarianceofportfolio:SecurityapproachVar(RP)=0.40x(.125-.095)2+0.60x(.075-.095)2=.0006PortfolioapproachThesumofthevariancesisnotthevarianceoftheportfolioVar(RP).50xVar(RA)+.50xVar(RB)FtthisweekOlympus–sagacontinues–resignationofPresident,openletterbymajorshareholder,questions(atlast!)byJapanesePressandGovernment.Eurozone–thedeal–moreofthesame,bigger(voluntary)haircuts,moreausteritybutthedebtorstri