风险回报与资本成本论述(英文版)(ppt 75页).ppt

Return Risk andtheSecurityMarketLine TypesofReturnsExpectedReturnsandVariancesPortfoliosAnnouncements Surprises andExpectedReturnsRisk SystematicandUnsystematicDiversificationandPortfolioRiskSystematicRiskandBetaTheSecurityMarketLineTheSMLandtheCostofCapitalSummaryandConclusions TypesofReturns TotalMonetaryreturn DividendIncome CapitalGainEganinvestmentof 1000risesinvalueto 1500providingacapitalgainof 500 Overthesameperiodthedividendincomeis5 50 Totalreturnisthen 500 50 550 Totalmonetaryreturnisanabsolutemeasureofreturns Ittellsyouhowmuchmoneyyouhavemadein s ItisoftenmoreusefultoknowthePercentageReturn ThePercentageReturnisthetotalmonetaryreturndividedbytheamountofcapitalinvested PercentageReturn Dividends CapitalGainsamountinvestedOrRit Dit Pit Pit 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 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 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 00378Tocalculatethevariancewecalculatethedeviationforeachday sreturnfromtheexpectedreturn squaretomakeitpositiveandthendividebyn 1 Inthiscasen 6 CalculatingExpectedReturnsandVarianceinpractice 3 Measuringrisk Ifweweretoplotthedailyreturnsonasecurityoveralongperiodthenitmightlooksomethinglikeanormaldistribution picturenextslide Whatwewanttodoistosummarisethispictureassimplyaspossible Themeanistheexpectedreturn thespreadorvariationisthestandarddeviationorvariance WearguethatthisspreadrepresentsrisktoinvestorsandhencethattheSt Dev orvarianceisameasureoftheriskofashare Infactreturndistributionsdon tusuallylookexactlylikethis 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 Olympus sagacontinues resignationofPresident openletterbymajorshareholder questions atlast byJapanesePressandGovernment Eurozone thedeal moreofthesame bigger voluntary haircuts moreausteritybutthedebtorstrikesback Greekreferendum MFGlobalcollapse broker dealersufferingfromeurozoneratingsdowngrades 6 3bnexposure Managementgreed hugeincreaseinseniormanagementpayoverlastyear 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 RAt E RAt RAt E RAt Covariance average deviationofreturnonAfromitsmean deviationofreturnonBfromitsmean CAB E RAt E RAt RBt E RBt CorrelationisastandardisedCovariance CorrelationbetweenAandBistheCovariancebetweenAandBdividedbythestandarddeviationofAtimesthestandarddeviationofB AB CovAB A B CovarianceandCorrelation Theriskofaportfolioiscomprisedoftheriskoftheindividualsecuritiesplusthecorrelationbetweenthem Iftherearetwosecuritiesthentheriskoftheportfoliocanbecalculatedfromthevarianceofeachsecurityplusthecorrelationbetweenthem Fortwosecuritieswehave 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 Cov21 TwosecurityPortfolioSelectionExample Rpt X1R1t X2R2tE Rpt E X1R1t X2R2t X1E R1t X2E R2t p2 E Rpt E Rpt 2 p2 E X1R1t X2R2t X1E R1t X2E R2t 2 p2 E X1 R1t E R1t X2 R2t E R2t 2Fromalgebraweknowthat a b 2 a2 b2 2ab p2 X12E R1t E R1t 2 X22E R2t E R2t 2 2X1X2E R1t E R1t R2t E R2t X12 12 X22 22 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 353 64 andderivedfromE J EltonandM J Gruber RiskReductionandPortfolioSize AnAnalyticSolution JournalofBusiness50 October1977 pp 415 37 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 P2 CovAV PeterBernsteinonRiskandDiversification Bigrisksarescarywhenyoucannotdiversifythem especiallywhentheyareexpensivetounload eventhewealthiestfamilieshesitatebeforedecidingwhichhousetobuy Bigrisksarenotscarytoinvestorswhocandiversifythem bigrisksareinteresting Nosinglelosswillmakeanyonegobroke bymakingdiversificationeasyandinexpensive financialmarketsenhancethelevelofrisk takinginsociety PeterBernstein inhisbook CapitalIdeas Howcorrelationaffectsrisk TheEfficientFrontier FTthisweek Olympus admitswrongdoing Eurozone manyinterestingarticleshighlightingthe power ofGreece Germanroleandinterest dangerstoItalyandothers Focusononearticle RobertJenkins Insight nov 8 Greekrestructuring exitfromtheeurozoneGreekgovtdecidesonexit Greekcitizensandcompanieswithdraweurodepositswhilsttheyarestilleuros Foreignlendersstoplendingandrecallloansasquicklyaspossible Govt announcesanewdrachma Capitalcontrolsareintroduced Govtdebtisredenominatedindrachma Olympusshareprice FTthisweek cont Greekrestructuring Valueofthedrachmaplunges Greekinflationsoars Disputesoverprivatesectordebt Aretheyindrachmaoreuros Ifdrachmathenforeignbankshaveaproblem assetvalueshavefallen IfineurosthenGreekborrowershaveaproblemContagioncommences Portugesecitizensthinkitmighthappentothemandmoveouteurosfromthebanks Similarmovesinseveralothercountries Europeanbanksindifficultiesbecauseofexposuretoeurodebtofvariouscountrieswithlikelydifficulties Counterpartyriskmeansmarketinbankloansdriesup Banklendinghalts BankscollapseunlessGovtrescuethem TheStorytodate TheriskofaportfoliodependsontheCovarianceorCorrelationbetweenassets Varianceisimportantforanindividualassetbutbecomeslessandlessimportantasaportfolioincludesmoreandmorestocks Theriskofaportfoliodependsontheaveragecovariancebetweenstocks Therelationshipbetweenriskandreturncanberepresentedgraphicallybyaquadraticfrontier ThebestcombinationsofriskandreturnareontheEfficientFrontier Theshapeofthefrontierarisesfromthecovariancebetweenassets HowCorrelationaffectsrisk ariskfreeasset HowCorrelationaffectsrisk ariskfreeasset 2 Tobin sSeparationTheorem SimplifyingourRiskMeasure Ourmessagesofarhasbeenthatwhenweaddsecuritiestogetherriskisaffectedbythecorrelation covariance betweenthem Becausesecuritiesarelessthanperfectlycorrelated riskisreduced Whilstthisisusefulasaconceptitisoperationallyverydifficulttouse Thenumberofcorrelationsthatweneedtoconsidertoconstructoptimalportfoliosusingthissortofapproachisverylarge Weneedtofindsomeothermeasureofriskthatwillenableustosimplifytheproblem Onesuchmeasureisthebetaofasecurityorportfolio Thebetaofasecuritycanbethoughtofas the standardised sumofthesecurity scovariancewithallsecuritiesSinceallsecuritiesisjustanotherwayofsayingthemarket thebetaofasecurityis the standardised covarianceofthesecuritywiththemarket EstimatingBeta Betaisusuallyestimatedusinglinearregression BetaisanoutputfromtheMarketModel Thisassumesthatthereisalinearrelationshipbetweenthereturnonthemarketandthereturnonashare Returnsonashareareregressedagainstreturnsonamarketindex Rit ai biRmtcitaiisthealphaofshareIbiisthebetaofshareI BetaCoefficientsforSelectedCompanies Table10 7 BetaCompanyCoefficient i Alcatel Lucent1 44L Oreal0 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 Whatdeterminesanasset sexpectedreturn Therisk freerate thepuretimevalueofmoneyThemarketriskpremium therewardforbearingsystematicriskThebetacoefficient ameasureoftheamountofsystematicriskpresentinaparticularassetTheCAPM E Ri Rf E RM Rf xi CapitalAssetPricingModel 2 Expectedreturnonassetiisalinearfunctionoftheriskfreerateandtheassetsmarginalrisk beta timestheexpectedriskpremiumonthemarket E Ri Rf E Rm Rf i iisthebetaofasecurity Itisderivedfromthemarketmodelandrepresentsthemarginalriskofanasset Theinvestorisassumedtoberational Assuchtheinvestorwillknowthatbyholdingadiversifiedportfolioofassetss hecangetridofalltheunsystematicrisk Theinvestorcan thowever 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 Vocabulary thefollowingallmeanthesamething a Requiredreturnb Appropriatediscountratec Costofcapital orcostofmoney 2 Thecostofcapitalisanopportunitycost itdependsonwherethemoneygoes notwhereitcomesfrom 3 Fornow assumethefirm scapitalstructure mixofdebtandequity isfixed TheWeightedAverageCostofCapital Capitalstructureweights1 Let E themarketvalueoftheequity D themarketvalueofthedebt Then V E D soE V D V 100 2 Sothefirm scapitalstructureweightsareE VandD V 3 Interestpaymentsondebtaretax deductible sotheaftertaxcostofdebtisthepretaxcostmultipliedby 1 corporatetaxrate Aftertaxcostofdebt RDx 4 ThustheweightedaveragecostofcapitalisWACC E V xRE D V xRDx 1 Tc Example EastmanChemical sWACC 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 EastmanChemical sWACC concluded Costofequity SMLapproach RE 05 1 1x 085 05 0935 1435 14 4 Costofdebt Multiplytheproportionoftotaldebtrepresentedbyeachissuebyitsyieldtomaturity theweightedaveragecostofdebt 6 2 Capitalstructureweights Marketvalueofequity 80millionx 62 375 4990mMarketvalueofdebt 521m 543m 226m 1290mV 4990m 1290m 6280mD V 1 29 6 28 2054 21 E V 4 99 6 28 7946 79 WACC 79x 144 21x 062x 65 1222 12 2 Example TheSMLApproach AccordingtotheCAPM RE Rf Ex RM Rf 1 Gettherisk freeratefromfinancialpress manyusethe1 yearTreasurybillrate say6 2 Getestimatesofmarketriskpremiumandsecuritybeta a Riskpremiumhistorical b Beta historical 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 TheWACCiscalculatedasWACC E V xRE D V xRDx 1 Tc whereTcisthecorporatetaxrate Eisthemarketvalueofthefirm sequity Disthemarketvalueofthefirm sdebt andV E D TheSecurityMarketLineandtheWeightedAverageCostofCapital Expectedreturn Beta SML WACC 15 8 Incorrectacceptance Incorrectrejection B A 161514 Rf 7 A 60 firm 1 0 B 1 2 IfafirmusesitsWACCtomakeaccept rejectdecisionsforalltypesofprojects itwillhaveatendencyt