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ReturnandRisk:TheCapitalAssetPricingModel(CAPM)

ReturnandRisk:TheCapitalAWisdomDon’tputallyoureggsinonebasket.

----AnonymousThereasonwhycorporationsdonotentergambleswithvolatilepayoffsandsmallpositiveexpectedreturnsisthatmanagersknowthatgenerallyvolatilitymatters.----ReneM.StulzWisdomDon’tputallyourMini

Case

Riskandreturnareconceptsthatwedealwitheveryday.Formanypeopleitisquiteacceptibletorisk$20everyweekinthelottery,inviewofpotentialreturnsofhundredsofthousands(orevenmillions)ofdollars.Whenyoubuyalotteryticket,theriskoflosingyour$20isveryhigh(howoftenhaveyouwonanythingatlotto).MiniCaseRi

Ingeneral,inordertotakeahigherrisk,youwouldexpectamuchgreaterpotentialpayoff.Consideralotterywhereeachticketcosts$2000.Wouldyoubuyaticketiftheoddswerethesameasinthelotterywheretheticketcosts$20?Probablynot---youwouldexpectmuchbetteroddsofwinninginordertorisksuchabigamountofmoney.Ingeneral,inord

“Betterodds”meansthatyouwouldexpectamuchhigherprobabilityofwinningbackyourbet.Howmuchyouwillbewillingtorisk,givenasetprobabilityofwinningorlosing,dependsonyourcharacter---youmaybearisk-loveroryoumayberiskaverse.“Betterodds”meansoddStange,unusualSeperatedfromapartorsettowhichitbelongsto

eg.twooddsocksThatcan’tbedividedexactlyby2Nothappeningregularly

eg.Helikestheodddrinks.oddStange,unusualNearinnumber

eg.Theylivedabroadfor30oddyears.Oddjobs:smallpracticaljobsthatyoudoinyourhomeNearinnumberoddsThepossibilitythatsomethingwillorwillnotbehappen

eg.TheoddsarethathewillfailtheexamThispossiblityexpressedinnumberswhenmakingabet打賭的賠率

eg.Ifyoubet$1onahorsewiththeoddsat10to1andthehorsewins,youget$11back.oddsThepossibilitythatsometChapterOutline11.1IndividualSecurities11.2ExpectedReturn,Variance,andCovariance11.3TheReturnandRiskforPortfolios11.4TheEfficientSet11.5RisklessBorrowingandLending11.6Announcements,Surprises,andExpectedReturn11.7Risk:SystematicandUnsystematic11.8DiversificationandPortfolioRisk11.9MarketEquilibrium11.10RelationshipbetweenRiskandExpectedReturn(CAPM)ChapterOutline11.1Individual11.1IndividualSecuritiesKeyTermsexpectedreturn期望報酬率variance方差standarddeviation標準差covariance協(xié)方差correlation相關(guān)性betacoefficient系數(shù)11.1IndividualSecuritiesKeyThecharacteristicsofindividualsecuritiesthatareofinterestarethe:ExpectedReturnVarianceandStandardDeviationCovarianceandCorrelation(toanothersecurityorindex)Thecharacteristicsofindivid11.2ExpectedReturn,Variance,andCovarianceI.ExpectedreturnandVarianceKeyTermsstateofeconomy經(jīng)濟狀況depression經(jīng)濟蕭條期recession經(jīng)濟衰退期normal一般boomtimes經(jīng)濟繁榮期multiply…by…乘11.2ExpectedReturn,VarianceII.CovarianceandCorrelationKeyTermsapositivedependency正依賴性apositiverelationship正相關(guān)giveriseto引起anegativedependency副依賴性anegativerelationship負相關(guān)offset補償divide…by…除II.CovarianceandCorrelatiopositivelycorrelated正相關(guān)的positivelycorrelation正相關(guān)negativelycorrelated負相關(guān)uncorrelated不相關(guān)standardize標準化interrelated相關(guān)的perfectpositive/negative/correlation完全正相關(guān)nocorrelation不相關(guān)positivelycorrelated正相關(guān)的1.DefinitionCovarianceandcorrelationmeasurehowtworandomvariablesarerelated.協(xié)方差和相關(guān)性是反映兩個隨即變量相關(guān)程度的計量工具。2.CalculationandanalysisofCovariancepositiverelationshipnegativerelationshipnorelation3.CalculationandanalysisofCorrelation1.DefinitionAispositively/negativelyrelatedtoBAandBarepositively/negativelycorrelated.AandBareuncorrelated.Thereisapositive/negativerelationbetweenAandB.ThereisnorelationbetweenAandB.Aispositively/negativelyrI.Expectedvs.UnexpectedReturnsRealizedreturnsaregenerallynotequaltoexpectedreturns.Thereistheexpectedcomponentandtheunexpectedcomponent.Atanypointintime,theunexpectedreturncanbeeitherpositiveornegative.Overtime,theaverageoftheunexpectedcomponentiszero.11.6Announcements,surprises,andexpectedreturnsI.Expectedvs.UnexpectedRetII.AnnouncementsandNewsAnnouncementsandnewscontainbothanexpectedcomponentandasurprisecomponent.Itisthesurprisecomponentthataffectsastock’spriceand,therefore,itsreturn.ThisisveryobviouswhenwewatchhowstockpricesmovewhenanunexpectedannouncementismadeorearningsaredifferentthananticipatedII.AnnouncementsandNewsTotalReturn=expectedreturn+unexpectedreturn11.7Risk:SystematicandUnsystematicTotalReturn11.7Risk:SystemRiskfactorsthataffectalargenumberofassetsAlsoknownasnon-diversifiableriskormarketriskIncludessuchthingsaschangesinGDP,inflation,interestrates,etc.I.SystematicriskRiskfactorsthataffectalarRiskfactorsthataffectalimitednumberofassetsAlsoknownasuniqueriskandasset-specificriskIncludessuchthingsaslaborstrikes,partshortages,etc.II.UnsystematicriskRiskfactorsthataffectalimIII.ReturnsTotalReturn=expectedreturn+unexpectedreturnUnexpectedreturn=systematicportion+unsystematicportionTherefore,totalreturncanbeexpressedasfollows:TotalReturn=expectedreturn+systematicportion+unsystematicportionIII.ReturnsTotalReturn=exp11.8DiversificationandPortfolioRiskI.TheEffectofDiversification:AnotherLessonfromMarketHistoryII.ThePrincipleofDiversificationIII.DiversificationandUnsystematicRiskIV.DiversificationandSystematicRiskV.Conclusion11.8DiversificationandPortf11.8DiversificationandPortfolioRiskDiversificationcansubstantiallyreducethevariabilityofreturnswithoutanequivalentreductioninexpectedreturns.Thisreductioninriskarisesbecauseworsethanexpectedreturnsfromoneassetareoffsetbybetterthanexpectedreturnsfromanother.However,thereisaminimumlevelofriskthatcannotbediversifiedaway,andthatisthesystematicportion.11.8DiversificationandPortfDiversifiableRiskTheriskthatcanbeeliminatedbycombiningassetsintoaportfolioOftenconsideredthesameasunsystematic,unique,orasset-specificriskIfweholdonlyoneasset,orassetsinthesameindustry,thenweareexposingourselvestoriskthatwecoulddiversifyaway.DiversifiableRiskTheriskthaTotalRiskTotalrisk=systematicrisk+unsystematicriskThestandarddeviationofreturnsisameasureoftotalrisk.Forwell-diversifiedportfolios,unsystematicriskisverysmall.Consequently,thetotalriskforadiversifiedportfolioisessentiallyequivalenttothesystematicrisk.TotalRiskTotalrisk=systema11.10RiskandReturn(CAPM)ExpectedReturnontheMarket:Expectedreturnonanindividualsecurity:MarketRiskPremiumThisappliestoindividualsecuritiesheldwithinwell-diversifiedportfolios.11.10RiskandReturn(CAPM)ExExpectedReturnonaSecurityThisformulaiscalledtheCapitalAssetPricingModel(CAPM):Assumebi=0,thentheexpectedreturnisRF.Assume

bi=1,thenExpectedreturnonasecurity=Risk-freerate+Betaofthesecurity×MarketriskpremiumExpectedReturnonaSecurityTRelationshipBetweenRisk&ReturnExpectedreturnb1.0RelationshipBetweenRisk&ReRelationship