ReturnandRisk:TheCapitalAssetPricingModelChapter11Copyright?2021bytheMcGraw-HillCompanies,Inc.Allrightsreserved.McGraw-Hill/IrwinKeyConceptsandSkillsKnowhowtocalculateexpectedreturnsKnowhowtocalculatecovariances,correlations,andbetasUnderstandtheimpactofdiversificationUnderstandthesystematicriskprincipleUnderstandthesecuritymarketlineUnderstandtherisk-returntradeoffBeabletousetheCapitalAssetPricingModelChapterOutline11.1IndividualSecurities11.2ExpectedReturn,Variance,andCovariance11.3TheReturnandRiskforPortfolios11.4TheEfficientSetforTwoAssets11.5TheEfficientSetforManyAssets11.6Diversification11.7RisklessBorrowingandLending11.8MarketEquilibrium11.9RelationshipbetweenRiskandExpectedReturn(CAPM)11.1IndividualSecuritiesThecharacteristicsofindividualsecuritiesthatareofinterestarethe:ExpectedReturnVarianceandStandardDeviationCovarianceandCorrelation(toanothersecurityorindex)11.2ExpectedReturn,Variance,andCovarianceConsiderthefollowingtworiskyassetworld.Thereisa1/3chanceofeachstateoftheeconomy,andtheonlyassetsareastockfundandabondfund.ExpectedReturnExpectedReturnVarianceVarianceStandardDeviationCovariance“Deviation〞comparesreturnineachstatetotheexpectedreturn.“Weighted〞takestheproductofthedeviationsmultipliedbytheprobabilityofthatstate.Correlation11.3TheReturnandRiskforPortfoliosNotethatstockshaveahigherexpectedreturnthanbondsandhigherrisk.Letusturnnowtotherisk-returntradeoffofaportfoliothatis50%investedinbondsand50%investedinstocks.PortfoliosTherateofreturnontheportfolioisaweightedaverageofthereturnsonthestocksandbondsintheportfolio:

PortfoliosTheexpectedrateofreturnontheportfolioisaweightedaverageoftheexpectedreturnsonthesecuritiesintheportfolio.PortfoliosThevarianceoftherateofreturnonthetworiskyassetsportfoliois

whereBSisthecorrelationcoefficientbetweenthereturnsonthestockandbondfunds.PortfoliosObservethedecreaseinriskthatdiversificationoffers.Anequallyweightedportfolio(50%instocksand50%inbonds)haslessriskthaneitherstocksorbondsheldinisolation.11.4TheEfficientSetforTwoAssetsWecanconsiderotherportfolioweightsbesides50%instocksand50%inbonds.100%bonds100%stocksTheEfficientSetforTwoAssets100%stocks100%bondsNotethatsomeportfoliosare“better〞thanothers.Theyhavehigherreturnsforthesamelevelofriskorless.PortfolioswithVariousCorrelations100%bondsreturn100%stocks=0.2=1.0=-1.0Relationshipdependsoncorrelationcoefficient-1.0<

r

<+1.0Ifr=+1.0,noriskreductionispossibleIfr=–1.0,completeriskreductionispossible11.5TheEfficientSetforManySecuritiesConsideraworldwithmanyriskyassets;wecanstillidentifytheopportunitysetofrisk-returncombinationsofvariousportfolios.returnPIndividualAssetsTheEfficientSetforManySecuritiesThesectionoftheopportunitysetabovetheminimumvarianceportfolioistheefficientfrontier.returnPminimumvarianceportfolioefficientfrontierIndividualAssetsAnnouncements,Surprises,andExpectedReturnsThereturnonanysecurityconsistsoftwoparts.

First,theexpectedreturnsSecond,theunexpectedorriskyreturnsAwaytowritethereturnonastockinthecomingmonthis:Announcements,Surprises,andExpectedReturnsAnyannouncementcanbebrokendownintotwoparts,theanticipated(orexpected)partandthesurprise(orinnovation):Announcement=Expectedpart+Surprise.Theexpectedpartofanyannouncementisthepartoftheinformationthemarketusestoformtheexpectation,R,ofthereturnonthestock.Thesurpriseisthenewsthatinfluencestheunanticipatedreturnonthestock,U.DiversificationandPortfolioRiskDiversificationcansubstantiallyreducethevariabilityofreturnswithoutanequivalentreductioninexpectedreturns.Thisreductioninriskarisesbecauseworsethanexpectedreturnsfromoneassetareoffsetbybetterthanexpectedreturnsfromanother.However,thereisaminimumlevelofriskthatcannotbediversifiedaway,andthatisthesystematicportion.PortfolioRiskandNumberofStocksNondiversifiablerisk;SystematicRisk;MarketRiskDiversifiableRisk;NonsystematicRisk;FirmSpecificRisk;UniqueRisknInalargeportfoliothevariancetermsareeffectivelydiversifiedaway,butthecovariancetermsarenot.PortfolioriskRisk:SystematicandUnsystematicAsystematicriskisanyriskthataffectsalargenumberofassets,eachtoagreaterorlesserdegree.Anunsystematicriskisariskthatspecificallyaffectsasingleassetorsmallgroupofassets.Unsystematicriskcanbediversifiedaway.Examplesofsystematicriskincludeuncertaintyaboutgeneraleconomicconditions,suchasGNP,interestratesorinflation.Ontheotherhand,announcementsspecifictoasinglecompanyareexamplesofunsystematicrisk.TotalRiskTotalrisk=systematicrisk+unsystematicriskThestandarddeviationofreturnsisameasureoftotalrisk.Forwell-diversifiedportfolios,unsystematicriskisverysmall.Consequently,thetotalriskforadiversifiedportfolioisessentiallyequivalenttothesystematicrisk.OptimalPortfoliowithaRisk-FreeAssetInadditiontostocksandbonds,consideraworldthatalsohasrisk-freesecuritieslikeT-bills.100%bonds100%stocksrfreturn11.7RisklessBorrowingandLendingNowinvestorscanallocatetheirmoneyacrosstheT-billsandabalancedmutualfund.100%bonds100%stocksrfreturnBalancedfundCMLRisklessBorrowingandLending Witharisk-freeassetavailableandtheefficientfrontieridentified,wechoosethecapitalallocationlinewiththesteepestslope.returnPefficientfrontierrfCML11.8MarketEquilibrium

Withthecapitalallocationlineidentified,allinvestorschooseapointalongtheline—somecombinationoftherisk-freeassetandthemarketportfolioM.Inaworldwithhomogeneousexpectations,Misthesameforallinvestors.returnPefficientfrontierrfMCMLMarketEquilibriumWheretheinvestorchoosesalongtheCapitalMarketLinedependsonherrisktolerance.ThebigpointisthatallinvestorshavethesameCML.100%bonds100%stocksrfreturnBalancedfundCMLRiskWhenHoldingtheMarketPortfolioResearchershaveshownthatthebestmeasureoftheriskofasecurityinalargeportfolioisthebeta(b)ofthesecurity.Betameasurestheresponsivenessofasecuritytomovementsinthemarketportfolio(i.e.,systematicrisk).EstimatingbwithRegressionSecurityReturnsReturnonmarket%Ri=a

i+biRm+eiSlope=biCharacteristicLineTheFormulaforBetaClearly,yourestimateofbetawilldependuponyourchoiceofaproxyforthemarketportfolio.11.9RelationshipbetweenRiskandExpectedReturn(CAPM)ExpectedReturnontheMarket:Expectedreturnonanindividualsecurity:MarketRiskPremiumThisappliestoindividual