CF_L1-L2 risk and return

CapitalMarketsandthePricingofRiskLectures1-2,CorporateFinance(DUOversion)1Outline1.CapitalMarketsandthePricingofRisk2.OptimalPortfolioChoice3.CostofCapital21.CapitalMarketandRiskPricing-Introductiontoriskandreturn-Measuresofreturn/Historicalreturns-Relationshipbetweenriskandreturn-Diversification-SystematicRisk31.1Introduction:Wherewouldweinvestmoney?•WorldPortfolio•Corporatebonds•Largecompanies’stocks•Smallcompanystocks•TreasureBills/Governmentsecurities•Lotteries•Whichwouldgiveusthehighest/lowestyield?4Figure10.1Valueof$100InvestedattheEndof1925Source:ChicagoCenterforResearchinSecurityPrices(CRSP)forU.S.stocksandCPI,GlobalFinanceDatafortheWorldIndex,Treasurybillsandcorporatebonds.5WhowouldinvestinthislotteryFlipacoin:Head:-10poundsTail:+12pounts61.2Measurements●Whatdowewanttoknowaboutourreturns?●Probabilitydistribution●Expectedreturn●Varianceandstandarddeviation7ProbabilityDistributionsWhenaninvestmentisrisky,therearedifferentreturnsitmayearn.Eachpossiblereturnhassomelikelihoodofoccurring.Thisinformationissummarizedwithaprobabilitydistribution,whichassignsaprobability,PR,thateachpossiblereturn,R,willoccur.8ExpectedReturnExpected(Mean)ReturnCalculatedasaweightedaverageofthepossiblereturns,wheretheweightscorrespondtotheprobabilities.ExpectedReturnRRERPR9VarianceandStandardDeviationVarianceTheexpectedsquareddeviationfromthemeanStandardDeviationThesquarerootofthevarianceBotharemeasuresoftheriskofaprobabilitydistribution()()SDRVarR22()RRVarRERERPRER10Frompasttofuture●RealizedReturn●VarianceandVolatilityofReturns●Forecasts11RealizedReturnitisthereturnthatactuallyoccursoveraparticulartimeperiod.–MicrosoftExample111111DividendYieldCapitalGainRatetttttttttDivPDivDivPRPPP12AnnualRealizedReturnIfastockpaysdividendsattheendofeachquarter,withrealizedreturnsRQ1,...,RQ4eachquarter,thenitsannualrealizedreturn,Rannual,iscomputedas:annual12341(1)(1)(1)(1)QQQQRRRRR13TheVarianceandVolatilityofReturnsVarianceEstimateUsingRealizedReturnsTheestimateofthestandarddeviationisthesquarerootofthevariance.211()1TttVarRRRT1415UsingPasttoPredictFutureWecanuseasecurity’shistoricalaveragereturntoestimateitsactualexpectedreturn.However,theaveragereturnisjustanestimateoftheexpectedreturn.StandardError–Astatisticalmeasureofthedegreeofestimationerror16StandardErrorStandardErroroftheEstimateoftheExpectedReturn95%ConfidenceIntervalFortheS&P500(1926–2004)Orarangefrom7.7%to19.9%(IndividualRisk)(AverageofIndependent,IdenticalRisks)NumberofObservationsSDSDHistoricalAverageReturn(2StandardError)20.36%12.3%212.3%4.6%79171.3Risk–ReturnTrade-offLargePortfoliosExcessReturnsisthedifferencebetweentheaveragereturnforaninvestmentandtheaveragerisk-freerateTable10.5VolatilityVersusExcessReturnofU.S.SmallStocks,LargeStocks(S&P500),CorporateBonds,andTreasuryBills,1926–200818Figure10.5TheHistoricalTradeoffBetweenRiskandReturninLargePortfolios,1926–2005Source:CRSP,MorganStanleyCapitalInternational19TheReturnsofIndividualStocksIsthereapositiverelationshipbetweenvolatilityandaveragereturnsforindividualstocks?Asshownonthenextslide,thereisnopreciserelationshipbetweenvolatilityandaveragereturnforindividualstocks.–Largerstockstendtohavelowervolatilitythansmallerstocks.–Allstockstendtohavehigherriskandlowerreturnsthanlargeportfolios.20Figure10.6HistoricalVolatilityandReturnfor500IndividualStocks,bySize,UpdatedQuarterly,1926–2005211.4DiversificationCommonVSIndependentRiskCommonRiskRiskthatisperfectlycorrelated,affectsallsecuritiesIndependentRiskRiskthatisuncorrelated,affectsaparticularsecurityDiversificationTheaveragingoutofindependentrisksinalargeportfolio22Firm-SpecificVersusSystematicRiskFirmSpecificNews–Goodorbadnewsaboutanindividualcompany–Duetofirm-specificnewsAlsoknownas:–Firm-SpecificRisk–IdiosyncraticRisk–UniqueRisk–UnsystematicRisk–DiversifiableRiskMarket-WideNews–Newsthataffectsallstocks,suchasnewsabouttheeconomy–Duetomarket-widenewsAlsoknownas:–SystematicRisk–UndiversifiableRisk–MarketRisk23DiversificationWhenmanystocksarecombinedinalargeportfolio,thefirm-specificrisksforeachstockwillaverageoutandbediversified.Thesystematicrisk,however,willaffectallfirmsandwillnotbediversified.24ExampleConsidertwotypesoffirms:TypeSfirmsareaffectedonlybysystematicrisk.Thereisa50%chancetheeconomywillbestrongandtypeSstockswillearnareturnof40%;Thereisa50%changetheeconomywillbeweakandtheirreturnwillbe–20%.Becauseallthesefirmsfacethesamesystematicrisk,holdingalargeportfoliooftypeSfirmswillnotdiversifytherisk.TypeIfirmsareaffectedonlybyfirm-specificrisks.Theirreturnsareequallylikelytobe35%or–25%,basedonfactorsspecifictoeachfirm’slocalmarket.Becausetheserisksarefirmspecific,ifweholdaportfolioofthestocksofmanytypeIfirms,theriskisdiversified.25DiversificationActualfirmsareaffectedbybothmarket-widerisksandfirm-specificrisks.Whenfirmscarrybothtypesofrisk,onlytheunsystematicriskwillbediversifiedwhenmanyfirm’sstocksarecombinedintoaportfolio.Thevolatilitywillthereforedeclineuntilonlythesystematicriskremains.26Figure10.7Volatilit