Lecture3 Risk,Return,and The Opportunity Cost of C

CenterforAccountingStudiesofXiamenUniversity2007Lecture3AdvancedFinancialManagementRisk,Return,andTheOpportunityCostofCapitalProfessorYuanlueFuXiamenUniversity–AdvancedFinancialManagementFU-2Sub-topicsCovered•OveraCenturyofCapitalMarketHistory•MeasuringPortfolioRisk•CalculatingPortfolioRisk•BetaandUniqueRisk•Diversification&ValueAdditivity•MarkowitzPortfolioTheory•RiskandReturnRelationship•ValidityandtheRoleoftheCAPM•SomeAlternativeTheories(Chapter7-8)XiamenUniversity–AdvancedFinancialManagementFU-31.TheValueofanInvestmentof$1in1900$1$10$100$1,000$10,000$100,00019001910192019301940195019601970198019902000StartofYearDollarsCommonStockUSGovtBondsT-Bills15,578147612004XiamenUniversity–AdvancedFinancialManagementFU-41.TheValueofanInvestmentof$1in1900$1$10$100$1,00019001910192019301940195019601970198019902000StartofYearDollarsEquitiesBondsBills7196.812.802004RealReturnsXiamenUniversity–AdvancedFinancialManagementFU-52.AverageMarketRiskPremia(bycountry)4.34.75.15.35.85.95.96.36.46.67.68.18.28.69.31010.701234567891011DenmarkBelgiumSwitzerlandSpainCanadaIrelandGermanyUKAverageNetherlandsUSASwedenSouthAfricaAustraliaFranceJapanItalyRiskpremium,%CountryXiamenUniversity–AdvancedFinancialManagementFU-62.AverageMarketRiskPremium---RatesofReturn1900-2003Source:IbbotsonAssociates-60%-40%-20%0%20%40%60%80%190019201940196019802000YearPercentageReturnStockMarketIndexReturnsXiamenUniversity–AdvancedFinancialManagementFU-73.MeasuringRisk1141012191524133204812162024-50to-40-40to-30-30to-20-20to-10-10to00to1010to2020to3030to4040to5050to60Return%#ofYearsHistogramofAnnualStockMarketReturnsHistogramofAnnualStockMarketReturnsXiamenUniversity–AdvancedFinancialManagementFU-83.MeasuringRiskVariance-Averagevalueofsquareddeviationsfrommean.Ameasureofvolatility.StandardDeviation–squarerootofvariance.Ameasureofvolatility.XiamenUniversity–AdvancedFinancialManagementFU-93.MeasuringRiskCoinTossGame-calculatingvarianceandstandarddeviation(1)(2)(3)PercentRateofReturnDeviationfromMeanSquaredDeviation+40+30900+1000+1000-20-30900Variance=averageofsquareddeviations=1800/4=450Standarddeviation=squareofrootvariance=450=21.2%XiamenUniversity–AdvancedFinancialManagementFU-103.MeasuringRiskDiversification-Strategydesignedtoreduceriskbyspreadingtheportfolioacrossmanyinvestments.UniqueRisk-Riskfactorsaffectingonlythatfirm.Alsocalled“diversifiablerisk.”MarketRisk-Economy-widesourcesofriskthataffecttheoverallstockmarket.Alsocalled“systematicrisk.”XiamenUniversity–AdvancedFinancialManagementFU-113.MeasuringRiskPortfoliorateofreturn=fractionofportfolioinfirstassetxrateofreturnonfirstasset+fractionofportfolioinsecondassetxrateofreturnonsecondasset(((())))XiamenUniversity–AdvancedFinancialManagementFU-123.MeasuringRisk051015NumberofSecuritiesPortfoliostandarddeviationXiamenUniversity–AdvancedFinancialManagementFU-133.MeasuringRisk051015NumberofSecuritiesPortfoliostandarddeviationMarketriskUniqueriskXiamenUniversity–AdvancedFinancialManagementFU-144.PortfolioRisk2222211221122121122112212121σxσσρxxσxx2Stockσσρxxσxxσx1Stock2Stock1Stock==ThevarianceofatwostockportfolioisthesumofthesefourboxesXiamenUniversity–AdvancedFinancialManagementFU-154.PortfolioRiskExampleSupposeyouinvest60%ofyourportfolioinExxonMobiland40%inCocaCola.TheexpecteddollarreturnonyourExxonMobilstockis10%andonCocaColais15%.Theexpectedreturnonyourportfoliois:%12)1540(.)1060(.ReturnExpected=×+×=XiamenUniversity–AdvancedFinancialManagementFU-164.PortfolioRisk222222211221211221222121)3.27()40(.σx3.272.18160.40.σσρxxCola-Coca3.272.18160.40.σσρxx)2.18()60(.σxMobil-ExxonCola-CocaMobil-Exxon×=××××=××××=×=ExampleSupposeyouinvest60%ofyourportfolioinExxonMobiland40%inCocaCola.TheexpecteddollarreturnonyourExxonMobilstockis10%andonCocaColais15%.Thestandarddeviationoftheirannualizeddailyreturnsare18.2%and27.3%,respectively.Assumeacorrelationcoefficientof1.0andcalculatetheportfoliovariance.XiamenUniversity–AdvancedFinancialManagementFU-174.PortfolioRiskExampleSupposeyouinvest60%ofyourportfolioinExxonMobiland40%inCocaCola.TheexpecteddollarreturnonyourExxonMobilstockis10%andonCocaColais15%.Thestandarddeviationoftheirannualizeddailyreturnsare18.2%and27.3%,respectively.Assumeacorrelationcoefficientof1.0andcalculatetheportfoliovariance.%18.39.333DeviationStandard9.33318.2x27.3)2(.40x.60x]x(27.3)[(.40)]x(18.2)[(.60)VariancePortfolio2222===++=XiamenUniversity–AdvancedFinancialManagementFU-184.PortfolioRisk)rx()r(xReturnPortfolioExpected2211+=)σσρxx(2σxσxVariancePortfolio21122122222121++=XiamenUniversity–AdvancedFinancialManagementFU-194.PortfolioRiskTheshadedboxescontainvarianceterms;theremaindercontaincovarianceterms.123456N123456NSTOCKSTOCKTocalculateportfoliovarianceadduptheboxesXiamenUniversity–AdvancedFinancialManagementFU-205.BetaandUniqueRiskbetaExpectedreturnExpectedmarketreturn10%10%-+-10%+10%stockCopyright1996byTheMcGraw-HillCompanies,Inc-10%1.Totalrisk=diversifiablerisk+marketrisk2.Marketriskismeasuredbybeta,thesensitivitytomarketchangesXiamenUniversity–AdvancedFinancialManagementFU-215.BetaandUniqueRiskMarke