ChapterTwenty-FourPortfolioPerformanceEvaluationIfmarketsareefficient,investorsmustbeabletomeasureperformanceoftheirassetmanagersDiscussmethodstoevaluateinvestmentperformanceConventionalapproachestoriskadjustmentOverview?2021McGraw-HillEducation24-2Time-weightedaverageGeometricaverageisatime-weightedaverageEachperiod’sreturnhasequalweightTime-WeightedReturns?2021McGraw-HillEducation24-3Dollar-weightedrateofreturnistheinternalrateofreturnonaninvestmentReturnsareweightedbytheamountinvestedineachperiodDollar-WeightedReturns

(1of2)?2021McGraw-HillEducation24-4Considerastockpayingadividendof$2annuallythatcurrentlysellsfor$50.Youpurchasethestocktoday,collectthe$2dividend,andsellitfor$53atyear-end.UsingDCFapproach,theIRRisequalto:Thetime-weighted(geometricaverage)returnis7.81%Dollar-WeightedReturn

(2of2)?2021McGraw-HillEducation24-5SimplestandmostpopularwaytoadjustforriskistocompareratesofreturnwiththoseofotherinvestmentfundswithsimilarriskcharacteristicsComparisonuniverseisthesetofmoneymanagersemployingsimilarinvestmentstyles,usedforassessingtherelativeperformanceofaportfoliomanagerAdjustingReturnsforRisk?2021McGraw-HillEducation24-6UniverseComparison?2021McGraw-HillEducation24-7Sharpe’sratiodividesaverageportfolioexcessreturnoverthesampleperiodbythestandarddeviationofreturnsoverthatperiodMeasuresrewardto(total)volatilitytrade-offRisk-AdjustedPerformance:Sharpe?2021McGraw-HillEducation24-8Treynor’smeasureisaratioofexcessreturntobeta,liketheSharperatio,butitusessystematicriskinsteadoftotalriskRisk-AdjustedPerformance:Treynor?2021McGraw-HillEducation24-9Jensen’salphaistheaveragereturnontheportfoliooverandabovethatpredictedbytheCAPM,giventheportfolio’sbetaandtheaveragemarketreturnRisk-AdjustedPerformance:Jensen?2021McGraw-HillEducation24-10Informationratiodividesthealphaoftheportfoliobythenonsystematicriskoftheportfolio,called“trackingerror”intheindustryMeasuresabnormalreturnperunitofriskthatinprinciplecouldbediversifiedawaybyholdingamarketindexportfolioRisk-AdjustedPerformance:InformationRatio?2021McGraw-HillEducation24-11Focusesontotalvolatilityasameasureofrisk,butitsriskadjustmentleadstoaneasy-to-interpretdifferentialreturnrelativetothebenchmarkindexM2

MeasureandtheShapeRatio?2021McGraw-HillEducation24-12M2ofPortfolioP?2021McGraw-HillEducation24-13AppropriatePerformanceMeasure?2021McGraw-HillEducation24-14ApositivealphaisnecessarytooutperformthepassivemarketindexThoughnecessary,it’snotenoughtoguaranteeaportfoliowilloutperformtheindexMostwidelyusedperformancemeasureTheRoleofAlphain

PerformanceMeasures?2021McGraw-HillEducation24-15PerformanceStatistics?2021McGraw-HillEducation24-16IfPorQrepresentstheentireinvestment,QisbetterbecauseofitshigherSharpemeasureandbetterM2IfPandQarecompetingforaroleasoneofanumberofsubportfolios,QalsodominatesbecauseitsTreynormeasureishigherIfweseekanactiveportfoliotomixwithanindexportfolio,PisbetterduetoitshigherinformationratioInterpretationof

PerformanceStatistics?2021McGraw-HillEducation24-17Mustdetermine“significancelevel”ofaperformancemeasuretoknowwhetheritreliablyindicatesabilityToestimatetheportfolioalphafromtheSCL,regressportfolioexcessreturnsonthemarketindexThen,toassesswhetherthealphaestimatereflectstrueskillandnotjustluck,computethet-statisticofthealphaestimateEvenmoderatelevelsofstatisticalnoisemakeperformanceevaluationextremelydifficultRealizedReturnsversusExpectedReturns?2021McGraw-HillEducation24-18Regardlessoftheperformancecriterion,somefundswilloutperformtheirbenchmarksinanyyear,andsomewillunderperformRecall,performanceinoneperiodisnotpredictiveoffutureperformanceLimitingasampleoffundstothoseforwhichreturnsareavailableoveranentiresampleperiodintroducessurvivorshipbiasSurvivorshipBiasandPortfolioEvaluation?2021McGraw-HillEducation24-19Styleanalysis,

atooltosystematicallymeasuretheexposuresofmanagedportfolios,wasintroducedbyWilliamSharpeIdeaistoregressfundreturnsonindexesrepresentingarangeofassetclassesRegressioncoefficientoneachindexwouldthenmeasurethefund’simplicitallocationtothat“style”R2ofregressionwouldmeasurepercentageofreturnvariabilityattributabletostylechoiceratherthansecurityselectionInterceptmeasuresaveragereturnfromsecurityselectionofthefundportfolioStyleAnalysis?2021McGraw-HillEducation24-20StyleAnalysisforFidelity’s

MagellanFund?2021McGraw-HillEducation24-21FidelityMagellanFundCumulativeReturnDifference?2021McGraw-HillEducation24-22AverageTrackingErrorfor636MutualFunds,1985-1989?2021McGraw-HillEducation24-23Risk-adjustmenttechniquesallassumethatportfolioriskisconstantovertherelevanttimeperiod,whichisn’tnecessarilytruePerformanceManipulationandtheMRARManagersmaytrytogamethesystem,giventheircompensationdependsonperformanceOnlymeasureimpossibletomanipulateisMRARPerformanceMeasurementwithChangingPortfolioComposition?2021McGraw-HillEducation24-24MRARScoreswithandwithoutManipulation?2021McGraw-HillEducation24-25Initspureform,markettiminginvolvesshiftingfundsbetweenamarket-indexportfolioandasafeassetTreynorandMazuy:HenrikssonandMerton:MarketTiming?2021McGraw-HillEducation24-26CharacteristicLines?2021McGraw-HillEducation24-27PerformanceofBills,Equities,andPerfect(Annual)MarketTimers?2021McGraw-HillEducation24-28Keytovaluingmarkettimingabilityistorecognizethatperfectforesightisequivalenttoholdingacalloptionontheequityportfolio–butwithouthavingtopayforit!ValuingMarketTimingasaCallOption?2021McGraw-HillEducation24-29PerformanceattributionstudiesattempttodecomposeoverallperformanceintodiscretecomponentsthatmaybeidentifiedwithaparticularleveloftheportfolioselectionprocessAcommonattributionsystemdecomposesperformanceintothreecomponents:Broadassetallocationchoicesacrossequity,fixed-income,andmoneymarketsIndustry(sector)choicewithineachmarketSecuritychoicewithineachsectorPerformanceAttributionProcedures

(1of2)?2021McGraw-HillEducation24-30BogeyisdesignedtomeasurethereturnstheportfoliomanagerwouldearnifheorsheweretofollowacompletelypassivestrategyInthiscontext,“passive”hastwoattributesItmeanstheallocationoffundsacrossbroadassetclassesissetinaccordwithanotionof“usual”allocationacrosssectorsItmeansthatwithineachassetcl