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1、OTCOT n-0一鼠法wallt:I君臣W+灵车8吧皿肾一Rgf藤三ThirdBuildingBlock:SizingPositionsPositionsizingbalancesmanagersconfidenceintheiralphaandfactorinsightswhilemitigatingidiosyncraticriskscomingfromconcentratedpositions.Positionsizingwillaffectallthreesourcesofactiverisk,butthemostdramaticimpactwillbeonidiosyncratic
2、risk./Thegeneralruleisthatsmallerpositionsinagreaternumberofsecuritieswilldiversifyawayidiosyncraticriskandleadtolowerportfoliovolatility.Afactor-orientatedmanagerwhospreadstheirportfolioacrossmanyassetsislikelytominimizetheimpactofidiosyncraticrisk.Astock-pickerislikelytoholdmoreconcentratedpositio
3、nsbasedontheirinsightsintoindividualsecurities,andhence,deliberatelyassumeaHgheFegFeef4disyGFatie44sk2ActiveShareandActiveRiskAActiveSharemeasuresthedegreetowhichthenumberandsizingofthepositionsinamanager,sportfolioaredifferentfromthoseofabenchmark,andisgivenbythefollowingequation:liNActiveShare=2IW
4、eightPOrtfoliO/-Weightbenchmark,!IActiveSharetakesavaluebetweenOand1.IfaportfoliohasanActiveShareof0.5,wecanconcludethat50%oftheportfolioisidenticaltothatofthebenchmarkand50%isnot.Iftwoportfolioswiththesamebenchmarkinvestonlyinbenchmarksecurities,theportfoliowiththefewersecuritiesandthereforehigherd
5、egreeofconcentrationinpositionswillhaveahigherlevelofActiveShare.AActiverisk,alsocalledtrackingerror,isthestandarddeviationofactivereturns(portfolioreturnsminusbenchmarkreturns).Asanequation:AResearchconclusionsonthecompositionofactivereturninclude:Highnetexposuretoariskfactorleadstohighlevelofactiv
6、erisk.AportfoliowithnonetfactorexposurewillhaveactiveriskattributedentirelytoActiveShare.ActiveriskattributabletoActiveShareisinverselyproportionaltothenumberofsecuritiesintheportfolio.Activeriskincreasesasfactorandidiosyncraticrisklevelsincrease.InvestmentStyleDescriptionActiveShareandActiveRiskPur
7、eindexingNoactivepositions:portfolioisequaltothebenchmarkZeroActiveShareandzeroactiveriskFactorneutralNoactivefactorbetsidiosyncraticrisklowifdiversifiedLowactiveriskActiveSharelowifdiversifiedFactordiversifiedBalancedexposuretoriskfactorsandminimizedidiosyncraticriskthroughhighnumberofsecuritiesinp
8、ortfolioReasonablylowactiveriskhighActiveSharefromlargeamountofsecuritiesusedthatareunlikelytobeinthebenchmarkConcentratedfactorbetsTargetedfactorbetsidiosyncraticrisklikelytobehighHighActiveShareandhighactiveriskConcentratedstockpickerTargetedindividualstockbetsHighestActiveShareandhighestactiveris
9、k巨业创新憎值一UJBqS SA-OVLowActiveShareandActiveRiskInvestmentStyles,ActiveShare,andActiveRiskHighConcentrated泪NConcentratedstockPicksDiversifiedFactorBetsFactorNeutralandIactorBetsDiversifiedStockPicksClosetIndexing*PureIndexingHighActiveRiskAManagerstylescanalsobeidentifiedthroughobservingtheirsectorand
10、securityspecificconstraints.Forexample:Asectorrotatorwouldneedtohavelargepermitteddeviationsinsectorweights;Astockpickerwouldneedtohavelargepermitteddeviationsinindividualsecurityweights;Adiversifiedmulti-factorinvestorwouldnotneedsuchlargedeviationsfromindexweights,butwouldstillneedsomeflexibilityi
11、nordertogenerateamoderatelevelofactiveriskandreturn.3.AllocatingtheRiskBudgetingAllocatingtheRiskBudgetingRiskbudgetingisaprocessbywhichthetotalriskofaportfolioisallocatedtoconstituentsoftheportfoliointhemostefficientmanner.Itisanintegralpartofaneffectiveriskmanagementprocess.Aneffectiveriskmanageme
12、ntprocesshasthefollowingfoursteps:Determinewhichtypeofriskmeasureisappropriategiventhefundmandate./Absoluteriskmeasuresareappropriatewhentheinvestmentobjectiveisexpressedintermsoftotalreturns./Relativeriskmeasuresareappropriatewhentheinvestmentobjectiveistooutperformamarketindex.Understandhoweachasp
13、ectofthestrategycontributestorisk.Determinewhatlevelofriskbudgetisappropriate.Properlyallocateriskamongindividualpositions/factors.AllocatingtheRiskBudgetingACausesandSourcesofAbsoluteRiskAbsoluteriskmeasuresfocusonthesizeandcompositionofabsoluteportfoliovariance.Thecalculationoftotalportfoliovarian
14、ce(Vp):尊片芸7嘤安2Inotherwords,theportfolaFanceisthesumofeachasset,scontributiontoportfoliovariance.Thecontributionofassetitoportfoliovariance(CVi)isgivenbytheequation:粤/羲assetjsweightintheportfolio/翻*thecovarianceofreturnsbetweenassetiandassetj/畿*=thecovarianceofreturnsbetweenassetiandtheportfolioAlloc
15、atingtheRiskBudgetingACausesandSourcesofRelative/ActiveRiskRelativeriskbecomesanappropriatemeasurewhenthemanagerisconcernedwithherperformancerelativetoabenchmark.Onemeasureofrelativeriskisthevarianceoftheportfoliosactivereturn(AVp):驾蠢浴邀吐/xi=theasset,sightintheportfolio/bi=thebenchmarkweightinasseti/
16、IhecovarianceofrelativereturnsbetweenassetiandassetjThecontributionofeachassettotheportfolioactivevariance(CAVi)is/RCipisthecovarianceofelafvereturnsbetweenassetiandtheportfolio.AllocatingtheRiskBudgetingATheimportantpointstonoteare:Contributiontoactivevarianceisafunctionofactiverisknotabsolutestand
17、arddeviation./E.g.Whilecashhasaverylowstandarddeviation,ithasanactiverisktwicethatoftheindexescomprisingthebenchmarkduetothelowcorrelationofcashversusthebenchmark.Thisleadstocashcontributingto100%oftheactivevariance.ThecorrelationoftheactivereturnsofindexAandindexBis-1.Thisisbecausethebenchmarkisane
18、quallyweightedaverageofthetwoindiceswhenoneisoutperformingthebenchmark(sohaspositiveactivereturns)thentheothermustbeunderperformingthebenchmark(givingnegativeactivereturns).Example:AbsoluteriskattributionAportfoliohasthefollowingcharacteristicsPortfolioWeightStandardDeviationAssetA40%20%AssetB50%12%
19、AssetC10%6%Portfolio100%11.92%CovarianceAssetAAssetBAssetCAssetA0.0400000.0096000.002400AssetB0.0096000.0144000.001440AssetC0.0024000.0014400.003600ACalculatetheabsolutecontributiontoportfoliovarianceofassetA.AGiventhatthetotalvarianceis0.014212fcalculatetheproportionoftotalportfoliovariancecontribu
20、tedbyAssetA.Example:AbsoluteRiskAttributionWeightofAssetAWeightofAssetACovarianceofAssetAwithAssetA0.400.400.04+WeightofAssetAWeightofAssetBCovarianceofAssetBwithAssetA0.400.500.0096+WeightofAssetAWeightofAssetCCovarianceofAssetCwithAssetA+0.400.100.0024=AssetAscontributiontototalportfoliovariance=0
21、.0084161.CovarianceofreturnsbetweenassetAandtheportfolio:A2.TheproportionoftotalportfoliovariancecontributedbyAssetAis,therefore,0.008416/0.014212=59.22%.Example:Factor-basedriskbudgetingThefollowingtablepresentstherisk-factorcoefficientsandvariance/covariancematrixforamanagerrunningaportfoliousinga
22、two-factormodel(marketandsize)CoefficientMarketSizeValueMomentumCoefficient1.0800.098-0.4010.034Varianceofthemarketfactorreturnandcovarianceswiththemarketfactorreturn0.001090.000530.00022-0.00025Portfoliosmonthlystandarddeviationofreturns3.74%Calculatetheportionoftotalportfolioriskthatisexplainedbyt
23、hemarketfactorinFundl,sexistingportfolioisclosestto:.Example:AbsoluteRiskAttributionATheportionoftotalportfolioriskexplainedbythemarketfactoriscalculatedintwosteps.Thefirststepistocalculatethecontributionofthemarketfactortototalportfoliovarianceasfollows:nCVrnarketfaCtor=/marketfactorjmf,jj=CVmarket
24、factor=(1.0800.001091.080)+(1.0800.000530.098)+(1.0800.00022-0.401)+(1.080-0.000250.034)CVmarketfactor=0.001223AThesecondstepistodividetheresultingvarianceattributedtothemarketfactorbytheportfoliovarianceofreturns,whichisthesquareofthestandarddeviationofreturns:Portionoftotalportfolioriskexplainedbythemarketfactor=0.001223(0.0374)2=87%
