EquityPortfolio

Management

CFA三級(jí)培訓(xùn)項(xiàng)目

講師：BobHong

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1.BuildingBlocks

UsedinPortfolio

Construction

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BuildingBlocksUsedinPortfolioConstruction

Thethreemainbuildingblocksofportfolioconstructionare:

Factorweightings.

Alphaskills.

Positionsizing.

Thesethreebuildingblocksareintegratedintoasuccessfulportfolio

constructionprocessthroughafourthcomponent:breadthofexpertise.

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BuildingBlocksUsedinPortfolioConstruction

FirstBuildingBlock:Overweight/UnderweightRewardedFactors

Thisrelatestothemanagertakingexposurestorewardedrisksthat

differfromthoseofthebenchmark.Thiscanbethoughtofasactive

returnduetodifferencesinbeta.

Withexposurestorewardedfactorsincreasinglyaccessibleviarules-

basedindexproducts,simplestaticexposuretorewardedfactorsisno

longerwidelyconsideredasourceofalpha.

Irrespectiveofthemanager’sapproach,whethertheyexplicitlytarget

factorexposuresortargetindividualsecurities,theirperformancecanin

partbeattributedtosensitivitytothesebetafactors.

Thisbuildingblockrelatesprimarilytoactivereturnsourcenumberone:

differencesinexposurestolong-termrewardedfactors.

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BuildingBlocksUsedinPortfolioConstruction

SecondBuildingBlock:AlphaSkills

Alphaskillsareexcessreturnsrelatedtotheuniqueskillsandstrategies

ofthemanager.

Amanagercangeneratealphathroughfactortiming,whichisskill

inidentifyingwhenafactormightoutperform/underperformits

averagereturn.

Thiscouldapplytoarewardedfactor,butitcouldalsoapplyto

unrewardedfactors,suchascorrectlytiminggeographicalor

industrysectorexposures,commodityprices,orevensecurity

selection(adiscretionarymanagermightrefertotheseasthematic

exposures).

Thisbuildingblockrelatesprimarilytoactivereturnsourcenumbertwo:

identifyingmispricings.

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BuildingBlocksUsedinPortfolioConstruction

ThirdBuildingBlock:SizingPositions

Positionsizingbalancesmanagers’confidenceintheiralphaandfactor

insightswhilemitigatingidiosyncraticriskscomingfromconcentrated

positions.

Positionsizingwillaffectallthreesourcesofactiverisk,butthemost

dramaticimpactwillbeonidiosyncraticrisk.

Thegeneralruleisthatsmallerpositionsinagreaternumberof

securitieswilldiversifyawayidiosyncraticriskandleadtolower

portfoliovolatility.

Afactor-orientatedmanagerwhospreadstheirportfolioacrossmany

assetsislikelytominimizetheimpactofidiosyncraticrisk.

Astock-pickerislikelytoholdmoreconcentratedpositionsbasedon

theirinsightsintoindividualsecurities,andhence,deliberatelyassumea

higherdegreeofidiosyncraticrisk.

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2.ActiveShare

andActiveRisk

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ActiveShareandActiveRisk

ActiveSharemeasuresthedegreetowhichthenumberandsizingofthe

positionsinamanager’sportfolioaredifferentfromthoseofabenchmark,

andisgivenbythefollowingequation:

N

ActiveShare=1

2

∣Weightportfolio,i?Weightbenchmark,i∣

i=1

ActiveSharetakesavaluebetween0and1.IfaportfoliohasanActive

Shareof0.5,wecanconcludethat50%oftheportfolioisidenticalto

thatofthebenchmarkand50%isnot.

Iftwoportfolioswiththesamebenchmarkinvestonlyinbenchmark

securities,theportfoliowiththefewersecuritiesandthereforehigher

degreeofconcentrationinpositionswillhaveahigherlevelofActive

Share.

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ActiveShareandActiveRisk

Activerisk,alsocalledtrackingerror,isthestandarddeviationofactive

returns(portfolioreturnsminusbenchmarkreturns).Asanequation:

2

e

?=?2(∑(β?β)×Fk)+?

?

pk

bk

?

Researchconclusionsonthecompositionofactivereturninclude:

Highnetexposuretoariskfactorleadstohighlevelofactiverisk.

Aportfoliowithnonetfactorexposurewillhaveactiveriskattributed

entirelytoActiveShare.

ActiveriskattributabletoActiveShareisinverselyproportionaltothe

numberofsecuritiesintheportfolio.

Activeriskincreasesasfactorandidiosyncraticrisklevelsincrease.

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ActiveShareandActiveRisk

InvestmentStyle

Description

ActiveShareandActiveRisk

Noactivepositions:portfolioZeroActiveShareandzero

Pureindexing

isequaltothebenchmark

activerisk

Noactivefactorbets—

idiosyncraticrisklowif

diversified

Lowactiverisk—ActiveShare

lowifdiversified

Factorneutral

Balancedexposuretorisk

factorsandminimized

Reasonablylowactiverisk—high

ActiveShare

Factordiversifiedidiosyncraticriskthroughhighfromlargeamountofsecurities

numberofsecuritiesin

portfolio

usedthatare

unlikelytobeinthebenchmark

Targetedfactorbets—

idiosyncraticrisklikelytobe

high

Concentrated

factorbets

HighActiveShareandhigh

activerisk

ConcentratedTargetedindividualstock

stockpickerbets

HighestActiveShareand

highestactiverisk

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ActiveShareandActiveRisk

InvestmentStyles,ActiveShare,andActiveRisk

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ActiveShareandActiveRisk

Managerstylescanalsobeidentifiedthroughobservingtheirsectorand

securityspecificconstraints.Forexample:

Asectorrotatorwouldneedtohavelargepermitteddeviationsinsector

weights;

Astockpickerwouldneedtohavelargepermitteddeviationsin

individualsecurityweights;

Adiversifiedmulti-factorinvestorwouldnotneedsuchlargedeviations

fromindexweights,butwouldstillneedsomeflexibilityinorderto

generateamoderatelevelofactiveriskandreturn.

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3.Allocatingthe

RiskBudgeting

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AllocatingtheRiskBudgeting

Riskbudgetingisaprocessbywhichthetotalriskofaportfoliois

allocatedtoconstituentsoftheportfoliointhemostefficientmanner.Itis

anintegralpartofaneffectiveriskmanagementprocess.Aneffectiverisk

managementprocesshasthefollowingfoursteps:

Determinewhichtypeofriskmeasureisappropriategiventhefund

mandate.

Absoluteriskmeasuresareappropriatewhentheinvestment

objectiveisexpressedintermsoftotalreturns.

Relativeriskmeasuresareappropriatewhentheinvestment

objectiveistooutperformamarketindex.

Understandhoweachaspectofthestrategycontributestorisk.

Determinewhatlevelofriskbudgetisappropriate.

Properlyallocateriskamongindividualpositions/factors.

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AllocatingtheRiskBudgeting

CausesandSourcesofAbsoluteRisk

Absoluteriskmeasuresfocusonthesizeandcompositionofabsolute

portfoliovariance.Thecalculationoftotalportfoliovariance(V):

p

??

?=???

?

????

?=1?=1

Inotherwords,theportfoliovarianceisthesumofeachasset’s

contributiontoportfoliovariance.Thecontributionofassetito

portfoliovariance(CV)isgivenbytheequation:

i

?

??=???=??

????????

?=1

?=assetj’sweightintheportfolio

?

?=thecovarianceofreturnsbetweenassetiandassetj

??

?=thecovarianceofreturnsbetweenassetiandtheportfolio

??

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AllocatingtheRiskBudgeting

CausesandSourcesofRelative/ActiveRisk

Relativeriskbecomesanappropriatemeasurewhenthemanageris

concernedwithherperformancerelativetoabenchmark.Onemeasure

ofrelativeriskisthevarianceoftheportfolio’sactivereturn(AV):

p

??

??=(???)??????

?

?????

?=1?=1

x=theasset’sweightintheportfolio

i

b=thebenchmarkweightinasseti

i

??=thecovarianceofrelativereturnsbetweenassetiandassetj

??

Thecontributionofeachassettotheportfolioactivevariance(CAV)is

i

???=?????

?????

RCisthecovarianceofrelativereturnsbetweenassetiandthe

ip

portfolio.

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AllocatingtheRiskBudgeting

Theimportantpointstonoteare:

Contributiontoactivevarianceisafunctionofactiverisknotabsolute

standarddeviation.

E.g.Whilecashhasaverylowstandarddeviation,ithasanactive

risktwicethatoftheindexescomprisingthebenchmarkduetothe

lowcorrelationofcashversusthebenchmark.Thisleadstocash

contributingto100%oftheactivevariance.

ThecorrelationoftheactivereturnsofindexAandindexBis–1.Thisis

becausethebenchmarkisanequallyweightedaverageofthetwo

indices—whenoneisoutperformingthebenchmark(sohaspositive

activereturns)thentheothermustbeunderperformingthebenchmark

(givingnegativeactivereturns).

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Example:Absoluteriskattribution

Aportfoliohasthefollowingcharacteristics

PortfolioWeight

StandardDeviation

AssetA

AssetB

AssetC

Portfolio

40%

50%

20%

12%

10%

6%

100%

11.92%

Covariance

AssetB

AssetA

AssetC

AssetA

AssetB

AssetC

0.040000

0.009600

0.002400

0.009600

0.014400

0.001440

0.002400

0.001440

0.003600

CalculatetheabsolutecontributiontoportfoliovarianceofassetA.

Giventhatthetotalvarianceis0.014212,calculatetheproportionoftotal

portfoliovariancecontributedbyAssetA.

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Example:AbsoluteRiskAttribution

1.CovarianceofreturnsbetweenassetAandtheportfolio:

WeightofAssetA×WeightofAssetA×

0.40×0.40×0.04

CovarianceofAssetAwithAssetA

+WeightofAssetA×WeightofAssetB×

0.40×0.50×0.0096

CovarianceofAssetBwithAssetA

+WeightofAssetA×WeightofAssetC×

+0.40×0.10×0.0024

CovarianceofAssetCwithAssetA

=AssetA’scontributiontototalportfoliovariance

=0.008416

2.TheproportionoftotalportfoliovariancecontributedbyAssetAis,

therefore,0.008416/0.014212=59.22%.

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Example:Factor-basedriskbudgeting

Thefollowingtablepresentstherisk-factorcoefficientsand

variance/covariancematrixforamanagerrunningaportfoliousing

atwo-factormodel(marketandsize)

Coefficient

Market

Size

Value