EquityPortfolio

Management

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1-21

1.BuildingBlocks

UsedinPortfolio

Construction

2-21

BuildingBlocksUsedinPortfolioConstruction

?Thethreemainbuildingblocksofportfolioconstructionare:

zFactorweightings.

zAlphaskills.

zPositionsizing.

?Thesethreebuildingblocksareintegratedintoasuccessfulportfolio

constructionprocessthroughafourthcomponent:breadthofexpertise.

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BuildingBlocksUsedinPortfolioConstruction

?FirstBuildingBlock:Overweight/UnderweightRewardedFactors

zThisrelatestothemanagertakingexposurestorewardedrisksthat

differfromthoseofthebenchmark.Thiscanbethoughtofasactive

returnduetodifferencesinbeta.

zWithexposurestorewardedfactorsincreasinglyaccessibleviarules-

basedindexproducts,simplestaticexposuretorewardedfactorsisno

longerwidelyconsideredasourceofalpha.

zIrrespectiveofthemanager’sapproach,whethertheyexplicitlytarget

factorexposuresortargetindividualsecurities,theirperformancecanin

partbeattributedtosensitivitytothesebetafactors.

zThisbuildingblockrelatesprimarilytoactivereturnsourcenumberone:

differencesinexposurestolong-termrewardedfactors.

4-21

BuildingBlocksUsedinPortfolioConstruction

?SecondBuildingBlock:AlphaSkills

zAlphaskillsareexcessreturnsrelatedtotheuniqueskillsandstrategies

ofthemanager.

9Amanagercangeneratealphathroughfactortiming,whichisskill

inidentifyingwhenafactormightoutperform/underperformits

averagereturn.

9Thiscouldapplytoarewardedfactor,butitcouldalsoapplyto

unrewardedfactors,suchascorrectlytiminggeographicalor

industrysectorexposures,commodityprices,orevensecurity

selection(adiscretionarymanagermightrefertotheseasthematic

exposures).

zThisbuildingblockrelatesprimarilytoactivereturnsourcenumbertwo:

identifyingmispricings.

5-21

BuildingBlocksUsedinPortfolioConstruction

?ThirdBuildingBlock:SizingPositions

zPositionsizingbalancesmanagers’confidenceintheiralphaandfactor

insightswhilemitigatingidiosyncraticriskscomingfromconcentrated

positions.

zPositionsizingwillaffectallthreesourcesofactiverisk,butthemost

dramaticimpactwillbeonidiosyncraticrisk.

9Thegeneralruleisthatsmallerpositionsinagreaternumberof

securitieswilldiversifyawayidiosyncraticriskandleadtolower

portfoliovolatility.

zAfactor-orientatedmanagerwhospreadstheirportfolioacrossmany

assetsislikelytominimizetheimpactofidiosyncraticrisk.

zAstock-pickerislikelytoholdmoreconcentratedpositionsbasedon

theirinsightsintoindividualsecurities,andhence,deliberatelyassumea

higherdegreeofidiosyncraticrisk.

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2.ActiveShare

andActiveRisk

7-21

ActiveShareandActiveRisk

?ActiveSharemeasuresthedegreetowhichthenumberandsizingofthe

positionsinamanager’sportfolioaredifferentfromthoseofabenchmark,

andisgivenbythefollowingequation:

N

1

ActiveShare=??Weightportfolio,i?Weightbenchmark,i?

2

i=1

zActiveSharetakesavaluebetween0and1.IfaportfoliohasanActive

Shareof0.5,wecanconcludethat50%oftheportfolioisidenticalto

thatofthebenchmarkand50%isnot.

zIftwoportfolioswiththesamebenchmarkinvestonlyinbenchmark

securities,theportfoliowiththefewersecuritiesandthereforehigher

degreeofconcentrationinpositionswillhaveahigherlevelofActive

Share.

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ActiveShareandActiveRisk

?Activerisk,alsocalledtrackingerror,isthestandarddeviationofactive

returns(portfolioreturnsminusbenchmarkreturns).Asanequation:

2

e

??

?

?

?2(∑(β?β)?Fk)+?

pkbk

?Researchconclusionsonthecompositionofactivereturninclude:

zHighnetexposuretoariskfactorleadstohighlevelofactiverisk.

zAportfoliowithnonetfactorexposurewillhaveactiveriskattributed

entirelytoActiveShare.

zActiveriskattributabletoActiveShareisinverselyproportionaltothe

numberofsecuritiesintheportfolio.

zActiveriskincreasesasfactorandidiosyncraticrisklevelsincrease.

9-21

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

Concentrated

stockpicker

Targetedindividualstock

bets

HighestActiveShareand

highestactiverisk

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ActiveShareandActiveRisk

?InvestmentStyles,ActiveShare,andActiveRisk

11-21

ActiveShareandActiveRisk

?Managerstylescanalsobeidentifiedthroughobservingtheirsectorand

securityspecificconstraints.Forexample:

zAsectorrotatorwouldneedtohavelargepermitteddeviationsinsector

weights;

zAstockpickerwouldneedtohavelargepermitteddeviationsin

individualsecurityweights;

zAdiversifiedmulti-factorinvestorwouldnotneedsuchlargedeviations

fromindexweights,butwouldstillneedsomeflexibilityinorderto

generateamoderatelevelofactiveriskandreturn.

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3.Allocatingthe

RiskBudgeting

13-21

AllocatingtheRiskBudgeting

?Riskbudgetingisaprocessbywhichthetotalriskofaportfoliois

allocatedtoconstituentsoftheportfoliointhemostefficientmanner.Itis

anintegralpartofaneffectiveriskmanagementprocess.Aneffectiverisk

managementprocesshasthefollowingfoursteps:

zDeterminewhichtypeofriskmeasureisappropriategiventhefund

mandate.

9Absoluteriskmeasuresareappropriatewhentheinvestment

objectiveisexpressedintermsoftotalreturns.

9Relativeriskmeasuresareappropriatewhentheinvestment

objectiveistooutperformamarketindex.

zUnderstandhoweachaspectofthestrategycontributestorisk.

zDeterminewhatlevelofriskbudgetisappropriate.

zProperlyallocateriskamongindividualpositions/factors.

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AllocatingtheRiskBudgeting

?CausesandSourcesofAbsoluteRisk

zAbsoluteriskmeasuresfocusonthesizeandcompositionofabsolute

portfoliovariance.Thecalculationoftotalportfoliovariance(V):

p

?

?

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?????

??????

zInotherwords,theportfoliovarianceisthesumofeachasset’s

contributiontoportfoliovariance.Thecontributionofassetito

portfoliovariance(CV)isgivenbytheequation:

i

?

??????????

???

?

?

?

??

???

9?=assetj’sweightintheportfolio

?

9?=thecovarianceofreturnsbetweenassetiandassetj

??

9???=thecovarianceofreturnsbetweenassetiandtheportfolio

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AllocatingtheRiskBudgeting

?CausesandSourcesofRelative/ActiveRisk

zRelativeriskbecomesanappropriatemeasurewhenthemanageris

concernedwithherperformancerelativetoabenchmark.Onemeasure

ofrelativeriskisthevarianceoftheportfolio’sactivereturn(AV):

p

?

?

????????????????

??

?

?

?

?

??????

9x=theasset’sweightintheportfolio

i

9b=thebenchmarkweightinasseti

i

9??=thecovarianceofrelativereturnsbetweenassetiandassetj

??

zThecontributionofeachassettotheportfolioactivevariance(CAV)is

i

?????????

??

?

?

?

9RCisthecovarianceofrelativereturnsbetweenassetiandthe

ip

portfolio.

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AllocatingtheRiskBudgeting

?Theimportantpointstonoteare:

zContributiontoactivevarianceisafunctionofactiverisknotabsolute

standarddeviation.

9E.g.Whilecashhasaverylowstandarddeviation,ithasanactive

risktwicethatoftheindexescomprisingthebenchmarkduetothe

lowcorrelationofcashversusthebenchmark.Thisleadstocash

contributingto100%oftheactivevariance.

zThecorrelationoftheactivereturnsofindexAandindexBis–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

AssetA

AssetB

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.

18-21

Example:AbsoluteRiskAttribution

?1.CovarianceofreturnsbetweenassetAandtheportfolio:

WeightofAssetAhWeightofAssetAh

0.40h0.40h0.04

CovarianceofAssetAwithAssetA

+WeightofAssetAhWeightofAssetBh

0.40h0.50h0.0096

CovarianceofAssetBwithAssetA

+WeightofAssetAhWeightofAssetCh

+0.40h0.10h0.0024

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

Valu