15433 20a Active Management

7/31/2019 15433 20a Active Management

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15.433INVESTMENTSClass20:ActivePortfolioManagement

Spring2003


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Financial instrumentsare increasing innumberandcomplexity

Supranationals

Interest rate-options

Cross-currency hedgesCurrency- Currency-

forwards options AgenciesAgencies Proxy hedgesComplex domestic markets

Government FuturesFuturesIndex-linked bonds

Semigovernments SwapsSwaps

Volatility optionsAgenciesAgencies Inflation protectedSupranationalsSupranationals government bonds

SwaptionsCDO / MBA

Exotic currency options


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Keyquestion forevery investorWhatisthegoalforthetotalportfolio?

Whatisthetimeframeforachievingthatgoal?

What isthetolerance for loss/uncertaintywithinashorterterm(one-,three-,six-month)period?

Whichkindsofriskareacceptable/unacceptable?

What are you willing to pay for active risk management? (e.g. cur-rencyhedges)

Howdoyoumonitor/evaluateyourriskmanagement?


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Therisk-versus-returncompassIncreasingcompensatedriskscanincreasereturns

Twomajortypesofcompensatedrisk:

CreditMarket

Aretheseareasofskill?OptimizetheriskexposureInsufficientevidenceofskill?Ignore,hedgeortransfertherisk?

Same RiskMore Return

Less Risk

Starting

Portfolio

Starting

PortfolioMore Risk

Same Return Same Return

Same Risk

Less Return


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HigherMomentsofAsset

Asset Return Risk

(asset) =return changeinvalueofasset

(return)=risk speedofchange

(risk) =highermomentsof risk profileofspeed


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Activevs. PassivemanagementActive management means allocation of resources based on an activestrategy.

Usually

active

management

is

performed

against

abenchmark,

requiringintendedover-/underweightsofpositions.

Passive management means following an index, benchmark or anotherportfolio using quantitative techniques, such as principal componentanalysistoreplicateanindex.

The discussion of active vs passive management is linked to the effi-cientmarketdiscussion: Caninformationaddvalue(performance).

Strategic Asset

Allocation

Tactical AssetAllocation

Stock Picking

Top-Down

Bottom-Up

Figure3: Bottom-upvs. topdownapproach


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FromWheredoesSuperiorPerformanceCome?

From Where does Superior Performance Come? Superior performancearises fromactive investmentdecisionswhichdifferentiatetheportfoliofromapassivebenchmarkThesedecisionsinclude:Market Timing: Altering market risk exposure through time to

makeadvantageofmarketfluctuations;Sectoralemphasis: Weightingtheportfoliotowards(orawayfrom)

company attributes, such as size, leverage, book/price, and yield,andtowards(orawayfrom)industries;

Stock selection: Markingbets intheportfoliobasedon informa-tionidiosyncractictoindividualsecurities;

Trading: largefundscanearnincrementalrewardbyaccommodat-inghurriedbuyersandsellers.


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SomeDefinitionsActivemanagement: The pursuit of transactions with the objective ofprofiting

from

competitive

information

- that

is,

information

that

would

loseitsvalueifitwereinthehandsofallmarketparticipantsActiveman-agementischaracterizedbyaprocessofcontinuedresearchtogeneratesuperiorjudgment, which is then reflected in the portfolio by transac-tions that are held in order to profit from thejudgment and that areliquidatedwhentheprofithasbeenearned.

Alpha: The risk adjusted expected return or the return in excess ofwhatwouldbeexpected fromadiversifiedportfoliowiththesamesys-tematic risk When applied to stocks, alpha is essentially synonymouswith misvaluation: a stock with a positive alpha is viewed as under-valued relative to other stocks with the same systematic risk, and astock with a negative alpha is viewed as overvalued relative to otherstockswiththesamesystematicriskWhenappliedtoportfolios,alphaisadescriptionofextraordinaryrewardobtainablethroughtheportfoliostrategy. Here it is synonymous with good active management: a bet-teractivemanagerwillhaveamorepositivealphaatagivenlevelofrisk.

Alpha,historical: Thedifferencebetweenthehistoricalperformanceandwhatwouldhavebeenearnedwithadiversifiedmarketportfolioatthesamelevelofsystematicriskoverthatperiod. Underthesimplestproce-dures,historicalalphaisestimatedastheconstantterminatimeseriesregressionoftheassetorportfolioreturnuponthemarketreturn.


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Alpha, judgmental: The final output of a research process, embody-inginasinglequantitativemeasurethedegreeofunderorovervaluationofthestocksJudgmentalalphaisaproductofinvestmentresearchanduniquetotheindividualororganizationthatproducesitisderivedfromaforecastofextraordinaryreturn,butithasbeenadjustedtobetheexpectedvalueofsubsequentextraordinaryreturn. Forexample,amongthosestocksthatareassignedjudgmentalalphasof2percent,theaver-ageperformance(whencomparedtootherstocksofthesamesystematicriskwithalphasofzero)shouldbe2percentperannum. Thus,averageexperienced performance for any category ofjudgmental alpha shouldequal the alpha itself. Ajudgmental alpha is a prediction, not retro-spectiveexperience.

Alpha, required: The risk adjusted expected return required to causetheportfolioholdingtobeoptimal,inviewoftherisk/rewardtradeoff.Therequiredalphaisfoundbysolvingforthecontributionofthehold-ing toportfolio riskandbyapplyingarisk/rewardtradeofftofindthecorrespondingalpha. Itcanbeviewedasatranslationofportfolioriskexposureintothejudgmentwhichwarrantsthatexposure.


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CAPM

Expected

R

eturn

Beta ()

Securit

yMark

etLine

M

(rf)

= 1

(rM

)Expected

RiskPremium

defensive aggressive

Risk free Investment Investment in Market

Figure: CAPMandmarket-aggressivityE(ri)rf

i = (1)E(rM)rf

cov(ri, rM)i =

2(2)

M


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APTAPTsays:Expected excess return for any asset is a weighted combination of

theassetsexposuretofactors.

APTdoesnotsay:Whatthefactorsareorwhattheweightsare.

Sowhat?CAPMforecastscanbeusedforperformancemeasurement,i.e. beat

theindex;APT forecastsaredifficulttouse forperformance- rememberthey

arearbitrary;A

good

APT

forecast

can

help

you

to

outperform

the

index;

APTisanactivemanagementtoolbasedonamultifactormodel.


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FactorModels

R2

= 1var(i)

(3)

var(ri)

ri = [bi,1F1+bi,2F2+ +bi,nFn] (4)

Afactormodelstriestoexplainthevariationofreturn,whichisatrans-formationoftheoriginallevel: assetbehavior.Some techniques help to understand what moves the assets and thusdetermines return and risk. The principal component analysis is fre-quentlyused,but...firsthand interpretation ismaybenot intuitive.


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ShallIgo longprincipalcomponent2andshortprincipalcomponent4?

LePenseur,Rodin1880


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TheTreynor-BlackModelMixSecurityAnalysiswithPortfolioTheory

Supposethatyoufindseveralsecuritiesappeartobemispricedrelativetothepricingmodelofyourchoice,saytheCAPM.

According to the CAPM, the expected return of any security with kis:

CAPM =rf +k (E(rM)rf) (5)kLet A be subset with mis-priced securities. For any securitykA,youfindthat

CAPMrk =k +k +k (6)wherek istheperceivedabnormalreturn.

You would like to exploit the mis-pricing in the subset A. For this,yourformaportfolioA,consistingofthemis-pricedsecurities. Atthesame

time,

you

believe

that

the

rest

of

the

universe

is

fairly

priced.

The rest of the portfolio allocation problem then becomes a standardone:

Theobjectiveisthatofamean-varianceinvestor.

Thechoice

of

assets:

1.ThemarketportfoliowithM andM2.Theportfolioofmis-pricedsecuritiesA,3.withA andA


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4.Theriskfreeasset.Thesolution: sameastheoneweconsideredinClass5.


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TheBlack-LittermanModelMixBeliefswithPortfolioTheory

The Black-Litterman asset allocation model, developed when both au-thors were working for Goldman Sachs, is a significant modification ofthetraditionalmean-varianceapproach. Inthemean-varianceapproachofMarkowitz,theuserinputsacompletesetofexpectedreturnsandthevariance-covariancematrix,andtheportfoliooptimizergeneratestheop-timalportfolioweights. Duetothecomplexmappingbetweenexpectedreturnsandportfolioweights,usersofthestandardportfoliooptimizersoften

find

that

their

specification

of

expected

returns

produces

output

portfolioweightswhichmaynotmakesense. Theseunreasonableresultsstemfromtwowellrecognizedproblems:

1.Expected returns are very difficult to estimate. Investors typicallyhaveknowledgeableviewsaboutabsoluteorrelativereturnsinonlya few markets. A standard optimization model, however, requiresthemtoprovideexpectedreturnsforallassets.

2.The optimal portfolio weights of standard asset allocation modelsareextremelysensitivetothereturnassumptionsused.

These two problem compound each other; the standard model has nowaytodistinguishstronglyheldviewsfromauxiliaryassumptions,andthe optimal portfolio it generates, given its sensitivity to the expectedreturns, often appears to bear little or no relation to the views the in-vestorwishestoexpress.


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In practice, therefore, despite the obvious attractions of a quantitativeapproach, few global investment managers regularly allow quantitativemodels to play a major role in their asset allocation decision. In theBlack-Litterman model, the user inputs any number of views or state-mentsabouttheexpectedreturnsofarbitraryportfolios,andthemodelcombinestheviewswithequilibrium,producingboththesetofexpectedreturns of assets as well as the optimal portfolio weights. Since publi-cation of 1990, the Black-Litterman asset allocation model has gainedwideapplicationinmanyfinancialinstitutions.


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Howrelevantare factors inrelationtodifferentstyles?

100%

90%

80%

70%

60%

50%

40%

30%

20%

10%

0%

100%

90%

80%

70%

60%

50%

40%

30%

20%

10%

0%

PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 9 PC 10 PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 9 PC 10

FactorsforValueportfolio FactorsforGrowthportfolio

Dependingonthenatureoftheinvestments,theinfluencingfactorsaredifferent. Thus, the principal components, reflecting the explanatorypowerofexisting,butunknownfactorsaredifferentinstructureanddimension. Whatmakesagoodfactor?Interpretable: It isbasedon fundamentalandmarket-relatedchar-

acteristicscommonlyusedinsecurityanalysisIncisive: ItdividesthemarketintowelldefinedslicesInteresting: It contributes significantly to risk, or it has persistent

orcyclicalpositiveornegativeexceptionalreturn

WhyFactors?Change inbehavior(companyrestructuring, newbusinessstrategy

etc),


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reflected in sensitivities to factors; Screening of universe for ade-quateinvestments,dependingoninvestmentobjective;

Handlingofinformation-overflow

SomeexamplesofStyle-definitions:LargeCapValue: StocksinStandard&Poors500indexwithhigh

book-to-priceratiosLargeCapGrowth: StocksinStandard&Poors500indexwithlow

book-to-priceratiosSmallCapStocks: Stocksinthebottom20Eachstylesreactsdifferentandthusfitsdifferentclientsindifferent

ways


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FactorDefinitions:Size: Capturesdifferencesinstockreturnsduetodifferencesinthemar-ket

capitalization

of

companies

This

index

continues

to

be

asignificant

determinantofperformanceaswellasrisk.

Success: Identifiesrecentlysuccessfulstocksusingpricebehaviorinthemarketasmeasuredbyrelativestrength. Therelativestrengthofastockissignificantinexplainingitsvolatility.

Value: Captures the extent to which a stock is priced inexpensivelyinthemarket. Thedescriptorsareasfollows:ForecastEarningstoPrice;ActualEarningstoPrice;ActualEarningstoPrice;Yield.

Variability in Markets (VIM): Predicts a stocks volatility, net of themarket, based on its historical behavior. Unlike beta, this index mea-suresthestocksoverallvolatility.

Growth: Uses historical growth and profitability measures to predictfutureearningsgrowth. Thedescriptorsareasfollows:DividendpayoutratiooverfiveyearsComputedusingthe lastfive

yearsofdataondividendsandearnings;Variabilityincapitalstructure;


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Growthrateintotalassets;Earningsgrowthrateoverlastfiveyears;Analyst-predictedearningsgrowth;RecentearningschangeMeasureofrecentearningsgrowth.


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ReturnDecompositionTotal

Return

ActiveNormal

Risk-FreeTotal

Excess

ActiveSpecific

ActiveSystematic

Figure: Returndecomposition

RiskDecompositionCommon Risk

21 x 21 = 441

Specific Risk

4.5 x 4.5 = 20.25

Total Risk

21.48 x 21.48 = 461.25

Figure: Riskdecomposition,


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ReturnandRisk,ATwoFactorLinearModel

Return:rp = ap+bp,1F1+bp,2F2+p

rBM = aBM +bBM,1F1+bBM,2F2+BM (7)ExcessReturn:

rprBM = ap+ (bp,1bBM,1)F1+ (bp,2bBM,2)F2

+ (ap+paBMBM) (8)VarianceofExcessReturn:

2 2var(rprBM) = (bp,1bBM,1) var(F1) + (bp,2bBM,2) (F2)

+ 2(bp,1

bBM,1) (bp,2

bBM,2)

cov

(F1, F2)

+ var(p) + var(BM)2cov(p, BM) (9) TrackingError:

2 2 (bp,1bBM,1) var(F1) + (bp,2bBM,2) (F2)TE= varprBM =

+2(bp,1bBM,1) (bp,2bBM,2)cov(F1, F2) (10)

+var(p) + var(BM)2cov(p, BM)

23 MITSloan15.433


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TrackingErrorThe tracking error is defined as: the standard deviation of active re-turn.

A = std[rAP] = [rP][rBM]

= AP =PBM (11)

Thetracking errormeasuresthedeviation from thebenchmark, as therp isthesumoftheweightedreturnsofallpositionsintheportfolioandrBM isthesumoftheweightedreturnsofallpositionsinthebenchmarks.Portfolioandbenchmarkdonotalwayscontainthesamepositions!

Trackingerroriscalledaswellactiverisk.


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InformationRatioInformationRatio: Ameasureofaportfoliomanagersabilitytodeliver,relating

the

relative

return

to

the

benchmark

and

the

relative

risk

to

the

benchmark:ExpectedActiveReturn(alpha)ActiveRisk

expectedactivereturn IR = = (12)

activerisk TEImpliedalpha: Alphabacked-outthroughreverseengineering;howmuchhas my expected return to be tojustify all other parameters ceterisparibus


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ForecastsSomeexamples:MCAR:HowmuchdoesactiveriskincreaseifIincreasetheholding

xby1%andreducecashby1%MCTCFR:HowmuchdoescommonfactorriskincreaseifIincrease

theholdingxby1%andreducecashby1%MCASR: How much does specific active risk increase if I increase

theholdingxby1%andreducecashby1%


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PerformanceAttributionThe identification of individual return components can be performedquiteeasily,subjecttothehistoryoftherestructuringoftheportfolio.

The straight forward approach is based on the definition of a passivebenchmark portfolio, which reflects the long-term investment strategy.Inthecontextofthe investmentstrategy(orthestrategicassetalloca-tion)the investmentmanagementdecideswhichassetcategories(equi-ties,fixed income,currencies,etc.) areover-/underweighted relativetothe benchmark (strategy). The weights of specific asset categories - asdeterminedintheinvestmentstrategy- arecallednormalweights.Foreachassetcategoryoftheportfolioexistsacorrespondingassetcat-egory of the benchmark (index), relative to which the performance iscalculated. Thereturnofthese indicesarecallednormalreturns. It isobvious,thatthethenormalreturn isareturnofapassive investmentinthecorrespondingassetcategoryofthebenchmark.

For equities, fixed income and for currencies exist different indices, re-flectingdifferentneeds.

Thenormalweightoftheassetcategoryi(ws,i)multipliedwiththenor-malreturn(rs,i) isthereturnofthis intendedassetcategory. Summedupoverallreturns fromthedifferentassetcategories,theportfoliohasthefollowingstrategy/-benchmarkreturn:

Nrstrategy = i=1ws,irs,i


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Against this benchmark-portfolio we want to know the realized returnof the actively managed portfolio. We have a positive excess-return, ifthe effectively realized portfolio return (rportfolio) exceeds the strategyreturn(rstratey):rexcess return =rstrategyrportfolioThe current portfolio return (rportfolio) is calculated from the effectivebreakdownoftheportfoliointhedifferentassetcategories(wp,i)aswellastheeffectivelyrealizedreturns(rs,i)oftheindividualassetcategories:

Nrportfolio = i=1wp,i rp,iThe difference between the strategy return and the realized portfolioreturnresultsfromthefact,thattheportfoliomanagerrestructurestheportfoliothroughmarkettimingstrategiesbasedontheontheassump-tion of predicting the direction of the performance. Overperformanceby timing the market can be achieved by adjusting the overall marketexposureoftheportfolio. Varioustechniquesexisttotimethemarket:tacticalover- andunderweightsofcategoriesandthusdeviatesfrom

thenormalweightsthourghchangesintheassetclassmix(especiallystockandcashpositions),alsocalledrotation(sectorrotation,assetclass

rotation)

timingwithinanassetclass: changingthesecuritymixbyshifting

theproportionsofconservative(lowbeta)anddynamic(highbeta)securities.


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derivatives instruments: especially indexfuturesandtheuseofop-tions.

Security selection is the identification of over/-under priced securities.Soasuperiorvaluationprocess isneededtocomparethetruevalue forasecuritywiththecurrentmarketvalue.

Overall,thereturnofaportfoliocanbedecomposedinfourreturncom-ponents,whichsummedupagainresultin(rportfolio):

Nrstrategy = i=1ws,i rs,i

Nrtiming = i=1rs,i (wp,iws,i)

Nrselectivity = i=1ws,i(rp,irs,i)

Nrcumulative effect = i=1(wp,iws,i)(rp,irs,i)

Figure1highlightsthedecompositionoftheportfolioreturn inthe in-dividualcomponentsandtheirrelationshiptoaactiverespectivelypas-sive portfolio management. Quadrant (1) is put together from passiveselectivity and passive timing. It represents the long-term investmentstrategyandservesasthebenchmarkreturnfortheobservationperiodinexamination. Iftheportfoliomanagementperformsapassivemarkettiming, we receive the return in quadrant (2). It represents the returnfromtimingandstrategy. Weunderstandtimingasthedeviationintheweightoftheindividualassetcategoryfromthenormalweight. Withinthe individual asset categories we invest in a passive index portfolio.Through subtraction of the strategy return from quadrant (1) we re-ceivethenetresultfromtiming.


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Quadrant3reflectsthereturnsfromselectivityandstrategy. Selectivityistheactivechoiceofindividualsecuritieswithinanassetstrategy. Thenormal weights are kept equal. The return from selectivity is receivedthroughsubtractionofthestrategyreturninquadrant(1)fromquadrant(3). In quadrant(4)we finallyfindthe realized return of the portfolioovertheobservationperiodinexamniation,calculatedastheproductofthe current weights of the individual asset categories with the currentreturns within the asset categories. Not obvious from the figure is thefourthcomponent,thecumulativeeffect(alsocalled interactioneffect),which isbasedoncrossproductofreturn- andweightdifferences. Theresidual term can be derived from the interaction between timing andselectivity. Itisbasedonthefactthattheportfoliomanagerputsmoreweight on the asset categories with a higher return than in the bench-markindex(selectivity).

selectivity

market

timing

active

passive

active

(4)realizedreturnNi=1wp,i rp,i

(3)selectivity&strategyNi=1ws,i rp,i

passive

(2)timing&strategyNi=1wp,i rs,i

(1)strategy

Ni=1ws,i rs,i


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Timing=(2)-(1)

Selectivity=(3)- (1)

Residual=(4)-(3)-(2)+(1)Figure1: Performancecomponentsinanactiveportfolio


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ExamplewithoutCurrencyComponentsAllreturnsarecalculatedinthedomesticcurrency. Allforeignexposuresareperfectlyhedgedbackintothedomesticportfoliocurrency. Theup-per

part

of

the

table

contains

the

normal

weights

and

normal

returns

required to calculate the passive strategy of the individual asset cate-gories.Inthesecondpartofthetablearetheeffectiveweightsandthecurrentreturnsoftheindividualassetcategoriesinthespecificquarters.The current weights and returns are adjusted from quarter to quartertoreflecttherestructuringofthetacticalassetallocationandthestockpickingandresultintheactiveover/-underweights. In the lower part of the table are the individual performance compo-nentsresultingintheindividualquarters. Theyarecalculatedusingtheequationsinthepreviousequations.

From the results in Table 1 it is obvious that the return from activemanagementvariessubstantiallyfromquartertoquarterandreflectsnoconstant pattern. The timing-return varies between -0.15% in the 4thquarter x1 and max 0.28% in the 1st quarter x1. Selectivity has evenmore variation: min is -0.18% in and 1.48% in the 1st quarter. Theresidualtermshaveasurprisingbigimpact,with0.18%oftheportfolioreturn in 1st quarter and 2n quarter and reducing the portfolio returnwith-0.39%!.


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x0/3 x0/4 x1/1 x1/2 x1/3 x1/4 x2/1 entire period

FI $ 57.50 57.50 57.50 57.50 57.50 57.50 57.50FI Euro

normal

weights

12.50 12.50 12.50 12.50 12.50 12.50 12.50Eq $ 22.50 22.50 22.50 22.50 22.50 22.50 22.50Eq Euro 7.50 7.50 7.50 7.50 7.50 7.50 7.50

FI $ -0.75 1.26 4.53 2.09 0.46 0.91 3.26

FI Euro

normal

-19.37 2.50 14.52 3.31 -0.99 -3.16 7.07Eq $

return

s

-28.62 1.39 16.02 0.85 -1.12 -2.18 7.79Eq Euro -1.94 4.37 6.71 4.48 2.15 2.18 5.71

FI $ 57.50 53.70 55.70 52.30 54.50 53.80 52.40FI Euro

weights

12.50 16.50 15.80 16.10 15.90 15.70 16.50Eq $

current

22.50 22.10 22.30 23.60 23.50 23.10 23.20Eq Euro 7.50 7.70 6.20 8.00 6.10 7.40 7.90

FI $ -0.32 0.81 4.22 2.12 1.15 0.78 2.32FI Euro -2.06 4.15 7.05 4.68 1.74 2.33 5.93Eq $

current

returns

-26.19 1.99 16.69 0.97 0.16 -3.89 10.09Eq Euro -21.61 2.37 17.75 4.89 -2.97 -3.24 7.08

strategy -9.44 1.68 8.53 2.14 0.05 -0.20 4.94 7.70timing 0.00 0.06 0.28 0.04 -0.09 -0.15 0.19 0.33selectivity 1.48 -0.07 -0.13 0.25 0.64 -0.18 -0.06 1.93interaction 0.00 0.08 -0.39 0.05 0.16 0.18 0.02 0.10realized -7.96 1.74 8.29 2.48 0.76 -0.35 5.09 10.06

return from active manag 1.48 0.06 -0.24 0.34 0.71 -0.15 0.16 2.36

Table1: Example forperformancecomponentswithoutcurrencyexpo-sure

The active management contributed in 5 out of 7 quarters positivelyto the overall return. Over the time period of 7 quarters the activemanagementadded2.36%,withcontribution fromtimingof0.33%,se-lectivitycontributed1.93%andtheresidualterm0.10%. Lookingattherealized return of the portfolio (10.06%), the contribution from activemanagementwith2.36%issubstantial!

Evenmoreimportantisthecontributionfromthestrategy,whichadded7.70%totheportfolioreturn,andthusisthemostimportantcomponent.Thisexampleshowsquitenicely,thatthemost importantcontributiontothereturnisfromthestrategicassetallocation. Thesubstantialpartoftheachievedinvestmentperformanceisbasedonthestrategyandnotfromtheactivemanagementthroughtheportfoliomanager.


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strategy

timing

selectivity

residual

Brinson/Hood/Beebower (1986) Brinson/Singer/Beebower (1991)

return components(%)

variancecomponents (%)

return components(%)

variancecomponents (%)

10.11

-0.66

-0.36

-0.07

93.6

1.7

4.2

0.5

13.49

-0.26

0.26

-0.07

91.5

1.8

4.6

2.1

total 9.01 100 13.41 100

comments

91 pension funds, USA 1974-1983,

n=43

82 pension funds, USA 1977-1987,

n=45

Table2: PerformancecomponentsforUSpensionfundsTable 2 the study has be carried out over a time period of 10 years.Inthefirstanalysisthepension fundsrealizedareturnof9.01%. Thisis 1.10% below the strategy return of 10.11. The active managementdestroyed value worth 1.10% (0.66% timing, 0.36%). For the secondanalysis the results look not better. The selectivity added in average0.26%totheannualreturn,howevertheactivereturndoesnotlookbet-ter,activemanagementloweredthereturnsby8basispointsinaverage.Acomparisonbetweenthedimensionofstrategyreturnandtheaddedvalueofactivemanagementshowsinbothstudiesthattheactivecom-ponentisonlyasmallfractionofthetotalreturn.


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PerformanceAttributionwithacurrencycomponent

We know from previous classes and from own experience that diversi-fication

can

improve

the

performance

of

the

portfolio.

Diversification

can be generated through investments in e.g. different assetcategoriesorindividualsectors,industriesetc. Especiallythediversificationacrosstheborder lines is important,addingadditional lowcorrelationstotheportfolio. Lookingattheperformanceattributionofinternationaldiver-sified portfolios, we want to know the impacts of strategy, timing andselectivity and as well the contribution from fx-components from theportfolio allocation. Exposure to foreign currencies can be generatedthrough direct investments in fx (buy, sell), or through investments inforeign securities, without completely hedging the fx exposures. Theportfolio return is increases through the fx-return by carrying the fx-exposuresduringtheobservationperiod.

We define with fs,j the strategic component in currencyj and fp,j theeffectivelyheldexposuretocurrencyj. Thereturnofaninternationallydiversifiedportfolioincludingfx-exposurescanbecalculatedasfollowing:

N Nrportfolio = i=1wp,i rp,i+ i=1fp,i rfx,j wp,i isagainthecurrentportfolio weight forassetcategory i. Thecur-rentreturn of anactively managed portfolioyieldsrp,i isno longer ex-clusively in the domestic currency (1 to 1), but in the local currencyof the particular investment. Thus, the first sum of previous equationincludes the weighted return of the investments in different securities,


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measuredinthelocalcurrencyofthecorrespondingmarket. Forinvest-ments in American securities it reflects e.g. the local equity return inUS$. With the second term in the previous equation we add an addi-tional return components coming from the fx-return for the exposureheld in the particular currency. The currency return rfx,j is weightedwiththecorresponding fx-component intheportfolio. Intheexample,wheree.g. 20%oftheequityportfolioareinvestedinEuro-denominatedsecurities(withouthedgingtheportfolioagainsttheEuro-exposure),wehavetoaddtothe localUS-equityreturna20%-investment(exposure)in Euro-currency. For a portfolio, which is exclusively invested in thedomesticportfoliocurrency,thesecondtermsisdropped.

The strategy return is calculated analogous to the portfolio return us-ingthepassivestrategyweightsandnormalreturnsinthelocalcurrency:

N Nrstrategy = i=1ws,irs,i+ i=1fs,i rfx,j

Again, here as well we add a fx-component. The different fx-returnsareweightedaccordingtheircorrespondingstrategicfx-weightsfs,j.

Thedecision,tovarytheproportionsofindividualcurrencyexposuresintheportfolioisconsideredpartofthetacticalassetallocation. Throughconsciousdeviationsfromstrategiccurrencyweightstheactiveportfoliomanagercanadd(loose)anadditionalreturncomponenttothedomes-ticportfolioreturn.Independent from the previous statement is the decision to invest inlocalmarketsandassetcategoriestobenefitfromthelocalperformance.


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Accordingly,thetiming-componentofan internationaldiversifiedport-folio issplit intotwoparts: one inamarket-component, whichreflectsthe investment decisions regarding the specific market and asset cate-gories, and a second part which reflects the currency component fromtheallocationdecisionindifferentcurrencyexposures:

Nrmarkets = i=1rs,i (wp,iws,i)Nrcurrency = i=1rfx,j (fp,jfs,j)

Themarketcomponent iscalculatedthroughmultiplicationofthepas-sive normal returns rs,j, measured in the specific local currency of theinvestmentposition,withdeviationoftheportfolioweightsfromnormalweights. Thereturn,coming fromthedeviation fromthestrategiccur-rencyallocation,isreflectedinthefx-component.

Thereturncomponentfromselectivityisdefinedas:Nrselectivity = i=1ws,i (rp,irs,i)

The portfolio return,rp,i, and as well the normal return,rs,i, are mea-suredinthelocalportfoliocurrency. Theperformancecomponentfromselectivitydecisionsisthusnotbeaffectedfromthecurrencyofspecificinvestments,but iscalculatedexclusivelythroughthechoiceofspecificsecuritieswithinamarketoranassetcategory.


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Legend:ws,i strategyweight(normalweight)forassetclassi

rs,i strategyreturn(normalreturn)forassetclassi

wp,i portfolioweight(effectiveweight)forassetclassi

rp,i portfolioreturn(effectivereturn)forassetclassi

Similarterms:Timing: AllocationCumulativeeffect: Interactioneffect


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PerformanceMeasureCapitalMarketorientedView

Sharpesmeasure:

rprfSharpe= (13)

pDivides average portfolio excess return over the sample period by thestandarddeviationofreturnsoverthatperiod. Itmeasurestherewardto(total)volatilitytrade-off?

Treynorsmeasure:

Treynor s=rprf (14)p

Givesexcessreturnperunitofriskoverthesampleperiodbythestan-darddeviationofreturnsoverthatperiod. Itusessystemicriskinsteadof

total

risk.

Jensensmeasure:

Jensen s =rp[rf +p(rMrf)] (15)ItistheaveragereturnontheportfoliooverandabovethatperdictedbytheCAPM,giventheportfolioos betaandthe averagemarketreturn.Jensensmeasureistheportfoliosalphavalue.Appraisalratio:


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pAppriasalRatio= (16)

pIt divides the alpha of the portfolio by the nonsystematic risk of theportfolio. Itmeasuresabnormalreturnperunitofriskthatinprinciplecouldbediversifiedawaybyholdingamarketindexportfolio.


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SummaryThe (simple) performance attribution allows to figure out where theportfoliomanagermanageraddedvalueandwherehedestroyedvalue.

It is key to learn from past errors and not to repeat them. Perfor-mance attribution is an essential element in investment to ensure thatexposuresarerewardedwiththeappropriateriskpremium.

Thecapitalmarketorientedperformanceattributionisanotherapproachtoanalyzetheperformance. Itallowstocalculatetheriskpremiumsforthefactors/stylestowhichtheportfolioisexposed.

Focus:BKMChapter26p. 874-883,890-897(learngeneraldefinitionsandassumptions)

typeofpotentialquestions: Conceptcheckquestions,p. 899ff. question2,3,4,5

BKMChapter27p. 917-933 (objectives of active portfolios, market timing, security

selection, portfolio construction, multifactor models and portfoliomanagement,

quality

of

forecasts)

typeofpotentialquestions: Conceptcheckquestions,p. 899ff. question2,3,4,5


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Thomas (2000), p. 26 f. information ratio Strongin, Petsch andSharenow (2000), p. 18 dealing with stock-specific benchmark, p.23f. portfoliomanagerpatterns


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Preparation forNextClassPleaseread:

Kritzman(1994a),Kritzman(1994b),Ross(1999),andPerrold(1999).

Video(Optional):TrillionDollarBet,(aPBSDocumentary). Ihavejustonecopyofthevideotape. It istobedistributedbyJoonChae([email protected])onafirstcomefirstservebasis. Ifthere isexcessdemand, somealternativemeansofdistributionwillbeworkedout. PleasecontactJoondirectly.

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15433 20a Active Management