CFA三级知识点必备：Trading,Performance Evaluation,and Manager Selection-打印版

Trading,

Performance

Evaluation,and

Manager

Selection

&

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䇨ᐾφ-&<ꢀ

1

.Algorithmic

Trading

2-28

AlgorithmicTrading

¾

¾

Algorithmictradingisthecomputerizedexecutionoftheinvestment

decisionfollowingaspecifiedsetoftradinginstructions.

Tradingalgorithmsareprimarilyusedfortwopurposes—tradeexecution

andprofitgeneration.

zExecutionalgorithms.Anexecutionalgorithmistaskedwith

transactinganinvestmentdecisionmadebytheportfoliomanager.

9

Themanagerdetermineswhattobuyorsellonthebasisofhis

investmentstyleandinvestmentobjectiveandthenenterstheorder

intothealgorithm.

zProfit-seekingalgorithms.Aprofit-seekingalgorithmwilldetermine

whattobuyandsellandthenimplementthosedecisionsinthemarket

asefficientlyaspossible.

9

Profit-seekingalgorithmsareusedbyelectronicmarketmakers,

quantitativefunds,andhigh-frequencytraders.

3-28

2.

Implementation

Shortfall

4-28

ImplementationShortfall

¾

Theimplementationshortfallmeasureisthestandardformeasuringthe

totalcostofthetrade.IScomparesaportfolio’sactualreturnwithits

paperreturn(wheretransactionsarebasedondecisionprice).

zThepaperreturnshowsthehypotheticalreturnthatthefundwould

havereceivedifthemanagerwereabletotransactallsharesatthe

desireddecisionpriceandwithoutanyassociatedcostsorfees(with

nofriction).

zIS=Paperreturn–Actualreturn

5-28

ImplementationShortfall

¾

¾

Paperreturn=ࡼ࢔െࡼࢊࡿൌࡿࡼ࢔െࡿࡼࢊ

zSrepresentsthetotalordershares

9

9

S>0indicatesabuyorder

S<0indicatesasellorder

zܲௗrepresentsthepriceatthetimeoftheinvestmentdecision

zܲ௡representsthecurrentprice

Actualreturn=ሺσ•ሻሺࡼሻെσ•’െ࢙ࢋࢋࡲ

࢐

࢔

࢐

࢐

z•and’representthenumberofsharesexecutedandthetransaction

௝

௝

priceofthejthtrade

zσ•௝representsthetotalnumberofsharesoftheorderthatwere

executedinthemarket

z“Fees”includesallcostspaidbythefundtocompletetheorder

6-28

ImplementationShortfall

¾

¾

IS=σ•’െσݏܲ൅ࡿെσݏࡼ࢔െࡼࢊ൅࢙ࢋࢋࡲ

௝

࢐

௝

ࢊ

௝

Executioncost

Opportunitycost

ꢀ

ꢀ

ExpandedIS=

ሺσݏሻܲെሺσݏሻܲ൅σݏ݌െσݏܲ൅ࡿെσݏࡼ࢔െࡼࢊ൅࢙ࢋࢋࡲ

௝

૙

௝

ࢊ

௝

࢐

௝

૙

௝

Delaycost

Tradingcost

Opportunitycost

Executioncost

ܲ଴

representsthearrivalprice

7-28

Example

¾

¾

OnMonday,thesharesofImpulseRoboticscloseat£10.00pershare.

OnTuesday,beforetradingbegins,aportfoliomanagerdecidestobuy

ImpulseRobotics.Anordergoestothetradingdesktobuy1,000sharesof

ImpulseRoboticsat£9.98pershareorbetter,goodforoneday.The

benchmarkpriceisMonday’scloseat£10.00pershare.Nopartofthe

limitorderisfilledonTuesday,andtheorderexpires.Theclosingpriceon

Tuesdayrisesto£10.05.

zAdditional:Thebuy-sidetradingdeskreleasestheordertothemarket

30minutesafterreceivingit,whenthepriceis£10.03.

¾

¾

OnWednesday,thetradingdeskagaintriestobuyImpulseRoboticsby

enteringanewlimitordertobuy1,000sharesat£10.07pershareorbetter,

goodforoneday.Duringtheday,700sharesareboughtat£10.07per

share.Commissionsandfeesforthistradeare£14.SharesforImpulse

Roboticscloseat£10.08pershareonWednesday.

NofurtherattempttobuyImpulseRoboticsismade,andtheremaining

3

00sharesofthe1,000sharestheportfoliomanagerinitiallyspecifiedare

canceled.

8-28

Example

¾

¾

Solution:

WecanbreakthisISdownfurther,asfollows:

DelaycostTradingcostFixedcosts

700@10.07

#

Monday

Tuesday

Wednesday

£

10.00£10.03£10.05

£10.08

Paperportfolio

#1000@$10.00

Opportunitycost

zDelaycost,whichreflectstheadversepricemovementassociated

withnotsubmittingtheordertothemarketinatimelymannerand

isbasedontheamountofsharesexecutedintheorder:(700˜

£10.03)–(700˜£10.00)=£7,021–£7,000=£21.

9-28

Example

zTradingcost,whichreflectstheexecutionpricepaidonshares

executed:(700˜£10.07)–(700˜£10.03)=£7,049–£7,021=£28.

zOpportunitycost,whichisbasedontheamountofsharesleft

unexecutedandreflectsthecostassociatedwithnotbeingableto

executeallsharesatthedecisionprice:(1,000shares–700shares)

˜

(£10.08–£10.00)=£24.

zFixedfees,whichareequaltototalexplicitfeespaid:£14.

zTherefore,expandedimplementationshortfall(£)=£21+£28+

£24+£14=£87.

zTheexpandedISprovidesfurtherinsightintothecausesoftrade

costs.Thedelaycostis£21,whichaccountsfor24.1%(£21/£87)of

thetotalIScost,whereastheopportunitycostof£24accountsfor

27.6%(£24/£87)ofthetotalIScost.Quiteoften,delaycostand

opportunitycostaccountforthegreatestquantityofcostduring

implementation.Thesecostscanoftenbeeliminatedwithproper

transactioncostmanagementtechniques.

10-28

3

.Evaluating

Trade

Execution

11-28

EvaluatingTradeExecution

¾

¾

¾

Costintotaldollars($)

ݐݏ݋ܥꢀ̈́ൌܵ݅݀݁ൈሺܲെܲכሻൈ݄ܵܽݎ݁ݏ

Costindollarspershare($/share)

ݐݏ݋ܥꢀ̈́Ȁݏ݄ܽݎ݁ൌܵ݅݀݁ൈሺܲെܲכሻ

Costinbasispoints(bps)

ሺܲെܲכሻ

ݐݏ݋ܥꢀܾݏ݌ൌܵ݅݀݁ൈ

ൈͳͲǡͲͲͲꢀܾݏ݌

ܲ

כ

zSide:+1Buyorder;-1Sellorder

zܲ=Averageexecutionpriceoforder

zܲכ=Referenceprice

zShares=Sharesexecuted

12-28

EvaluatingTradeExecution

¾

¾

¾

VWAP

zPortfoliomanagersusetheVWAPbenchmarkasameasureofwhether

theyreceivedfairandreasonablepricesoverthetradingperiod.

zSincetheVWAPcomprisesallmarketactivityovertheday,allbuying

andsellingpressureofallothermarketparticipants,andmarketnoise,it

providesmanagerswithareasonableindicationofthefaircostfor

marketparticipantsovertheday.

ሺܲെܸܹܣܲሻ

VWAPcost(bps)=ܵ݅݀݁ൈ

ൈͳͲସꢀܾݏ݌

ܸܹܣܲ

13-28

EvaluatingTradeExecution

Market-AdjustedCost

zThemarket-adjustedcostisaperformancemetricusedbymanagers

andtraderstohelpseparatethetradingcostduetotradingtheorder

fromthegeneralmarketmovementinthesecurityprice.

zThemarket-adjustedcostiscalculatedbysubtractingthemarketcost

duetomarketmovementadjustedforordersidefromthetotalarrival

costofthetrade.

Market-adjustedcost(bps)=Arrivalcost(bps)–βhIndexcost(bps)

Where,

βrepresentsthestock’sbetatotheunderlyingindex

ሺܫ݊݀݁ݔꢀܸܹܣܲെܫ݊݀݁ݔꢀܽݎݎ݅ݒ݈ܽꢀݎ݌݅ܿ݁ሻ

Indexcost(bps)=ܵ݅݀݁ൈ

ൈͳͲସꢀܾݏ݌

ܫ݊݀݁ݔꢀܽݎݎ݅ݒ݈ܽꢀݎ݌݅ܿ݁

14-28

EvaluatingTradeExecution

AddedValue

zAnothermethodologyusedbyinvestorstoevaluatetrading

performanceistocomparethearrivalcostoftheorderwiththe

estimatedpre-tradecost.

zThismetrichelpsfundmanagersunderstandthevalueaddedbytheir

brokerand/orexecutionalgorithmsduringtheexecutionoftheorder.

zAddedvalue(bps)=Arrivalcost(bps)–Est.pre-tradecost(bps)

15-28

4

.Performance

Appraisal

16-28

PerformanceAppraisal

¾

TheSharperatiomeasurestheadditionalreturnforbearingriskabovethe

risk-freerate,statedperunitofreturnvolatility.Inperformanceappraisal,

thisadditionalreturnisoftenreferredtoasexcessreturn.

ꢂ୅െ”௙

ɐ୅

ꢁ୅

ൌ

zOneweaknessoftheSharperatioisthattheuseofstandarddeviation

asameasureofriskassumesinvestorsareindifferentbetweenupside

anddownsidevolatility.

¾

TheTreynorratiomeasurestheexcessreturnperunitofsystematicrisk.

ܴ஺

Ⱦ

െݎ௙

ꢃ୅ൌ

୅

zBecauseofitsrelianceonbeta(onlyconsiderssystematicrisk),the

Treynorratioshowshowafundhasperformedinrelationnottoitsown

volatilitybuttothevolatilityitwouldbringtoawell-diversifiedportfolio.

17-28

PerformanceAppraisal

¾

Theinformationratio(IR)isasimplemeasurethatallowstheevaluatorto

assessperformancerelativetothebenchmark,scaledbyrisk.

ꢅሺ”ሻെꢅሺ”ሻ

୔

୆

ꢄꢂൌ

ɐሺ”െ”ሻ

୔

୆

zTheimplicitassumptionisthatthechosenbenchmarkiswellmatched

totheriskoftheinvestmentstrategy.

9

Theinformationratio(IR)isusedtomeasureaportfolio’s

performanceagainstthebenchmarkbutaccountingfordifferences

inrisk.

18-28

PerformanceAppraisal

¾

Theappraisalratio(AR)isareturns-basedmeasure.Itistheannualized

alpha(Jensen’salpha)dividedbytheannualizedresidualrisk

(unsystematicrisk).Theappraisalratiomeasurestherewardofactive

managementrelativetotheriskofactivemanagement.

Ƚ

ꢆꢂൌ

ɐக

Where,

ߪequalsthestandarddeviationofߝ.

ఌ

௧

zThealphaandtheresidualriskarecomputedfromafactorregression.

zTheappraisalratioisalsoreferredtoastheTreynor–Blackratioorthe

Treynor–Blackappraisalratio.

19-28

PerformanceAppraisal

¾

TheSortinoratioisamodificationoftheSharperatiothatpenalizesonly

thosereturnsthatarelowerthanauser-specifiedreturn.

ଵȀଶ

ꢅݎ௣െݎ்

ߪ஽

ݎ௣െݎ்

ߪ஽

σ୒‹ሺݎെݎǡͲሻଶ

ꢁꢂୈ

ൌ

ꢁꢂୈ

ൌ

ɐୈ

ൌ

୲ୀଵ

௧

்

ܰ

whereݎistheminimumacceptablereturn(MAR),whichissometimes

்

referredtoasatargetrateofreturn.

zTheSortinoratiousesameasureofdownsideriskknownastarget

semi-standarddeviationortargetsemideviation.

zTheSortinoratiopenalizesmanagersonlyfor“harmful”volatilityand

isameasureofreturnperunitofdownsiderisk.

zSortinoratioofferstheabilitytoaccuratelyassessperformancewhen

returndistributionsarenotsymmetrical.

zEssentially,theSortinoratiopenalizesamanagerwhenportfolioreturn

islowerthantheMAR;itismostrelevantwhenoneoftheinvestor’s

primaryobjectivesiscapitalpreservation.

zCross-sectionalcomparisonsofSortinoratiosaredifficulttomake

applicabletoeveryinvestor,becausetheMARisinvestor-specific.

20-28

PerformanceAppraisal

¾

Captureratios

zTheupside/downsidecapture,orsimplythecaptureratio(CR),

CR(mB,t)=UC(m,B,t)/DC(m,B,t)

zTheupsidecaptureratioUC(m,B,t)=R(m,t)/R(B,t)ifR(B,t)≥0

9

UC>100%,outperformthemarket.

zThedownsidecaptureratio(DC),DC(m,B,t)=R(m,t)/R(B,t)ifR(B,t)<0

9

where

9

DC<100%,outperformthemarket.

R(m,t)=returnofmanagermfortimet

R(B,t)=returnofbenchmarkBfortimet

9

zItmeasurestheasymmetryofreturn(e.g.convexity,gamma).

9

9

Acaptureratiogreaterthan1indicatespositiveasymmetry,ora

convexreturnprofile;

Acaptureratiolessthan1indicatesnegativeasymmetry,ora

concavereturnprofile.

21-28

PerformanceAppraisal

R(m)

ConvexandConcaveReturnProfiles

Convex

Concave

R(B)

22-28

PerformanceAppraisal

¾

¾

Drawdownismeasuredasthecumulativepeak-to-troughlossduringa

continuousperiod.

Drawdowndurationisthetotaltimefromthestartofthedrawdownuntil

thecumulativedrawdownrecoverstozero,whichcanbesegmentedinto

thedrawdownphase(starttotrough)andtherecoveryphase(trough-to-

zerocumulativereturn).

ܯܽݔ݅݉ݑ݉ꢀܦܦሺ݉ǡݐሻꢀൌꢀ‹ሺꢀܸ

ሺ݉ǡݐሻꢀȂꢀܸሺ݉ǡݐכሻ

ǡͲሻ

ܸ

ሺ݉ǡݐכሻ

where

V(m,t)=portfoliovalueofmanagermattimet

V(m,t*)=peakportfoliovalueofmanagerm

t>t*

23-28

5

.TypeIand

TypeIIErrorsin

Manager

Selection

24-28

ManagerSelectionProcess

¾

Hypothesis

zꢇ଴:themanageraddsnovalue.

zꢇୟ:themanageraddspositivevalue.

TypeI:Hiringorretainingamanagerwhosubsequentlyunderperforms

expectations.(worrymore)

¾

¾

TypeII:Nothiringorfiringamanagerwhosubsequentlyoutperforms,or

performsinlinewith,expectations.

TypeIandTypeIIErrors

Re