百題frm二級投資組合

RiskManagementandInvestmentManagement

KeyPoint:FactorTheory

FactorsandCAPM

Factorsdefinition

Factorsaretoassetswhatnutrientsaretofood.

Factorrisksaredrivingforcebehindassets’riskpremiums.

Factorsmatter,notassets.

Assetsarebundlesoffactors.

Differentinvestorsneeddifferentriskfactors.

Factorrisksarebad.

Factortheoryspecifiesdifferenttypesofunderlyingfactorrisk.

CAPManditsassumptions

Assumptions:

Notransactioncosts.

Assetsareinfinitelydivisible.

Theabsenceofpersonalincometax.

Anindividualcannotaffectthepriceofastockbyhistrading.

Investors’decisionmakingsolelydependontermsofreturnsandstandarddeviationsofthereturns.

Unlimitedshortsalesareallowed.

Unlimitedlendingandborrowingattherisklessrate.

Allinvestorshaveidenticalexpectations.

Allassetsaremarketable.

CAPMriskpremiumsdependonlyontheassets’beta,whichmeansonlyonefactor–marketportfolio.

ShortcomingsofCAPMcomefromitsassumptions.

BasicintuitionsoftheCAPMstillholdstrue:riskpremiumsare

compensationforinvestors’lossesduringbadtimes.

EfficientMarketTheoryandhowmarketscanbeinefficient.Lossesduringbadtimesarecompensatedforbyhighreturns.

重要知識點

基礎題

Q-1. Whichofthefollowingconceptsmostlikelytobeafactor?

USTreasuryBill.

CorporateBonds.

PrivateEquity.

HedgeFund.

Q-2.AndrewAngdevelopsananalogy,writing"factorsaretoassetswhatnutrientsaretofood."HistheoryoffactorriskpremiumsincludeseachofthefollowingthreeideasEXCEPTwhichisnotinthetheory?

Assetsarebundlesoffactors(justasmostfoodsarecombinationsofnutrients)

Factorsdomatterbutassetclassesdonot(justashealthyeatingisaboutthenutrientsnotthelabels)

Differentinvestorspreferand/orneeddifferentfactors(justasdifferentpeoplehavedifferentnutritionalneeds)

Becausefactorsrepresentdifferentgoodtimes,mostinvestorsshouldseekexposuretomostinvestablefactors(justasmostpeopleshouldseekabalanceddietofmostnutrients)

Q-3.Inregardtothecapitalassetpricingmodel(CAPM),whichofthefollowingassumptions(orimplications)oftheCAPMisagenuinesuccesssuchthatitisbothtrueinpracticeandusefultous?

Informationiscostlessandavailabletoallinvestors:technologyhasreducedinformationfrictiontoroughlyzero

Riskisfactorexposure:Theriskofanindividualassetismeasuredintermsofthefactorexposureofthatasset

Investorshavemean-varianceutility:assetownerscareonlyaboutmeans(whichtheylike)andvariances(whichtheydislike)

Investorshavehomogeneousexpectations:investorshaveidenticalexpectationswithrespecttothenecessaryinputsintotheportfoliodecision

Q-4.Whichofthefollowingstatementsisalimitationofthecapitalassetpricingmodel(CAPM)?

Investorshaveasingleperiodinvestmenthorizon.

Themarketisnottransparent

Investorshaveheterogeneousexpectations.

Peopleneedtopayaliquiditypremiumtodotransaction.

Q-5. Assetsthathavebigprofitsduringperiodsoflowmarketreturnshave:

Lowbetasandlowriskpremiums.

Lowbetasandhighriskpremiums.

Highbetasandlowriskpremiums.

Highbetasandhighriskpremiums.

Q-6. Whichbehaviordoesassetpayoffsand“badtimes”eventswouldmostlikelyperform?

Theexpectedpayoffofanassetinbadtimesisunrelatedtotheasset’sexpectedreturn,becausearbitrageurseliminateanyexpectedreturnpotential.

Theexpectedpayoffofanassetinbadtimesisunrelatedtotheasset’sexpectedreturn,becauseitdependsoninvestorpreferences.

Thehighertheexpectedpayoffofanassetinbadtimes,thehighertheasset’s

expectedreturn.

Thehighertheexpectedpayoffofanassetinbadtimes,thelowertheasset’sexpectedreturn

KeyPoint:Factors

Factors

FactorsInvesting

ValueInvestingandValuePremium

Avalue-growthstrategyislongvaluegrowthstocksandshortgrowthstocks.

Avaluestockhasahighbook-to-marketratio,agrowthstockhasalowbook-to-marketratio.

Macroeconomicriskfactors

Economicgrowth,inflation,andvolatilityarethethreemostimportantmacrofactorsthataffectassetprices.

Ratherthanlevelofafactor,itistheunanticipatedchangetoariskfactorthataffectsassetprices.

MitigatingvolatilityriskandChallenges

Twobasicapproachestomitigatevolatilityrisk:

Investinless-volatileassetslikebonds.

Buyvolatilityprotectioninthederivativesmarket.

Dynamicriskfactor

TheFama-Frenchmodelexplainsassetreturnsonthreedynamicfactors:

TraditionalCAPMmarketriskfactor.

Afactorthatcapturessizeeffect(SMBorsmallcapminusbigcap)

A factor that captures value/growth effect (HML or highbook-to-marketvalueminuslowbook-to-marketvalue.

Valueandmomentuminvestmentstrategies

重要知識點

Amomentumstrategyislong“winners”andshort“l(fā)osers”.

Valuestrategyisanegativefeedbackstrategy,momentumisapositivefeedbackstrategy.

Momentumstrategiesaresubjecttocrashes.

Differentstrategybasedondifferentsituationsandneeds.

基礎題

Q-7. Ahighbook-to-marketvalueratioisindicativeofa:

Small-capstock.

Large-capstock.

Valuestock.

Growthstock

Q-8. WhichofthefollowingstatementsisTRUEaboutthemomentumfactor?

Momentumisanegativefeedbackstrategywhichisinherentlystabilizing

ThemomentumfactorisobservedinequitiesbutisNOTobservedinbonds,commoditiesandrealestate

Momentuminvestingbydefinitionisananti-valuestrategy;correlationsbetweenHMLandWMLarestronglynegative

Thecumulatedprofitsonmomentumstrategieshavebeenanorderofmagnitudelargerthancumulatedprofitsoneithersizeorvalue

Q-9. WhichofthefollowingisafactorintheFama-Frenchthree-factormodel?

InvestmentGrowth.

Thesmallcapitalizationminusbigcapitalizationriskfactor.

Thewinnersminuslosersriskfactor.

Inflation.

Q-10. Whichofthefollowinginvestmentstrategiesdestabilizesassetpricesmost?

Avaluestrategy.

Asizeinvestmentstrategy.

Amomentuminvestmentstrategy.

Value,momentum,andsizestrategiesallstabilizeassetprices.

KeyPoint:AlphaandtheLow-RiskAnomaly

.AlphaandtheLow-RiskAnomaly

重要知識點

Alpha,trackingerror,informationratio,Sharperatio.

Alphaistheaverageperformanceofaninvestorinexcessoftheirbenchmark.

Thestandarddeviationofexcessreturnisknownastrackingerror.Informationratioistheratioofalphatoitstrackingerror.

IR=

Ifaninvestorisusingriskfreerateasbenchmark,Sharperatiois:

E(RP)?Rf

SR=

σ

IdealBenchmarkshouldbe:

Welldefined.Tradable.

ReplicableAdjustedforrisk.

Grinold’sfundamentallawofactivemanagementsuggestsatradeoffbetweenthenumberofinvestmentbetsplaced(breadth)andtherequireddegreeofforecastingaccuracy(informationcoefficient)

IR≈IC×√BR

FactorRegression

TraditionalCAPM,APT,Fama-French.

ApplicationofFactorRegression:Styleanalysis

AlphasfornonlinearstrategiesRiskAnomaly

Riskanomaly–thestockswithlowbetasandlowvolatilitieshavehighreturns.

Explanations:

DataminingLeverageconstraintsAgencyProblemsPreferences

Acomprehensiveexplanationforriskanomalyiselusive.

基礎題

Q-11. Whichofthefollowingstatementsisincorrectconcerningthelow-riskanomaly?

Thelow-riskanomalyconflictswiththeCAPM.

Thefirmswithhigherbetaperformindifferentlywiththelowerbetafirms.

Thelow-riskanomalypointtoanegativerelationshipbetweenriskandreward.

Thelow-riskanomalysuggeststhatlow-betastockswilloutperformhigh-betastocks.

Q-12. Whichofthefollowingstatementsisnottrueregardingbenchmark?

Abenchmarkshouldbewell-defined.

Abenchmarkshouldbereplicable.

Abenchmarkshouldbeequallyappliedtoallriskyassetsirrespectiveoftheirriskexposure.

Abenchmarkshouldbetradeable.

Q-13. FollowingGrinold’sfundamentallawofactivemanagement,oneshouldfind:

sectorallocationisthemostimportantfactorinactivemanagement.

tomaximizetheinformationratio,activeinvestorsneedtoeitherhavehigh-qualitypredictionsorplacealargenumberofinvestmentbetsinagivenyear.

asmallnumberofinvestmentbetsdecreasesthechancesofmakingamistakeand,therefore,increasestheexpectedinvestmentperformance.

investorsshouldfocusonincreasingonlytheirpredictiveabilityrelativetostockpricemovements。

Q-14. Whywouldaninvestorincludemultiplefactorsinaregressionstudy?

ToattempttoimprovetheadjustedR2measure.

Tosearchforabenchmarkthatismorerepresentativeofaportfolio’sinvestment

style.

Toincreasethetestsofstatisticalsignificance.

Ionly.

BothIandIII.

BothIandII.

I,II,andIII.

Q-15. Regardingoftheriskanomaly,whichofthefollowingcharacteristicsisapossiblereason?

Investorpreferences.

Thepresenceofhighlyleveragedretailinvestors.

Lackofshortsellingconstraintsforinstitutionalinvestments.

Lackoftrackingerrorconstraintsforinstitutionalinvestments.

KeyPoint:PortfolioConstruction

PortfolioConstruction

PortfolioConstructionTechniques

Screens

Stratification

LinearProgramming

QuadraticProgramming

重要知識點

基礎題

Q-16.Whichstatementaboutriskcontrolinportfolioconstructioniscorrect?

Quadraticprogrammingallowsforriskcontrolthroughparameterestimationbutgenerallyrequiresmanymoreinputsestimatedfrommarketdatathanothermethodsrequire.

Thescreeningtechniqueprovidessuperiorriskcontrolbyconcentratingstocksinselectedsectorsbasedonexpectedalpha.

Whenusingthestratificationtechnique,riskcontrolisimplementedbyoverweightingthecategorieswithlowerrisksandunderweightingthecategorieswithhigherrisk.

Whenusingthelinearprogrammingtechnique,riskiscontrolledbyselectingtheportfoliowiththelowestlevelofactiverisk.

KeyPoint:PortfolioRiskMeasures

PortfolioRiskMeasures

PortfolioVaR

VaRforuncorrelatedpositions(ρ=0):

UndiversifiedVaR(ρ=1)

MarginalVaR,IncrementalVaRandComponentVaR

MVaR

Cov(RA,RP)

重要知識點

IncrementalVaRA≈MVaRA×WA(anyamount)

ComponentVaRA=MVaRA×VA

GlobalMinimumPortfolio:MVaRi=MVaRj

OptimalPortfolio:

Positionireturn?riskfreerate Positionjreturn?riskfreerate

MVaR MVaR

LiquidityDuration:Itisanapproximationofthenumberofdaysnecessaryto

disposeofaportfolio’sholdingswithoutasignificantmarketimpact.

numberofsharesofasecurity

LD=desiredmaxdailyvolume(%)×dailyvolume

基礎題

Q-17. AwealthmanagementfirmhasaportfolioconsistingofUSD48millioninvestedinUSequitiesandUSD35millioninvestedinemergingmarketsequities.The1-day95%VaRforeachindividualpositionisUSD1.2million.ThecorrelationbetweenthereturnsoftheU.S.equitiesandemergingmarketsequitiesis0.36.Whilerebalancingtheportfolio,themanagerinchargedecidestosellUSD8millionoftheUSequitiestobuyUSD8millionoftheemergingmarketsequities.Atthesametime,theCROofthefirmadvisestheportfoliomanagertochangetheriskmeasurefrom1-day95%VaRto10-day99%VaR.Assumingthatreturnsarenormallydistributedandthattherebalancingdoesnotaffectthevolatilityoftheindividualequitypositions,byhowmuchwilltheportfolioVaRincreaseduetothecombinedeffectofportfoliorebalancingandchangeinriskmeasure?

USD4.529million

USD6.258million

USD7.144million

USD7.223million

Q-18. Thebank’stradingbookconsistsofthefollowingtwoassets:

Asset

AnnualReturn

VolatilityofAnnualReturn

Value

A

10%

25%

100

B

20%

20%

50

Correlation(A,B)=0.2

HowwouldthedailyVaRat99%levelchangeifthebanksells50worthofassetAandbuys50worthofassetB?

Assumethereare250tradingdaysinayear.(μ1?day=0）

0.2286

0.4578

0.7705

0.7798

Q-19.Aportfoliomanagerisevaluatingtheriskprofileforaportfolioofstocks.Currently,theportfolioisvaluedatCAD20millionandcontainsCAD5millioninstockXYZ.ThestandarddeviationofreturnsofstockXYZis15%annuallyandthatoftheoverallportfoliois12%annually.ThecorrelationofreturnsbetweenstockXYZandtheportfoliois0.3.Assumingtheportfoliomanagerusesa1-year99%VaRandthatreturnsarenormallydistributed,whatistheestimatedcomponentVaRofstockXYZ?

CAD162,972

CAD234,906

CAD523,350

CAD632,152

Fund

ExpectedReturn

Volatility

Alpha

5%

20%

Omega

7%

25%

Q-20.ConsideraUSD1millionportfoliowithanequalinvestmentintwofunds,AlphaandOmega,withthefollowingannualreturndistributions:

Assumingthereturnsfollowthenormaldistributionandthatthereare252tradingdaysperyear,whatisthemaximumpossibledaily95%Value-at-Risk(VaR)estimatefortheportfolio?(μ1?day=0)

USD16,587

USD23,316

USD23,459

USD32,973

Q-21. Aportfolioconsistsoftwopositions.TheVaRofthetwopositionsare$10millionand

$20million.Ifthereturnsofthetwopositionsarenotcorrelated.TheVaRoftheportfoliowouldbeclosestto:

$5.48million

$15.00million

$22.36million

$25.00million

Q-22. Aportfolioiscomposedoftwosecuritiesandhasthefollowingcharacteristics:InvestmentinX: USD1.8million

InvestmentinY: USD3.2million

VolatilityofX: 8%

VolatilityofY: 4%

CorrelationbetweenXandY: 15%

TheportfoliodiversifiedVaRatthe95%confidencelevelisclosestto:

$14,074

$206,500

$404,740

$340,725

Q-23.ThemanageroftheBetaBalancefund,abalancedglobalequityandfixed-incomeportfolio,believesthatglobalizationiscausingthecorrelationsofequityandfixed-incomereturnsacrossdifferentmarketstoriseovertime.HedecidestoadjustthecorrelationsinhisVaRanalysisforthecomingyeartoreflectthehighercorrelationsheexpects.Ifhisexpectationturnsouttobeincorrect,whatisthemostlikelyresult?

TherewillbenoimpactontheportfoliobecauseVaRisonlyaprediction,andportfolioreturndependsonwhatactuallyhappens.

Theportfolioreturnwillbelowerthanitshouldhavebeen,giventheexpectedrisklevel,becauseassetallocationwillnothavebeenoptimal.

Theriskoftheportfoliowillhavebeenunderstatedbecauseoftheincorrectestimateofcorrelationamongglobalmarkets.

Theportfolioreturnwillbehigherthanitshouldhavebeen,giventheexpectedrisklevel,becauseofthehighercorrelationamongassetclasses

Thenexttwoquestionsarebasedonthefollowinginformation.

Asset

Position

IndividualVaR

MarginalVaR

VaRContribution

1

USD100

USD23.3

0.176

USD17.6

2

USD100

USD46.6

0.440

USD44.0

Portfolio

USD200

USD61.6

USD61.6

Ariskmanagerassumesthatthejointdistributionofreturnsismultivariatenormalandcalculatesthefollowingriskmeasuresfora2-assetportfolio:

Q-24. Ifasset1isdroppedfromtheportfolio,whatwillbethereductioninportfolioVaR?

USD15.0

USD38.3

USD44.0

USD46.6

Q-25.Letβi=ρσi/σp,whereρdenotesthecorrelationbetweenthereturnofassetiandthereturnoftheportfolio,σiisthevolatilityofthereturnofassetiandσpisthevolatilityofthereturnoftheportfolio.Whatisβ2?

0.714

1.429

1.513

Cannotdeterminefrominformationprovided.

Q-26. Considerthefollowingtwoassetportfolios:

Asset

PositionValue

(InThousandsofUSD)

ReturnStandardDeviation(%)

Beta

A

400

3.60

0.5

B

600

8.63

1.2

Portfolio

1,000

5.92

1

CalculatethecomponentVaRofassetAandmarginalVaRofassetB,respectively,atthe95%confidencelevel.

USD21,773and0.1306

USD21,773and0.1169

USD19,477and0.1169

USD19,477and0.1306

Q-27.Ariskanalystisevaluatingtherisksofaportfolioofstocks.Currently,theportfolioisvaluedatEUR200millionandcontainsEUR15millioninstockA.ThestandarddeviationofreturnsofstockAis16%annuallyandthatoftheoverallportfoliois21%annually.ThecorrelationofreturnsbetweenstockAandtheportfoliois0.37.Assumingtheriskanalystusesa1-year99%VaRandthatreturnsarenormallydistributed,howmuchisthecomponentVaRofstockA?

EUR2.066million

EUR2.326million

EUR5.582million

EUR7.327million

Q-28.Aportfoliomanagercurrentlyholds8,000sharesofGFInc.inaparticularportfolio.ThedailyvolumeofGFsharestradedonthestockexchangeis2,000.Additionally,onany

givenday,theportfoliomanagerwishestotradenomorethan25%ofthedailytradingvolumeofGF.WhichofthefollowingamountsisclosesttotheliquiditydurationofGFinthisportfolio?

0.06

0.40

6.50

16.00

Asset

ExpectedReturn

BetatotheIndex

BetatothePortfolio

A

12%

1.2

0.90

B

10%

0.7

0.90

C

10%

0.6

0.85

D

8%

0.3

1.10

Q-29.Aportfoliomanagerwantstoinvestasmallamountofnewmoneythathasrecentlycomeintoafund.Thefundisbenchmarkedtoanindexand,ratherthanaddinganewholding,themanagerisconsideringincreasingtheholdingsofoneofthefourassetsdescribedinthefollowingtable:

TheportfoliomanagerwantstoselecttheassetthathasthelowestmarginalVaRaslongasitsTreynorratioisatleast0.1.Assumingtheriskfreerateis2%,whichassetshouldtheportfoliomanagerselect?

AssetA

AssetB

AssetC

AssetD

KeyPoint:PortfolioRiskManagement

trackingerror

Relevantreturnisthetrackingerror(TE),whichisexcessreturnofassetoverbenchmark.

policymixedVaR

thepolicymixriskistheriskofadollarlossowingtothepolicymixselectedbythefund.

SurplusatRisk

重要知識點

Surplus(S)isthedifferencebetweenthevalueoftheassets(A)andtheliabilities(L).Thechangeinthesurplus(ΔS)isequaltothechangeinassets(ΔA)minusthechangeinliabilities(ΔL).Ifwenormalizebytheassets,thereturnonthesurplusisgivenby:

Expectedsurplus=A×(1+RA)?L×(1+RL)

σSurplus=√A2σA2+L2σL2?2AσALσLρ

Surplusatrisk=zα×σSurplus

Fundingriskshouldbemeasuredasthepotentialshortfallinsurplusoverthehorizon,thisissometimescalledsurplusatrisk.

RiskBudgeting

BudgetRiskacrossAssetClasses:BudgetingriskacrossassetclassesmeansselectingassetswhosecombinedVaRsarelessthanthetotalallowed.ThebudgetingprocesswouldexaminethecontributioneachpositionmakestotheportfolioVaR.

BudgetRiskacrossActiveManagers:Forallocatingacrossactivemanagers,ifthetrackingerrorsofthemanagersareindependentofeachother,itcanbeshownthattheoptimalallocationisachievedwiththefollowingformula:

IRi×(Portfolio′strackingerrorvolatility)

weightofportfoliomanagedbymanageri=

IRP×(Manager′strackingerrorvolatility)

Foragivengroupofactivemanagers,theweightsmaynotsumtoone.Theremainderoftheweightcanbeallocatedtothebenchmark,whichhasnotrackingerror.

基礎題

Q-30.YouareevaluatingtheperformanceofValance,anequityfunddesignedtomimictheperformanceoftheRussell2000Index.Basedupontheinformationprovidedbelow,whatisthebestestimateofthetrackingerrorofValancerelativetotheRussell2000Index?

AnnualvolatilityofValance:

35%

AnnualvolatilityoftheRussell2000Index:

40%

CorrelationbetweenValanceandtheRussell2000Index:

0.90

A. 3.1%

17.5%

39.6%

53.2%

Q-31.OnJanuary1,2006,apensionfundhasassetsofEUR100billionandisfullyinvestedintheequitymarket.IthasEUR85billioninliabilities.During2006,theequitymarketdeclinedby15%andyieldsincreasesby1.2%.Ifthemodifieddurationoftheliabilitiesis12.5,whatisthepensionfund’ssurplusonDecember31,2006?

EUR15.00billion

EUR12.93billion

EUR12.75billion

EUR12.57billion

Q-32.Attheendof2007,Chad&Co.’spensionhadUSD350millionworthofassetsthatwerefullyinvestedinequitiesandUSD180millioninfixed-incomeliabilitieswithamodifieddurationof14.In2008,thewidespreadeffectsofthesubprimecrisishitthepensionfund,causingitsinvestmentinequitiestoloss50%oftheirmarketvalue.Inaddition,theimmediateresponsefromthegovernment–cuttinginterestrates–tosalvagethesituation,causedbondyieldstodeclineby2%.Whatwasthechangeinthepensionfund’ssurplusin2008?

USD-55.4million

USD-124.6million

USD-225.4million

USD-230.4million

PensionAssets

Assets

Liabilities

Amount(inUSDmillion)

100

90

ExpectedAnnualGrowth

6%

7%

ModifiedDuration

12

10

AnnualVolatilityofGrowth

10%

5%

Q-33.AnanalystreportsthefollowingfundinformationtotheadvisorofapensionfundthatcurrentlyinvestsingovernmentandcorporatebondsandcarriesasurplusofUSD10million.

Toevaluatethesufficiencyofthefund’ssurplus,theadvisorestimatesthepossiblesurplusvaluesattheendofoneyear.Theadvisorassumesthatannualreturnsonassetsandtheannualgrowthoftheliabilitiesarejointlynormallydistributedandtheircorrelationcoefficientis0.8.Theadvisorcanreportthat,withaconfidencelevelof95%,thesurplusvaluewillbegreaterthanorequalto:

USD-11.4million

USD-8.3million

USD-1.7million

USD0million

Q-34. Whichofthefollowingstatementsaboutriskmanagementinthepensionfundindustryiscorrect?

Apensionplan’stotalVaRisequaltothesumofitspolicy-mixVaRandactivemanagementVaR.

Pensionfundriskanalysisdoesnotconsiderperformancerelativetoabenchmark.

Inmostdefined-benefitpensionplans,ifliabilitiesexceedassets,theshortfalldoesnotcreateariskfortheplansponsor.

Fromtheplansponsor’sperspective,nominalpensionobligationsaresimilartoashortpositioninabond.

Q-35.Acompany'spensionfundisestablishedasadefinedbenefitplan,andthereforetheboardmustconsiderfundingrisk.Whichofthefollowingstatementsaboutthepensionfund’sfundingriskiscorrect?

Thelongerthehorizonforexpectedpayouts,thelowerthefundingrisk.

Decreasesininterestrateswillreducefundingrisk.

Thefundingriskhasbeeneffectivelytransferredtotheemployees.

Fundingriskrepresentsthetruelong-termrisktotheplansponsor.

Q-36.TheAT&Tpensionfundhasanallocationof$60milliondevotedtoU.S.equities.Nowthefundwantstoallocatethis$60milliontotwomanagers.Thisisequivalenttoariskbudgetof$3.948million.EachmanagerhasaTEVof6%.Thefundmanagershavedifferentcapabilities,theirIRsare0.6(manager1)and0.4(manager2).ToachieveanexactTEVof4%andinformationratioof0.725,theweightforeachshouldbe?

Manager1:55.17%,Manager2:36.78%

Manager1:55.17%,Manager2:44.83%

Manager1:36.78%,Manager2:55.17%

Insufficientinformationtocalculate

KeyPoint:PerformanceMeasurementandEvaluation

重要知識點

PortfolioPerformanceMeasurement

PerformanceAnalysis

E(RP)?Rf

SR=

TR=

IR=

E(RP)?E(RB)

σ2

PerformanceAttribution

Referstothesetoftechniquesusedbyperformanceanalyststoidentifythesourcesofvalueadditiontotheportfolio.Forexample,howmuchoftheperformance(excessreturnsabovebenchmark)isattributabletotheselectionoftherightassetclassesorhowmuchisattributabletoselection

ofrightsectororsecuritywithinanassetclass.

基礎題

Q-37.Amanagerwhoobtainsanaveragealphaof2.5%withatracking-errorof4%.Ifhewishtheresulttobesignificantto95%,howmanyyearsitisnecessarytoobservetheportfolioreturn?

8.8years

9.8years

10.8years

11.8years

Q-38. Basedon60monthlyreturns,youestimateanactivelymanagedportfolioalpha=1.24%andstandarderrorofalpha=0.1278%.Theportfoliomanagerwantstogetduecreditforproducingpositivealphaandbelievesthattheprobabilityofobservingsuchalargealphabychanceisonly1%.Calculatethet-statistic,andbasedontheestimatedt-valuewouldyouaccept(orreject)theclaimmadebytheportfoliomanager.

t=9.70,accept

t=2.66,accept

t=2.66,reject

t=9.70,reject

Q-39. Considerthefollowingperformancedateforasampleperiod:

Portfolio(P)

Market(M)

Averagereturn

15%

9%

Beta

1.6

1.0

Standard

deviation

32%

24%

Trackingerror

20%

0

Riskfreerate

—

3%

IfthePortfolio(P)isonesub-portfoliothatiscombinedwithseveralotherportfoliosintoalargeinvestmentfund,whichistheappropriaterisk-adjustedperformancemeasure(RAPM)andwhatisitsvalueforPortfolio(P)?

Sharpeof25.0%

Treynorof6.0%

Treynorof7.5%

Informationratioof12.0%

Q-40.Considerthefollowingperformancedateforasampleperiod:

Portfolio(P)

Market(M)

Averagereturn

15%

8%

Beta

0.9

1.0

Standarddeviation

27%

15%

Trackingerror

20%

0

Riskfreerate

—

2%

IfthePortfolio(P)representstheactiveportfoliotobeoptimallymixedwiththepassiveportfolio,whichistheappropriaterisk-adjustedperformancemeasure(RAPM)andwhatisitsvalueforPortfolio(P)?

Sharpeof0.4815

Jensen(alpha)of0.0760

Treynorof14.44%

Informationratioof0.380

Q-41. RickMaslerisconsideringtheperformanceofthemanagersoftwofunds,theHCMFundandtheGRTFund.Heusesalinearregressionofeachmanager’sexcessreturns(ri)againsttheexcessreturnsofapeergroup(rB):

ri=ai+bi×rB+ei

Theinformationhecompilesisasfollows:

Fund

Initial

Equity

Borrowed

Funds

TotalInvestment

Pool

ai

bi

HCM

USD100

USD0

USD100

0.0150

0.9500

(t=4.40)

(t=12.1)

GRT

USD500

USD3,000

USD3,500

0.0025

3.4500

(t=0.002)

(t=10.20)

Basedonthisinformation,whichofthefollowingstatementsiscorrect?

Theregressionsuggeststhatbothmanagershavegreaterskillthanthepeergroup.

Theaitermmeasurestheextenttowhichthemanageremploysgreaterorlesseramountsofleveragethandohis/herpeers.

IftheGRTFundweretolose10%inthenextperiod,thereturnonequity(ROE)wouldbe-60%.

ThesensitivityoftheGRTfundtothebenchmarkreturnismuchhigherthanthatoftheHCMfund.

Q-42.Aportfoliohasanaveragereturnoverthelastyearof13.2%.Itsbenchmarkhasprovidedanaveragereturnoverthesameperiodof12.3%.Theportfolio’sstandarddeviationis15.3%,itsbetais1.15,itstrackingerrorvolatilityis6.5%anditssemi-standarddeviationis9.4%.Lastly,therisk-freerateis4.5%.Calculatetheportfolio’sinformationRatio(IR).

0.569

0.076

0.138

0.096

Q-43. PortfolioQhasabetaof0.7andanexpectedreturnof12.8%.Themarketriskpremiumis5.25%.Therisk-freerateis4.85%.CalculateJensen’sAlphameasureforPortfolioQ.

7.67%

2.70%

5.73%

4.27%

Benchmark

Portfolio

MarketSector

Weight

AnnualReturn

Weight

AnnualReturn

Equity

20%

8%

40%

6%

FixedIncome

50%

4%

55%

5%

Cash

30%

2%

5%

3%

Q-44.Ariskmanagerrunsaperformanceattributionanalysisonanactivelymanagedportfoliousingaselectedbenchmark.Theweightsandperformanceofthedifferentmarketsectorswithintheportfolioandthebenchmarkaregivenbelow: