FRM schweser part 2 book 4 2013 (1of 2)

• Transactions costs:Likecovariance, transaction costs are animportant input for portfolio construction, however,thesecostsalsocontain adegree of uncertainty.Transaction costs must beamo

KAPLAN

1 of 2

FRM PART II BOOK 4: RISK

MANAGEMENT; CURRENT ISSUES IN

FINANCIAL MARKETS

READING ASSIGNMENTSANDAIMSTATEMENTS

RISK MANAGEMENTANDINVESTMENT MANAGEMENT

53:PortfolioConstruction

54:Portfolio Risk: AnalyticalMethods

55:VaRand Risk Budgetingin InvestmentManagement

56:Risk Monitoringand Performance Measurement

57:Empirical EvidenceonSecurityReturns

5H:PortfolioPerformance Evaluation

59:OverviewofHedge Funds

60:HedgeFundInvestment Strategies

61: OverviewofPrivateEquity

62:HedgeFunds

63: Risk Management for Hedge Funds:Introduction andOverview

64:TrustandDelegation

65:MadolF:ARiotof RedFlags

CURRENT ISSUES IN FINANCIAL MARKETS

66: SovereignCreditworthiness andFinancialStability:

An InternationalPerspective

67:Of Runes and Sagas: PerspectivesonLiquidityStressTesting

UsinganIcelandExample

6K:Tailsof the Unexpected

69:TheDogand the Frisbee

70:Challengesof FinancialInnovation

71:Exchange-Traded Funds, MarketStructureanddie Flash Crash

SELF-TEST; RISK MANAGEMENT ANDINVESTMENT

MANAGEMENT;CURRENTISSUES IN FINANCIAL MARKETS

PASTFRM EXAM QUESTIONS

57

63 HI

103

112

125135

22H

235

253 259

271

275

279

FKM PART IJ ROOK 4: RISK MANAGEMENT AND INVESTMENT MANAGEMENT; CURRENT

ISSUES IN FINANCIAL MARKETS

£>201 3 Kaplan, foe., d.b.a Kaplan Schweser All rights reserved.

Printed in the Uni Led States of America.

GARP FRM Practice Ream Questions are reprinted with permission, Copyright 2012, Global Association of

Risk Professionals All rights reserved,

Thesematerials may HOL be copied w id torn written permission from die audio r The unauthorised duplication

of diese notes is a violation of global copyright laws Your assistance in pursuing potential violators of this law is

greatly appreciated.

Disclainier:Tbe SchweserNotes should lie used in conjunction with die original readings as set forth by

GARP®.The information am tail ted in these books is based on the original readings and is believed to be

accurate However, dieir accuracy cannot be guaranteed nor is aov warranty conveyed as to your ultimate exam success.

Kaplan.,Inc.

Page2

READING ASSIGNMENTS AND

Thefollowingmaterialis a reviewofthe RiskManagementandInvestmentManagement, and

CurrentIssuesinFinancial Marketsprinciplesdesignedtoaddress the AIMstatements setforth

by theGlobalAssociationofRiskProfessionals.

READING ASSIGNMENTS

RiskManagementand InvestmentManagement

Richard Grinoldand RonaldKahn,ActiveForfolioManagement:A Quantitative

Approach for ProducingSuperiorReturnsandControllingRisk,2nd Edition(NewYork:

McGraw-Hill, 2000).

53 “PortfolioConstruction,”Chapter14

PhilippeJorion, Value-at-Risk: TheNewBenchmarkforManaging Financial Risk,

3rdEdition (NewYork: McGrawHill, 2007)

(page12)

54 “Portfolio Risk:AnalyticalMethods,” Chapter7 (page24)

(page41)

55 “VaR and RiskBudgetingin InvestmentManagement,”Chapter17

RoherLLittermanand theQuandcative Resources Group,Modem Investment

Management:AnEquilibrium Approach(Hoboken,NJ: JohnWiley& Sons, 2003).

56 “RiskMonitoringand PerformanceMeasurement,” Chapter 17

ZviBodie, Alex Kane, andAlanJ.Marcus, Investments,9thEdition (New York

McGraw-Hill, 2010)

57 “EmpiricalEvidenceonSecurityReturns,” Chapter13

58 “Portfolio PerformanceEvaluation,”Chapter 24

DavidP Stowed, AnIntroduction toInvestmentBanks,HedgeFunds,andPrivateEquity

(Academic Press, 2010).

59 “Overview ofHedgeFunds,”Chapter11

60. “HedgeFund InvestmentStrategies,” Chapter12

ReadingAssignments and ATM Statements

61.""Overview ofPriva.ceEquity/ Chapter16

G Constantinides,M.HarrisandR.Stulz.Ed.,HandbookoftheEconomicsofFinance,

Volume2B (Oxford: Elsevier, 2013)

(page125)

63 AndrewW.Lo,"Risk Management forHedge Funds: IntroductionandOverview/

FinancialAnalystsJournal,Vol.57, No.6 (Nov to Dec, 2001),pp.16-33 (page146)

64 StephenBrown,WilliamGoetzmann, BingLiang, ChristopherSchwarz,“Trustand

65.GregN GregoriouandFranÿois-Serge Lhabitant, ARiotofRedFlags/

CurrentIssuesin FinancialMarkets

66.JaimeCaruana and Stefan Avdjiev, ''Sovereign Creditworthiness and FinancialStability:

An International Perspective.11 BanquedeFrance FinancialStabilityReview,No.16

(April2012), pp.71-85

67.Li LianOngandMartinCihdk,“OfRunesandSagas:PerspectivesonLiquidityStress

Testing UsinganIcelandExample/IMF WorkingPaperWP/10/156,

July2010

68.AndrewG.HaldaneandBenjamin Nelson, “Tails of theUnexpected.” Speech from

“TheCreditCrisis FiveYears On:Unpackingthe Crisis1’ Conferenceat theUniversityofEdinburgh(BankofEngland,June82012)

69.AndrewG.Haldane andVasileiosMadouros, “The Dog and the Frisbee/Speechfromthe FederalReserveBank ofKansasCity's36thEconomicPolicySymposium (BankofEngland,August31 2012)

GeraldRosenlield,JayLorsch,RakeshKhurana(eds.), ChallengestoBusinessinthe

Twenty-First Century,(Cambridge:AmericanAcademyofArts & Sciences, 2011).

70.“Challenges of FinancialInnovation/ Chapter2

Book4ReadingAssignments and AIM Statements

AIM STATEMENTS

53 PortfolioConstruction

Candidates,aftercompleting this reading,should be able to:

1 Identify theinputsto the portfolio constructionprocess, {page 12)

2. Describe the motivation andmethodsfor refiningalphas in die implementation

process, {page 12)

3. Describe neutralization andmethodsforrefiningalphas to beneutral, (page13)

4 Describe theimplicationsoftransaction costs onportfolioconstruction, (page 14)

5 Explain practicalissuesin portfolioconstructionsuchasdeterminationof risk

aversion,incorporation ofspecific riskaversion,and properalphacoverage

{page 14)

6. Describe portfoliorevisionsand rebalancingand the tradeoffs between alpha,risk,

transaction costsanti timehorizon, (page 16)

7 Describe theoptimalno-trade region forrebalancingwith transaction costs.

54 Portfolio Risk: Analytical Methods

Candidates,aftercompleting this reading,should be able to:

1 Defineand distinguish between individualVaR, incrementalVaR anddiversified

portfolioVaR (page24)

2. Explain the role correlation hason portfoliorisk, (page25)

3 ComputediversifiedVaR,individualVaR,and undiversifiedVaRofa portfolio

{page 24)

4 Define,compute,and explain theusesofmarginalVaR,incrementalVaR,and

componentVaR (page28)

5 Describe the challengesassociatedwithVaR measurement as portfoliosize increases.

(page29)

6. Demonstratehowone can use marginal VaR toguidedecisionsabout portfolio

VaR (page33)

7 Explain the differencebetween risk managementand portfoliomanagement, and

demonstratehowtousemarginal VaR inportfolio management,(page34)

55 VaRand Risk BudgetinginInvestmentManagement

Candidates,aftercompleting thisreading,should be able to:

1 Define riskbudgeting, (page41)

2 Describe theimpact ofhorizon,turnoverand leverageonthe riskmanagement

process in theinvestment management industry (page4l)

3 Describe theinvestment processof largeinvestorssuchaspension funds, (page42)

4 Describe the riskmanagementchallenges with hedgiefunds,{page43)

ReelingAssignments and AIM Statements

5 Defineanddescribe diefollowingtypesof risk:absolute risk, relativerisk,

policy-misrisk,active managementrisk, fundingrisk and sponsorrisk,(page 43)

6. Describe howVaRcan beused to check compliance, monitor riskbudgetsand

reverse engineer sources ofrisk,(page46)

7 ExplainhowVaRcanbe usedin dieinvestmentprocessand development of

investmentguidelines, (page48)

8. Describe the riskbudgetingprocessacross assetclassesandactive managers

(page49)

56 RiskMonitoringandPerformanceMeasurement

Candidates,aftercompletingthis reading, shouldbeable to:

1 Define, compareandcontrastVaR andtrackingerror as risk measures, (page 57}

2. Describe risk planning includingobjectives and participantsin itsdevelopment

(page 58)

3. Describe risk budgetingand the roleofquantitativemethods,(page59)

4. Describe risk monitoringand itsrolein an internal controlenvironment,(page59)

5 Identifysourcesof riskconsciousnesswithinanorganization, (page 59)

6. Describe dieobjectivesofarisk management unit in an investment management

firm, (page60)

7 Describe how riskmonitoringconfirms thatinvestment activities are consistent

withexpectations, (page61)

8 Explain dieimportanceof liquidity considerations fora portfolio, (page61)

9. Describe dieobjectivesofperformancemeasurement, (page62)

10 Describecommon features ofa performancemeasurement framework,(page62)

57 EmpiricalEvidenceonSecurity ReturnsCandidates,aftercompleting thisreading,should be ableto:

1. Interpretdieexpected return-betarelationship impliedin theCAPM,anddescribe

the methodologies forestimatingthesecuritycharacteristic line and thesecuritymarket linefromaproperdataset,(page68)

2 Describe thetwo-stageprocedure employed inearlytestsof dieCAPMandexplaintheconcernsrelated totheseearlytest results,(page69)

3- Describeandinterpret Rolls critique to theCAPM, aswellasexpansions of Rolfscritique, (page 69)

4 Describe themethodologiesforcorrectingmeasurement error in beta,andexplainhistorical test resultsof thesemethodologies, (page70}

5 Explainthetestof thesingle-indexmodels thataccountsforhumancapital, cyclical

variationsandnontraded business,(page71)

6 Summarizethetestsof multifactor CAPMandAPT. (page72)

7 Describeand interpret theFama-French three-factor model, andexplain historical

testresultsrelatedto thismodel, (page 73)

8. Summarizedifferent models used to measurethe impact ofliquidity1'on asset

pricingandasset returns, (page 74)

9 Explain die"equity premiumpuzzle"anddescribe thedifferent explanationsto diis

observation,(page75)

Bonk4ReadingAlignments and AIM Statements

53 PortfolioPerformance Evaluation

Candidates,aftercompleting this reading,should he able to:

1. Differentiate between thetime-weightedanddoliar-weightedreturnsofa portfolio

and theirappropriateuses,{pageSi)

2. Describe the different risk-adjusted performance measures, such asSharpe’s

measure,Treynor’smeasure,Jensen'smeasure (Jensen’salpha),and information

ratio,(page84)

3. Descrihe the uses for theModigliani-squaredand Treynor’s measure incomparing

two portfolios, and thegraphicalrepresentationof thesemeasures, (page 84)

4 Descrihe the statisticalsignificanceofaperformancemeasure usingstandarderror

and thet-statisric.(page91)

5 Explain thedifficulties in measuringtheperformances of hedgefunds,(page92)

6. Explainhowportfolioswithdynamicrisk levelscanaffect the useof theSharpe

ratio to measureperformance, (page92}

7 Descrihe techniquesto measurethe market timing abilityof fundmanagerswitha

regressionandwithacall optionmodel,(page 93)

8 Descrihe style analysis, (page94)

9 Descrihe theassetallocationdecision,(page94)

59 Overviewof Hedge Funds

Candidates,after completing this reading, shouldbe able to:

1 Descrihe thecommoncharacteristics attributed tohedgefunds, and how they

differentiatefromstandard mutual funds,(page103)

2. Explain theinvestmentstrategiesused by hedge funds to generate returns.

(page104)

3 Describe how hedge fundsgrewinpopularity and theirsubsequentslowdownin

2008 (page K)4)

4 Explain the feestructurefor hedgefunds,and theuseofhigh-watermarksand

hurdle rates,(page 105)

5 Assessacademicresearchon hedge fund performance, (page105)

6 Explain how hedge fundshelped progress die financial markets,(page 106)

7 Descrihe theliquidityofhedgefund investmentsand dieusageoflock-ups,gates

and side pockets, (page106)

8. Comparehedge funds to private equityand mutualfunds,(page 107)

9 Descrihe fundsoffundsand provideargumentsforandagainst using themas an

investment vehicle, (page107)

60 Hedge Fund Investment Strategies

Candidates,aftercompleting this reading,should he able to:

1 Descrihe equity-basedstrategiesof hedge fundsand their associatedexecution

mechanics, return sources and costs, (page ] 12)

2 Summarize howmacrostrategiesareused to generate returnsby hedgefunds*

(page113)

3. Explain thecommon arbitrage strategies ofhedgefunds,including

fixed-income-basedarbitrage,convertiblearbitrage and relative value arbitrage, (page113)

4 Descrihe the mechanicsofanarbitragestrategyusinganexample,(page115)

5 Descrihe event-driven strategies,includingactivism, mergerarbitrageand distressed

securities, (page 116)

Reading Assignment; and AIM Statements

6 Explain themechanic;involvedinevent-driven arbitrage, includingtheir upsidebenefitsand downsiderisks,(page I IS)

7 Describeandinterpret a numerical example of thefollowingstrategies:mergerarbitrage,pairstrading, distressedinvesting and global macro strategy, (page 119}

6 1 OverviewofPrivateEquityCandidates,aftercompleting thisreading, shouldbe able to:

I Describeanddifferentiate between majortypesof private equityinvestment

4 Describe the key characteristics ofaprivate equitytransaction,(page 127)

5 Identifythe keyparticipantsin aprivate equitytransacdonand the rolesthey play

(page127)

6. Identifyand describe methodsof fundingprivate equity transactions,(page12B)

7 Identifyissues related to theinteraction between private equityfirmsand die

managementoftarget companies,(page129)

8. Describetypicalways ofcapitalizinga private equityportfoliocompany, (page129)

9 Describe the potentialimpactofprivate equitytransactions,including leveraged

recapitalizations,on targetcompanies, (page130)

62. HedgeFunds

Candidates,after completing thisreading, shouldbe able to:

I Describe die characteristicsof hedge funds and die hedge fund industry,and

comparehedgefunds widi mutualfunds,(page135)

2 Explain die evolution of the hedge fund industry and describe landmarkevents

which precipitatedmajorchangesin thedevelopmentof theindustry, (page135)

3 Describe die different hedge fundstrategies, explain their returncharacteristics,and

describe the inherent risksof eachstrategy,(page136)

4 Describe die historical performancetrendof hedgefundscompared toequityindices,and evaluatestatistical evidence relatedto thestrategyofinvesting in a

portfolioof top performing hedge funds, (page139)

5 Descrihe the marketeventswhich resultedinaconvergence of risk factors for

differenthedgefund strategies, andexplainthe impact ofsucha convergenceon

portfoliodiversificationstrategies, (page140)

6. Describe the problem of risksharingasymmetryhetween principals andagents in

thehedgefundindustry, (page141}

7 Explain theimpactof institutionalinvestors ondiehedge fundindustry andassess reasonsfor the trend towardsgrowingconcentrationofassets undermanagement

(AUM}indie industry, (page 141}

63 RiskManagementlorHedgeFunds:IntroductionandOverview

Candidates,after completingthisreading, should be able to:

1. Compareandcontrast theinvestmentperspectives betweeninstitutional investors

antihedgefundmanagers, (page146)

2. Explain how proper riskmanagement can itself hea sourceofalphafor a hedge

fund, (page147)

Book4ReadingAssignments and AIM Statements

3 Explain die limitationsof the VaR measureincapturing thespectrumofhedge

fund risks,{page148)

4 Explain howsurvivorshipbias posesa challengefor hedgefundreturnanalysis

(page150)

5 Describe how dynamicinvestmentstrategies complicate the riskmeasurement

process for hedgefunds, (page 151)

6 Describe how the phase-locking phenomenonand nonlinearitiesin hedge fund

returns can heincorporated intoriskmodels, (page153)

7 Explain how autocorrelation ofreturns canbe usedas a measureof liquidity of the

asset, (page155)

64 Trustand Delegation

Candidates,aftercompletingthis reading, shouldhe able to:

1 Explain theroleof third partyduediligence firmsin the delegatedinvestment

decision-makingprocess, (page161)

2 Explain howpastregulatoryandlegalproblems with hedge fundreportingrelates to

expectedfutureoperationalevents, (page1 63)

3- Explain the roleof theduediligenceprocessinsuccessfully identifyinginadequate

orfailed internalprocess, (page164)

65 Madoff:ARiotof Red Flags

Candidates,aftercompleting thisreading, shouldbe able to:

1. DescribeBernardMadofFInvestmentSecurities (BMIS) anditsbusinesslines

(page169)

2. Explainwhatis asplit-strikeconversion strategy, (page 170)

3. Describe thereturnsreportedonMadoiF’sfeederfunds, (page171)

4. Explainhow the securitiesfraudat BMLS wascaught,(page171)

5 Describe the operational red flagsat BMISconflictingwith the investment

professions standard practices, (page 171)

6. Describeinvestmentredflags that demonstratedinconsistencies in BMIS'

investmentstyle,(page172)

66 SovereignCreditworthinessandFinancial Stability:An InternationalPerspective

Candidates,aftercompletingthis reading, shouldbe able to:

1 Explain three key initial conditions that helped spread of the economiccrisis

globallyamongsovereigns, (page178)

2 Describe threeways in which the financialsector risksare transmittedtosovereigns

(page179)

3 Describe five waysinwhich sovereign risksare transmitted to thefinancialsector.

(page ISO)

4 Summarize the activity of hanks and sovereigns in dieEuropean Union duringdie

2002-2007 period leadinguptodieeconomic crisis,(page 180)

5 Summarizetheactivityof banksandsovereigns in theEuropean Unionduringdie

economic crisis, (page181)

6 Describe how risksweretransmittedamongbanksandsovereigns inthe European

Unionduring theeconomic crisis,giving specific examples, (page1H1 )

7 Describe theeconomicconditionof the European financialsectorin 2012,and

explainsome possihlepolicyimplementation thatcan helpmitigatethespreadof

futurecrises,(page183)

Reading Assignments and ATM Statements

67 Of RunesandSagas: PerspectivesonLiquidityStress Testing Usingan Iceland

Example

Candidates,aftercompleting this reading, shouldhe able to:

I Summarize theeventsof the Icelandicdebtcrisis, (page IS!))

2. Descrihe the typicalsolvencyandliquidityscenarios present at Icelandic hanksin

the periodsleadinguptotheIcelandicdebtcrisis,(page190)

3 Explain how the weightingof shocksinshort-termassetsand short-term liabilities

areadjustedin stress testsdrataccountforaliquiditycrisis,(page 191)

4 Contrast thestress testmethodsof the FinancialSupervisoryAuthority(FME) and

Sedlabanki,andcompare their results todie resultantfundinggapatSedlabanki

from the actualshocks, (page ]94)

5 Descriheseveralwaystoimprove diemanagementofsolvencyriskatbanks

(page197) 6S TailsoftheUnexpected

Candidates,after completingthisreading, should be able to:

J Summarize thehistoryofnormalityin physical,social,andeconomic systems.

(page204}

2. Describe theevidenceoffattails, theimplicationsoffat tails,andexplanationsfor

fattails, (page206)

3. Identify examples of system-basedinteractionsthat canleadtofit tails,(page210)

4. Describenon-normalityin regards to asset pricingand riskmanagementtook

(page210)

69 TheDogand the FrisbeeCandidates,aftercompleting thisreading, shouldbe ableto:

]. Describe heuristics and explain why using heuristicrulescan beanoptimalresponse

to acomplexenvironment,(page215)

2. Descrihe theadvantagesanddisadvantagesof usingsimpleversuscomplex rulesin a

decision making process, (page216)

3. Descriheidealconditionsandsituations wheresimple decisionmakingstrategies

canoutperformcomplexrulesets,(page217)

4 Summarize theevolutionofregulatorystructuresandregulatoryresponses

tofinancialcrises,and explaincriticismsof the level ofcomplexityin current

regulatorystructures,(page218)

5 Compare the effectivenessofsimpleandcomplex capitalweightingstructures in

predicting hank failuregivensmaller and larger samplesizes, andexplain the results

of thestudyofFDIC-insuredbanks,(page219)

6. Comparethe results provided by simpleandcomplexstatistical modelsin

estimatingasset returnsand portfolioVaRovervaryingtimeperiodsand portfolio

Book4ReadingAssignments and AIM Statements

70 Challengesof Financial Innovation

Candidates,aftercompleting thisreading,should be able to:

1 Describecrucial functionsofafinancialsystem, (page228}

2. Describe howaccountingsystemsand protocolscanaffect how riskispresented

(page229}

3 Describe significantissues relatedto risk in thesavings market,{page230}

4. Describe the useofhedgingversus raising equitycapitalas itrelates to managing

risk, (page 230)

5 Describe theinteractionbetween speculativebehaviorandfinancialinnovation.

(page231)

71. Exchange-Traded Funds, Market Structureand the Flash Crash

1 Describe thechronologyof the Flash Crashandthe possible triggers for thisevent

discussed in recent research, (page235)

2. Describe the dataset, measurements, flags, andmultiple regression modelsused in

thestudy, (page238)

3 Calculate themaximumdrawdown,concentration ratio,and thevolume and quote

Herfindahlindex, (page238}

4 Summarize the resultsof thestudy including thedescriptivestatistics, the time

series variationinfragmentation,and thedeterminantsof fragmentation and

drawdown, (page 244)

The following is 1 neview of ihe Riitlt ManIÿIIKIILanil IfivcaUheni MafiagtcnefU principle* designed lu address foe AIM siatemefiLS set font iiy GART® This topic Is also covered in:

die position alphaswithin aportfolio.This topic also goesinto detail regarding transactions

costs and bow they influence allocation decisions with regard to portfolio monitoring and

rebalancing.Fortheexam,payattention to thediscussionsofrefiningalphaandthe implications

of transactions costs.Also,he familiar with the different techniques used co constructoptimalportfolios

THE PORTFOLIOCONSTRUCTION PROCESS

AIM53.1: Identify theinputstotheportfolio construction process.

The processof constructingan investmentportfolio has severalinputswhichinclude:

* Currentportfolio:Theassetsandweightsin thecurrentportfolio Reladvetothe other

inputs, thecurrent portfolioinputcan be measured with themostcertainty

* Alphas:Theexcess returnof eachasset Thisinputissubject to errorand bias andas a

resultis somedmesunreasonable

* Covariances Covariancemeasures how diereturnsof theassets in theportfolioare

related Estimatesofcovarianceoften display elements ofuncertainty

• Transactions costs:Likecovariance, transaction costs are animportant input for portfolio

construction, however,thesecostsalsocontain adegree of uncertainty.Transaction

costs must beamortizedover the investmenthorizoninorder todetermine the optimalportfolio adjustments

* Activeriskaversion:Thisinputmust heconsistentwith thespecified target active risk

level.Activeriskis another namefortrackingerror,whichis the standarddeviationof

active return(i.e.,excessreturn)

REFINING ALPHAS

AIM53.2: Describe themotivation and methodsfor refining alphasin the

implementation process

Themotivationforrefining alphais toaddressthevarious constraints that eachinvestor

or manager might have.For theinvestor, constraints might includenothavinganyshort

positionsand/or a restriction on dieamountof cashheldwithin theportfolio.Forthe

manager, theconstraintsmight include restrictions onallocations to certainstocks

and/or making theportfolioneutralacross sectors.The resultingportfoliowill be differentfrom acorresponding unconstrainedportfolioandas aresult willlikelyhe less efficient

©2013 Kaplan,Inc.

Page12

Topic 53

Cross Reference to CARP AssignedReading—Grinold & Kahn, Chapter14

Constrainedoptimization methods forportfolioconstruction areoften cumbersometo

implement

Amethod that involves refining die alphascanderivethe optimal portfolio, given the

consideration of portfolioconstrain ts, in alesscomplicatedmanner.This method refines

the optimalpositionalphasand then adjusts each position'sallocation Inotherwords,if

noshort sales areallowed, then the modifiedalphaswould bedrawncloser to zero,and

the optimization that would followwouldcallfora zero percentallocation tothose short

positions If,inaddition toshortsales,all longpositionallocationswererequired to more

closelyresemblethe benchmarkweights,dien all modifiedalphaswouldhe pulledcloser

to zerorelative to dieoriginalalphas, indicating that die constrained portfoliowouldmore

closelyresemble the benchmark portfolio(i.e., sincealphaIscloserto zero, thereturns

between die benchmarkandportfolioare nowcloser).Themain ideato this approach is

that refiningalphas and then optimizingposition allocadonscan replaceeven themost

sophisticated portfolioconstruction process

A managercanrefine thealphas by proceduresknown asscalingandtrimming By

consideringthestructureof alpha, we can understand how touse the technique of scaling

alpha= (volatility)x(information coefficient)x(score)

hi this equation,scorehasa mean ofzeroandstandarddeviation ofone.This meansthat

alphaswillhavea mean zeroanda range thatisdeterminedby the volatility(i.e., residual

risk) and die Information coefficient (i.e., correlation between actual and forecasted

outcomes).The managercan rescale thealphas tomake them have the proper scale for the

portfolioconstruction process Forexample, if dieoriginalalphas had astandarddeviation

of2%, the rescaledalphascouldhavealowerstandarddeviationof 0.5%

Trimmingextremevaluesis another methodofrefining alpha.The managershould

scrutinize alphas thatarelargeinabsolute valueterms.‘‘Large11mightbedefinedas

three timesdie scaleof thealphas.It may be diecase that suchalphasare the resultof

questionabledata, and theweightsfor those position allocations should heset to zero.

Thoseextremealphas thatappeargenuinemay bekept but lowered to bewithinsomelimit,

say, three times the scale

AIM 53.3:Describe neutralization and methodsforrefining alphas to be neutral

Neutralization is the process ofremovingbiasesand undesirable betsfromalpha.There

areseveral typesof neutralization:benchmark, cash, and risk-factor In allcases, the typeof

neutralizationand thestrategyfor the process should bespecifiedbefore the process begins

Benchmark neutralization involvesadjustingthebenchmark alphato zero.Thismeans the

optimal position that uses thebenchmarkwillhavea betaofone.Thisensures that the

alphasarebenchmark-neutral and avoidsanyissues with benchmark timing Forexample,

suppose thata modifiedalphahasa betaof1.2.By makingthisalpha benchmark-neutral,a

newmodified alpha will be computed where the heta isreducedto one.Making the alphas

cash-neutralinvolvesadjustingthealphasso that the cash position willnot he active Itis

possibletosimultaneously make alphas both cash andbenchmark-neutral

Cross Reference to GARP AssignedReading-Grinold & Kahn,Chapter l4

The risk-factor approachseparates returnsalongseveral dimensions (e.g.,industry) The

managercan identifyeachdimension as a source of either riskorvalue added.The manager

should neutralize thedimensionsorfactors that are a sourceof risk(forwhich themanager

does not have adequateknowledge)

TRANSACTIONS COSTS

AJM53.4: Describe theimplicationsoftransactioncosts on portfolioconstruction

Transactions costs arethecostsof moving fromone portfolioallocationtoanother.They

need tobeconsideredin addition to thealphaandactiverisk inputsin the optimizationprocess.When considering only alpha andactiverisk, anyprobleminsetting the scale of

thealphascan heoffset by adjusting active riskaversion.Theintroduction oftransactions

costs increases theimportanceof the precision of the choice ofscale.LSome researchers

propose that the accuracy ofestimatesof transactions costs is asimportantas tire accuracy

of alphaestimates Furthermore,theexistenceof transactions costs increases dieimportance

ofhaving more accurate estimatesof alpha

When consideringtransactions costs, it isimportant torealize thatdiesecostsgenerally

occurat a pointin timewhile the benefits (i.e., theadditionalreturn) are realizedover a

timeperiod Thismeansthat themanager needs tohavearuleconcerning howto amortize the transactions costs over agiven period.Beyond theimplicationsoftransactions costs, a

full analysis wouldalso consider thecausesoftransactionscosts,howto measurethem,and

how toavoid them.

Toillustrate the roleoftransactions costsand howto amortize them, wewillassume

forecastscan he made with certainty and the risk-freerate is zero.Thecostof buyingand

sellingstockis $0.05 ThecurrentpricesofstockAand Bare both $10 The forecastsare

for dre price ofstockAto he $11 in oneyear andthe price of stock B tobe $12 in two

years; therefore, the annualized alphasarethesame at10%.Also, neither stock willchange

invalueafter reachingthe forecastedvalue Now, assume ineachsuccessiveyear that the

manager discoversastock with the samepropertiesasstock A and everytwoyearsastock

exactly like stock B.Themanagerwouldtrade the stock-Atypestocks eachyear andincur

$0.10in transactions costs at theend of each year Thealpha is 10%,and the transactions

casts are1% for type-Astocksfora net returnof 9%.For the type-Bstocks, the annual

return is also 10%,but thetransactions costsper yearareonly0.5% hecause theyare

incurredeveryotheryear Thus,on anannualizedbasis,theafter-cost-return oftype-Bstocks isgreater than drat oftype-Astocks

PORTFOLIO CONSTRUCTION ISSUES

AIM53.5: Explain practical issues in portfolioconstructionsuchas determination

ofrisk aversion, incorporation ofspecificriskaversion,and proper alpha coverage.

Practical issuesin portfolioconstructionincludetire levelof riskaversion, theoptimalrisk,

andthealphacoverage

Cross Reference to GASP AssignedReading-Grinold & Kahn,Chapter l4

Measuringthe level ofrisk aversion is dependenton accurate measuresof theinputsin the

followingexpression:

information ratio

risk aversion =

2xacrive risk

Forexample, assumingdiat the information ratio is 0,8and die desired levelofactive risk

is 10%,dien die implied level of riskaversion is0.04.Beingabletoquantify riskaversion

allows the manager tounderstandaclient’s utilityin a mean -varianceframework Utility

can hemeasured as: excessreturn -{riskaversion x variance)

trackingerror.

Aversion tospecific factor riskis importantfortwo reasons.Itcanhelp themanager

address therisks associatedwith havingapositionwith the potential for hugelosses,and die

potential dispersion acrossportfolios when the manager managesmore dianoneportfolio

This approach canhelpamanager decide die appropriateaversion

riskfactors

andspecific

Properalphacoverage refers toaddressing thecasewherethemanagerhasforecasts of

stocks thatare not in the benchmark and themanagerdoesn’t haveforecasts forassets in

the bench mark When the manager has information onstocksnot in the henchmark,a

benchmarkweight ofzeroshould heassignedwithrespect tobenchmarking, butactive

weightscan heassignedto generate activealpha

When thereis not aforecast forassets indie henchmark,alphascan beinferredfrom the

alphas ofassetsfor which thereaueforecasts.Oneapproachis tofirstcompute thefollowing

two measures:

value-weighted fractionof stocks widi forecasts=sumofactiveholdingswithforecasts

(weightedaverageofthealphaswith forecasts)

averagealphafor the stocks with forecasts=

(value-weightedfractionof stocks with forecasts)

Thesecondstep is tosuhtract this measure from each alphafor which thereis aforecast

andsetalphato zeroforassetsthatdo nothaveforecasts This providesa setof

benchmark-neutralforecasts whereassetswithoutforecastshaveanalphaof zero.

Topic 53

Cross Reference to GARP AssignedReading—Grinold & Kahn,Chapterl4

PORTFOLIO REVISIONSAND REBALANCING

AIM53.6:Describeportfolio revisionsandrebalancingandthetradeoffs between

alpha, risk, transaction costsand timehorizon

AIM53.7:Describe theoptimalno-traderegionfor rebalancingwith transaction

costs.

Iftransactions costs are zero, a manager should revise a portfolioevery time new

informationarrives However, inapractical setting, themanagershouldmaketrading

decisions based on expectedactivereturn, activerisk,and transactions costs.The managermay wish co heconservativedue to dieuncertaintiesof thesemeasuresand the manager's

ability cointerpret them Underestimatingtransactions costs,for example, willlead to

trading toofrequendy.In addition, thefrequent tradingand short time-horizonswould

causealphaestimates toexhibita greatdealofuncertainty Therefore, the managermust

chooseanoptimal timehorizon where thecertainty of thealpha issufficient to justifya

tradegiven the transactions costs.

Therebalancing decision dependson thetradeoffhetween transactions costs and the value

addedfrom changing the position.Portfolio managersmust be awareof dieexistenceof

die no-trade region where die benefitsarelessthan die costs.The benefit of adjusting die

numberof sharesinaportfolio ofagivenassetIs given by the followingexpression:

marginalcontribution tovalueadded-(alpha ofasset} -[2x (risk aversion) x (activerisk)

x (marginal contribution to activeriskofasset)]

Aslongas thisvalueisbetween the negative costofsellinganddiecostofpurchase,the

manager wouldnot trade that particularasset.In otherwords, theno-traderangeis as

folloWSt

—(costofselling) <(marginalcontributiontovalueadded) <(costofpurchase)

Rearranging thisrelationshipwithrespect toalphagivesa no-trade range foralpha:

[2x (risk aversion) x (active risk) x (marginal contributionto activerisk)]- (costof

selling) <alpha ofasset < [2 x (riskaversion) x (activerisk) x(marginal contribution co

activerisk)] + (costof purchase)

Thesizeof dieno-traderegionisdetermined bytransactions costs, riskaversion,alphaand

the riskinessof theassets.

©2013 Kaplan,Inc.

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Topic 53

Cross Reference to GARP AssignedReading-Grin old & Kahn,Chapterl4

PORTFOLIO CONSTRUCTION TECHNIQUES

AJM 53-S: Describe tbefollowing portfolio construction techniques, including

strengths and weaknesses:

* Screens

Stratification

* Linear programming

* Quadraticprogramming

Thefollowingfour genericclassesof procedurescover mostof the applications of

institutionalportfolioconstruction techniques:screens,stratification,linearprogramming,

andquadratic programming.In eachcase thegoalis thesame: high alpha, lowactive risk,

and lowtransactions costs.The success ofa manager isdeterminedby the valuetheycan

addminusanytransaction costs:

(portfolio alpha)- (risk aversion) x (activerisk)- (transactions costs)

Screens

Screens areaccomplished by ranking theassetsbyalpha, choosingdietop performing

assets,andcomposing eitheranequally weightedorcapitalization-based weighted portfolio

Screens canalso rebalance portfolios; for example, themanagercan sorttheuniverseof

portfolios hy alpha;then, (1) divide the universeofassets into buy,hold, and selldecisions

basedonthe rankings, (2) purchaseanyassets onthe buylist not currently in theexisting

portfolio,and(3) sell any stocksin theportfoliothatare on the sell list

Screens areeasytoimplementand understand.There is a clearlinkbetween the cause

(being in the buy/hold/sellclass)and theeffect(beinga partof thepotcfolio).This

techniqueis alsorobust in thatextreme estimatesof alpha will not bias dieoutcome.It

enhances returnbyselectinghigh-alphaassetsandcontrols risk by havingasufficient

numberofassetsfordiversification Shortcomingsof screeningincludeignoring

information within therankings,diefact there will beerrors in therankings,and excluding

those categories ofassets that tend tohave low alphas (e.g., utilitystocks).Also,other chan

havingalargenumher ofassetsfordiversification, this technique does not properlyaddress

riskmanagementmotives.

Stratification

Stratification buildson screensby ensuring that each category or stratumofassets is

representedin theportfolio.Themanager canchoose tocategorize theassets byeconomic

sectorsand/or by capitalization If thereare fivecategoriesandthree capitalization levels

(i.e.,small,medium and large), then there will be 15 mutually exclusive categories The

manager would employa screen oneachcategory tochooseassets The managercould

thenweight the assetsfrom eachcategorybasedon their corresponding weights in the

benchmark

Topic 53

Cross Reference to GASP Assigned Reading-Grinnid & Kahn.Chapter l4

Stratification has thesamebenefitsasscreeningandonefewershortcomingin thatithas

solved theproblemof thepossibleexclusionofsomecategoriesofassets However, this

technique still suffers from possibleerrors in measuring alphas

Linear Programming

Linearprogramming usesa typeof stratification basedon characteristicssuch as industry,

size,volatility,beta,etc.without making thecategoriesmutually exclusive* The linearprogrammingmethodology willchoose dieassets thatproduceaportfoliowhichclosely

resembles the benchmark portfolio.This techniquecanalso includetransactions costs,

reduce turnover,andsetpositionlimits

Linearprogramming’sstrengthisthat the objectiveis to create a portfolio that closely

resembles thebenchmark.However, the resultcanbe verydifferent from the benchmark

withrespect to thenumberofassetsandsomerisk characteristics

lead to alarge deviation from dieoptimal portfolio, thisis not necessarily thecase since

small mistakes tend tocancelout in the overall portfolio

Thefollowinglossfunction providesa measurethat illustrates howa certainWeiof

mistakes mayonlylead to asmall loss, hut the lossesincreasedramaticallywhen die

mistakes exceeda certain level:

2 1 2

actual market volatilityloss

1-value added estimated marketvolatility

Ifactual marketvolatilityis 20%, an underestimateof1%willonly producealoss-to-value

ratioof 0.0117 Underestitnations of 2% and3%will produce loss-to-valueratios equal to

0.055and 0*1475,respectively.Thus, theincrease in loss increasesrapidlyin responseto

givenincrea*sesin error*

PORTFOLIO RETURN DISPERSION

AJM53.9:Describedispersion, explain itscausesanddescribemethodsfor

controllingforms ofdispersion.

Dispersionis a measureof how much eachindividualclient’s portfolio might hedifferent

from die compositereturnsreported bythemanager.One measure is thedifferencebetween

themaximum returnand minimum return forseparate account portfolios The basiccauses

ofdispersionaredie different histories and cash flowsof each of theclients.

©2013Kaplan,Inc.

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Topic 53

Cross Reference to CARP AssignedReading-Grinold & Kahn,Chapter14

Managerscan controlsomeforms of dispersion lint unfortunately notall forms.Onesource

of dispersion beyond themanager'scontrolisthe differingconstraints chateach client has

(e.g., notbeingableto invest inderivativesorother classesof assets}.Managersdo, however,

have the abilitytocontrol the dispersioncausedby different betassincethis dispersion

oftenresultsfrom thelackof proper supervision.Iftheassetsdiffer betweenportfolios, the

managercancontrol thissourceof dispersion bytrying to increase die proportionofassets

that are common to all theportfolios

Theexistenceoftransactions costsimpliesthat thereis someoptimallevelofdispersion*

Toillustrate die roleoftransactions costs incausingdispersion,wewillassume a manager

has onlyoneportfolio that isinvested60% stocksand 40% bonds The manager knows

theoptimal portfoliois62% stocksand38% bonds, but transactions costswouldreduce

returns more than thegainsfrom rebalancing the portfolio If themanageracquiresa

secondclient, hecan dien chooseaportfoliowith weights62%and 38% for thatsecond

client.Since oneclient hasa60/40 portfolio andthe other hasa62/38 portfolio,there

will be dispersion Clearly, higher transactions costs canleadto a higher probability of

dispersion

Ahigherlevel of risk aversionand lowertransactionscostsleadstolower trackingerror.

Withouttransactions costs, there will benotrackingerror ordispersion because all

portfolioswill beoptimal.Thefollowingexpressionshowshowdispersionis proportional to

Adding moreportfolios willtend to increasethe dispersion because thereis ahigherchance

ofan extremevaluewith moreobservations.Over time, asdieportfoliosaremanaged to

pursuethe samemoving target,convergencewilloccur However, thereis nocertaintyas to

tiieratethismightoccur

Cross Reference to GASP Assigned Reading-Giinold & Kahn.Chapter l4

AIM53.1

The inputsintodie portfolioconstruction processarethecurrent portfolio, thealphas,

covariance estimates, transactions costs,and active riskaversion.Withtheexceptionof the

current portfolio, all of thesearesubject to errorand.possiblehias

AIM53.2

Refiningalpha is onemethodforincludingboth investor constraints(e.g.,noshort

selling) and managerconstraints(e.g., proper diversification) Usingrefinedalphasand

thenperformingoptimizationcan achieve thesamegoatas acomplicatedconstrained

optimizationapproach

AIM53.3

Neutralization is the process of removing hiases and undesirablehetsfromalphas*

Benchmarkneutralization involves adjusting the benchmarkalphato zero. Gash

neutralizationeliminates the needforactivecashmanagement.Risk-factorneutralizationneutralizesreturndimensions thatareonlyassociated with riskand donotaddvalue.

AIM53.4

Transactions costs haveseveral implications.First, they may makeitoptimalnot toadjust

even in thefaceofnewinformation.Second, transactions costs increase the importance of

making alphaestimates morerobust

Including transactions costs can be complicatedbecause they occurat onepoint in time,

hut the benefitsof the portfolio adjustmentsaremeasuredoverthe investment horizon

toaddressing thecasewhere the manager makes forecasts of stocks thatare notin the

benchmark and themanager nothavingforecasts forassets indie benchmark*

AIM53.6

In the process of portfolio revisionsandrebalancing, therearetradeoffs hetween alpha,risk,

transaction costs,and time horizon.Themanager may wish toheconservativehasedon

theuncertaintiesof theinputs Also,the shorter thehorizon, themore uncertain thealpha,

whichmeans themanagershouldchooseanoptimal timehorizonwhere the certainty of the

alphaissufficient tojustifyatrade given the transactionscosts*

©2013Kaplan,Inc.

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Topic 53

Cross Reference to CARPAssigned Reading-Giinold & Kahn,Chapter 14AIM 53.7

Becauseof transactions costs, there willbe anoptimalno-trade region whennew

information arrivesconcerning the alpha ofan asset.Thatregionwould hedetermined

bydie levelof riskaversion, active risk,themarginalcontributiontoactive risk, and the

transactions costs.

AIM 53.8

Portfolioconstruction techniques indudescreens,stratification,linear programming, and

quadratic programming Stratification builds on screens,and quadratic programming builds

onlinear programming,

Screenssimplychoose assetsbasedon rawalpha.Stratificationfirstscreensand then chooses

stocks basedon thescreenandalsoattempts to includeassetsfrom allasset classes.

Linear programmingattempts to construct aportfolio that dosely resembles the benchmark

by usingsuchdiaracteristicsas industry,size,volatility,andbeta.Quadratic programming

buildson the linear programmingmethodologyby explicitlyconsideringalpha,risk,and

transactions costs.

AIM53.9

Fora manager with several portfolios, dispersionis die resultof portfolioreturns notbeing

identical The basiccausesofdispersion are thedifferenthistories and cash flows of each

of theclients,Amanagercan control thissourceof dispersion by tryingto increasethe

proportion ofassetsthatare common toallportfolios

A Noreliahle methodexists.

B By refining the alphasandthen optimizing,it ispossibletoincludeconstraints

of hoth theinvestor anddiemanager

C By refiningthe alphasanddien optimizing,itispossibletoincludeconstraints

of the investor, but notthemanager

D* By optimizing and thenrefiningthe alphas,itispossibletoinclude constraints

of both theinvestor anddiemanager

C Both I andTI

D NeitherInor II

Whichof thefollowingstatements mostcorrectlydescribesaconsideration chat

complicates theincorporationof transactions costs intothe portfolio constructionprocess?

A The transactions costsand the benefitsalwaysoccurintwodistincttime

periods

B The transactions costs are uncertainwhilethe benefitsarerelativelycertain.

C Thereare nocomplicatingfactors from the introduction of transactionscosts.

D The transactions costs musthe amortizedover thehorizonof the benefit from

thetrade

4

Amanagerhasforecasts of stocksA, B,andC,but notofstocksDandE.StocksA

B,and D arein the benchmark portfolio StocksCand Eare notin the benchmarkportfolio Which of die followingare correctconcerning specific weights the

managershouldassignin tracking the benchmarkportfolio?

Topic 53

Cross Reference to GASP AssignedReading—Grinold & Kalin, Chapter l4

CONCEPT CHECKER ANSWERS

1 „ C The currentportfoliois theonlyinput that isdirectlyobservable,

2 B The approach of first refiningalphasand then optimizing canreplaceeven the most

sophisticated portfolioconstruction process With thistechniqueboth the investor and

manager constraints arc considered,

3, C This is evident from the definition of the no-tradc region for thealphaof the asset,

[2 x (risk aversion) x (active risk) x(marginalcontribution to active risk)!-(cost ofselling)

<alphaof asset < [2 x {risk aversion) x [active risk) x (marginalcontribution to active risk)] +

(cost ofpurchase)

4, D Achallengeis tocorrectlyassign the transactions costs to projected future benefits The

transactions costs must he amortized over the horizon of the benefit from the trade The

benefits (c,g,, the increase inalpha) occurs over rime while the transactions costsgenerally

occur at aspecificrime when theportfolioisadjusted,

5, A The manager should assign atrackingportfolio weight equal to zero for stocks for which

there is a forecast hut that arc not in the benchmark, Aweightshould beassignedto Stock

D, and it should he a function of thealphasof the other assets,

The following i* i ttrtriew bf lie Risk Management and InveiUheJll Management principles JesigheJ lb ailiires.H the AIM vLit-etticfitis iel forth by GART® Tibi topic is also cuvefeil fo:

PORTFOLIO RISK: ANALYTICAL METHODS

Topic54

EXAM FOCUS

Due to diversification,the valueat risk (VaR) ofa portfolio willbeless than orequal to the

sum of the VaRs of the positions in die portfolio If all positions are perfectly correlated,then the portfolio VaRequals thesumof theindividual VaRs A managercan makeoptimaladjustments to the riskofa portfolio with such measures as marginalVaR, incrementalVaR,

andcomponentVaR.This topicis highlyquantitative Be able tofind dieoptimal portfolio

using the excess-return-to-marginal VaR ratios. For theexam, understand how correlations

impact the measure of portfolio VaR Also,it is important that you know how to compute

incremental VaR and componentVaR using the marginal VaR measure.We have included

severalexamples tohelp widi application of dieseconcepts.

Portfolio theorydependsaloton statistical assumptions In finance, researchersand analystsoftenassume returns arenormally distributed.Suchanassumption allows us toexpress

relationships in conciseexpressions suchasbeta.Actually, beta and other convenient

concepts canapply ifreturnsfollowanellipticaldistribution,whichis abroader classof

distributions thatincludes the normaldistribution In what follows, we willassume returns

followanellipticaldistribution unlessotherwise seated

AIM 54.1:Define anddistinguish between individual VaR,incremental VaRand

diversified portfolioVaR

AIM 54.3: ComputediversifiedVaR, individualVaR,and undiversifiedVaR ofa

portfolio.

Professor's Note: AIM54.1 isaddressedthroughoutthis topic

DIVERSIFIED PORTEQUOVAR

Diversified VaR issimplythe VaRof theportfoliowhere thecalculationtakesinto account

the diversificationeffects The basic formula is:

VaRp = Zcx(1ÿx P

where:

Zc = die3-scoreassociated with die levelof confidencec

Up -the standard deviationof die portfolioreturn

P =the nominalvalueinvestedinthe portfolio

Topic 54

Cross Reference to GARP AssignedReading—Jorion, Chapter 7

Examining theformulafor thevarianceof the portfolio returns isimportant becauseit

revealshow the correlationsof thereturnsof theassets in theportfolioaffectvolatility.The

varianceformulais:

ap2 -thevarianceof theportfolioreturns

w. - the portfolioweight investedin position i

a. - the standard deviationof thereturn in position i

pjj -thecorrelationbetween thereturnsofasset iand assetj

Thestandarddeviation,denoted tSpi is:

i=l Ul j<i

Up

-Clearly dievariance andstandard deviation arelower when the correlations are lower,

In ordertocalculatedelta-normalVaRwithmorethanoneriskfactor,weneeda covariance

matrix thatincorporatescorrelations between each riskfactorin die portfolio and volatilities

of each riskfactor.Ifwe knowthe volatilitiesandcorrelations,we canderive thestandard

deviationof the portfolioandthecorresponding VaRmeasure."Wewill discuss how to

calculate VaR usingmatrixmultiplicationlaterin diis topic,

Individual VaR is the VaRofan individual position in isolation. Ifthe proportion orweight

in theposition is tit, dien we can define theindividualVaRas:

VaRj= Zcx ajx|P;|= ZcxtT;x |wj|xP

where:

P = the portfoliovalue

R = thenominalamount invested inpositioni

Weuse the absolute valueof theweightbecause bothlongand short positions pose risk

AIM54.2: Explaintke role correlation hason portfoliorisk

Ina two-asset portfolio, the equation for the standard deviationis:

CFp = + w22ff22 +2w1w2p1ÿcr1ai

andthe VaR is:

VaRp =ZtPÿw1V13 +w2“cs 2ÿ +2 WiWÿPi,ÿ!ÿ

Cross Reference to GARP Assigned Reading—Jorion, Chapter?

WecansquareZcand P and put[hem under chesquare-rooLsign.This allowsus toexpress

VaRpas afunctionof the VaRs of dieIndividualpositions,whichweexpressasVaRjforeach posidon i. Fora two-asset portfolio we will haveVaR, andVaRj Ifthe correlationis

zero, pj2 =0, then thethird termunder theradicalis zeroand:

VaRfor uncorrelaced positions:VaRp= iJVaR2 +VaR33

The otherextreme is whenthecorrelation is one,p,2=1- If die correlation equalsone,dien

thereis nobenefitfromdiversification For the two-asset portfolio,wefind:

UndiversifiedVaR= VaRP = +VaRz5 +2VaR,VaR2 =VaR, + VaR2

Ingenera], undiversifiedVaR is diesumof all die VaRs of theindividual positionsin the

portfolio when noneof those positionsareshortpositions.

NoticehowevaluatingVaR using bodiacorrelationofzeroandacorrelationofonewill

placealower and upper boundon the total (orportfolio)VaR.Total VaRwill he less if the

positionsare uncorrelated andgreaterif the posidonsarecorrelated.Thefollowing examples

illustrate this point*

Example: ComputingportfolioVaR (part1)

An analystcomputes the VaRfor die twopositions in her portfolio.The VaRs:

VaR|= $2.4 millionandVaR3 = $1*6 million.ComputeVaRpifdiereturns of thetwo assets are uncorrelated

Answer:

Foruncorrelatedassets:

VaRp = yjv aR,2 +VaRz3 = +1.62 )($millions)2 = ,/8-32($milIions)2

VaRp =$2.8844million

Example:Computing portfolioVaR (part2)

An analystcomputes the VaR forthe twopositionsin her portfolio.TheVaRs:

VaRj = $2.4 millionandVaRz = $1,6million ComputeVaRpifdiereturns of thetwo assets are perfectly correlated

Answer:

Forperfectlycorrelatedassets:

VaRp =VaRj+VaR3 =$2.4million +$1.6 million =$4 million

©2013Kaplan,Inc.

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Cross Reference to GARP AssignedReading—Jorum,Chapter7

Undercertainassumptions, the portfolio standard deviationofreturnsfara portfoliowith

more than two assetshasa veryconciseformula.Theassumptionsare:

* Theportfolioisequally weighted,

• All theindividualpositionshave thesamestandard deviationof returns,

• The correlations between each pair ofreturns are thesame.

The formula isthen:

°p~

VN + f— NJP

where:

N=thenumberofpositions

tr =thestandarddeviation chatisequalfor allNpositions

p = the correlation between the returnsofeach pairofpositions

Prf)fe no r sNote:Thisformulagreatlysimplifiestheprocess ofhavingto

calculateportfoliostandard deviation with a covariance matrix ,

To demonstrate die benefitsofdiversification,we cansimplysetupa2 x 2table where

thereis asmall and largecorrelation (p) columnandasmall and largesamplesize {N) row.

Assumingthat thestandarddeviation of returns is20% for bothassets, we seehow the

portfoliovariance isaffected by thedifferentinputs,

Figure I:Portfolio StandardDeviation

Example: ComputingportfolioVaR (part 3)

A portfolio has five positionsof$2 million each.Thestandarddeviation of the returns is

30%for each position.The correlations between each pairof returns is 0.2.Calculate the

VaR usinga Z-valueof2.33

AIM54.4:Define, compute, andexplainthe usesof marginalVaR,incremental

VaR, andcomponent YhR

MarginalVaRappliesto a particularposition in aportfolio, and it is theperunitchange

in aportfolioVaRthatoccursfromanadditionalinvestment inthatposition Mathematically

speaking,it isthe partialderivativeof the portfolioVaR with respect to theposition:

t)VaRp -zcÿ.zccov(Rj,RP)Marginal VaR MVaR; =ÿ

(ÿmonetary investmentin i) (?W; Op

UsingCAPM methodology,weknowaregression of thereturnsofasingleasset i in a

portfolioonthereturnsof theentire portfolio givesabeta,denoted ff,whichis a concise

measure thatincludesthe covarianceof thepost cion’s returns with the total portfolio:

oov(Ri, Rp)

ft- 2

~PUsing theconceptof beta gives another expression for marginalVaR;

MarginalVaR - MVaR5 =

portfoliovalue

©2013 Kaplan,Tnc.

Page2H

Gross Reference to GARP AssignedReading—Jorion,Chapter7

Example: ComputingmarginalVaR

AssumePortfolioX hasaVaRof €400,000 Theportfolioismade up of fourassets: Asset

A,AssetB,AssetC,andAsset D.Theseassets ateequallyweightedwithin the portfolio

andare eachvaluedaL €1 ,000,000 AssetA hasa betaof1.2 Calculate the marginal VLR

IncrementalVaR Iscite changein VaRfrom die addition ofa newposi Jon in a portfolio,

Since itapplies to an enureposition,it isgenerallylargerthanmarginalVaRandmay

Include nonlinearrelationships,which marginalVaR generallyassumes away The problem

with measuring incrementalVaRis that, inordertoheaccurate, afull revaluationof the

portfolioafter theaddidonof die new positionwouldhe necessary.Theincremental VaR

isthedifferencebetween the newVaR from the revaluation minus theVaRbefore che

addition.Therevaluation requiresnotonlymeasuring the risk of the position itself,hut

it alsorequiresmeasuringthechangein the riskof theocherpositions thatarealreadyin

the portfolio.Foraportfolio withhundredsor thousandsof positions, thiswould he time

consuming Clearly,VaR measurement becomes moredifficultas portfoliosize increases

given theexpansionofthe covariance matrix.Usingashortcutapproach for computing

incrementalVaRwould be beneficial

Forsmalladditions to aportfolio,we canapproximate the incremental VaR with the

followingsteps:

Step1: Estimatethe riskfactors of dienewposidon and include diemIna vector[q]

Step2: Forthe portfolio,estimate thevectorofmarginal VaRsfor the risk factors[MVaR-]

Step3: Take the crossproduct

This probablyrequiresless workandisfastertoimplementbecause it islikely the managers

already haveestimatesof thevectorof MVaR values: in Step2.

Beforewetakealookathowto calculateincrementalVaR, let’sreview the calculationof

delta-normalVaR usingmatrix notation (i.e., usinga covariance matrix).

Cross Reference to GASP AssignedReading—Jorion, Chapter 7

Example: Computing VaR usingmatrix notation

AportfolioconsistsofassetsAandB.Theseassets arethe riskfactorsin the portfolio.The

volatilitiesare 6%and 14%,respectively.There are$4 million and$2 million investedin

diem,respectively Ifwe assume theyareuncorrelatedwitheachother, computedie VaR

ofthe portfolio usingaconfidenceparameter, Z,of 1.65

Professors Note:Matrixmultiplication consistsofmultiplyingeach rotaby each

column.Forexample:(4 x 0.062) + (2 x 0) = 0.0144; 0.0144 x 4 = 0.0576.Had the positions beenpositively correlated, somepositive value would replace

the zerosin thecovariance matrix.

Example:ComputingincrementalVaR

AportfolioconsistsofassetsAandB.The volatilitiesare6%and14%, respectively.Thereare$4 million and$2 million investedill themrespectively Ifwe assumethey are

uncorrelatedwith eachother,computethe incrementalVaR foran increaseof$1(>,000in

Asset A Assume aZ-score of1.65

Cross Reference to CARP AssignedReading—Jorum, Chapter 7

Themarginal VaRsof thetwo riskfactorsare:

ooy(RA,RP)_ 0,0144

=0.0644281.65x

Sincethe two assets are uncorrelated, the incrementalVaRofan ajdditional $10,000

investment in PositionA wouldsimply be$10,000 times 0.064428, or$644.28

COMPONENT VAR

Component VaRforpositioni, denotedCVaR, is theamountof riska particular fund

contributesto a portfoliooffunds.Tt will generally he lessthan theVaRof thefund hyitself

(be.,standaloneVaR) becauseofdiversification benefitsatthe portfolio level Enalarge

portfoliowith many positions, theapproximationissimplydiemarginal VaR multipliedby

the dollar weight in position i:

Example: ComputingcomponentVaR(Example 1)

AssumePortfolioXhasaVaRof€4(10,000 The portfoliois made upof fourassets: Asset

A, Asset B, Asset C,andAsset D.Theseassets areequallyweighted widiin theportfolio

andareeach valuedat €1 ,O0O,000.AssetAhasa betaof1.2.Calculate diecomponent

Topic 54

Cross Reference to CARP Assigned Reading—Jorion, Chapter 7

Example: ComputingcomponentVaR (Example2,Part1)

Recallour previousincrementalVaR exampleofaportfolioinvested £4 millioninA and

$2millioninB Using their respectivemarginal VaRs,0.064428and0.175388, compute

the componentVaRs

Answer:

CVaRA = (MVaRA) x (wAxP)=(0.064428) x ($4million)= $257,713

CVaRB = (MVaRB)*(wBxP) = (0.175388) x ($2million)= $350,777

Example:ComputingcomponentVaR(Example 2,Part 2)

Using the resultsfrom the previousexample,compute die percentof contribution toVaR

Normal distributionsare asubsetof the class of distributions calledellipticaldistributions

As aclass,ellipticaldistributionshavefewer assumptions than normal distributions

Risk managementoftenassumesellipticaldistributions,and the procedures to estimate

componentVaRs upto this point haveapplied to ellipticaldistributions

Ifthereturnsdonotfollow anellipticaldistribution,we can employotherproceduresto compute componentVaR.If the distribution ishomogeneousofdegreeone,for example,

then we can use Euler’s theorem to estimate the componentVaRs.Thereturnofaportfolio

of assets ishomogeneous ofdegreeone because, forsome constant, k,we can write:

Cross Reference to CARP AssignedReading ~Jorion, Chapter 7

Thefollowingsteps can help usfindcomponentVaRsfor a non-ellipticaldistribution using

historicalreturns:

Step1: Sort the historicalreturnsof theportfolio,

Step2: Find the returnof the portfolio,whichwewilldesignateRP(VaR}= that corresponds

to a return chatwouldbe associated with the chosenVaR,

Step3: Find thereturnsof dieindividual positionsthatoccurredwhenRP(VaR)occurred

Step4: Useeachof the positionreturnsassociated with RP(VaR)lor componentVaRfor

that posidon

To improve the esdmatesof thecomponent VaRs, ananalyst should probablyobtain returns

for each individual posidonlor returnsof the portfolioslightlyabove and belowRÿÿÿy,

Foreachsecofreturnsfor each position, theanalystwouldcompute anaverage to better

approximate thecomponentVaRof theposidon

MANAGING POUTPOLIOS USING VAR

AIM 54.6:Demonstratehowone can usemarginalVaR to guidedecisions about

portfolioVaR

AmanagercanloweraportfolioVaRby lowering allocationstothepositions withthe highest

marginalVaR If the manager keepsdie total investedcapitalconstant, this wouldmean

increasingallocations to posidonswith lower marginalVaR.Portfolio risk will heat aglobal

minimumwhere all die marginal VaRsareequal for alliandy:

MVaR- = MVaR

Wecan use our earlierexample to see how we can use marginal VaRstomake decisions

LOlower the riskof theentire portfolio In the earlier example,PositionA has the smaller

MVaR; therefore,wewillcompute themarginalVaRsandtotal VaR for a portfoliowhich

hasJ5million investedinA and$] millionin B,Theportfoliovariance is:

TheVaR of$546,247 isless dian die VaRof 5608,490, whichwas producedwhen Portfolio

A hadalower weight.Wecan seethat themarginal VaRsare now much closerin value:

cov(RA,Rp)l _[0.062 0 1[$5|_ [0.0180'

COV(RB,RP)]- o 0.142 j$l] _ [O.0196

Cross Reference to GARP Assigned Reading—Jorion, Chapter 7

The marginalVaRsof dietwo positionsare:

AIM 54.7: Explain the difference between riskmanagementand portfolio

management,anddemonstrate bowto usemarginal VaRin portfoliomanagement

Asthenameimplies, riskmanagementfocusesonrisk andways to reducerisk; however,

minimizing risk maynotproducetheopdmal portfolio.Portfolio management requiresassessing both riskmeasuresand return measures tochoose the optimal portfolio

Traditionalefficient frontier analysis tellsus that die minimum varianceportfoliois not

optimal.Weshouldnote chatthe efficient frontieris the plotof portfoliosthat have the loweststandard deviationfor each expectedreturn (orhighest returnfor eachstandard

deviation)when plottedon a planewith the verticalaxismeasuringreturnandthe

horizontalaxismeasuring thestandard deviation.The optimal portfolio isrepresented by

the pointwherearayfrom die risk-freerate Is just tangent to die efficient frontier Thatoptimal portfoliohas diehighestSharperatio:

(portfolioreturn - risk-free race)

Sharpe ratio=

(standard,deviationof portfolioreturn)

Wecan modify this formula by replacing diestandard deviationwidiVaRso that the focusthen becomes theexcess returnof the portfoliooverVaR:

(portfolioreturn-risk-freerate)

(VaRof portfolio)

Thisratio ismaximizedwhen theexcess return ineach position divided byitsrespective

marginalVaRequalsa constant.In otherwords, at theoptimum:

(Positioni return—risk-freerate)_ (Positionj return— risk-freerace)

(MVaR j )

for all positionsiandj

(MVaRj)

optimalportfolio. Thisdiffers from equatingjustthe MVaRs, as in the last

AIM, which obtains theportfoliowith the lowestportfolio VaR.

Cross Reference to GARP AssignedReading—Jorion,Chapter7

Assumingthat thereturnsfollowellipticaldistributions, we can represent the condicion

ina more concisefashion byemployingbetas, fh, whichareohtainedfrom regressing each

positionsreturn on theportfolio returnt

(Positionireturn risk-freerate)_ (Position jreturn—risk-freecate)

for all positionsi andj

Theportfolio weightsthat make these ratiosequal will he die optimal portfolio.We now

turn ourattention todetermining theopdmal portfolio for ourexample portfolio ofAand

B Wewillassume theexpectedexcess returnof Ais6%andthat of Bis11% Even without

thisinformation,weshould know that theopdmalportfolio will havean allocation inA

less than $5 millionand inB greaterthan $1 million.This isbecausethemarginalVaRs

were almostequalwith diose allocadons That, theretakingportfolio would he closetothe

minimum variance,which willnotbe optimal.Wemightwant tofindout howtoadjust

theallocation with respecL to theoriginalvaluesof$4millioninA and$2 millioninB.By

comparing theratiosof thetwo assets wefind:

ExcessreturnofA 0.06

=0.93130.064428

MVaRA

Excessreturnof B 0.11

=0.6272

MVaRfl 0.175388

Weseethat thereis toomuchallocatedin B.Beforeweadjustdieportfolio,we compute

the excess-return-to-VaR radofor theentire portfolio.Thereturn is:

Now,becausethereturn toMVaR ratio wasgreaterforA, wewillincreasethe allocationin

Ato$4.5million and decrease that inB to$1.5million With thosechanges, the portfolio

Cross Reference to GASP Assigned Reading-Jorion, Chapter 7

En thiscase, die marginalVaRsarefoundbyr

eov(RA,Rp)l _[o.062 0 |[$4.5l _ [0.0162 ct>v(RBlRP)J_ o 0.142 1-5j [0.0294

ThemarginalVaRsof the twopositionsarethem

cov{RA,Rp)y 0.0162MVaRA = Zcx 1.65x =0.0781

$564,387

Thisisgreater than the0.7559valueassociated with dieoriginal $4million and$2 million

allocations Theresultis a moreoptimal portfolio allocadon

©2013Kaplan,Inc.

Page 36

Cross Reference to CARP AssignedReading—Jarion, Chapter 7

AIM 54.1

Diversified VaRissimplythe VaRof the portfoliowhere the calculation takesinto account

thediversification effects

IndividualVaR is dieVaR ofanindividual position inisolation

AIM 54.2

Fora two-assetportfolio, twospecialcases are:

1.VaRforuncorrelatedpositions:

VaRP=ÿ/VaR12 +VaR23

2.VaRfor pertecdycorrelatedpositions:

UndiversifiedVaR =VaRp = v\foR j3 +VaR22 +2VaR}VaR2 = VaR:4-VaR2

AIM 54.3

Diversified VaRissimplythe VaRof the portfoliowhere the calculation takesinto account

thediversification effects* The basic formulais:

VaR -Z x a x P

F c F

where:

Z = die associated with die levelof confidencec

tip =ÿ thestandard deviationof the portfolioreturn

P = the nominal value investedin the portfolio

Individual VaRisthe VaRofanindividualpositioninisolation.Ifthe proportionorweight

in die positionis w-,then we can define theindividualVaR as:

VaRÿ - Zÿx (Tj x|P.|= Zcx ctj x|w|xP

where:

P = the portfoliovalue

R - the nominalamountinvestedin position i

AIM 54.4

Marginal VaR isdiechangein a portfolioVaR thatoccursfroman additionalone unit

investmentin agiven position Usefulrepresentationsare:

Cross Reference to GARP Assigned Reading—Jorion, Chapter 7

IncrementalVaRisthechangeinVaR from theadditionofa newpositionin aportfolio*It

can hecalculated precisely froma total revaluation of the portfolio,hut thiscanhecostly.A

less costlyapproximationisfound by(l)breaking down thenew positionintoriskfactors, (2) multiplyingeach newriskfactortimesthecorrespondingpartialderivativeof die

portfolio withrespect LO die risk factor,andthen (3}adding upall die values

ComponentVaRforpositioni, denoted CVaRj,is the amount a portfolioVaRwould

changefromdeletingdiat positionin aportfolio Inalargeportfoliowith many positions,

theapproximation issimplythe marginalVaR multiplied by the dollar weightin positioni:

CVaRj= (MVaRj) x (w;xP) = VaR x p;x w;

Thereis amethodforcomputingcomponentVaRsfor distributions thatare notelliptical

Theprocedureis to sortthe historical returnsof theportfolioand designatea portfolio

return that correspondsto the lossassociatedwith theVaRand then findthereturnsof each

of thecomponentsassociated with that portfolioloss.Thoseposidon returns canbe used to compute componentVaRs

AIM54.5

The incremental VaRisthe difference between the new VaR from die revaluation minus

theVaR before the addidon The revaluation requiresnotonly measuring the risk of the

position itself, butit also requiresmeasuringthechangein therisk of die other positions

thatarealreadyin the portfolio,for aportfolio withhundredsorthousandsofpositions,this would be timeconsuming

AIM54.6Portfolio risk will beat aglobalminimum whereall the marginalVaRsareeqnal for alli

When computingindividualVaR, it isproperto:

A. usethe absolute valueof the portfolioweight.

B useonlypositiveweights

C useonly negative weights

D* computeVaRfor each assetwidtin theportfolio

A portfolioconsistsoftwopositions.TheVaRof dietwopositionsare$1 Qmillion

and $20 million If thereturnsof the twopositionsare notcorrelated, theVaRof

theportfoliowouldhe closestto:

Whichof thefollowingis truewithrespect tocomputing incrementalVaR?

Compared m usingmarginalVaRs,computingwidifullrevaluationis:

A morecostly,hut lessaccurate.

B less casdy, butmore accurate.

C. lesscostly,butalsoless accurate.

D* morecostly, hut alsomore accurate.

Aportfolio hasanequalamount investedin two positions, XandY.Theexpected

excess returnofXis9%andthat ofYis12% Their marginalVaRsare 0.06and

0.075 respecdvely.Tomovetowardtheoptimal portfolio, the manager will probably:

A increasetheallocationinY and/or lower thatinX

B increasethe allocationin Xand/orlower thatin Y

C. donothingbecause theinformation isinsufficient

D notchangetheportfolio becauseit isalready optimal

Foradditional Book 4’

Topic54practice questionssee:

4.

5

Self-TestQuestions: #1—2(page253)

Past FRM Exam Questions: 43-12(page259)