CFA level 3 study notebook3 2015

StudySession 10Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I EnhancedIndexing by MatchingPrimary Risk Factors Duetothe numberof different b

BOOK 3 - FIXED-INCOME PORTFOLIO

PORTFOLIO MANAGEMENT

StudySession10-Fixed-IncomePortfolioManagement(1). 7

StudySession11-Fixed-Income Portfolio Management(2) 65

Self-Test-Fixed-Income Portfolio Management 110

StudySession 12 -Equity PortfolioManagement 113

Self-Test- Equity PortfolioManagement 166

SCHWESERNOTES™ 2015CFALEVEL III BOOK3:FIXED-INCOME

MANAGEMENT

©2014 Kaplan,Inc.All rights reserved

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Printedinthe United StatesofAmerica

ISBN:978-1-4754-2785-1/1-4754-2785-9

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The

READINGS AND

READINGSThefollowing materialisa reviewofthe FixedIncomePortfolioManagement, FixedIncome

Derivatives,and EquityPortfolioManagementprinciples designedtoaddress the learning

outcome statements setforthby CFAInstitute

Reading Assignments

Fixed-IncomePortfolioManagement(1),CFA Program 2015Curriculum,Volume4,

LevelIII

21.Fixed-Income Portfolio Management—PartI

22.Relative-ValueMethodologiesfor Global Credit Bond Portfolio

EquityPorfolioManagement, CFA Program 2015Curriculum,Volume4,LevelIII

Book 3- Fixed-IncomePortfolio Management (1, 2)andEquity Portfolio Management

Readingsand Learning Outcome Statements

LEARNINGOUTCOME STATEMENTS(LOS)The CFAInstitutelearningoutcome statementsarelistedinthefollowing Thesearerepeated

ineachtopicreview However,the order may have been changedinorderto getabetterfit

with theflow ofthereview.

Thetopicalcoveragecorrespondswith thefollowingCFAInstituteassigned reading:

21. Fixed-Income PortfolioManagement—PartI

The candidate should be ableto:

a. compare,withrespect toinvestmentobjectives, theuseof liabilitiesas a

benchmarkand theuseofabond indexas a benchmark,(page7)

b compare pure bond indexing, enhanced indexing, andactiveinvesting with

respect tothe objectives, advantages, disadvantages, andmanagementof each

(page8)

c. discussthecriteriaforselectingabenchmark bond index and justify theselectionofaspecific index when givenadescription ofaninvestor’s risk

aversion,income needs,andliabilities,(page11)

d critique theuseof bond market indexesas benchmarks,(page12)

asduration matching and theuseofkeyratedurations,by whichanenhanced indexermayseektoalign the risk

exposuresof the portfolio with those of the benchmark bondindex,(page13)

f contrastand demonstrate theuseof totalreturnanalysis andscenarioanalysisto

assessthe risk andreturncharacteristics ofaproposedtrade,(page16)

g formulateabondimmunizationstrategy toensurefunding ofapredeterminedliability and evaluate thestrategyundervarious interestrate scenarios,(page18)

h demonstrate theprocessof rebalancingaportfoliotoreestablishadesired dollarduration,(page25)

i explain theimportanceof spreadduration,(page27)

j discuss theextensionsthat have been madetoclassicalimmunizationtheory,including the introduction of contingentimmunization,(page29)

k explain the risks associated with managingaportfolio againstaliabilitystructure

includinginterestraterisk,contingent claimrisk,andcaprisk,(page32)

1 compareimmunizationstrategies forasingle liability,multipleliabilities,andgeneral cashflows,(page33)

immunizationstrategies,(page35)

The topical coverage corresponds with thefollowing CFAInstituteassigned reading:

22 Relative-Value Methodologies for Global Credit Bond Portfolio ManagementThe candidate should be ableto:

a. explain classic relative-value analysis, basedontop-down andbottom-upapproachestocredit bond portfoliomanagement,(page52)

b discuss the implications of cyclical supply and demand changes the primary

Book 3 -Fixed-Income Portfolio Management(1, 2)andEquityPortfolio Management

Readings andLearning Outcome Statements

c. explain the influence of investors’ short- and long-term liquidity needson

portfoliomanagement decisions,(page54)

d discuss commonrationalesfor secondary market trading, (page54)

e. discusscorporatebond portfolio strategies thatarebasedonrelative value

(page56)

The topical coverage corresponds with thefollowing CFAInstituteassigned reading:

23 Fixed-Income Portfolio Management—PartII

The candidate should be ableto:

;eonportfolio duration andinvestmentreturns.

a.

(page65)

b discuss theuseof repurchaseagreements(repos)tofinance bond purchases and

thefactors that affect thereporate,(page68)

c. critique theuseof standarddeviation,target semivariance,shortfallrisk,and

valueatriskasmeasuresof fixed-income portfoliorisk,(page70)

d demonstratethe advantages of using futures instead of cash marketinstruments

toalter portfoliorisk,(page72)

e. formulate and evaluatean immunizationstrategybasedoninterestratefutures

(page74)

f explain theuseofinterestrateswaps and optionstoalter portfolio cash flows

andexposuretointerestraterisk,(page79)

g comparedefaultrisk,credit spreadrisk,and downgrade risk and demonstrate

theuseof credit derivativeinstrumentstoaddress each riskinthecontextofa

fixed-income portfolio, (page82)

h explain the potentialsourcesofexcess returnforaninternational bond portfolio

(page85)

aforeignbond when domesticinterestrateschange and2)the bond’s contributiontodurationinadomestic portfolio, giventhe durationof the foreign bond and thecountry beta,(page86)

j recommend and justify whethertohedgeor nothedgecurrencyriskinan

international bondinvestment,(page88)

k describehow breakeven spread analysiscanbe usedtoevaluate the riskin

seeking yield advantagesacrossinternational bondmarkets,(page94)

1 discuss the advantages and risks of investinginemerging marketdebt,(page95)

m discuss thecriteriaforselectingafixed-income manager, (page96)

i.

STUDY SESSION 12

The topicalcoveragecorresponds with thefollowingCFAInstituteassigned reading:

24 EquityPortfolioManagement

The candidate should be ableto:

a. discussthe roleof equitiesinthe overall portfolio, (page113)

the rationalesfor passive, and

Book 3- Fixed-IncomePortfolio Management (1, 2)andEquity Portfolio Management

Readingsand Learning Outcome Statements

d distinguishamongthe predominant weighting schemes usedintheconstruction

of major equity market indices (page116)

toanequity

market,including indexedseparateorpooledaccounts,index mutualfunds,

exchange-tradedfunds,equity indexfutures,and equity totalreturnswaps

(page118)

f comparefull replication, stratified sampling, and optimizationasapproachestoconstructinganindexed portfolio andrecommend anapproach when givena

description of theinvestmentvehicle and the indextobetracked, (page120)

g explain and justify theuseof equity investment-style classifications and discussthe difficultiesinapplyingstyle definitions consistently, (page121)

h explain the rationales and primaryconcernsof valueinvestorsand growth

investorsand discuss thekey risks of eachinvestmentstyle, (page122)

i comparetechniques for identifyinginvestmentstyles and characterize the style

ofan investorwhen givenadescription of the investor’s security selection

method,detailsonthe investor’s security holdings,orthe resultsofa basedstyle analysis, (page124)

returns-j comparethe methodologies usedto constructequity styleindices,(page130)

k interpretthe resultsofanequitystyle box analysis anddiscusstheconsequences

of styledrift,(page131)

1 distinguish between positive and negativescreensinvolving socially responsibleinvestingcriteriaand discuss their potential effectson aportfolio’s stylecharacteristics,(page132)

m compare long-short and long-onlyinvestmentstrategies,including their risksand potential alphas, and explain whygreaterpricing inefficiencymay exist on

the short side of themarket,(page133)

n. explain howamarket-neutral portfoliocanbe “equitized”togain equity marketexposure and compareequitized market-neutral and short-extension portfolios

(page135)

e.

esofactiveinvestors,(page137)

p contrastderivatives-based and stock-based enhanced indexing strategies andjustify enhanced indexingonthe basisof risk control and the informationratio

s distinguishamongthecomponentsof totalactivereturn(“true” activereturnand“misfit”activereturn)and their associatedriskmeasuresand explain theirrelevancefor evaluatingaportfolio of managers, (page145))

t. explain alpha and beta separationas anapproachtoactivemanagementanddemonstrate theuseof portable alpha, (page147)

u describe theprocessofidentifying, selecting,and contracting with equitymanagers,(page148)

v contrastthe top-down and bottom-up approachestoequityresearch,(page150)

imi o.

The following is a review of the Fixed-Income Portfolio Management (1) principles designed to address

the learning outcome statements set forth by CFA Institute This topic is also covered in:

Study Session 10

EXAM FOCUS

Fixedincome isgenerallyanimportant topicand highly integratedintothe

overwhelming theme of LevelIII,portfoliomanagement.Theconceptsof duration and

spreadwill carryoverfromearlier levelsoftheexamwithextensionsfromwhat has

beenpreviously covered.Assetliabilitymanagement (ALM)willbeaprominenttheme

Immunizationandits variations isALMwith math Also be preparedtodiscusspros

andconsof thevariousapproaches.Fixed incomewill address the detailsofhedgingto

modifyportfolioriskand touchon someaspectsof currency riskmanagement.Don’t

overlook the seemingly simple discussions of benchmarks andactiveversuspassive

managementbecausetheseareprominent themesatLevelIII.Expectboth questions

with math andconceptualquestions

BOND PORTFOLIO BENCHMARKS

LOS 21.a:Compare, withrespecttoinvestmentobjectives,theuseof liabilities

asabenchmark and theuseofabond indexasabenchmark

CFA®ProgramCurriculum,Volume4,page125UsingaBond Indexas aBenchmark

Bond fundmanagers(e.g., bond mutualfunds)arecommonly comparedto abenchmark

thatisselectedorconstructedtoclosely resemble the managed portfolio.Assume,for

example,abond fundmanagerspecializesinone sectorof thebondmarket.Instead

ofsimply accepting thereturngenerated by themanager, investorswant tobeable

todetermine whether themanagerconsistentlyearnssufficientreturns tojustify

managementexpenses.In thiscase, a custombenchmarkisconstructedsothatany

differencein return isduetostrategiesemployed bythe manager,notstructural

differences betweentheportfolio and thebenchmark

Anothermanager mightbecomparedto awell-diversified bond index Ifthe manager

mostlyagreeswith marketforecasts andvalues,she will followapassivemanagement

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

If themanagerbelieves she hasasuperiorabilitytoforecastinterest ratesand/or identifyunder-valued individualbondsorentiresectors,shefollowsanactivemanagementapproach

Shewillconstructthe portfoliotoresemble the indexin many waysbut,throughvariousactivemanagementstrategies, shehopestoconsistentlyoutperform the index.Activebondportfoliomanagementstrategiesarediscussed throughout this topicreview.

Using LiabilitiesasaBenchmarkTheinvestmentobjective whenmanagingabond portfolioagainstasingleliabilityor set

of liabilities(ALM) isratherstraightforward; the managermustmanagetheportfoliotomaintainsufficient portfolio valueto meetthe liabilities

BOND INDEXINGSTRATEGIES

LOS21.b: Compare pure bondindexing,enhancedindexing,andactiveinvesting with respecttotheobjectives, advantages, disadvantages,and

managementof each

CFA®Program Curriculum,Volume4,page127

Asyou may surmisefrom thisLOS,therearemanydifferent strategies thatcanbefollowedwhenmanagingabond portfolio.Forexample, themanagercan assume a

completelypassiveapproach andnothavetoforecastanything.In otherwords,the

managerwho feels he hasno reason todisagree with market forecasts hasno reason to

assumehecanoutperformanindexingstrategythroughactivemanagement.Ontheotherhand,amanagerwhoisconfidentinhis forecasting abilities and hasreason to

believe marketforecastsare incorrect can generatesignificantreturnthroughactive management.

The differences between thevarious activemanagementapproachesaremostlymatters

of degree Thatis,bond portfoliomanagementstrategies formmore orlessacontinuum

fromanalmost do-nothing approach(i.e.,purebond indexing)to ado-almost-anythingapproach(i.e.,full-blownactivemanagement)asdemonstrated graphicallyinFigure1

Figure1 :IncreasingDegrees ofActiveBond Portfolio Management

Increasing active management

Increasingexpectedreturn

Increasingtrackingerror

Pure bond

indexing

Full-blown active management

InFigure1,youwillnoticetheincreaseof three characteristicsasyoumovefrompure

bond indexingtofull-blownactivemanagement.Thefirst,increasingactive management, can be definedasthe gradual relaxation ofrestrictions onthe manager’sactions toallowhimtoexploit hissuperiorforecasting/valuationabilities Withpurebond indexing, the

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21- Fixed-IncomePortfolio Management—Part I

exposuresasthe index Asyoumovefrom lefttoright, therestrictionsonthe manager’s

actions arerelaxed and the portfolio risk factorexposuresdiffermoreandmorefrom

thoseof the index

Thenextcharacteristic,increasingexpectedreturn, referstotheincrease inportfolio

expectedreturnfromactionstakenby the manager Unless the manager hassome

superior ability that enables himtoidentify profitablesituations,he should stick with

purebond indexingor atleast match primary risk factors

The thirdcharacteristic, increasingtrackingerror,referstothe degreetowhich the

portfolioreturntracks that of the index Withpurebond indexing,eventhough

managementfees andtransactionsare incurred,the reducedreturnonthe portfolio will

closely track thereturn onthe index.As youmove tothe right, the composition and

factorexposuresof the portfolio differmoreandmorefrom the index Each enhancement

isintendedtoincreasethe portfolioreturn,butisnotguaranteedtodoso.Thus,the

amountby which the portfolioreturnexceeds the indexreturncanbe quite variable

from periodtoperiod andevennegative The difference between theportfolio and index

returns(i.e.,the portfolioexcessreturn) isreferredto asactivereturn.The standard

deviationofactivereturnacrossseveral periodsisreferredto astrackingrisk,thusit is

thevariabilityof the portfolioexcess returnthatincreasesasyou movetowardsfull-blown

activemanagement.This increased variability translatesintoincreaseduncertainty

The five classificationsof bond portfoliomanagementcanbe describedas:(1)purebond

indexing,(2)enhanced indexing by matchingprimaryriskfactors,(3)enhanced indexing by

small riskfactormismatches, (4)active managementby larger riskfactormismatches,and

(5)full-blownactive management

FortheExam:Generally, donot expectfirm distinctions among these five categories

Instead, view No.1 aspurely passive andNo.5ashavingnorestrictionsonthe

manager.In betweenisacontinuumandexactdistinctionsaresubjective Moving

from No.1toNo.5,the potential for adding valueincreasescomparedtotheindex,

butsodoes risk Generally:

• No 1allowsnodeviations from the index

• Nos 2and 3 allowsomedeviations but will matchatleast the overall durationof

the benchmark

• Nos.4 and5involve deviating from theaveragedurationof the benchmarkas

wellasother deviations

PureBondIndexing

Thisistheeasieststrategy todescribeaswellasunderstand Inapurebondindexing

strategy,the manager replicateseverydimensionof the index.Every bondinthe indexis

purchased anditsweightinthe portfolioisdetermined byitsweightinthe index.Due

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

EnhancedIndexing by MatchingPrimary Risk Factors

Duetothe numberof different bondissues inthe typical bond indexaswellastheinefficiencies andcostsassociated withpurebond indexing, thatstrategyisrarelyimplemented.Instead,managers will enhance the portfolioreturnbyutilizinga

samplingapproachtoreplicate the index’s primary risk factors while holding only

a percentageof the bondsinthe index Sampling reduces thecostsassociated withconstructing theportfolio, and matching the risk factorsmeansthe portfolioisexposed

tothesameriskfactorsasthe index Thismeansthe portfolio will track the indexclosely, andsincelowertransactionscostsare incurred,thisstrategywilloutperforma

pure bond indexingstrategy.

EnhancedIndexingby Small Risk Factor MismatchesThisisthe first levelof indexing thatisdesignedtoearnabout thesamereturn as

the index While maintaining theexposuretolarge riskfactors,suchasduration,themanagerslightlytilts the portfolio towardsother,smaller riskfactors by pursuingrelativevalue strategies (e.g.,identifyingundervaluedsectors)oridentifyingotherreturn-enhancing opportunities The small tiltsareonly intendedto compensateforadministrativecosts.

ActiveManagementbyLarger Risk Factor MismatchesTheonly difference between thisstrategyand enhanced indexing by small risk factormismatches(thepreceding strategy)isthe degree of the mismatches In otherwords,

the managerpursues moresignificantquality and value strategies (e.g.,overweightqualitysectorsexpectedtooutperform, identify undervaluedsecurities) In addition,

themanagermight alter the duration of the portfolio somewhat Theintent isearningsufficientreturn tocoveradministrativeaswellasincreasedtransactionscostswithoutincreasing the portfolio’s riskexposurebeyondanacceptable level

Full-BlownActiveManagementThereareno restrictions onhow the portfoliocandeviatefrom the index Figure2

isasummaryof the advantages and disadvantages of the bond portfolio strategiesdiscussed.Notethatineachcase,relative phrases (e.g.,lower, increased)referto thecell immediately above theone inwhichthe phraseis written.For example, less costlyto

implement, under advantages for enhanced indexing by matching primary riskfactors,

referstolowercoststhan those associated withpurebond indexing

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21 - Fixed-Income Portfolio Management—Part I

Figure2:Advantages and Disadvantages ofBondPortfolio Management Strategies

DisadvantagesAdvantages

lowtrackingerror)

Same risk factor exposures

Increased management fees

Increasedexpectedreturn

Few if any manager

restrictions

No limits on duration

Increased risk Increasedtrackingerror

Increased management fees

Increasedmanagement fees

SELECTINGABENCHMARK BONDINDEX

LOS21.c:Discuss the criteriaforselectingabenchmark bond index and justify

the selectionofaspecific index when givenadescription ofaninvestor’s risk

aversion,income needs,and liabilities

CFA®ProgramCurriculum, Volume4,page 129Out-performingabond indexon a consistentbasisisdifficultatbest,especiallywhen

riskandnet return areconsidered.Theprimary benefitstousinganindexing approach

include diversification and lowcosts.The typical broad bond market indexcontains

thousandsof issues withwidelyvaryingmaturities,couponrates,and bondsector

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

Regardless of thestrategyemployed, themanagershould be judged againstabenchmark,

and the benchmark should match the characteristics of the portfolio Amongothers,

therearefour primary considerations whenselectingabenchmark:(1)market valuerisk,(2) income risk, (3)creditrisk,and(4)liabilityframeworkrisk

Market value risk The market valuesof long duration portfoliosare more sensitivetochangesinyield than the market values of shorter duration portfolios.Fromamarketvalue perspective,therefore,thegreatertheinvestor’sriskaversion,the shorter theappropriate duration of theportfolio and the selected benchmark

Income risk.If the clientisdependentuponcash flows from the portfolio, those cashflows should beconsistentand low-risk Longertermfixed-rate bonds will lockinanincomestream.The longer thematurityof the portfolio andbenchmark, therefore,thelower theincomerisk.Investorsdesiringastable,long-term cash flow shouldinvest in

longer-termbonds and utilizelong-termbenchmarks

Credit risk Thebenchmark’s credit riskexposureshould beconsistentwith the client’sobjectives andconstraints.If the client seeks higherreturnand willaccepthigher credit

risk,selectabenchmark withgreatercredit risk exposure

Liability framework risk If therearedefinableliabilities,then ALMisthe preferredapproach The benchmark thatmostclosely matches the liabilities should be selected

LOS21.d: Critique theuseof bond market indexesas benchmarks

CFA®Program Curriculum,Volume4,page131

Avalid benchmark should be investableinordertoprovideavalid alternativetohiring

amanager.If the indexisnotinvestable, it isnot avalid benchmark The bond marketprovides several challengestothis requirement

First,bond marketsecuritiesare moreheterogeneous and illiquid.Issuesareuniquewithdifferencesinmaturity, seniority, and other featurescomparedtostocks,whichare

generally issuedasonetypeof stock Compounding the problem,many issuesdonottrade regularly and pricing dataisfrequently basedonappraisals and tradesareoftennot

publiclyreported These characteristics lead index providerstomake choices regardingwhattoincludein anindex and full index replicationislesscommonthan for equities

Second,theresultingindexes fromvariousvendorscanappearsimilar butbequitedifferentincharacteristics With different characteristics therecanbeunapparentrisks(e.g., whatisthe weight of callable and non-callable bonds? Of sinking fund bonds?

Whatcountriesareincludedinaglobalindex?)

Third,the risk characteristicscanchange quicklyovertimeas newissuesof bondsare

added and those approaching maturityaredeleted from the index

Fourthisthe “bums” problemascapitalized-weighted indexesmay carryincreased

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21- Fixed-IncomePortfolio Management—Part I

mitigate the bumsproblem,someindex providers impose weightlimits,make subjective

decisions,or useequal weights

Lastly,itcanbe difficult forinvestorstofindanindex that matches their risk profile.For

example, iflong-terminterestratesarehistoricallylow,bondissuerswill finance debt

longertermresultinginahigher durationinthe index whereasan investormayhavea

shorter durationtimehorizon

The resultismany active investorscreate custombenchmarksfromacomposite of

indexes and sub-indexestomatch the characteristicsofaparticularmanager Passive

investorsusesamplingtoreplicateanindex andALMportfoliosusethe liabilitiesasthe

benchmark

ALIGNING RISK EXPOSURES

LOS21.e:Describe and evaluate techniques, suchasdurationmatchingand

theuseof keyratedurations,by whichanenhanced indexermayseektoalign

the risk exposures of theportfoliowith thoseof the benchmark bond index

CFA®ProgramCurriculum,Volume4,page135

Anenhanced index portfolio closelymimics itsbenchmarktominimizetrackingerror

Enhancedindexing generally allowsnodeviation from the benchmark’s duration but

allows smaller deviationsinother riskfactorsinanefforttoadd value(active return).

The simplest but least precisewaytocontrol riskistomatchaggregateportfolio

exposuretobenchmark exposure.For example, if the benchmark hasadurationof1.8

and average credit quality ofAA,then match the portfolio’s duration and credit quality

tothesetworiskfactors

Cell matching(i.e.,stratified sampling) adds precision by matching individual cell

exposurewithin the riskfactor.Forexample, the benchmarkaverageduration and

qualityarecomposedasfollows:

Figure 3: Cell Matching

*midpointof rangeusedtocalculate contributiontoduration

The portfolio will match the weights of the benchmark by cell and therefore also match

Study Session 10

Cross-Reference to CFA Institute Assigned Reading #21—Fixed-Income Portfolio Management—Part I

I multifactor regression ofpastdatatofindaportfolio allocation by risk factors that

wouldhavemostclosely trackedpastbenchmarkreturns.).

The primary riskfactorsconsidered in anyof the approaches previously mentionedtypicallyinclude:

1 Duration(i.e.,effectiveduration)measuresexposuretointerestrateriskas

measured bysmallparallel changesin theyieldcurve.Aparallel shiftmeansall

interest rateschange by thesameAr.Forlarger changesinrates,matchingconvexitywill improveresults butconvexity also assumesparallelshifts.Matching duration

(andconvexity)of the benchmarkminimizes interest raterisk

Thinkofinterestrateriskas movementin thegenerallevelofinterestratesandyieldcurveriskasanynon-parallel changeinratesand theyieldcurve.Ina non¬

parallelshift,Arfordifferentmaturitieswill differ.Non-parallelshiftsarenormal

and thisisyieldcurverisk.Thecurve cantwist (interestrates atshorter and longer

maturitiesmoveinoppositedirections)orthecurve canchangeinotherways.Cellmatchingdurationof the benchmarkminimizesbothinterest rateandyieldcurverisks.(Notethat in spite ofparallel shifts beingrare,simple duration generallyexplainsmosto/whathappenstoportfolios when thecurvechanges.)

2 Keyratedurationor presentvalue distributionof cash flow matching achievesthe

sameresultascell matching of duration All threeminimizebothinterestrateandyieldcurverisk Keyrateduration breaks the yieldcurveintoafinite numberof

maturity pointsand analyzes changeinprice ofasecurityif onlyoneof thosepoints

ontheyieldcurvechanges.Forexample,abondhasa5-year keyratedurationof1.27.Ifthe5-yearinterest rate increases1%andnootherrateschange, the bondwill decline 1.27% Summingall ofabond’s keyratedurations willequalthebond’sduration

Becauseduration measures pricechange andpriceisthePV ofabond’sfuturecashflows,ifthepresentvalue distributionofcash flowsarematched,duration anddistributionsof durationarealso matched Figure 4 anditsdiscussion explain this

0.500

1.000

1.500

0.0150.015

0.970 1.000

0.005

0.010

0.007

0.0151.442

1.000

In the firstandsecondcolumns,thefuture cash flows and their timingareprojected

Because each cashflowisa onetime event,eachisequivalentto azero-coupon bond,

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21- Fixed-IncomePortfolio Management—Part I

The third column calculates thePVof each cash flow basedonthe bond’syield The

sumof the PVsisthe bond’s price

The forth column shows eachPVas a percentageof totalPV.The product of column2

(duration)andcolumn 4 (weighting)isthe contributiontototal duration of that cash

flow andisshownincolumn5.Summing each of theseproductsincolumn5isthe

bond’s duration

The final column finds the%weight of each duration contributiontototal duration

Ifamanager matches theweightsinthe final column foraportfoliotothoseof the

portfolio’sbenchmark,durations will be matchedaswellasexposurealong the yield

isultimately thesamething;it minimizesbothinterest rateand yieldcurve

risk Asalways,startworkingpracticequestionsafteryouhave completed eachreadingto seethe application expected

3 Sectorandqualitypercent.The manager matches the weights ofsectorsand

qualitiesinthe index

4 Quality spread duration contribution Themanagermatches the proportion of the

index durationthat iscontributed byeachqualityin theindex,where quality refers

tobonds with credit risk(i.e., notcredit risk-freeTreasurybonds).Spread duration

measureshow the price ofonebond will change relativetothe price of another bond

if the differenceinyield between thetwobonds(thespread) changes.Forexample,

aportfolio’s benchmark has30%investedinArated bonds withaspread duration

of 5.00 The product of weight and durationis1.50 andisthe spread duration

contribution ofArated bondstothe benchmark.If the spread ofArated bondsto

Treasurybondsincreases1.0%,then the value of the benchmark would fall 1.5%

inrelationtoTreasurybond prices.(Note:thereis no waytoknowfromthis data

ifTreasury pricesorthe benchmarkincreasesordecreasesinprice, only that there

isaprice decline relativetoTreasury prices.) Ifaportfolio matches this 1.50 spread

duration contributionforAratedbonds,then changeincorporatespreads should

notaffect the portfolio’s performance relativetothe benchmark

5 Sectorduration contributions Thesameanalysis appliedtoqualitycan be

appliedto sectors.Forexample,aportfolio’s benchmark hasa2.61spread duration

contributiontoindustrial bonds.If the portfolio matches this2.61,thenachangein

industrial bond spreads should have effect the portfolio’s performance relative

Study Session 10

Cross-Reference to CFA InstituteAssigned Reading#21—Fixed-Income Portfolio Management -Part I

I 6 Sector/coupon/maturity cellweights.Convexity isdifficultto measurefor callable

bonds.Oneway tomatch theconvexity istomatch thesector,coupon,andmaturity

weightsinthe portfoliotothat of the benchmark Forexample,holdcallablebonds

in theportfolioin similarweight andwith similar characteristicstothose in thebenchmark

7 Issuer exposure.After matching all of the risk factors previouslymentioned,thereisstillevent risk,andanindividual security could underperformforreasonsunrelated

tomarket circumstances(e.g.,the issuerdeclares bankruptcy) Holdingasmaller

numberof securitiesthan thebenchmarkincreasesthisrisk because eachsecurity

will havearelatively larger weightin theportfolio thaninthe benchmark

Figure5contains asummary of the risk exposures for non-MBSbonds.2Note that MBSprimaryriskexposuresincludesector, prepayment,andconvexity risk

Figure5: BondRiskExposures: Non-MBS

Primary Risk Factors Risk Interest Rate Yield Curve Spread Credit Optionality

CFA®ProgramCurriculum, Volume4,page145

Rather thanfocus exclusivelyontheportfolio’s expectedtotalreturnunderonesingle

setof assumptions,scenarioanalysisallowsaportfoliomanagerto assessportfoliototalreturnunder varyingsetsofassumptions(differentscenarios).Possiblescenarioswouldinclude simultaneous assumptions regardinginterestratesand spreadsatthe endof the

investmenthorizonaswellasreinvestment rates overthe investmenthorizon

PotentialPerformance ofaTradeEstimatingexpected totalreturnunderasinglesetofassumptionsonly providesapointestimateof theinvestment’sexpectedreturn (i.e., asinglenumber).Combining total

returnanalysiswithscenarioanalysisallows theanalystto assess notonlythereturn but

alsoitsvolatility(distribution) under differentscenarios.

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21 - Fixed-Income Portfolio Management—Part I

Example:Scenarioanalysis

Considera7-year, 10%semiannual,$100 parcorporatebond.Thebondispricedto

yield9%($105.11),andit isassumed thatcouponscanbe reinvestedat7%overthe

1-year investment horizon

The yieldcurveisexpectedtoremainflatatitscurrentlevel.However,theissue’s

creditspreadisexpectedtochange, but byanunknownamount Thus,the manager

hasoptedto usetotalreturnanalysisina scenarioanalysisframeworkto assessthe

range ofpotentialoutcomesand has generated the informationin the following figure

TotalReturn SensitivitytoHorizonYield:One-Year Horizon

Bond-EquivalentYield EffectiveAnnual Return

*Required return on the bond in one year.

Samplecalculation,assuming9%horizon yield(boldinthetable):

1 Horizonprice(in one year,the bond will havea6-yearmaturity):

N=6 X 2=12;FV=100;I/Y=9/2=4.5%;PMT=5;CPT-*ÿPV= 104.56

0 07)

horizonvalueof reinvested coupons=$5+ $5|1H—-— I =$10,175

total horizonvalue= 104.56+10.175=$114.735

PV=-105.11;FV= 114.735; N=2;CPT->I/Y =4.478%

3 BEY= 4.478%x 2=8.96%

4 EAR = (1.04478)2 -1=9.16%

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

Calculation assumingan11%horizon yield:

1 Horizonvalue=horizon price+reinvested coupons= 95.69+10.175= 105.865

2 Semiannualreturn=PV=-105.11;FV=105.865;N=2;CPT I/Y=0.3585%

and the effective annualreturnincreasesfrom0.72%to29.22%

Scenarioanalysis provides the tools for themanagertodoabetter jobinquantifying theimpact ofachangeinthe horizon yield assumptiononthe expected totalreturnof thebond.Amorecomplete scenario/totalreturnanalysis could include the simultaneousimpacts ofnonparallel shiftsintheyieldcurve,differentreinvestmentrates, et cetera.

Scenarioanalysiscanbe broken downintothereturnduetoprice change, coupons

received,andinterestonthe coupons Examining thereturn componentsprovides the

managerwithacheckonthe reasonableness assumptions.Forexample, if the price change

islargeand positive foradeclineinrates,but thesecuritiesaremortgage-backedwithnegativeconvexity,the manager could furtherexamineasomewhat surprising result

Assessing theperformance ofabenchmark indexoverthe planning horizonisdone

inthesame wayasfor the managed portfolio Whenyoucomparetheirperformances,the primaryreasonsfor different performance, other than the manager’sactive bets,areduration and convexity.Forexample, theconvexities(rateof changein duration)

for the benchmark and portfoliomaybe different duetosecurityselection,and themanagermaydeliberately change the portfolioconvexityand/or duration(relativetothe

benchmark) inanticipation oftwistsorshiftsinthe yieldcurve

IMMUNIZATION

LOS 21.g: Formulateabondimmunizationstrategytoensurefundingofa

predeterminedliability and evaluate thestrategyundervarious interestrate

scenarios

CFA®ProgramCurriculum,Volume4,page148ClassicalImmunization

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21- Fixed-IncomePortfolio Management—Part I

andreinvestmentraterisk.Price risk,also referredto asmarket valuerisk,referstothe

decrease(increase)inbond pricesasinterestratesrise (fall) Reinvestmentrateriskrefers

totheincrease(decrease)in reinvestment incomeasinterestratesrise (fall)

Itisimportantto notethat price risk andreinvestmentrateriskcauseopposite effects

Thatis, asinterestrates increase,prices fall butreinvestmentratesrise.Asinterestrates

decrease,pricesrisebutreinvestmentratesfall

Supposeyouhavealiability thatmustbe paidatthe endof fiveyears,andyouwould

liketoformabondportfolio that will fully fundit.However,youareconcerned about

theeffect thatinterestraterisk will haveonthe ending value ofyourportfolio Which

bonds shouldyoubuy?Youshouldbuy bonds that resultintheeffects of price risk and

reinvestmentriskexactly offsetting each other Thisisknownasclassicalimmunization

Reinvestmentraterisk makes matching thematurityofacoupon bondtothematurity

ofafuture liabilityaninadequatemeansof assuring that the liabilityispaid Because

futurereinvestmentratesare unknown,the totalfuture value ofabond portfolio’s

couponpaymentsplus reinvestedincome is uncertain

ClassicalSingle-PeriodImmunization

Classicalimmunization istheprocessof structuringabond portfolio that balancesany

changeinthe valueof the portfolio with thereturnfrom thereinvestmentof thecoupon

and principalpaymentsreceived throughout theinvestmentperiod The goal of classical

immunization istoformaportfoliosothat:

• Ifinterestrates increase,the gainin reinvestment income >lossinportfolio value

• Ifinterestratesdecrease,the gaininportfolio value>lossin reinvestment income

Toaccomplish thisgoal,we useeffective duration Ifyouconstruct aportfolio withan

effective duration equaltoyourliabilityhorizon,theinterestrateriskof the portfolio

will be eliminated.Inotherwords,price risk will exactly offsetreinvestmentraterisk

Professor’sNote:Recall duration works bestforsmall, immediate,parallelshifts

in theyieldcurve.Therefore, additional rules will beaddedshortly

ImmunizationofaSingle Obligation

To effectivelyimmunizeasingle liability:

1 Selectabond(orbond portfolio) withaneffective duration equaltothe durationof

the liability Foranyliability payableonasingledate,the durationistakentobe the

timehorizon untilpayment.Forexample, payablein3years isadurationof 3.0

2 Set thepresentvalue of the bond(orbond portfolio) equaltothepresentvalue of

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

Forexample,suppose youhavea$100millionliability withadurationof8.0and

a presentvalue of$56,070,223.Yourstrategyshould betoselectabond(orbondportfolio) withadurationof8.0anda presentvalueof$56,070,223

Theoretically, this shouldensurethat the value ofyourbond portfolio will equal

$100 millionineightyears,evenif thereisasmallone-time instantaneousparallel shift

inyields Any gainorlossin reinvestment incomewill be offset byanequal gainorloss

inthe valueof the portfolio

What doesit meanif the durationof the portfolioisnotequaltothe durationof theliability?

• If portfolio durationisless than liabilityduration,the portfolioisexposedtoreinvestmentrisk Ifinterestratesaredecreasing, the losses from reinvestedcoupon

and principalpaymentswouldmorethan offsetanygains from appreciationinthevalueof outstanding bonds Under thisscenario,the cash flows generated fromassets

would be insufficientto meetthe targeted obligation

• Ifportfolio durationisgreaterthan liabilityduration,the portfolioisexposedtoprice risk Ifinterestratesareincreasing, this would indicate that the losses fromthe market valueof outstanding bonds wouldmorethan offsetanygains from theadditionalrevenuebeing generatedonreinvested principal andcouponpayments.

Under thisscenario,the cash flowsgeneratedfromassetswouldbe insufficientto

meetthe targeted obligation

Adjustmentstothe Immunized Portfolio

Without rebalancing, classicalimmunizationonly works foraone-time instantaneous

changein interestrates.Inreality,interestratesfluctuate frequently, changing thedurationof theportfolio and necessitatingachangeintheimmunizationstrategy.

Furthermore,themerepassage oftimecausesthe durationof both the portfolio andits

targetliabilitiestochange, althoughnotusuallyatthesamerate.

Remember,portfolioscease tobe immunizedforasingle liability when:

• Interestratesfluctuatemorethanonce

• Timepasses

Thus, immunization isnot abuy-and-holdstrategy.Tokeepaportfolioimmunized, it

mustbe rebalanced periodically Rebalancingisnecessarytomaintainequality betweenthe durationof the immunized portfolio and the decreasing duration of the liability

Rebalancing frequencyisacost-benefit trade-off.Transactioncostsassociated withrebalancingmustbeweighedagainst the possibleextent towhich the terminal valueofthe portfoliomayfall short ofitstargetliability

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21 - Fixed-Income Portfolio Management—Part IBond CharacteristicstoConsider

In practice, it is importanttoconsider severalcharacteristicsof theindividual bonds

thatareusedto construct animmunized portfolio Bond characteristics thatmustbe

considered withimmunizationinclude the following:

• Credit rating.Inimmunizingaportfolio,itisimplicitly assumed thatnoneofthe

bonds will default

• Embeddedoptions For bonds withembedded options,it maybe difficulttoestimate

duration becausecash flowsaredifficulttoforecast

• Liquidity Ifaportfolioistobe rebalanced,itwillbe necessarytosellsomeofthe

bonds.Thus,liquidityisanimportantconcern.

Optimizationproceduresareoftenusedtobuild immunized portfolios.These

procedures consider themany variationsthat typicallyexistwithinthe universe of

available bonds

ImmunizationAgainst NonparallelShifts

Animportant assumption of classicalimmunizationtheoryisthatanychangesinthe

yieldcurve areparallel Thismeansthat ifinterestrateschange, theychange by the

same amountandin thesamedirectionfor allbondmaturities Theproblemisthat in

reality, parallel shifts rarelyoccur Thus,equatingthedurationoftheportfolio with the

durationof the liability doesnot guaranteeimmunization

Immunizationriskcanbethoughtofas a measureof the relativeextent towhichthe

terminalvalueofanimmunized portfoliofalls shortofits targetvalueas aresultof

arbitrary (nonparallel) changesin interestrates.

Becausetherearemanybond portfolios thatcanbe constructedtoimmunizeagiven

liability,youshould select theonethatminimizes immunizationrisk

Howdoyoudothis? Asit turns out,immunized portfolioswith cashflowsthatare

concentrated around theinvestmenthorizon havethelowestimmunizationrisk.Asthe

dispersion of the cash flowsincreases, sodoes theimmunizationrisk Soundfamiliar?

Ingeneral, the portfolio that has the lowestreinvestmentriskisthe portfolio that will do

the bestjobof immunization:

• Animmunized portfolio consisting entirely ofzero-couponbonds thatmature

attheinvestmenthorizon will havezero immunizationrisk because there iszero

reinvestment risk

• If cash flowsareconcentrated around the horizon (e.g., bullets withmaturitiesnear

the liabilitydate), reinvestmentrisk andimmunizationrisk will be low

• Ifthere isahigh dispersionof cash flowsaboutthe horizondate(asinabarbell

strategy),reinvestmentriskandimmunization riskwillbehigh

Study Session 10

Cross-Reference to CFA Institute Assigned Reading #21—Fixed-Income Portfolio Management—Part I

I WARM-UP: DURATIONAS AMEASUREOFBOND PORTFOLIO RISK

FortheExam:This materialonduration,dollarduration,and duration contribution

isprovided solelyas a reviewof thebasicsrequired foracomplete understanding of

the material in LOS21.h

Themajorfactorthatdrives bond pricemovements(andreturns)ischanginginterestrates,and durationisusedtomeasureindividual bond and portfolioexposureto

changesininterestrates.Duration isoften considereda moreusefulmeasureof bondrisk than standard deviation derived from historicalreturns,because the numberof

estimatesneededtocalculate standard deviationincreasesdramaticallyasthenumber

ofbondsin theportfolioincreases,andhistoricaldatamaynotbereadily availableor

reliable Estimatingduration,onthe otherhand, is quitestraightforward anduseseasilyobtainable price, requiredreturn,and expected cash flow information

EffectiveDurationEffective durationofaportfolioorindexisthe weighted average of the individual

effective durationsof the bonds in theportfolio

Example: Calculating portfolioeffective duration

BrandonMason’sportfolioconsistsof thebondsshown in thefollowing figure

BondPortfolioof BrandonMason

Adurationof 5.8 indicates that the market valueofthe portfolio will change by

approximately5.8%forevery 1.0percentagepoint(100bps) parallel changein

interest rates.

The effective durationforabond indexiscomputedinthesamewayasthat forabond

portfolio In thiscase,however,we can usetheaverageeffective durationof thesectors

rather than thedurationsof theindividual bondsin thesectors,whichwouldbefar

moretedious:

DIndex — y>A — wlDl + W2D2 + w3D3 + + wnDn

i=l

where:

Index= tÿeeffective durationof theindex

= the weight ofsectori inthe index

=the effective durationofsectori

DURATION CONTRIBUTION

w;

Di

EffectiveDuration

Managerssometimesrelyon abondorsector’smarket-value weightintheir portfolioas

a measureof theexposuretothat bondor sector.Analternativeway to measureexposure

is tomeasure thecontributionofa sector orbondtotheoverall portfolio duration

Specifically, the contributionof anindividual bondor sector tothedurationof the

portfolioisthe weight of the bondor sectorinthe portfolio.Durationcontribution

isthe product ofthedurationofan asset (orgroupofassets)and their weightin the

portfolio.Itcapturesboth theirvolatility(duration)and also relativesize(weight)in the

portfolio

contributionof bondor sectoritothe portfolio duration =w;Dj

where:

W; =theweightofbondor sectori inthe portfolio

market valueof bondor sectori inthe portfolio

total portfolio value

Study Session 10

Cross-Reference to CFA Institute Assigned Reading #21—Fixed-Income Portfolio Management—Part I

Assume you havea10-yearcorporatebond inanactively managedportfolio.The

bond hasamarket valueof $5million andadurationof4.7,and theportfolio has

atotal valueof$20million andadurationof 6 Calculate the contribution of thecorporatebondtothe overall durationoftheportfolio

Answer:

Thecontributionof thecorporatebond tothedurationof theactively managedportfoliois:

contributiontoportfolio duration=($5million/ $20 million)x4.7=1.175

It contributes19.6% of theportfolio’sduration,1.175/6.0

DollarDuration

Duration measurespercentchangeinvalue.Dollar durationisrelated andmeasures

dollar changeinvalue Byconvention,it iscalculatedfora 100basis points(bp),a

1%changeinrates,and shownas apositivenumber.(It canbecalculatedforchangesother than100bp.Forexample, price value ofabasis pointisdollar durationfora 1bpchange.) Ifrates increase,thebondorportfolio declinesinpercentanddollaramount.

DDcanbecalculatedforanindividual bondorforaportfolioas:

DD = (duration)(0.01)(price)

Example: Dollar duration

Aportfolio withamarketvalueofGBP 47,500,000andapar valueofGBP50Mhas

adurationof 7.0 The managerusescash in theportfolio(duration=0) topurchaseGBP1,000,000marketvalue andpar ofabondwithadurationof4.0 Calculatethe

initial and after purchase “dollar duration” of the portfolio

Answer:

InitialDD= GBP47,500,000(7.0)(0.01)= GBP3,325,000

DD afterpurchase:

DDisasimple addition of the DD of theassetsin theportfolio Itisnot aweighted

average The cash used hadnoduration and contributednoDDtothe initial

portfolio.Thepurchased bondhasaDD of GBP1,000, 000(4.0)(0.01)=GBP40,000

DDafter purchase= GBP3,325,000 +40,000 = GBP 3,365,000

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21- Fixed-IncomePortfolio Management—Part I

Example:Contributiontoportfolio dollar duration

Assumeyouhavea10-yearcorporatebondinanactively managed portfolio The

bond hasamarket valueof $5 million andadurationof4.7.The portfolio hasa

total valueof$20million andadurationof 6.8 Calculate the contribution of the

corporatebondtothe dollar durationof the portfolio

The bond contributes$235,000tothe portfolio dollar duration of $1.36 millionor

about 17.3% of the portfolio dollar duration

ADJUSTING DOLLAR DURATION

LOS21.h: Demonstrate the process ofrebalancingaportfoliotoreestablisha

desired dollar duration

CFA®ProgramCurriculum,Volume4,page152Dollarduration, justlikeanyother durationmeasure,changesasinterestrateschange

orsimplyastime passes Therefore,the portfolio managermustoccasionallyadjustthe

portfolio’s dollar duration Therearetwoprimarysteps:

Step1: Calculate thenewdollar duration of the portfolio

Step2: Calculate the rebalancingratiowhichistheratioof the desired (targetor

original)DDtothenewDDof the portfolio.Subtracting1from thisratio

gives thepercentchangetomakeinthe holding of eachassetinthe portfolioto

restorethe desiredDD

Study Session 10

Cross-Reference to CFA Institute Assigned Reading #21—Fixed-Income Portfolio Management—Part I

I Example: Reestablishingtheportfoliodollar duration

Aportfoliowithadollar durationof$162,658 consistsoffour bondswith the

indicated weights,durations,and dollar durations:

Market Value x Duration x0.01= DollarDuration

$1,000,000 1,350,000

965,000883.000

2.6Portfolio

One yearlater,the yieldcurvehasshifted upwardwiththe followingresults:

Market Value x Duration x 0.01= DollarDuration

To readjust backtothe original dollar durationaswellasmaintainthecurrent

proportionsof each bondin theportfolio,wesubtract1.0from the rebalancingratio

to arrive atthe necessaryincreasein the value of each bond in theportfolioand, thus,

the totalincreasein theportfolio value(i.e.,required additionalcash):

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21 - Fixed-Income Portfolio Management—Part I

Toreturntheportfoliobacktoitsoriginaldollarduration,the manager could add

cashandpurchasethebondsin theamountsindicated Alternatively,the manager

could selectoneof the bondsto use as acontrollingposition Becausethe dollar

duration has fallen dramatically and Bond1has the longestduration,themanager

coulduseless additionalcash by increasing onlytheholdingin Bond1 (i.e.,using

Bond1 asthecontrollingposition):

Thus,insteadofinvesting$1,802,580inall thebonds,themanagercouldpurchase

another$1,354,007 (= $2,312,507-$958,500)of Bond1andreturnthe portfolio

dollar duration backtoitsoriginal level

Market Value x Duration x 0.01= DollarDuration

LOS21.i:Explain theimportanceof spread duration

CFA®ProgramCurriculum,Volume4,page 153

Durationmeasures thesensitivityofabondto a one-timeparallelshift in theyield

curve.Spread durationmeasures the sensitivity ofnon-Treasuryissuesto achangein

their spread aboveTreasuries ofthesamematurity

Although yield spread and spread durationcanbe defined and measuredfor individual

bonds,theyaretypically used forentireclassificationsofbonds,where classificationisby

ratingand/orsector.Calculatingthespreaddurationfora sectorallowsthe managerto

bothforecast thefuture performanceof thesectorandselect superiorbondsto represent

eachsectorinthe portfolio

Forexample, themanagermight forecastawideningofthe spreadforone sectorof

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

Therearethree spread durationmeasuresusedfor fixed-rate bonds:

1. Nominalspreadisthespread between the nominal yieldonanon-TreasurybondandaTreasury of thesame maturity.When spread durationisbasedonthe nominalspread,itrepresentsthe approximatepercentageprice change fora100basis pointchangeinthe nominal spread

2 Zero-volatility spread(orstaticspread)isthe spread thatmustbe addedtotheTreasuryspot ratecurvetoforce equality between thepresentvalueofabond’s cashflows(discountedattheTreasuryspot ratesplus thestaticspread) and the marketprice of the bondplus accruedinterest.Computingspread duration using thezero-volatility spreadmeasuresthepercentagechangeinprice givena one-time,100

basis point changeinthe zero-volatility spread

3 Option-adjusted spread(OAS) isdetermined usingabinomialinterestrate tree.

Sufficeittosaythat when spread durationisbasedonOAS, it isthe approximate

percentagechangeinprice fora100basis point changeintheOAS

Spread durationmaybe computed usinganyof these methods Asaresult,observeddiscrepanciesamongreported values for spread durationmaybearesultof the differentmethods used

Aportfolios spread durationisthe market value-weightedaverageof the individual

sectorspread durations

Example: Spread durationCompute thespread duration for the following portfolio

Interpretation:If the OAS of eachsectorincreasesby100basis points withnochange

inTreasury yields, the value of the portfolio will decrease by approximately3.13%

Aportfolio’sduration,whichisaweighted average of the individual bonddurations,

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21- Fixed-IncomePortfolio Management—Part I

theyieldcurve,whichcausestheyieldsonall bondstoincreaseordecrease thesame

amount.Spread durationmeasuresthepercentagechangeinthe total value of the

portfolio givenaparallel100bps changeinthe spreadoverTreasuries

Intheformer(duration),theparallel shiftintheyieldcurvecould be caused byachange

ininflation expectations, whichcausestheyieldsonallbonds,includingTreasuries, to

increase/decrease thesame amount.In the latter(spreadduration),the shiftisinthe

spread only, indicatinganoverallincreaseinriskaversion (riskpremium) for all bonds

in agiven class

By weighting classes(sectors)differentlyinthe bond portfolio, the managerexposesthe

portfoliotospread risk(i.e.,the risk that the spread foragiven class willchange) Of

course,theactive managertypically weights thesectorsinaportfolio differently from

the benchmarkinaneffortto capturefavorable changesinspreads

EXTENSIONSTOCLASSICAL IMMUNIZATION

LOS 21.j:Discusstheextensionsthat have been madetoclassical

immunizationtheory, includingthe introductionof contingentimmunization

CFA®ProgramCurriculum,Volume4,page155Thusfar,wehave lookedatclassicalimmunizationasif therewerefewuncertainties.For

instance, weassumedanychangesinthe yieldcurve wereparallel andinstantaneousso

thatwecouldimmunize ourportfolio using duration strategies

Whenthe goalistoimmunizeagainstaliability,however,we mustalsoconsider

changesinthe valueof the liability, whichinturncould change theamountofassets

neededfor theimmunization.Wemustalso consider theabilitytocombine indexing

(immunization)strategies withactiveportfoliomanagementstrategies.Notethatsince

activemanagementexposestheportfoliotoadditionalrisks, immunizationstrategiesare

also risk-minimizing strategies

The bottom lineisthat classicalimmunizationstrategiesmaynotbe sufficientin

managingaportfoliotoimmunizeagainstaliability To address the deficienciesin

classicalimmunization,fourextensionshave been offered:(1)multifunctionalduration,

(2)multiple-liabilityimmunization, (3)relaxationoftheminimumrisk requirement, and

(4)contingentimmunization

The first modificationor extensiontoclassicalimmunizationtheoryistheuseof

multifiinctional duration(a.k.a.keyrateduration).To incorporate multifunctional

durationintoourimmunizationstrategy,themanagerfocusesoncertainkeyinterest

ratematurities.Forexample, the manager’s portfolio mightcontainmortgage-backed

securities,whichareexposed to prepaymentrisk Unlike other fixed-incomesecurities

thatincrease invalue wheninterestratesfall,MBSactlike callablecorporatebonds that

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

The secondextension ismultiple-liabilityimmunization.The goal of multiple-liability

immunization isensuringthat the portfoliocontainssufficient liquidassets to meetallthe liabilitiesastheycomedue Thatis,rather thanmonitorthe valueof the portfolio

asif the liabilityis its minimumtargetvalueat asingle horizondate,therecanbe

numerouscertainor evenuncertainliabilities with accompanyingnumeroushorizondates

The thirdextension isallowing for increasedrisk,orotherwise relaxing theminimum

risk requirement of classicalimmunization.Aswill be demonstrated whenwediscusscontingentimmunization, aslongasthe manager doesnotjeopardize meeting theliabilitystructure,hecanpursue increased risk strategies that could leadto excess

portfolio value(i.e., aterminal portfolio valuegreaterthan the liability)

The fourthextension iscontingentimmunization,whichmixes activeand passive

(i.e., immunization)strategies

ContingentImmunizationContingentimmunization isthe combinationofactivemanagementwith passive

immunizationtechniques Likeimmunization,theremustbeadefined liabilityor

liabilitiesfor knownamountsonknown dates allowinga presentvalueof liabilitiestobecomputed Unlikeimmunization,the beginning value of the portfoliomustexceed the

PV of theliabilities The differenceiscalledan economicsurplusorsurplus Theinitialsurplusisrelatedtoandcanonlyexistif theinvestorwillaccept afloorreturnless thanthe availableimmunizationrate.Theimmunizationrateavailableinthe marketminus

theinvestor’s minimumfloorreturniscalled the cushion spread

The basicstepsincontingentimmunization consistof determining thePVof theliability and comparing thistothePVof theassets(theirmarketvalue)todeterminethe valueof the surplus Astimeand/or market conditions change, the PV ofassetsandliabilities will changeaswell The surplusmustbe continually recomputed As longas

the surplusispositive theportfoliocanbe actively managed

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21 - Fixed-Income Portfolio Management—Part I

Example: Contingentimmunization

Aninvestordecidestopursueacontingentimmunizationstrategy over a3-yeartime

horizon Theinvestorhas$20,000,000 to invest,theavailable3 year immunization

rateis 4%,and theinvestorwillaccept aminimumsafetynet returnof3.2%

Determinethe:(a)cushion spread,(b)required terminal value[futurevalueof liability

(FVL)], (c) presentvalueof liabilities(PVL),and(d)initialsurplusamount.

• (a)The cushion spreadis4%-3.2%=0.8%,whichmeanstheremustbean

initialpositive surplus

• (b)Therequiredterminalvalue(FVL) isusuallygiven In thiscase it is notand

mustbecomputedfrom the initialinvestedamount[the PVofassets (PVA)]and

minimumacceptablereturn: $20,000,000[1+(,032/2)]3x2=$21,998,458

• (c)ThePVL is the FVLdiscountedattheavailableimmunizationrate:

$21,998,458/ [1+ (,04/2)]3x2=$19,534,001

• (d)ThesurplusisPVA- PVL,initiallythis is:

$20,000,000-19,534,001=$465,999

Assume theinvestorhad initially expectedafall ininterest ratesand had purchased

$20,000,000parof4.5%, 10-yearbonds.Nowassume oneyearhas passed and

thebondnowtradesat a3.9%YTMand the 2-year immunizationrateis3.4%

Determinethe:(e)requiredterminalvalue, (f)presentvalueof liabilities(PVL),and

(g)PVofassets (PVA).

• (e) Requiredterminalvalue only changes ifa newtargetvalueis set bythe client

andmanager;it isstill$21,998,458andis nowduein2years

• (f)ThenewPVL isbasedonthe terminalvalue,remaining2-year time horizon,

andnewavailableimmunizationrate.ThePVL isnow:

$21,998,458/ [1+ (0.034/2)]2x2=$20,564,039

• (g)Theoriginal purchase of$20,000,000parof4.5%, 10-year bonds hada4.5%

YTM andis now a9-yearbond yielding3.9% Itsnewmarketvalueis:

PMT=$20,000,000 x (0.045/2)=$450,000,N=9x 2=18

I/Y=3.9/2=1.95%, FV=$20,000,000:

CPT—> PV =$20,903,489

Assuming themanageralso collected$900,000of couponsandreinvestmentearnings

of$2,500,(h)computethenewsurplusamount, (i)determine if themanagercan

continuetoactivelymanage theportfolio,and(j)stateandexplainwhat willhappen

tothesurplus ifratesimmediatelyrise (no calculations).

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

• (h)The surplusisthenew PVA-PVL.The PVAisthe ending market value pluscoupons collected andreinvestmentearnings:

$20,903,489+900,000 + 2,500- 20,564,039=$1,241,950

• (i)Withapositivesurplus the managercan continuetoactively manage

• (j) The results of the previousyeardemonstrate that theassetduration exceeds theliability duration The higherassetduration would be thereason theassets rosein

valuemorethanthe liabilities whenratesfell and createdalarger surplus Ifratesimmediatelyrisethen theassetvalue will drop bymorethan theliability value andsurplus will decline

Forthe Exam: Acontingentimmunizationstrategyisacomplextimevalueofmoney

strategy.The datacanbe presentedinavarietyofwayssoexaminethe informationcarefullytodetermine howtosolve the question Determining the surplusorwhathas happenedtosurplusisgenerally important Surplusisa conceptthat pervadesany

form ofassetliabilitymanagementand contingentimmunization isaform ofALM

Tocomputesurplus be preparedtocalculate the PVA andPVLifnotgiven directly.A

couple of hints:

• Assumesemiannual compoundingasinthe example unless directed otherwise

• Ifassetduration andconvexitymatch thoseof the liability the surplus will berelatively stable (essentially thismeansthe portfoliois immunized).If durationand convexity ofassetsand liability donotmatch,the surplus will changeasmarket conditions change andtimepasses

• If the initial surplus and cushion spreadarelarge,alarger adversemovementin

market conditionscan occurbefore the surplusisexhausted

• Before the surplus becomes negative, the portfoliomustbe immunized and

activemanagementisnolonger allowed If the surplus becomes negative,it isno

longer possibletoimmunizeand reach thetargetvalue because thecurrentvalue

ofassetsisnotlarge enoughtoreach the terminal valueatthe prevailing market

immunizationrates.

IMMUNIZATIONRISKS

LOS 21.k:Explainthe risks associated with managingaportfolioagainsta

liabilitystructureincludinginterest raterisk,contingent claimrisk,and caprisk

CFA®Program Curriculum,Volume4,page 160Three risks that the portfoliomanagermustbeawareof relatetomarketinterestratesand thestructureof the bondsintheportfolio Theyare(1)interestraterisk,

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21- Fixed-IncomePortfolio Management—Part I

Interestrateriskisthe primaryconcernwhen managingafixed-income portfolio,

whether againstaliabilitystructure or abenchmark Because the values ofmost

fixed-income securities moveoppositetochangesin interestrates,changinginterestrates

areacontinualsourceof risk As alreadymentioned,tohelp avoidinterestraterisk,

themanagerwill match the duration andconvexityof the liability and the portfolio

Convexitycanbe difficulttomeasureforsomefixed-incomesecurities,especially those

with negative convexity Thisistheconcernwhenfixed-incomesecurities aresubjectto

earlyretirement(e.g., mortgage-backedsecurities,callablecorporatebonds)

Contingent claim risk(a.k.a.call riskorprepaymentrisk).Callable bondsaretypically

called only afterinterestrateshave fallen Thismeansthat themanagernotonly loses

the higherstreamofcouponsthatwereoriginally incorporatedintotheimmunization

strategy,sheisfaced with reinvesting the principalat areducedrateofreturn.Thus,

contingent claim risk hassignificant potentialtoaffect theimmunizationstrategy

throughitseffectonthe valueof the portfolio To adjust for this potential, rather than

simply comparing the portfolio durationtothat of the liability, themanagermust

consider the convexity of the bonds

Cap risk Ifanyof the bondsinthe portfolio havefloatingrates,theymaybesubject

tocaprisk If thecoupon onthe floatingratebond doesnotfullyadjustupward for

risinginterestrates,the market valueof the bond will adjust downward Theassetsand

liabilities willnotadjustin syncand the surplus will deteriorate

IMMUNIZINGSINGLE LIABILITIES,MULTIPLELIABILITIES,ANDGENERAL

CASHFLOWS

LOS21.1: Compareimmunizationstrategies forasingleliability,multiple

liabilities,andgeneralcash flows

CFA®ProgramCurriculum,Volume4,page160

Ifamanagercouldinvest inazero-coupon Treasury withamaturityequaltothe liability

horizon,he has constructedanimmunizationstrategywithnorisk Because thisisrarely

thecase,however,the managermusttakesteps tominimizerisk

Onestrategyisminimizingreinvestmentrisk(i.e.,the risk associated with reinvesting

portfolio cashflows).Toreduce the risk associated withuncertain reinvestmentrates,

the manager shouldminimizethe distributionof thematuritiesof the bondsinthe

portfolio around the (single) liability date If themanagercanhold bulletsecuritieswith

maturities veryclosetothe liabilitydate, reinvestmentriskislow

Concentrating thematuritiesof the bonds around the liability dateisknownas abullet

strategy.Thinkofa strategyemployingtwobonds One bondmaturesoneyearbefore

the liability date and the othermaturesoneyearafter the liability date When the first

matures,the proceedsmustbe reinvestedfor onlyoneyear Atthe dateof the liability,

the maturity of the other off only the the first

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

Nowconsiderabarbellstrategywhere the first bondmaturesseveralyearsbefore theliability date and the other severalyearsafter the liability date The face value of the firstmustbe reinvested whenitmatures, sothe managermustbe concerned with both the

reinvestmentrateand, sincethenewbond will have severalyearsuntilmaturity,all theother riskfactors associated with suchabond The secondbond, since itmaturesseveral

yearsafter the liabilitydate, issubjecttosignificantinterestraterisk

Obviously,asthematuritiesof the bulletstrategy moveawayfrom the liability date andthematuritiesof the barbellmovetoward the liabilitydate,the distinction betweenthetwowill begintoblur Rather than base thestrategyonsubjective judgment, themanagercan minimizeM-Square (M2)(a.k.a maturityvariance).

Maturity variance isthevarianceof the differencesinthematuritiesof the bonds used

in theimmunizationstrategyand thematuritydateof the liability.Forexample, if allthe bonds have thesamematurity dateasthe liability,M2is zero Asthe dispersion ofthematuritydatesincreases,M2increases

MultipleLiabilitiesThe keytoimmunizingmultiple liabilitiesistodecompose the portfoliopayment

streamsinsuchawaythat thecomponent streamsseparatelyimmunizeeachof themultiple liabilities Multiple-liabilityimmunization ispossible if thefollowingthreeconditionsaresatisfied {assumingparallelrateshifts):

1. Assetsand liabilities have thesamepresentvalues

2 Assetsand liabilities have thesameaggregatedurations

3 The range of the distribution of durations of individualassetsinthe portfolio exceedsthe distribution of liabilities Thisisanecessaryconditioninordertobe abletouse

cash flows generated fromourassets(whichwill include principalpaymentsfrommaturingbonds) tosufficientlymeeteachofourcash outflow needs

Apoint of clarification for the second conditionis inorder.Evenifaliabilitystructureincludes individual liabilities that exceed 30years induration (e.g.,apensionfund),

amultiple-liabilityimmunizationstrategycanstill be used effectively The conditionrequires that the weighted average durations of the liabilities andassetsareequal.Because

of the additivepropertyofduration,thisstrategywill workaslongasthe weight of theshort-duration liabilitiesissufficienttobringthe average below 30years

Itisimportantto notethat satisfying these three conditions willassureimmunization

only against parallelrateshifts In thecaseof nonparallelratechanges,linearprogramming modelscanbe usedto constructminimum-risk immunized portfolios formultiple liabilities The procedureistominimizea measureofimmunizationriskformultiple liabilities and nonparallelratechanges Theminimizationprocedureissubject

totheconstraintsimposed by the conditions required forimmunizationunder theassumption ofaparallel shift along withanyother relevantinvestment constraints

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21- Fixed-IncomePortfolio Management—Part IGeneral Cash Flows

General cashflowsinthiscasereferstousing cashas partofan immunizationstrategy

eventhough the cash hasnot yetbeen received.Forexample, expectingacash flow

in six months,the portfoliomanagerdoesnot puttheentireamountrequired for

immunization intothe portfolio today Instead he looksatthe expected cash flowas a

zeroand incorporatesitspayoff and durationintotheimmunizationstrategy.

Let’sassumethe managerexpects toreceiveacash flowin sixmonths Treating this like

a zero,the durationis0.5 Toconstructthe portfoliotoimmunizealiability duein1.5

yearswithaduration of1.0,themanagercould combine the cashtobe received withan

appropriateamountof bonds with durationsgreaterthan1.0, sothat the conditions for

immunizationare met,includingaweighted average portfolio duration of1.0

RISK MINIMIZATIONVS.RETURNMAXIMIZATION

LOS21.m:Compare riskminimizationwithreturnmaximization in

immunizedportfolios.

CFA®ProgramCurriculum,Volume4,page 165Onestandard conditionfor classicalimmunization isriskminimization.Aswehave

discussedinseveralsectionsof this topicreview,the portfoliomanagerhasmanytools

tominimize exposuretorisks faced when immunizingaportfolioto meet aliability.We

haveneglectedtomentionthe relationship of riskminimizationtothe levelof portfolio

expectedreturn.

Return maximization istheconceptbehind contingentimmunization.Consider the

managerwho has the abilitytolockinanimmunizedrateofreturnequalto or greater

than the required safetynet return.Aslongasthatmanagerfeels hecan generate even

greater returns,he shouldpursue activemanagementinhopes of generatingexcessvalue

CASH FLOW MATCHING

LOS21.n:Demonstratetheuseof cash flowmatchingtofund afixedsetof

future liabilities and compare theadvantagesanddisadvantagesof cash flow

matchingtothoseofimmunizationstrategies

CFA®ProgramCurriculum,Volume4,page 166

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

Cash flow matchingisusedto construct aportfolio that will funda streamof liabilitieswith portfoliocouponsand maturity values Cash flow matching will alsocausethedurationstobematched,butit is morestringent thanimmunizationbymatchingduration The timing andamountsofassetcash flowsmustalso correspondtotheliabilities.Becauseofthis,the durations willstaymatchedastime passesand rebalancingshouldnotbe needed Toconstructthe portfolio, themanager:

• Selectsabond withamaturitydate equaltothat of the lastliabilitypaymentdate

• Buysenoughin parvalue of this bond such thatitsprincipal and finalcouponfullyfund the last liability

• Usingarecursiveprocedure(i.e.,workingbackwards),chooses another bondsothat

its maturityvalue and last coupon plus the coupononthe longer bond fully fundthe second-to-last liabilitypaymentandcontinuesuntil all liabilitypaymentshavebeen addressed

Professor’sNote: An easy wayto constructacashflowmatchistopurchaseonlyzero-couponbonds Simply buyfaceamountsequaltoeach liabilityonthe needed

payoutdates.However,thisis more restrictiveinthe bonds thatcanbe usedand,hence,could bemoreexpensivethanusingcouponbonds.Knowthatzeros istheeasyway and bepreparedforthe toughercouponbond calculationsifaskedonthe

exam

Whileapurecash flow matchisthesafestwaytofund theliabilities,someclients andtheir managers allowaslightdeviationinmatchingthe dates.Abondmightbe usedthat providesacash flow slightly beforeit isneeded andamodestreinvestmentrate

might be factoredin.Alternatively,abond withacash flow just after whatisneededcould be selectedonthe assumptionitcould be usedascollateral and the funds bor¬

rowedforabrief periodtomakethe distribution

The followingarethe differences between cash flow matching and multiple-liability

immunization:

• Cash flow matching depends upon all the cash flows of the portfolio,soexpectationsregarding short-termreinvestmentrates orborrowingrates arecritical.Forthisreason,managersmust useconservativeassumptions.Deviationsfroma truecashflow match should be modest and be associated withasignificantexpectedcostsaving This tendstoincreasethe overallcost topurchase the cash flow matchedportfolio.Immunizationby matching durationislessrestrictiveandmaycostless

• Owingtotheexactmatching problem, onlyassetflowsfromacash-flow-matchedportfolio thatoccur priortothe liabilitymaybe usedto meetthe obligation.An

immunized portfolioisonly requiredtohave sufficient valueonthe dateof eachliability because fundingisachieved through portfolio rebalancing.(Hint:the

statementabout cash flows occurringjustpriortothepayoutdate and the earlierdiscussion aboutallowingcashflowstooccurafter thepayoutdatearebothintheCFAtext Yes,they contradict each other The focus hereisthat the control of cashflowsismuchmorerestrictivefor cash flow matching than forimmunization.)

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21- Fixed-IncomePortfolio Management—Part I

Professor’sNote: Youshould conclude cashflowmatchingismore restrictive,

simplertounderstand,andsafer(though bothare verysafewhen done correctly)but generally makes the purchasepriceoftherequiredportfolio higher

Youshould also have gathered that the divisionpointbetweenone strategyandanothercan sometimesbeblurry

These approachescanalso be combined and blended together

Combination matching, also knownashorizon matching,isacombinationof

multiple-liabilityimmunizationand cash flow matching thatcanbe usedtoaddress theassetcash

flow/liability matching problem Thisstrategy creates aportfolio thatisduration

matched During the first fewyears,the portfolio would also be cash flow matchedin

ordertomakesurethatassetswereproperly dispersedto meetthenear-termobligations

Combination matching offers thefollowing advantagesovermultiple-liability

immunization:

• Provides liquidityinthe initial period

• Reduces the risk associated with nonparallel shiftsinthe yieldcurve.The initial

cash needsaremetwithassetcash flows Thereisnorebalancing neededto meetthe

initial cash requirements

The primary disadvantage of combination matchingisthatittendstobemoreexpensive

than multiple-liabilityimmunization

Study Session 10

Cross-Reference to CFA InstituteAssigned Reading#21—Fixed-Income Portfolio Management -Part I

LOS 21.a

Portfoliosthatarebeing usedtofund measurableliabilitiestypicallyusethe liabilities

astheportfoliobenchmark Thelowriskstrategyistomatch theassetcharacteristicsto

thoseof the liabilities Themostimportantmatchisduration

Portfolios without definableliabilitiesoftenuse abond indexas abenchmark andtheir

performanceisevaluatedversusthat benchmark The low riskstrategyistomatch the

characteristicsofthebenchmark

LOS21.b

Strategy

Pure bondindexing(PBI):

managerreplicatesthe index

•Tracks the index (zero or very lowtrackingerror)

•Same risk factor exposures

as theindex

•Lowadvisoryand administrative fees

•Less costly toimplement

•Increasedexpectedreturn

•Maintains exposure to the index’s primary risk factors

•Costly anddifficultto

•Increased management fees

•Lowered ability to track the index (i.e.,increasedtrackingerror)

•Lowerexpectedreturn than the index

•Increased risk

•Increasedtrackingerror

•Increasedmanagement fees

Enhancedindexingby small risk factor mismatches: earns

the same return as the index;

tilt theportfolio towards

smaller risk factors by pursuingreturn-enhancing

opportunities

•Same duration as index

•Increasedexpectedreturn

•Reduced manager

restrictions

Active management bylarger

risk factor mismatches:

pursue moresignificantqualityand value strategies

•Increasedexpectedreturn

•Reducedmanager

restrictions

•Ability to tune the portfolio duration

•Increased expectedreturn

•Fewifany manager

restrictions

•No limits on duration

•Increased risk

•Increased trackingerror

•Increased management fees

Full-blownactive management:actively

pursuestilting,relative value,

and duration strategies

•Increasedrisk

•Increasedtrackingerror

•Increased management fees

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21- Fixed-IncomePortfolio Management—Part I

abilities justifyit

• Market value riskvariesdirectly with maturity Thegreaterthe riskaversion,the

lower the acceptable marketrisk,and theshorter the benchmark maturity

• Incomeriskvariesindirectly withmaturityThemoredependent the clientisupona

reliableincomestream,the longer thematurityof the benchmark

• Credit risk The credit risk of the benchmark should closely match the credit risk of

theportfolio

• Liabilityframeworkriskisapplicable onlytoportfolios managed accordingto a

liabilitystructureand shouldalways be minimized

LOS21.d

If the indexisnotinvestable, it isnot avalid benchmark

1.Bondsecuritiesareheterogeneous and illiquid.Issueshave unique differencesin

maturity, seniority,and otherfeatures;plusmany issuesdonottrade regularly and

pricing dataisfrequently basedonappraisals and tradesareoftennotpublically

reported

2.Indexescanappearsimilar but be quite differentinrisks

3 Risk characteristicscanchange quicklyover timeasnew issuesof bonds and those

approaching maturity leadtosignificant annual additions and deletions for the bondsin

anindex

4 The “bums” problemaslargeissuancebyanissuerleadsto greaterindex weight but

largeissuance isalsorelatedtoexcessiveleverageand subsequent credit problems

5.Difficulty forinvestors infindinganindex that matches their risk profile

LOS21.e

Duration.Effective duration(a.k.a.option-adjustedoradjustedduration),whichisused

toestimatethe changeinthevalueofaportfolio givenasmall parallel shiftinthe yield

curve,isprobably themostobvious riskfactortobe measured.Duetothe linearnature

ofduration,whichcausesittounderestimate theincreaseandoverestimatethe decrease

inthe value of the portfolio, the convexity effectisalso considered

Keyratedurationmeasuresthe portfoliossensitivitytotwists inthe yieldcurveby

indicating the portfolio’s sensitivitytocertain interestrates.Duetothe nearly endless

combinationsofassetsthat will have thesamedurationastheindex,the managermust

take thetimetoensurethat the portfolio also matches the index’s exposuretoimportant

keyrates.Mismatchescan occurwhen the portfolio and benchmarkcontaindifferent

combinationsof bonds with varyingmaturitiesand keyratedurations but thesame

overall effective duration

LOS 21.f

StudySession 10

Cross-Reference to CFA InstituteAssigned Reading#21-Fixed-Income Portfolio Management—Part I

Estimatingexpected totalreturnunderasinglesetof assumptions (predictions) onlyprovidesapointestimateof theinvestmentsexpectedreturn (i.e., asinglenumber)

Combiningtotalreturnanalysis withscenarioanalysis allows the analystto assess notonly thereturnbut alsoitsvolatility(distribution)under differentscenarios

LOS 21.g

To effectivelyimmunizeasingle liability:

1 Selectabond(orbond portfolio) withanelfective duration equaltothe durationoftheliability

2 Setthepresentvalue of the bond(orbondportfolio) equaltothepresentvalue ofthe liability

Without rebalancing, classicalimmunizationonly works foraone-time instantaneous

changein interestrates.Immunizationriskcanbe thought ofas ameasureof the relativeextent towhich the terminal value ofanimmunized portfolio falls short ofitstarget

valueas aresultof arbitrary (nonparallel) changesin interestrates.Ingeneral, theportfolio that has the lowestreinvestmentriskisthe portfolio that will do the best job of

immunization:

• Animmunized portfolio consisting entirely ofzero-couponbonds thatmature

attheinvestmenthorizonwill havezeroimmunizationrisk because thereiszeroreinvestmentrisk

• If cash flowsareconcentrated around the horizon(as inabullet), reinvestmentriskandimmunizationrisk will be low

• If thereisahigh dispersion of cash flows about the horizon date(asinabarbellstrategy),reinvestmentrisk andimmunizationrisk will be high

A managermustoccasionally adjust the portfolio’s dollar duration duetointerestrate

changesorthe passing oftime.Thetwo stepsinadjustingdollar durationare

(1)calculate thenewdollar duration and(2)calculate the rebalancingratioanduseittodetermine the requiredpercentagechangeinthe valueof the portfolio

rebalancingratio=targetDD / newDD

1 Nominal spreadisthe spread between the nominal yieldonanon-TreasurybondandaTreasury of thesame maturity