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

Topic 1 8Cross Reference to GARP AssignedReading—Mali, Chapter6 AIM18.6:Calculateexpectedloss from recovery rates*the loss given default*andtheprobability of default.. Topic 1 8 Cross Re

KAPLAN SCHWESER

FRM PART II BOOK 2:

MANAGEMENT

CREDIT RISK MEASUREMENTAND MANAGEMENT

IS:CreditandCounterpartyRisk

19:Default Risk:QuantitativeMethodologies

20:Credit Risks andCredit Derivatives

21:CreditDerivativesand Credit-Linked Notes

22:The StructuringProcess

23: Cash Collateralized DebtObligations

24:Spread Risk and Default Intensity Models

25:PortfolioCreditRisk

26:Structured Credit Risk

27:Securitization

28:Understanding theSecuritizationof SubprimeMortgageCredit

29: DefiningCounterparty Credit Risk

30:MitigatingCounterparty Credit Risk

31 :QuantifyingCounterpartyCredit Exposure, I

32:QuantifyingCounterpartyCreditExposure, II:TheImpactofCollateral 224

33:Pricing Counterpart}'CreditRisk, I

PAST FRM EXAM QUESTIONS

7082

91 104 120

136157167

FRM TARTnBOOK 2: CREDTT RISK MEASUREMENT AND MANAGEMENT

©2013 Kaplan, hie., d.b.a Kaplan Schweser All rights reserved.

Printed in die United States nf America.

ISBN: 978-1-4277ÿ467-8 1 1-4277-44A7-X PPN: 3200-3240

Required Disclaimer: GARP® does not endorse, promote, review, or warrant die accuracy of the products or services offered by Kaplan Schweser of FRM information, nor does it endorse any pass rates claimed

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Disclaimer: The SchweserNotes should lie used in conjunction with the original readings as set forth by GARP® The information contained in these books is based on die original readings and is believed to be accurate However, dieir accuracy cannot be guaranteed nor is any warranty conveyed as to your ultimate exam success.

©2013 Kaplan,Inc.

Page2

READING ASSIGNMENTS AND

Thefollowingmaterialis a reviewofthe Credit Risk Measurement andManagementprinciples

designedtoaddress theAIMstatements setforthby the GlobalAssociationofRiskProfessionals.

READING ASSIGNMENTS

Allan MaLz FinancialRiskManagement:Models,History;andInstitutions. Hoboken,NJ:

JohnWiley& Sons,2011

IS.“Creditand Counterparty Risk,”Chapter6

Arnaud tieServignyandOliyier Renault Measuring andManagingCreditRisk

NewYork;McGraw-Hill,2004

19."‘Default Risk:Quantitative Mediodnlogies,” Chapter 3

ReneStulz RiskManagement&Derivatives Florence,KY:ThomsonSouth-Western,

2002.

(page11)

(page32)

20.“CreditRisks andCreditDerivatives,”Chapter IS

ChristopherCulp.StructuredFinanceandInsurance:TheArtofManagingCapitaland

Risk Hoboken,NJ: JohnWiley& Sons, 2006.

21.“CreditDerivativesand Credit-LinkedNotes,*Chapter12

22.“The StructuringProcess,”Chapter 13

23 “Cash Collateralized Debt Obligations,” Chapter 17

Allan Malz FinancialRiskManagement:Models,History, andInstitutions. Hoboken,NJ:

JohnWiley &Sons,2011

24 “Spread Risk and DefaultIntensity Models,”Chapter7

25.“Portfolio Credit Risk,” Chapter8

26.“StructuredCreditRisk,”Chapter9

Christopher Culp.StructuredFinanceand Insurance: TheArtofManagingCapitaland

Risk.Hoboken,NJ: JohnWiley& Sons,2006

(page136)

(page157)

Book 2

ReadingAssignments and AIM Statements

28.Adam Ashcroft andTilSchuermann.“UnderstandingtheSecuritizationof

SubprimeMortgageCredit.” FederalReserveBankofNew YorkStaffReports,

No.3M(March2008).

Jon Gregory CounterpartyCredit Risk: TheNewChallengeforGlobalFinancialMarkets

WestSusses, UK;JohnWiley& Sons, 2010.

29- “DefiningCounterpartyCredit Risk/Chapter2

30 “MitigatingCounterpartyCreditRisk,”Chapter3

31 “QuantifyingCounterpartyCreditExposure,I,’Chapter4

32 “QuantifyingCounterpartyCreditExposure, II:The Impact ofCollateral,”

Boole 2

ReadingAssignments and AIM Statements

1a. Credit andCounterpartyRisk

Candidates,aftercompletingthisreading,should he ableto:

1 Descrihe securities with different typesofcreditrisks,suchas corporatedebt,

sovereigndebt, credit derivatives,and structuredproducts, (page1 1)

2. Differentiate between bookandmarketvaluesfora firm's capitalstructure,

5 Define thefollowingtermsrelated todefault andrecovery:defaultevents,

probabilityof default, credit exposure, and lossgivendefault,(page14)

6 Calculate expected loss from recoveryrates, die lossgiven default,andthe

probabilityofdefault, (page16)

7 Differentiate hetween a creditriskeventandamarket riskeventfor marketable

securities, (page 17}

8 Summarizecreditassessment techniquessuchas credit ratingsand rating

migrations, internal ratings,andriskmodels, (page17)

9 Definecounterparty risk,describeitsdifferentaspectsand explain howit is

mitigated, (page18)

10. Describe bowcounterpartyriskisdifferentfrom creditrisk* (page18)

11. Describe the Merton Model, and useit tocalculate the valueofafirm, the valuesof

afirm’s debt andequity,and default probabilities,(page21)

12. Explain the drawbacks andassesspossibleimprovements to the Merton Model, and

identifyproprietarymodelsof rating agencies thatattempt toaddress theseissues.

(page24)

13. Describecreditfactor models and evaluateanexampleofasingle-factor model

(page24)

14 DefineCreditVaR (Value-at-Risk) (page 25)

19. DefaultRisk:Quantitative Methodologies

Candidates,after completing thisreading,should be ableto:

1. Describe the Merton modelforcorporatesecuritypricing, includingits

assumptions,strengths andweaknesses:

• Illustrate andinterpretsecurity-holder payoffsbased ontheMerton model

* Using theMerton model,calculate the valueofafirm'sdebt andequity and the

volatility of firmvalue

* Describethe results and practical implications of empiricalstudies thatusethe

Mertonmodel tovaluedebt,

(page32)

2. Describe the Moody’sKMVCreditMonitorModel to estimate probabilityof

default usingequity prices,andcompare theMoodysKMV equity model with die

Merton model,(page 34)

3 Describecreditscoringmodels and the requisitequalifiesof accuracy, parsimony,

non-triviality, feasibility, transparencyand inrerpretability, (page37)

Bank 2

ReadingAssignments and AIM Statements

4 Defineanddifferentiateamongdie followingquantitativemethodologies for creditanalysis and scoring:

* Lineardiscriminantanalysis

* Parametricdiscrimination

* Knearest neighborapproach

* Supportvectormachines(page37)

3 Defineand differentiatethefollowingdecision rules:minimum error, minimum

risk, Neyman-PfearsonandMinimal (page3£)

6. Identifythe problemsand tradeoffsbetweenclassification and prediction modelsof

performance, (page39)

7 Describeimportantfactorsin the choiceofaparticular class ofmodel, (page39)

20.CreditRisks and Credit Derivatives

Candidates,aftercompletingtills reading,shouldheableto:

1. Explain the relationship of credit spreads,time to maturity, andinterest rates.

(page50)

2. Explain die differences between valuingsenior and subordinated debt usinga

contingent claim approach, (page52)

3 Explain, fromacontingent claim perspective, the impact stochasticinterest rates

haveondie valuationof riskybonds, equity,and die riskofdefault, (page 52)

4 Assess thecredit risksofderivatives, (page61)

5 Describe die fundamental differences between CreditRisk+,CreditMetricsandKMVcredit portfolio models, (page56)

6. Define and describeacreditderivative, credit defaultswap,and totalreturnswap

(page61)

7 Defineavulnerable option, and explain how credit risk can be incorporatedin

determining theoption’svalue,(page63)

8. Explain how to accountforcreditriskexposureinvaluingaswap, (pagje 64)

21.CreditDerivativesand Credit-LinkedNotesCandidates,aftercompletingthisreading,should he ableto:

1. Describe the mechanicsofasinglenamedcredit defaultswap (CDS),and describeparticular aspectsofCDSssuchassettlement methods, payments to the protectionseller,reference name,ownership, recoveryrights, trigger events,accruedinterest andliquidity, (pagie70)

2. Describeportfoliocredit default swaps,includingbasketCDS,Ndi toDefault

CDS, SeniorandSubordinatedBasketCDS (page72)

3 Describe the composition and useofiTraxx CDS indices, (page 74)

4 Explain the mechanicsofassetdefaultswaps, equitydefaultswaps, totalreturn

swapsand creditlinkednotes,(page75)

22.TheStructuring ProcessCandidates,aftercompletingdiisreading,shouldhe ableto:

1. Describe theobjectivesofstructuredfinance and explain the motivations forasset

securitization, (page 82)

2. Describe die process and benefits ofring-fencingassets, (pageS3)

3 Describe the roleofstructuredfinancein venturecapitalformation,risktransfer,agencycost reduction, and satisfactionofspecificinvestor demands,(page84)

Book 2

ReadingAssignments and AIM Statements

4 Explain diesteps involvedand die various playersinastructuringprocess

(page85)

5 Define and describe theprocessof Lranchingandsubordination, and describe die

roleof loss distributions and credit racings, (page86)

23.Gish Collateralized Debt Obligations

Candidates,afcercompletingthisreading,should be ableto;

1. Definecollateralizeddebt obligations(CDOs) anddescribediemotivationsof

CDObuyersandsellers, (page91)

2. Describe the typesof collateral used in CDOs.(page91)

3 Defineandexplain diestructureof balance sheetCDOsand arbitrageCDOs

(page93)

4 Describe die benefitsofandmotivationsfor balance sheetCDOsand arbitrage

CDOs.(page94)

5 Describecashflowvs. market valueCDOs.(page94)

6 Describestatic vs. managed portfolios ofCDOs*(page95)

24.SpreadRisk and DefaultIntensityModels

Candidates,aftercompletingdiisreading,shouldbeableto;

I. Define thedifferentwaysof represendng spreads Compareanddifferentiate

between thedifferent spread conventions andcompute onespread givenodiers

when possible,(page 104)

2. Defineandcomputethe Spread‘01. (page105)

3 Explain howdefault riskforasinglecompanycan bemodeledas aBernoulli trial

(page106)

4. Explain die relationshipbetweenexponentialand Poisson distributions, (page107)

5 Define the hazard rateanduse it todefineprobabilityfunctionsfordefault time

and conditional default probabilities,(page 107)

6. Calculaterisk-neutral default racesfromspreads,(page109)

7 Describe advantages of using theCDSmarket to estimatehazard rates,(page110)

8. Explain howa CDSspread canbe used toderiveahazard rate curve,(page111)

9 Constructa hazard ratecurvehima CDSspreadcurve, (page 112)

10 Constructadefault distributioncurvefromahazard rate curve,(page1 12)

11. Explain how thedefault distributionisaffectedbytheslopingof thespreadcurve.

(page113)

12. Definespreadriskandits measurementusingthe mark-to-market andspread

volatility,(page114)

25 Portfolio Credit Risk

Candidates,aftercompletingdiis reading,shouldbe ableto;

1. Define default correlationfor credit portfolios,(page120)

2 Identify drawbacksin usingthe correlation-based credit portfolio framework

(page121)

3 Assesstheeffects of correlation on acredit portfolioanditsCreditVaR (page122)

4 Describe howasinglefactor model can beused to measureconditional default

probabilities giveneconomic health, (page124)

5 Compute thevarianceof the conditional defaultdistribution and die conditional

probability ofdefault usingasingle-factormodel,(page125)

6. Explain therelationshipbetween thedefaultcorrelationamongfirmsandtheir

single-factormodel beta parameters.Apply this relationship to compute one

parameterfrom theother,(page 126)

Book 2

Reading Assignments and AIM Statements

7 Explain how Credit VaR ofa portfolioiscalculated using thesingle-factormodel,

andhow correlationaffects thedistribution oflossseverityfor intermediate values

between0and 1.{page 127)

8. Describe howCreditVaRcanhe calculated usingasimulationof joint defaultswith

acopula, (page129}

26.Structured Credit Risk:

Candidates,aftercompletingdiisreading,should beableto:

1. Identifycommon typesofstruerured products and the various dimensions thatare

importantto their valueandstructure, (page136)

2. Describe the roleofcapitalstructureand creditlosses in a securitization,(page137)

3 Evaluateawaterfall example ina securitization with multiple tranches, (page 138)

4 Identifythekeyparticipantsin a securitization,anddescribesome conflicts of

interest thatcan arisein theprocess, (page141)

5 Evaluateone or two iterationsofinterim cashflowsin a threetieredsecuritization

structure includingthe final cashflows toeach trancheholder, (page 142)

6 Describeasimulation approach tocalculatingcreditlossesfor different tranchesin

a securitizationofaportfolioofloans,(page145)

7 Explain how the probability of default anddefaultcorrelationamongthe

underlyingassetsofa securitizationaffects thevalue,losses and CreditVaRof

equity, junior,andsenior tranches, (page 146)

8. Defineanddescribe how defaultsensitivitiesfor tranchesare measured,(page148)

9 Summarize someof thedifferent typesof risks thatplayaroleinstructured

products, (page148)

10. Defineimpliedcorrelation and describe howit can hemeasured, (page 149)

11. Identifydie motivations for usingstructured creditproducts, (page149)

27.SecuritizationCandidates,aftercompleting thisreading,should he ableto:

1. Define securitizationanddescribe the processand therole theparticipants play.

(page157)

2. Analyze die differences in the mechanicsof issuingsecuritized productsusinga trustvs specialpurpose entity,(page158)

3 Describe thevarious typesof internal and external creditenhancements and

interpreta simplenumericalexample, (page 159)

4 Explain theimpact liquidity,interest rateandcurrency risk hason asecuritized

structure, and list securities thathedge theseexposures,(page161)

5 Describe thesecuritization process for mortgage backedsecuritiesandasset hacked

commercialpaper, (page163)

28.Understandingthe SecuritizationofSubprime MortgageCreditCandidates,aftercompleting thisreading,should be ableto:

1. Explain thesubprimemortgage creditsecuritization processin the UnitedStates.

(page167)

2. Identifyand describekeyfrictionsinsubprimemortgage securitization,and

assess the relative contributionof each factor to the subprimemortgage problems.(page167)

3 Describe the characteristics of diesubprimemortgage market,including the

creditworthinessof die typical borrower and thefeaturesandperformance ofa

subprimeJoan, (page 170)

Book 2

ReadingAssignments and AIM Statements

4. Explain thestructureof the securitization process of the subprime mortgageloans

(page170)

5 Describe thecredit ratingsprocess with respect tosubprimemortgagebacked

securities,{page 171}

6. Explain die implications ofcreditratingson dieemergenceof subprime related

mortgagebackedsecurities, (page171)

7 Describe die reladonship between diecreditratingscyde and the housing cycle

(page171)

8 Explain die implications of the subprimemortgagemeltdownon themanagement

of portfolios,(page 172)

9 Compare diedifferencebetween predatory lendingandborrowing, (page 172)

29 DefiningCounterpartyCredit Risk

Candidates,after completing this reading*shouldbe ableto;

1. Definecounterparty riskandexplain howitdiffersfromlending risk,(page177)

2. Identifytypesof transactionsthat carrycounterpartyrisk, (page177)

3 Explainsomewaysinwhichcounterpartyriskcan be mitigated,(page178)

4. Definethefollowingterminology related to counterparty risk;creditexposure*

creditmigration, recovery, mark-to-market,replacementcost,asymmetric exposure,

andpotentialfutureexposure, (page179)

5 Describe the different ways institutionscan managecounterpartyrisk, (page181)

6. Describe the drawbacksofrelyingon triple-Arated* “too-big-to-fail”institutionsas

amethodofmanagingcounterparty risk, (page1S2)

7 Summarize howcounterparty riskisquantifiedandbrieflydescrihe creditvalue

adjustment (CVA).(page182)

8. Summarize howcounterpartyriskishedged andexplain important factorsin

assessingcapitalrequirementsforcounterpartyrisk, (page183)

9 Definethefollowingmetricsfor creditexposure;expectedmark-to-market,

expectedexposure, potentialfutureexposure,expected positive exposure,effective

exposure* and maximum exposure,(page184)

30.MitigatingCounterpartyCredit Risk

Candidates,aftercompletingdiisreading,shouldhe ahleto;

1 Differentiate betweena two-wayandone-wayagreement,and explain the purpose

ofan ISDA masteragreement and creditsupport annex (CSA).(page191)

2 Identifytypesofdefault-remoteenduesand describe problems associated with the

assumption that theyare in factdefaultremote, (page192)

3 Describe how terminadonand walkaway features workin creditcontracts.

(page192)

4. Describenettingandclose-outprocedures (includingmultilateralnetting)* explain

their advantagesanddisadvantages,and describe how diey fitinto the frameworkof

theISDA master agreement,(page193)

5 Describe the effectivenessof nettinginreducingexposurebasedoncorrelation

betweencontractmark-to-marketvalues, (page196)

6. Describe theeffect of nettingonexposuremetrics, (page1 96)

7 Describe collateralization and explain themechanicsof die collateralization process,

includingthe roleofavaluationagent, thetypesof collateral thataretypicallyused*

andreconciliationof collateraldisputes, (page197)

8. Describe thefollowing featuresof collateralizationagreements;linkstocredit

quality* marginsand callfrequency, thresholds*minimum transfers, rounding,

haircuts,interest,and rehypothecadon.(page200)

Bonk 2

ReadingAssignments and AIM Statements

31.QuantifyingCounterparty CreditExposure,ICandidates,aftercompletingthisreading,should be ableto:

1. Explain thefollowing techniques used toquantifycreditexposure: add-ons,

semi-analytical methods,andMonteCarlosimulation,(page207)

2. Descrihe theMonteCarlo simulation technique for quantifyingexposure,and

explain the choiceof risk“hotspots'"on the exposureprofile, (page208)

3 Identify typicalexposure profiles for thefollowingsecuritytypes:loans, honds,repos, swaps, FX,options, and creditderivatives, (page210)

4 Explain howpaymentfrequenciesand exercisedates affect theexposureprofiles of

securities, (page212)

5 Explainthe difference betweenrisk-neutraland real probabilitymeasuresinthe

contextof how theyare usedincreditexposuremodels, (page213)

6. Descrihe theparameters used insimplesingle-factor modelsof dtefollowing

securitytypes:equities, FX,commodities,credit spreads, andinterest rates.

(page214)

7 Descrihe how nettingis modeled,(page216)

8 Defineandcalculate the nettingfactor,(page217)

9 Defineand calculate marginal expected exposure and theeffect of correlationon

totalexposure, (page 2IS)

32 QuantifyingCounterparty CreditExposure,II:TheImpactof CollateralCandidates,aftercompletingthisreading,should be ahleto:

1. Calculate theexpectedexposureandpotential futureexposureover the remargining

period given normaldistributionassumptions, (page 225)

2. Descrihe the assumptionsand parametersinvolved in modelingcollateral

(page227)

3. Identifydie impactdiat eachfactor of collateral modeling has on dieexposure

profile, startingfrom asimplecaseoffullcollateralization,(page228)

4 Explain the relevant risksinvolvedas aresult of enteringinto acollateralagreement.

(page230)

33.PricingCounterpartyCredit Risk,I

Candidates,after completing thisreading,should beahle to:

1. Explain themotivationof pricingcounterpartyrisk, (page236)

2. Defineandcalculatecreditvalueadjustment (CVA) when nowrong-way riskis present, (page236)

3 Descrihe the process ofapproximatingtheCVAspread,(page237)

4 Define and calculate the incrementalCVAand the marginal CVA.(page238)

5 Discusshow collateralization andnetting affect theCVAprice,(page239)

6. Explain challengesin pricingCVA arisingfrom the presence ofexoticproductsand

theissueof path dependency,(page 239)

7 DefineandcalculateCVA andCVA spread inthe presence ofabilateralcontract.

(page239)

8. Explain issues that need tobe considered in pricing bilateralCVA (page241)

The fbHmvillg is i review ill the CteJil Risk MetsuKlbaiL and MiifiajÿtineciL principles designed m -address die

AIM suLemenLS set Wit by GARP® This inpie is alsu oovered in:

Topic 1 8

EXAM FOCUS

In this topic, we introduce credit riskand provide an overviewof various definitions related

tocreditrisk These definitions provideafoundation fortindersLandingcreditrisk andwill he

importanttoknow whenmodelingdais risk.The main creditrisk model discussedindais topic

is the Merton model We will discuss this model's assumptions andprohlems,and provide a

detailedanalysis of the model’sparameters.Forthe exam,paycloseattendon to thecalculations

forprobabilityof default, lossgivendefault,andexpectedloss

AIM18.1:Describesecuritieswith differenttypesof creditrisks, suchascorporate

debt,sovereign debt,credit derivatives,and structured products.

Credit denotesan economicobligation to anoutside entity that is not oneof theownersof

thefirm’sequity.Credit risk iseither the riskofeconomic lossfromdefault,orchangesin

creditevents or credit ratings

Typesof creditriskysecuritiesincludecorporateandsovereign debt, credit derivatives,and

structuredcreditproducts.Theirinterest rates includeacredit spread abovecreditrisk-free

securities.

* Corporatedebtincludes fixed and floatingratebonds issuedbycorporationsandbank

loans,andtechnicallyrepresents the only credit riskysecuritythatcandefault

* Sovereign debtisdebtissued bycentral,state, provincialorlocalgovernments, or

state-ownedorcontrolledentities.

* Credit derivativesare contracts chat transfer credit riskandwhose payoffs dependon

payoffs of other credit risky securities.Thebestknownexample ofacredit derivativeis a

creditdefaultswap(CDS).

• Structuredcreditproductsarebonds backed bypoofsofmortgages or loans or some

other typeof collateral Theyaregenerally notdefaultable, however,theyarecredit risky

indiesensethatifsomeof theunderlyingassetsdefault, thevalueof thesesecurities

musthewrittendownand thecreditormust takealoss

Before wediscusscreditriskysecuritiesand their valuationsin greaterdetail, it isimportant

to understand the firm'sbasiccapitalstructure. In thisAIM,we will differentiate between

afirm’s bookvalueand marketvalue.Bookvaluerefers to the accountingbalancesheetof

thefirm, whereassets,debt, and equityaretypicallyenteredat book (historical)values.Thisdiffersfrom theeconomicbalance sheetof the firm, where thecomponentsof the balance

sheetarevaluedat market prices,or at someothervalue,includingoption pricing The

components of theeconomicbalance sheet also includeassetsthatarefinanced bydebtandequity(At= D( +E(},where.4 denotestheassetsof the firmat current marketprices,and

DtandEtdenotedebtandequityatmarket prices The equityratio, or E(l A(,is theratio

of equityover assets,andtheleverageratio, orAji E(,istheratioofassets overequity

Assets produce cash Howsand profits Debtis anobligation diat financesassetsand results

inaliability diat mustbe repaidin thefuture.Equityis thecapital invested by the firm’s

owners,andrepresents a residualinterest in thefirmonceall other creditors,includingdebtholders,are paid off Equity, therefore,absorbs all losses beforedebt takesaloss.Equity

owners arepaideither individendsorthrough reinvestedcapital in thefirm

AIM18.3:Identify and describe different debtsenioritiesandtheir respective

collateralstructure.

Within diecapitalstructure,differentsecuritieshave differentrights, including priority

on paymentsandcashflows Debtseniorityis theorderofrepayment on obligations—

typicallydebtor preferredshares—to creditors.Seniordehtisrepaidfirst, followed by

repayment on junior debt

Debt,especiallycorporate debt,can sometimes contain characteristicsof both equity anddebtsecurities.Threesecuritiesofnote arepreferredstock,convertiblebonds,and payment

inkind bonds

Preferred stock(i.e., prefshares) areessentially hybridsecurities that exhibit characteristics

of both bonds andequity,withapriority in dieeventof default betweencommonequity

and bonds.Similar to bonds,theypayafixed dividend and typically havenovoting rights

Similar to commonequity, theydonothaveafixed maturitydateand thereis nolegal

obligation topaydividends

Convertible bondsare bonds diatcan be convertedinto a predeterminednumberof

commonsharesduring thebonds’life As a result,it isofteneasier todiinkof thesebonds

as nonconvertible,plainvanillabondswitha calloptionon the firm’sequity.Mandatoryconvertiblebondsmustbe converted to common sharesat afuturedate(usually within

three years) Given their relativelyshortterm, the presentvalueof couponsisgenerallynot

alargecomponentof theirvalue.Oonverdble pref sharescan be convertibleinto afixed

numberofcommonshares

©2013Kaplan,Inc.

Page12

Topic 1 8 Cross Referent* to GARPAssigned Reading-Mali*Chapter 6

Paymentinkind(PIK) bondsare bondschat payinterest in kind, asadditionalpar value

bonds, rather than bypayinginterest incash* Thisisessentiallyadeferredcoupon where die

principal increases over time*PIK bondsareoften issuedas partofleveragedbuyouts where

the issuerislookingtodefer cash payment aslongaspossihle*PIK bondsare morejunior to

regular bondsas theyincreasethe firm's indebtednessandhence itsrisk

In addition toseniority,creditobligationscanalso he categorized basedonsecurityas

eithersecuredor unsecured Unsecuredobligations only haveageneralclaim on assets in

bankruptcy,whilesecuredobligationshaveaclaimonspecificassets ascollateral* This claim

on collateraliscalledalien, which allowsacreditor to seizespecificassetsunder afirms

bankruptcy, however, the proceedscan onlybe used to pay off thespecificsecureddebt,

andcannot beused to payoff other debt Anyamountsleftover must be paidto thefirm's

owner Liens are typicallyoil realestate but can involve other securitiesincludingbonds,

firmsubsidiaries, orspecificproperty.

Othertermsassociated with secured loansincludehaircut, recourse,and priority A haircut

incollateralized lending refersto areduction inthe collateral’s valuesothat thefullvalue

of collateral is notbeinglent. Increases and reductionsin haircuts is referred to as variation

margin, while the initialamountofreductioniscalled initialhaircut.Recourse insecured

lendingreferstodie lendersrightfor claims against theborrower’sassetsbeyond thevalue

of the collateralif the collateralis insufficient cosatisfywhat die lender Isowed-Ina non¬

recourse orlimited liabilityloan, the lender has nofurtherclaim beyond the collateral value

Priority refers tothe orderinwhich claims are satisfied underaborrower'sbankruptcy

LSecured debthaspriorityover unsecureddebt, andwithin unsecureddebtseniordebt has

priorityoverjunior debt (debenturesareexamplesof junior debt)

Asset classesoutsideof cash securities(e*g., bonds,notes, corporatedebt) canalsogiverise

cocredit risk.Theseinclude derivativeson anunderlyingcash security(e.g.,creditdefault

swaps)

ProfessorsNote; Creditdefault swaps(CDS)are notthefocus ofthistopic, but

will be discussedin detail later in this book

CREDIT CONTRACT FRICTIONS

AIM18.4: Describecommonfrictions thatariseduringthecreation of credit

contracts.

Despite their advantages in mitigating credit risk,creditcontractssuffer froma numberof

problems, including transacdon costs,fricdon,and conflictsofinterest issues*

Asymmetricinformationrefers todifferent parties to a transactionhaving different

informationsets.Forexample,incredittransactions the borroweroften hasmore or hetter

information than thelender Informationasymmetriescan beremedied through monitoring

by die lender andadequatedisclosuresby the borrower

Principal-agentproblemsarisewhenaprincipal hiresan agentfor specificduties,

however, the agenthas better information dian dieprincipal Examplesinclude investment

Topic 18

Cross Reference to GASP Assigned Reading—Mali,Chapter6

managementrelationships(e g.,an investor as the principal hiresan investment manageras

an agentfortrading, however, themanager'sincentive is to maximizeherown returns rather

chan che investor’s)anddelegated monitoring (e.g., theinterestsofa hank’sdepositorsor

creditorsas principalsconflict widr theinterestsof thebanks managersasagencs)

Riskshiftingoccurswhen risks and rewardsare transferredfrom onegroup of marketparticipants toanothergroupholdingdifferent positions inthe firm’s capitalstructure.

A classic conflictis between equity investors and lenders Equityinvestors benefitfromincreasing risktothe firm’sassets (e.g., from increasedborrowing)astheir investment Lslimitedtotheir equity while their returnpotential is unlimited, however,bondholders’

risk increases as theirreturns arefixed Therefore, risk shiftsfrom equityinvestors to

bondholders Institutions thataredeemed'koo-big-to-fail1’canalsocauserisk shifting when

risk isshiftedfrom protected debtholders (e.g.,secured or senior bondholders) toequity

holders

Moral hazardariseswhen buyinginsurance or someprotection that reduces theincentiveof

theinsured party to avoid the insuredevent.For moral hazardto arise, theinsuredparty has

theability tomitigate theriskbeinginsured, while cheinsurer cannot monitor theactions

of the insured.Aclassic exampleis the insurancebusiness.A homeownerinsuringa homeagainstlire may notpurchaseexpensive smokedetectors, or aperson with medical insurancemaynotlookafter his healthasmuchas apersonwithout insurance In finance,firms that

expect abailoutin bankruptcymayhe prompted to take greaterrisks

Adverse selection occurs when partiesto a transactionhaveasymmetricinformation.For

example, the entitysellingan asset may knowsomethingadverse about theasset that theprospective buyermaynotknow, however, this negative informationis notcaptured in the

asset’sprice In finance,abanksellingloansor securities in the markets may possessmore

information than thebuyers

Externalitiesare costs or benefits dialoccurwhenoneparty’sactions causeothers toabsorb

thecost or benefit.Forexample,asmallgroupof borrowersin the short-term marketscan

drive up thecostfor otherborrowers.Asymmetric informationarises aslenders have less

information than horrowerswhichalsocreatesexternalities

Collectiveactionproblems (i.e.,coordinationfailures)occur whenagroup of individuals

were to benefitcollectively ifthey all tooka courseofaction, butwouldnotbenefit ifan

individualalone took thesame courseofaction.Examples ofcoordination failures include

the Prisoner’s Dilemmaingame theory,or infinance where allcreditorsofa particular class

cannotagreeon termsandarealldisadvantaged under bankruptcy

DEFAULTAND RECOVERY

AIM IS.5:Define thefollowingterms relatedtodefault andrecovery: default

events,probabilityofdefault, creditexposure,and loss given default

Defaultis the failure to payafinancial obligation.Defaultincludes bothdistressedexchanges

andimpairment Underadistressed exchange, creditorsreceive new securitieswithlower

value than theiroriginalsecurities. Fromanaccounting perspective, defaultoccurswhen

the valueofafirm’sassets isless than the value ofitsliabilities(i.e., zero ornegativeequity)

Topic 1 8 Cross Reference to GARP Assigned Reading-Mail, Chapter 6

This may giverise toimpattnipltwheretheassetvaluesare written down. Note that

impairmentcan occurwithoutdefault.Ifafirm cannotsatisfyitsliabilities, it would be

forcedintobankruptcy, which is a legal procedureinwhich diefirmseeks protection from

itscreditorseithervia reorganization and restructuring (e.g.,Chapter 11 bankruptcy)or via

liquidadon (e.g,, Chapter7bankruptcy) In reality, firmsmayseek bankruptcyprotection

before their equityisfullydiminished in ordertoallow diefirm to continue itsoperations

while preventing creditors from suingthefirm,

The probability of default (PD) is thelikelihood thata borrower willdefaultwithina

specifiedtimehorizon.Probabilityofdefaultis therefore dieprobability ofarandomdefault

time t*<T,where Tis thespecifiedtime horizon.PD isdependentondireefactors:

I Time tfrom wherewe areviewingdefault (usuallyat present or t= 0,butcould bea

futuredate)

2 Thetimeinterval overwhichto measuredefault probabilities (usually beginningat t=0

until time Tin thefuture,althoughthe intervalcouldalsobegin in die future)

3. Arandom variabletime t*whendefaultoccurs.

Exposureatdefault(i.e.,exposure)isdieamountofmoneythelender can losein theevent

ofa borrowersdefault.Exposureforderivativescontractsdependsonwhether thecontract

islinear[e.g,, futureswhich havezeronet presentvalue(NPV) at initiation] or nonlinear

(e.g.,options which almostalways havea non-zero NPV).Exposurefor swapsincluding

interest rateswapsisdieNPVof theswap

Loss given default (LGD) istheamountofcreditorlossin theeventofadefault.When

defaultoccurs,creditors typically donotlose dieentire amountof theirexposure.The

fractionof exposurenotlost (recovered) at defaultisrecovery,an amountbetween0%and

K)0%.Lossgiven defaultistherefore:

exposure-recovery+LGD

Therecoveryamount istheamountowed that creditorsreceive under bankruptcy,and

dependsonseniority,assetvalues, and business conditions Recoveryisgenerallyexpressed

as therecoveryrate,RRr where RRis afraction between 0and1

LGDrecovery

RR =

Typicalrecoveryrateslor secured debtcanexceed75%,butareoften closeto0% for

junior unsecureddebt.Both LGDandrecoveryare random variablesthatare not known

inadvanceofadefault Inaddition, LGD maybe correlated with the default probability,

which may complicate themodel.Nevertheless, many applicationstreat LGD as aknown

quantity

Topic 1 8

Cross Reference to GARP AssignedReading—Mali, Chapter6

AIM18.6:Calculateexpectedloss from recovery rates*the loss given default*andtheprobability of default

Expectedloss (EL)is die expected value of the creditloss*and representsdie portionofloss

a creditor should provision for and treat as an expenseitem(e.g.*on theincomestatement)

If die only possible creditevent isdefault,expected lossisequalto:

EL= PD x(l —RR) x exposure = PD x LGD

Professor'sNote:In thisequation,LGD is indollar terms, however, itcould

Jiffo beexpressedas a percent(i.e., I - RR), On theexam, ifLGDisgivenas a

percent, EL = PD x LGD x exposure.

Ifdiecrediteventincludesdiepossibilityof hodi defaultand credit migration(e g.,potentialchangesincredit ratings},dien EListhe probability-weighted sumof changes in value

underdie differentscenarios.

Itisimportant to notethat bodi LGDand recoveryareconditional expectations, thatis,

theyareconditionalondefaultoccurring:

E[loss[default] =LGD=

P[default] PD

Consideranexposure of$100*000widia LGDof$30,000 thatisknownwithcertainty

The recoveryis therefore $70*000,and the recoveryrate, RR, is70%.If the probability of

default,PD, is1%* theexpected loss,EL, is 0.01 x $30,000=$300

Sowhywouldan investor invest in asecurity diat has ailexpected loss? Thesimpleanswer

is that theinvestor islookingtobecompensatedbya credit spread thatwould more than

offset theexpected loss For risk-free bonds,an investor over oneyearwouldreceive 1 + r*

wherer is the risk-freecoupon An investor would thereforeexpect to earn 1 + r+i on

a riskybond,wherezIs thecouponspread thatisexpectedto compensatefor default If

defaultcan only occur in oneyear justbefore acoupon payment,diereare twopossiblepayoffson theriskybond:

1. Tileinvestor receives 1 + r + z,with probability1 —PD

2 Theinvestor receives RR,with probabilityPD

Becausethefuturevalueof the risk-freebond isknown with certaintytohe1 + r*the

investormay prefer the riskybondaslongas:

Topic 1 8 Cross Reference to GARP Assigned Reading-Mali, Chapter 6

CREDITVS. MARKET RISK EVENTS

AJM IS.7:Differentiate betweenacredit riskevent anda market riskeventfor

marketablesecurities

Marketrisk is die riskofeconomiclossesfrommovements in market prices,including

market pricemovementsof credit-risky securities.Credit risk isthe riskof borrower default

oncontractualobligations,bm also includesodiet risks includingcreditdowngrades.An

issuerdowngradefrom Ato BBB withoutachangein Aspreadsor interest rates is a pure

creditevent,whileawideningspread betweenAand risk-freerates or a risein risk-freerates

is a pure marketevent.Notethat there lias historicallybeensomeambiguitybetween credit

andmarket risk.Forexample,achangein theperceptionofcreditquality,evenifitdoes

not result increditmigration, maycausespreads to increaseandgive rise to credit risk (this

specificcredit riskisreferred to as mark-to-market ritk)

CREDIT ASSESSMENTTECHNIQUES

AJM18.8:Summarizecreditassessment techniquessuchascredit ratings and

rating migrations, internal ratings, and riskmodels.

A credit ratingis analphanumeric gradeassignedbycredit ratingagenciesthatsummarizes

the creditworthinessofa particularsecurityorentity.Themost prominentcredit rating

agenciesareStandard andPoor’s (S&P),Moodys, and Fitch Ratings (Fitch), which have

been grantedspecial recognition bytheSecurities andExchangeCommission (SEC) in die

U.S.

Theratingsassigned by thecredit ratingagencies reflect the probability of default of

entitiesand debt issues AAA securitiesareconsideredvirtuallyfree ofdefaultrisk, while

aD ratingsignifiesdefault.Investmentgradesecuritiesrange from AAA to BBB-,while

non-investment (i.e.,speculative)gradesecurities range from BB+ to C.Rating agencies

alsoassessrating migration,orchangesin ratings Probabilityestimates aresummarizedin

transition matrices,whichshowdieestimated likelihoodofa rating change foracompany

within aspecified time period(usuallyoneyear) In other words, thematrix indicates the

probability thataparticular issuerwillenddie period withadifferentratingthan what

itinitially beganwith Atypical1-year ratings transition matrixbyS&P can beseen in

Figure1.

Topic 1 8

Cross Reference to CARP AssignedReading-Mali, Chapter 6

Figure 1: Transition Matrix

0.48

The largest percentages within thematrix areshownby diediagonal figures startingfrom

topleft, which show the probability that securities would finishayearwith unchangedratings Forexample,diereis a91.43%probabilitythat asingleA-ratedsecurity would

maintain itsAratingat theend of the year Note diat theprobabilityoffailureincreases

considerablyasthestartingcredit rating foils.Also,defaultisconsidereda terminal state;

thatis,diereis no transitionfromdefault

Itisimportant to understandthat die ratingsbusinessgives rise to an inherentconflictof

interest.Ratingsagenciesarecompensated for ratings by bondholders rather than by die

saleof datato investors(thisiscalled the issuer-pays model).Thisgivesrise to aconflictbetweenbondissuers,who benefitfrom receivingdiehighest ratings, and investors,who

expectratings to be basedon anobjectiveratingsmethodology.Pardydue to thisconflict,many firms carryout theirown internalassessmentof credit quality throughinternal models,andmay assign internaltarings to assistwithcredit-relatedor investmentdecisions

Credit riskmodelsarefrequently used to assesscreditriskofasinglefirm The two main types of modelsare reduced-form modelsandstructural models.Reduced-form modelsare

technicallynotrisk models whichestimatedefault probabilitiesor LGDas outputs,but

radier use dieseparameters asinputs to simulatedefault times.Structural modelsestimate

credit riskfrom fundamental inputs primarilyfrom balance sheetdata,

AIM 18.9:Definecounterparty risk, describeitsdifferentaspectsandexplain how

it is mitigated.

AIM18.10: Describe howcounterpartyriskisdifierentfrom credit risk

Counterparty riskis a typeofcredit riskthat oneofthe partiesto a transactionwillnot

fulfillitsobligations.In evaluatingcounterpartyrisk, twoconditionsmust besatisfied:(1)

the investment must be profitable,and (2) thecounterparty mustfulfill itsobligation to die

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Topic 1 8 Cross Reference to GARP Assigned Reading-Mali, Chapter 6

investor However, counterparty riskistypicallya two-way transaction withdie linebetween

borrowerand lenderblurred Thistypeof risk mayariseunder thefollowingscenarios:

1 OTCderivativestrading.Each derivativescontracthas twosides,andeidier side may be

exposed to counterpartyriskatanygiven time. Inaddition, OTCderivative tradesare

bilateralcontractsbetween twoprivate parties,whichcreates counterpartyriskatany

given time.In contrast, exchange-tradedinstruments,includingoptionsandfutures,

have significantly lesscounterpartyrisk given thataclearinghouseis atdiecenterof

each trademitigatingdiis risk

2. Brokeragerelationships.Historicallyit wasassumedthatonlythe brokerin abrokerage

reladonship hascounterpartyrisk, not the client Followingthesubprimecrisis,this

assumption haschanged followingclient lossesfromfailed brokerages,while broker

lossesonclientexposuresremained rare.

Nettingsignificantly reducescounterparty risk Nettingbecomes particularlyimportant

aspartiesfrequently trade multiplepositionswith eachother,often buying and selling

differentquantities of thesame contract widiina day Nettingprovidesagainto bodi

partiesasonly thenet amountof money needs tohe paid, reducingcounterparty risk

Multilateral nettingisnettingamongmuldplecounterparties.Exposuresunder multilateral

netdngare moredifficulttocalculate,however, thebenefitsaresimilaras under netting

Nettingandsetdement clearingaretheprimary reasonswhy clearinghouseswereintroduced

in the U.S infuturestrading.In addidon,counterpartyexposures and nettingareoften

governedthrough legal agreements including theISDAMaster Agreement

Itisimportanttodistinguishcounterparty riskfrom market risk Market riskis the risk

chat the valueofan underlyingposition willmoveagainst die trader due toadverse market

factors, which mayresult in a negative NPV of dieinvestment. Counterpartyriskis the

conditional risk chat dieNPVof theinvestment ispositive, however, thecounterpartyfails

to perform itsobligationsand therefore no profitisrealizedfromthetrade Toaccountfor

counterpartyrisk, the fair NPV ofthe positionmust be adjustedbya counterpartycredit

valueadjustment(CVA).

Onewayto protectagainstcounterparty riskin derivatives trading ismargin Marginis

aform of collateral posted by both counterpartiesto cover potentiallossesfromdefault

Initial marginistheamountof cash collateral posted by both sidesat tradeinitiation Initial

margin tends tobe small, particularlyfor mostswapcontracts,and the majority of margin

arisesfrom changesin theNPVofderivativescontractswhichareposted dailyas variation

margin.Notall cypesoftradeshave small initial margin, however Contractsincluding

CDSsandCDS-related tradestypicallyhavelargeinitial marginasthesecontractsrequire

significant upfrontpayment inexchange for tirecounterpartysellingprotection

Historically, derivativesdealers rypically required their clientsto postinitial marginon both

thelongand short sidesofaswap Itwasalso thedealer LhatconsideredmakingCVAs to

OTCderivatives, rather dian die client,to protect the dealer againstpotentialclientdefault

During the recentcreditcrisis, however, including the bankruptcy of LehmanBrothers,

the assumptions of such one-sided protection proved incorrect.Clients suffered significant

lossesas aresult of Lehman’sdefaultsinceLehman held margincollateral,which then

became partof diebankruptcyestate.This resulted in clientsbecoming unsecuredgeneral

creditorsof the Lehman bankruptcyestatefor both diemargin paid toLehmanandfor

their claimsfrom die derivativecontracts.

Topic 1 fi

Cross Reference to GASP Assigned Reading—Mali,Chapter6

Counterparty riskcan he mitigated by: (1) accurately measuringexposures, (2) maintaining assessmentof counterparty conditions, (3) dealingwithadiverse groupof counterparties,

and(4) minimizing exposurestoweaker counterparties

Reducingexposuresto aparticularcounterparty can beachieved bylimiting the volumeof

OTC contracts tradedwiththem, orhy increasing the amountof collateral requirementsagainsL them In thecontextofCDS trades, limiting the volume oftrades to a counterparty

isreferredto as CDS compression.When dierearemultiplelongand shortCDSpositionswitha counterparty,compression reducesthesetofCDStrades to asinglenet longorshortposition, which limitsexposuretothecounterparty.LSomedifficulties couldarise,however,

as contractsmay notbe identical regardingcounterparty, premium,andmaturity

VariationsofCounterparty Risk

Double default riskis the risk that a counterpartythat solddefault protectionon a third

partywill defaultatdiesame time asthe third party.Therefore,doubledefaultrisk isbodi

aform ofcounterparty riskandcorrelationrisk Oneof thebest-knownhistoricalexamples

ofdouble defaultriskwas thecaseofAmerican International Group(AIG).AIGis awellcapitalized,highly ratedUA-based insurance corporation thatsold significantamountsof

CDS protectionon avariety ofcreditexposures.Given AIG'sprominent market position,

the protection buyersconsideredcounterpartyrisk (i.e.,the potential forAIG todefault) to

be minimal Tooffsetitsexposures,AIG, diroughoneofitssubsidiaries, purchasedalargequantityofhighly rated mortgage-backedsecuritiesincluding collateralized debt obligations

(CDOs) Asthe credit crisisunfolded,AIG was unableto meet itsobligations under the

CDS contracts ithadwritten atdiesame time itsufferedmaterial impairments under theCDOcontractsitheldlong

Custodial riskrefers to the riskofdefaultbyacustodian.Custodians provide custodial

servicesbycollectingcash flowsincludingdividendsandinterest,and selling, lending,and

transferringsecurities tobe availablefor delivery.Custodiansalso maintaincustody of

securities inmarginaccounts inmarginlendingand primebrokeragerelationships.This

gives rise tocustodialrisk,as securities in marginaccounts are not in thecustomer’s name

but areinstreet name so that they could besold immediatelyto protect the lender againstpotentialcredit losses Thiscontrastswith securitiesincash and nonmarginaccounts,which

areincustomer nameandarethereforenotsubject tocustodial risk

Brokersoften providecustodialservicesinaddition to credit intermediationservices to

clients Collateral pledged byaclient that isheld bythe broker can oftenbe repiedged

by the brokerascollateral toborrow moneytofundits ownoperations Thisis referred

to asrehypothecation Rehypothecation becameaparticular concernduring the Lehmanbankruptcy as theassets, including unpledgedassets,of clients ofoneof Lehman’s

subsidiarieswere notsegregatedandwere thereforesubject torehypothecation.Asa result

theseclients becamecreditorsof Lehman duringthe bankruptcyproceedingsas potentially

Topic 1 8 Cross Reference to GARP Assigned Reading-Malz, Chapter 6

AIM18.11:Describe theMerton Model,anduse itto calculate the valueofafirm,

the values ofafirm’s debt and equity, and default probabilities.

Single-obligorcredit risk modelsaremodelsofasingleissuerof debt obligations.The model

chatisour primaryfocus is dieMerton model,which relates the firmls balance sheet

components tocredit riskusing the Black-Scholes-Merton option pricingmodel in order to

value credu-riskycorporatedebt.TheMerton model rests on anumberofassumptions:

1. The marketvalueofassets, and expectedreturn, p,arerelated Markets are in

equilibriumandinvestors expect to earn ariskpremium of p—r,wherer isdie

continuouslycompoundedrisk-free rate.

2 The basicfunctionofA( = E( + D(describes thefirm's balance sheet Debt consistsof

asinglezero-coupon bondwithanominal paymentof D,maturingat rime T.The

notation D refersto thenotionalvalue of debt, whileD(andEt indicatethevalueof

debtandequityat time t (marketvaluesofdebt andequity}.The model alsoassumes

that thefirmcandefault onlyon thematuritydateof die bond

3. Equityconsistsofcommonsharesonly

4 Debtholdershavelimited liabilityandhave no recourse toanyoiher assets onceequity

iseliminated

5 Contractsarestriedyenforcedand debtholder obligationsmust be fully satisfied before

equityowners canrealize any value Note diat thisassumptionissomewhat unrealistic,

asthereare typicallynegotiationsbetween debtholdersand equityowners onhowto

distributeassetsifafirm isundergoingreorganization

6. Tradingin marketsoccursnotonly for the firm's equity and dehtsecurities, but alsofor

its assets.Traderscanestablish hodilongand short positions

7 Thereare nocash flows priorto diematurityof the debt (includingdividends).

Default occurswhen the market valueof the firm'sassets isless chan theface value ofits

obligations,or whenAj-< D.Aq-—Discalled the distancetodefault.Therefore,we can

view the firm's debt and equityasEuropeanoptionson thevalueof the firm'sassecswith

diesame maturitybisthe firm’s zero-coupondebt.Optionscan then be Vbdued using the

Black-Scholes-Mertonoption formula,althoughcontrary to typicaloption pricingmodels,

herewe arelooking covaluecredit risk

Professor's Note:For thistopic,you are notrequiredto usethe

Black-Scholes-Merton (BSM) modelto valueoptions Calculations usingBSMwill he

demonstratedin Topic20. Yourfocushere should heon how to useprovided

option valuesto value thefirm'sdebt andequity

As mentioned,thesetof assumptions just outlinedis notentirelyrealistic, including the

assumption ofanabsenceofnegotiationsbetween debtholders andequityownersduring

Topic 1 8

Cross Reference to CARP AssignedReading-Mali, Chapter 6

reorganization In addition,it is unrealisticto assumethat thevalueandvolatilityof die

firm'sassetswould beknownatanygiventime.

Nowthatwehaveoutlined thesetofassumptions, equityanddebtvaluescan he computedusingoption-pricing modelsasfollows:

Equity valueoffirmzThe valueofassets, and thevolatilityofassets, are seen as

known quantities Equitycan he viewedas acall option on the firm'sassetswithan exercise

priceequal toD.Atmaturitydate T,if thefirm'sassets are greaterthan itsdebt, the firm

pays thevalueof debt.Ifthe valueofassets islessthan the value of debt, equity is zero

and the firm doesnot have sufficientresources topaydebtinfull The valueofequityat

maturitydate Tcan then beseen as:

Ep = masfAp- D,0)

The notation T=T- t represents thetime to maturity, and thecurrentvalueof equity,Et,

can then he valued using die Black-LScholes-Merton value ofaT-yearEuropean callat a

D(=De rr -(European putvalue with strikeat D)

Thefirm'sbalance sheet The halance sheet equation ofA( =Eÿ+ D(can be re-written asdie

valueofa portfolio of the risk-free discount hond plus along call anda short putoption

withstrike prices of thenominal valueof debt:

A(= E(+D(= (European call with strikeat D)+ De rr -(European putwith strikeat D)

Leverage*.Leverageissimplytheratioof equityto assets.

Probabilityofdefault(PDfi Theprobability of defaultis theprobabilityof exercising theput

and call options Itisimportant, however, todifferentiate between crue/actuarial/physicalprobability ofexerciseand therisk-neutral probability

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Topic 1 8 Cross Reference to CARPAssigned Reading-Mali, Chapter 6

The actuarial(true orphysical)PDcan becalculated using astochastic process usingthe

return on assets, p PD can then he calculatedusingalognormaldistributionofthefirths

assetswidi parameterspand oA:

Yieldtomaturityand creditspread:"We can nowalsocalculate dieyield to maturity of debt

and.itscreditspread-Theyield tomaturity of debt,yt is:

DteÿT =D

Theequation canbe re-arranged usingthecurrent market valueof die debt:

[De-rr-Europeanput optionwith strikeat D]ey tT= D

Aftertaking logarithms, the formula becomes:

yt — — logjÿl—e pEuropean putopdonwith strikeatDj

Finally,we can calculatethe creditspreadbysubtracting the risk-freerate from both sides:

r= —log|ÿ1 — e-1"7ÿ +European put optionwith strikeat Dj -r

yt-Loss givendefault(LCD): TheLGD dependsonhowmuchthe valueof the firm’s debt

exceeds the valueofassets atmaturity.In theMerton model, LGD is arandom variable

Note that theactuarial expecteddefaultlossis not thecurrentmarket valueof the put

opdon Rather, the value of theputopdonis greaterthan die actuarialexpected loss given

thecompensation to die put writerfor cakingon the risk and expectedcostof default

protection The actuarialexpecteddefaultlossescanthen he calculated as thefuture valueof

the actuarialdefaultputoption:

expecteddefaultlosses=erf (European putoptionwithstrikeat D)

Topic 18

Cross Reference to CARP AssignedReading-Mali, Chapter 6

Dividingtheactuarialexpected default lossesbythe PD gives ns the LGD:

je1"7 (European putoptionwith strikeatD)j

expectedLGD

PDFinally,we can compute theexpected recoveryrate as:

(expected LGD)

1

Profestor'sNote:The Merton model will be reviewed Again in Topics 19and20

AIM18.12:Explain the drawbacksand

Merton Model,andidentifyproprietary models of rating agencies thatattempt to

address these issues

possible improvements to the

assess

Asmentioned in the previousAIM,the Merton model makessome unrealisticassumptions

Another drawbackof the model is that itcouldresult inlow default probability valuesand

high recoveryratesfor firmswithhighleverage.Firms widihigh leveragein realitywould

typicallyhavehigherdefault probabilitiesand lower recoveryrates.

Despiteitsdrawbacks, the Merton model has provedpopularandhasbeen adapted

byseveralratingagencies in theirproprietary models,including Moody’sKMVand

RiskMetries’CreditGmdesmodels Thesemodels address theMerton model’s two main

shortcomings: (1) afirm's capitalstructure,especiallyitsdebtstructure, isgenerallymuch

morecomplex than themodelimplies, and(2) afirm’s assetvalueandvolatilityis not

direedyobservable in die market

CREDIT FACTOR MODELS

AIM18.13: Describe credit lactor models and evaluatean example ofasingle¬

factor model

Factormodels relate the riskof credit losstofundamentaleconomicquantities Asimple

versionofafactor model is asingle-factor model,which usesa randomassetvaluefrom the

Merton modelas thevaluebelow which thefirmdefaults

Asingle-factormodelcan beused tovaluea firm’sasset return.Withahorizonatthefuture

dateof T ™ t + T, asset return canbecalculated usinga logarithmicformula:

Topic 1 8 Cross Reference to GARPAssignedReading-Malz, Chapter 6

As weyepreviouslyseen,defaultoccurswhenAp< D.Thisisthenidentical to theevent

that;

D~A/ =

, A , -MfeH -log(equity ratio]

aT <log

In ocherwords,defaultoccurswhen dieasset return isnegative andgreaterinabsolute value

chan the initial equityratio(E, t A().

Asset return under this model is afunction of two randomvariables: (1) the return on a

marketfactor m that denotes the correlation between default and thestateof the economy,

and(2)ashock E-t thatcapturesidiosyncratic risk.Asset returnand thevarianceofasset

return can thenbe written asfunctionsof dieasset betas:

a-p — 3m "H>/l — 0ÿ£

Var[aT] = 0ÿ +1-/?2 =1

The0in themodelabove relatesto assetbeta radier thanequitybeta andcaptures the

co-movement of the firm’sreturnswithan unobservable market index

lasdy, thesingle-factor model uses adefault probabilityas an input(rather than an output

as under the Merton model) that values thedefault diresholdassetvalue (denotedas k)

based on the /'Z?-th quantile of usingastandard normaldistribution function.In

summary, thesingle-factor modeluses two parameters,8and£, whichcan heestimated

usingbalance sheetdataandstock price informationorfirmratingsandtransition matrices.

A practicalexample of the model would hetocalculate thevalue of0wheresystematicand

idiosyncraticrisk contributeequallyto total credit risk, as measuredbyreturn variance This

would heat a0valuewhere:

CREDIT VAR

AIM18.14: Define Credit VaR (Vaiue-at-Risk).

CreditVaRandthe previous models for estimatingcredit risk statistics(e.g., unexpected

loss) arerelatedbecause they incorporatepotential losses at afuture dateat agiven

probability Theydiffer, however,in two main respects First,thetime horizonfor

measuringcredit riskis typically muchlonger than for marketrisk,andisgenerallyaround

oneyear.As aresult, creditdriftforcredit riskcan be material andcanalsocreateissues that

areusuallynot a concernwidi market risk,includingdie treatmentof coupon payments

andcostoffundingpositions.Second, extreme skewness is amaterial concern in credit risk

Extremeskewnessarisesgiven,in the rare eventthatdefault doesoccur, returns arevery

Topic 1 8

Cross Reference to GARP AssignedReading-Mail,Chapter6

large and negative Skewness resultsin a higherconfidenceintervalfor measuring credit

VaR,usuallyat99th and99.9thpercentiles

Onceacreditloss occurs,losses can he broken down into threecomponents;expected

loss, unexpectedloss, and tail loss (lossbeyond unexpectedlosses).Expectedloss(EL) is thedifferencehetween die par valueofa bond and itsexpected futurevalue,factoringin

default probability andrecovery Unexpectedloss(UL) is aquantile ofcreditlossin excess

of expected loss,defined eitherasstandarddeviation ordie99thor99.9tb percentileloss

inexcessof expected loss.CreditVaRistypically definedin termsofULastheworst-case

portfoliolossat agivenconfidencelevelover aspecific holding period, minus the expectedloss This differs Irorn market risk, where market risk VaR isdefinedin termsofprofitand

loss,thatis,it comparesafuturevalue witha currentvalue.Credit riskVaR compares two

futurevalues

Jump-ta-defaultriskis an estimateof the lossifa position were to immediatelydefault

The jump-to-default value ofJC units ofabondwithavalueofpisxpRR,where RRis therecoveryrate.Notethat jump-co-defaultriskcanalso becalculated widioutdefault

probabilitiesas a form ofstress testing, by lookingat it as a worst-case scenario. Notethat

jnmp-tn-defaiilt riskcanbe misleadingfor portfolios for two reasons First, a portfolio

withlongand short positions thatareoffsettingwill haveartificiallylow jump-co-default

valuesalthough portfolio riskishigh.Second,aportfolio with only longpositionswill showartificially highjump-to-defaultvaluesas itdoesnot factorin diversification

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Topic 1 8 Cross Reference to GARP Assigned Reading-Malz, Chapter 6

KEY CONCEPTS

AIM1S.1

Creditis an economicobligationto anoutsideentitythat is not oneof theownersof the

firm’sequity.Creditrisk iseither the riskofeconomiclossfromdefault,orchangesincredit

events orcredit ratings Credit riskysecuritiesincludecorporateand sovereign debt, credit

derivatives,andstructuredcredit produces

AIM 18.2

Afirm’s bookvaluerefersto theaccounting balance slicetof diefirm, whereaseconomic

balance sheet of the firm refers to thecomponentsof the balancesheetvaluedat market

prices.Accordingto the basic balance sheet equation,assetsequaldebtplusequity The

equityratio isequityover assets,and die leveragerado is assets overequity

AIM18.3

Debtseniorityis die orderof repayment onohligadonsofsecuritieswithinafirm’s capital

structure.

LSecurides canincludehybrid securities thathave characteristiesof bothequidesanddebt,

includingpreferredshares, convertiblebonds andpayment in kind bonds

Unsecured ohligadonsonly haveageneral claimon assetsin bankruptcy, while secured

obligationshaveaclaimonspecificassets ascollateral

AIM18.4

Despitetheiradvantages, creditcontractshaveanumber of drawbacks,including

asymmetric information,principal-agent problems, riskshifting, moralhazard problems,

adverseselecdon, externalities,andcollectiveaction problems

AIM18.5

Defaultis die failuretopayafinancialobligation andincludesboth distressedexchanges

(creditors receivenew securities with lowervaluedian their originalsecurities)and

impairment (assetvaluesare writtendown)

Probabilityofdefault Is the likelihood that aborrower willdefaultwithin aspecified time

horizon.Probability of defaultisdependenton dietimefrom wherewe areviewingdefault,

thetimeintervaloverwhich tomeasuredefault probabilities,andarandom variabletime

when defaultoccurs

Exposureatdefaultis dieamountof money the lendercanlosein theeventofaborrower’s

default

Loss givendefault (LCD)is theamountofcreditorlossin theeventofadefault.LGD is

essentiallyexposurelessrecovery.Therecoveryamount istheamountowed that creditors

receive underbankruptcy,anddependsonseniority,assetvalues,andbusinessconditions,

Topic 1 8

Cross Reference to CARP AssignedReading-Mali, Chapter 6

AJM 18.G

Expectedlossis die expectedvalueof die creditloss, andisequal to the probability of

default times LCD.Creditmigration referstothe potentialchangesincredit ratings BothLCDandrecoveryareconditionalexpectations

AIM IS.7

Market riskis the riskofeconomiclossesfrom movementsin market prices.Credit risk is

the riskof borrower defaultoncontractualobligations,and includes other risks likecredit

downgrades

AIM18.8

A credit ratingis an alphanumeric gradeassignedby ratingagencies that summarizes the

creditworthinessofaparticular securityorentity

Ratingmigration refersto a changein ratings.Probabilityestimates aresummarizedin

transition matrices,which show the estimatedlikelihoodofa ratingchangeforacompanywithinaspecifiedtimeperiod-Theratingsbusinesssuffers from conflicts ofinterest,

includinga conflict between bondissuers and investors.

AJM 18.9

Counterpartyriskis a typeofcreditrisk thatoneof theparties to a transactionwillnot

fulfillitsobligations.Twoconditionsmust bemet inevaluatingcounterpartyrisk:(1)die

investmentmust beprofitable,and (2) thecounterparty mustfulfill itsobligationtodie

investor

AIM18.10

Credit riskis either the riskofeconomiclossfromdefault,orchangesincreditevents

or creditratings.Counterparty riskis a type of credit risk thatoneof die parties to a transactionwill notfulfillitsobligations.Market riskisthe risk that the value ofan

underlyingposidon will moveagainst dietraderdue toadverse marketfactors

AJM 18.11

TheMerton modelis asingle-obligorcredit risk model that relates the firms balance sheet

components tocredit riskusingthe Black-Scholes-Merton opdon pricingmodel inorderto

value credit-riskycorporatedebt.TheMertonmodelrests on anumberof simplifying and

at times unrealisticassumptions

AIM18.12

TheMerton model hasbeenadapted by several radng agencies in theirproprietary models,

including Moody’s KMVandRiskMetrics'CreditGradesmodels, whichcorrectseveralof

theMertonmodel’sshortcomings

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Topic 1 8 Cross Reference to GARP AssignedReading-Mali, Chapter 6

AIM IS.13

Factormodels rek.ee[he risk of credit losstofundamentaleconomicquantities A

single-factor modelcanhe usedtovalueafirmsasset return anddefaultevents.

AIM18.14

Unexpected losses and creditVaRare relatedconcepts sincethey bothincorporatepotential

lossesat afuture dateat a given probabilityhowever,differin that dietimehorizonfor

measuringcreditriskistypically muchlonger than for market risk, andextremeskewnessis

a materialconcern incredit risk

Lossesfollowingacreditlosscan be broken downintoexpectedloss,unexpectedloss,and

tail loss (lossbeyond unexpectedlosses)

Followingtheaggressive risk-takingbyoneof the largestAustralian hedgefunds, the

sis month AustralianLIBOR ratehas increasedfrom 3.5% to3.8% Which of the

followingeconomic termsbest describes thisscenario?

JemisFund Management Inc (Jemis)is amutual fundcompany diatfrequendy

tradesinterest rateswaps.Oneof the swapscurrentlyoutstandinghasa net present

value(NPV)of $2 millioninJemis7favor.AccordingtoJemis, the$2million

represents itspotentiallossintheeventof the counterparty's default Which of thefollowing termsbest describes this amount?

A. Exposureatdefault

B Recovery

C Expected loss

D Loss givendefault

A bank hasanoutstanding tradewith oneofitscounterpardeswith anexposure

of$500,000andarecoveryrateof 70%.Thehankestimatedthat thereis a2%

probabilitythat thecounterpartywill defaulton itsobligations.Whatisthe bank’s

A Transition matrices assessrating mlgradons, dialis, the probability thata

company starting with aparticular ratingwill hedowngradedwithin thestated

period

B Thediagonalelements in the transition matrix beginningat thetopleft show

theprobabilityofending the year withan unchanged rating

C Withina transition matrix,thereis no transidonfromdefaulttoanother rating

D The probabilityofarating migrationislowerfor lower raied companies

Foradditional Book2 Topic18practice questionssee:

SelfTestQuestions: #1—2(page247)PastFRM Exam Questions:#1(page252)

5

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Topic 1 8 Cross Reference to GARP AssignedReading-Malz, Chapter6

CONCEPT CHECKER ANSWERS

1 B The film’s equity is its assets less itsdebt*or $258,800-$150,000=$ 100,000,

The equity ratio is the ratio of equity to assets, or $100,000 l $250,000=0.4.

Theleverageratio is the ratio of assets to equity, or $250,000!$100,000 n2.5

2 C This scenario is anexampleof anexternality.Externalities arc costs or benefits that occur

when one party’s actions cause others to absorb the cost or benefit In this case, the aggressive

risk taking of one entity lead to an increase in short-termborrowingcosts for adprudent

borrowers in theAustralian fendingmarket

3 A Exposureatdefault(exposure)is thepotentialamount lenders would lose in the event of a

borrower’s default, Exposurefor interest rate swaps is the NPV of the swap Lossgivendefault

(LCD) is the amount of creditor loss in the event that a default does occur, and is calculated

as the exposure less recovery The fraction of exposure not lost at default is recovery.Expected

loss is theexpectedvalueof the credit loss, and is a factor of theprobabilityof default and

LGD.

4 A At a recovery tare of 70%, the recovery amount is $500,000 x 0.70=$350,000.

The loss givendefault(LCD) is $500,000-$350,000 =$1 50,000.

Expectedloss is(probabilityofdefault x LGD)=0.02 x$150,000=$3,000.

5 A Transition matrices assess theprobabilitythat a company’s rating will remain unchangedat

the end of astatedperiod.Rating migration measures theprobabilityof achangein letter

rating, however it encompasses both ratingupgradesanddowngrades

The fallowing is n review of the Qtiiii Riik Measurement and Management principles designed to address die

AIM statements set forth bv GARP®, This topic is also covered in:

METHODOLOGIES

Topic 19

EXAM FOCUS

In this topic,wewill discussmethodsfor computingdefaultrisk The Mertonmodelestimates

die value of the bondholder andstockholder claims, which are then used to calculate the

implied probability of default However, diis model requires many unrealisticassumptions

Moodys KMV model relaxes some of diese assumptions Other methods used to predict

defaultarecreditscoring models,includingparametricmethods andnonparamerricmediods.Note that the Merton model and die KMV model will hediscussed in greater detail in the

nexttopic{Topic20).Fordieexam,understand how theKMVmodel calculates probability of

defaultand haveageneral understanding of the credit scoringmodels discussed

AIM 19.L:Describe theMerton modelforcorporate securitypricing, includingits

assumptions,strengths and weaknesses:

* Illustrate andinterpret security-holder payoffsbasedontheMerton model

* Using theMerton model,calculate thevalueofafirms debt and equity and thevolatility offirm value

* Describe the resultsandpractical implicationsofempirical studiesthatuse theMerton modeltovalue debt

Professors Afate: The lasttwo bulletpointsfromAIM19.1 will be addressedin

Topic20.

Structuralmodelsof credit riskestimatedefaultriskas afunctionof thevalueof the firm

Given thevalueof the firm, the valueof debt and equitycan bedetermined Structuralmodelsin thiscontext arealsocalledvalue-based models

The Merton model isconsideredavalue-based model, where thevalueof the firm’soutstanding debt(D)andequity (£) areequal to the valueof thefirm{V}.Given an estimateofanytwo of the three values (V, E, orD),weknow the valueof the third

component. Forexample, given thefundamentalvalueof thefirmand the observed value

of diestock,ananalystcandetermine the valueof the bonds: D=V-E Also, given Vand other information, D and Ecan hedetermined.The valueof the debtcan serve as an

indicatorof the firm’sdefaultrisk.

SinceEandDarecontingentclaims,option pricingcan be used todetermine theirvalue?

TheMerton modelassumesthat the debt consistsofasinglezero-couponbond issuethat

matures at timeMatface value£>M.Atthe maturity of thedebt, ifthevalueof the firm’s

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Topic 19

Cross Reference to GARP AssignedReading—de Servigny Sc Renault, Chapter 3 assets isless than the value of the debt, then thefirm mustdefault.Thedebtholdersget

thevalueof thefirm, and they either breakeven or takea loss,while the equityholdersget

nothing.Thepayoffsatmaturityare asfollows:

payment todebtholders= Dw-max(DM-VM,0)

payment tostockholders- max(VM-DM,0)

The Mertonmodelassumes that Vfollowsa certaindistributionover time,such that the

valueof the stockholders’ claimcan bedeterminedby the Black-Scholes-Merton option

pricingmodel.This isbecausethe payment to the stockholdersatmaturityislike diepayoff

ofalongpositionin acall option The payolfofacall option isdenotedwith thefollowing

expression: max(priceof stock—exerciseprice, 0).Thedebtholders’payoff resembles that of

ashortputand risk-free bond

The relationship of theMerton model to the Black-Scholes-Merton modelrequiressome

other strong assumptions (e.g., the bondholderscannotforcebankruptcyprior to maturity}

the valueof thefirm, V, isobservable and follows theassumed time-seriesprocess; etc.)

Ifwe canassume theMertonmodelisvalid andthat theassumptions hold,we can use

the previous equationsto computethe payoffs For example,wewill assumethe bonds

haveamaturity,orfacevalue,of $80 Ifweconsidera case where the value of thefirm is

$200 when the bondsmature,then the payofftostockholdersis$120,and thepayoffto

bondholdersis $80,In anothercase, if thevalueof thefirmis $70,then thedebtholdersget

$70, and die stockholdersget$0 These resultsrequire theassumption that noadjustment

forliquidityisneeded

Diagrams of thepayoffs resemble thoseof option payoffs Figure1shows that thepayoff to

bondholders (D) increasesone-for-one with thevalueof thefirm (TO, D = V,untilV> DM,

when the maximum payofftothebondholders(DM)isreadied The payoff toshareholders

(.S)beginsat the pointwhereV= DMandincreasesdollar-for-dollarwith thefirmvaluefor

firmvaluesaboveDM.Itcan be viewedas acalloptionon firm value withan exerciseprice

ofDm, tiie maturity value of the debt

Figure1:Payoff to BondholdersandShareholdersatMaturity

Payoff to bondholders Payoff to shareholders

S D

DM

D* Firm Value Firm VaJue

Topic 1 9

Cross Reference to GARP AssignedReading-de Servigny & Renault,Chapter3

Thestrengthsof theMerton modelare itssimplicity when pricingcorporatedebt,aswell

as its intuitive nature.The weaknessesaredie numberofassumptions required,aswellas some practicalityissues. Forexample, the absenceofmarked to marketdebtvalues makesit

difficult toaccurately value thefirm In addition, itcanalso be difficult to hndan accurate

estimateofassetvolatility

AIM 19.2:Describe the Moodys KMVCredit Monitor Model toestimate

probability'of defaultusing equityprices, andcomparethe Moodys KMVequitymodel withthe Merton model

Batiks use theMertonand dieKMV approachtodeterminedefault rates.Default rate

informationis necessaryto determine die required capital needed to coverlosses Thefollowingis adiscussionof diesourcesoferror in thedeterminadonof default ratesusingthese methods

The Merton model usesmarket datasuch asstock value andcapitalstructure topredict

racesofdefault.TheMerton model relieson alistofunrealisticassumptions:

1. Thereisonlyone issueof equity and debt, andthedebtis intheform ofazero-coupon

bond that matures at agivendate.

2 Defaultcanonlyoccur at thematuritydace

3 The value of the firmisobservable and followsalognormal diffusion process(geometric

Brownian motion).

4. Therisk-freeinterest rate is constantthrough time.

5 Thereis nonegotiationbetweenequityand bondholders

6 Thereis noneedtoadjust for liquidity

The KMV model isbuilton the Merton model andtries toadjust forsomeof die

shortcomings,mostnotably (1)that all thedebtmatures at the same timeand(2) that the

valueof thefirmfollowsalognormal diffusion process

The KMVmodelassumes that thereareonly twodebtissues;die firstmaturesbefore thechosen horizon, and theochermaturesafter chat horizon The maturity value,ordefaultthreshold,is alinear combinadonof die values.Thedefaultthreshold (a.k.a thedefaultpoint)is in essencethe parvalueof the firm’sliabilities (or debt) In other words, thedefault

thresholdis acombinationof short-termandlong-term liabilities

Apractical rule fordeterminingthedefaultpoint (i.e.,default threshold)is:

short-term liabilities+0.5x long-termliabilities

Topic 1 9 Cross Reference to GARPAssigned Reading—de Serrigny & Renault,Chapter 3

Thisequation isapplicable when dieratioof long-term-liabilities-to-short-term-liabilities

isless than 1.5- Ifthisratio is greaterthan 1 ,5,die default point would bedeterminedas

follows:

0.3 x shore-termliabilities

long-termliabilites

Beforewe cancalculate the probability ofdefault using theKMV model,we mustderive the

distancetodefault (DD).The DD considers die distribution of the firm’sasset returns and

calculatesthe numberofstandard deviationsbetween themean of theassetdistributionand

thedefaultdireshold In equation form:

expectedassetvalue-default threshold

asset value

DD

Professor's Note: Onprevious FRMexams, the distanceto default has been

calculatedusingthefollowing expression:(asset value-liability value)l

(standarddeviation ofasset valueindollar terms).

Once die distance todefaultiscomputed, the expected default frequency(aÿk.a.die

probabilityof default) can be found We willsoon seehow the expecteddefaultfrequency

figureismapped onto acredit ratingsystem toidentify theratingofa particular firm

Figure2: Distance toDefault

Cross Reference to GASP AssignedReading-de Servigny & Renault,Chapter3

Since asset pricesarelognormallydistributed, the DDis morepreciselycalculated using the

followingformulaat timehorizon T%

E(ROA)=expected return on assets

= valueof thefirmassets

= standarddeviationof firmassets

V

Professor'sNote:"log(V)— log(defaultthreshold)" in the equation abovecan

also be written as “log(V1default threshold)."1Also, recall that the valueofthe

firm (i.e., valueofassets) ismade up ofboth debt and equity Therefore, like

the Merton model,oneofthe main driversofthe KMV modelisequity prices

(i.e.,stock prices)

This equation will also beseen inTopic20when we examine theprobabilityofdefaultusing theMerton model Thedifference, however, between MertonandKMVishowthisequationis utilized*Asyouwillsee inthenext topic, theMerton modelcomputes

the cumulative normaldistributionfor the negative value of die previous DD expression.Forexample, if theexpressionequals1,96, theMertonmodelwouldsaythat thereis N(—1.96)= 0.025or 2,5% probabilityofdefault Notethat this valueisfound byusingthecumulative normaldistribution table (i.e., cumulative z-table) in theappendixof this hook

TheKMVmodelon the otherband, usesthesame distance todefaultvalue (e.g.,1.96) and

assessesthe numberofdefaultsat a laterdate(e.g., 1 year) associated with diecomputed

DD value The number ofdefaultsfrom agiven sampleof firms Ls then used to compute

theexpecteddefaultfrequency(EDF).Again, EDF in the KMVmodelisalso known

as theprohahilityofdefault.The EDF will heassociatedwithaparticularcreditrating

(e.g.,BBB),Thefollowingexamplewill helpillustrate thecalculation of expected defaultfrequency

Example:Expected default frequency

Assumethe expectedassetvalueinoneyearfrom theassetvalue distributionis $800, andthedefault thresholdis found tobe $500 Calculatediedistance to defaultif the annual

assetstandarddeviation is 100.

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Topic 1 9 Cross Reference to CARP Assigned Reading-de Servigny & Renault, Chapter 3 Answer:

HOO 500

DD=

100

Tocompute EDF, assumethat 2,000firms last year UadaDD of3, and15of these firms

defaultedafteroneyear.The expected default frequency= 15/2,000= 0.75% This value

isassociated with the EDF of thefirmsincethisfirmalso hasaDD of3.An implied

credit ratingis then assigned basedon diis EDFvalue.Forexample,alowEDF,suchas

0.75%,would be assignedanAA-rating

Thecalculationof EDF is avaluableleadingindicatorofdefault andoftentimes predicts

defaultmonthsinadvance.Asharpincreaseinthe slope of the expected default frequencyis

agoodindicator thata creditratingdowngradeislikelyto occur in drenear future,

CREDIT SCORING MODELS

AJM 19.3:Describe credit scoring models and the requisite qualitiesof accuracy,

parsimony, non-triviality,feasibility,transparencyandinterpretability.

Creditscoring models assigna numerical valueto afirm, which indicateswhedierafirmis

likelytodefaultor not.Theirmainfunctionis to assess thecreditworthinessof small and

private firms For example,creditscoresenable small businessestogain approvalfor loansin

ashorteramountoftime.Featuresofoptimalcreditscoringmodelsinclude thefollowing:

• Accuracy-producesalow volumeoferrors.

• Parsimony- uses alimited numberof independent variables

• Non-triviality - producesappealingoutcomes.

• Feasibility— usesaccessible resourcesin a reasonableamountoftime.

* Transparency andInterpretability—dataiseasytofind andinterpret

AJM19.4:Define and differentiate among thefollowing quantitative

methodologiesfor credit analysisandscoring:

+ Lineardiscriminant analysis

Parametricdiscrimination

Knearest neighbor approach

+ Supportvector machines

Fisher linear discriminant analysis.A process thatsegregates alarger groupinto

homogeneous subgroups.Thelargergroupcould bepotential borrowers,for example, and

thesubgroups could begoodand bad borrowers.Anexample of linear discriminant analysis

is Altman’sZscore,

Parametric discrimination.A particularapproach todiscriminantanalysis that uses a

score function to determine die membersof thesubgroups Examplesof parametric

discriminationarelogitand probit models.Parametricdiscriminant analysis determines

Topic 19

Cross Reference to GARP AssignedReading-tie Servigny & Renault,Chapter3

a score usinga regression, logit,orother statistical technique.Whether the value of the

scorefalls aboveor belowa certain threshold determineswhich subgroup the observation is

placedin(e.g.,whedierafirm iscategorized into alikely-to-or not-likely-to-default group)

Professor'sNote:Logit modelsare basedonlinearprobabilitymodels, which

restrict the rangeofthedefaultprobability to be between 0andL

©

K-nearest neighbor.A nonparametricdiscriminanttechnique that usesthepropertiesof

firms diat havealreadyfalleninto thecategoriesof Interest (e.g.,defaultor notdefault) and

categorizesa new entrantbyhowcloselyit resembles the membersalreadyineachof the

groups

Supportvectormachines.Amethod that usesthe characteristicsof observations (firms) to create anequation thatdoesdie bestjobofdividingthelarger groupinto twosubgroups.The groupscan belinearandincludeplanesand hyperplanes They can henonlinearwheretheseparationcriteria is apolynomial

AIM19.5:Define and differentiate thefollowingdecision rules:minimumerror,

minimum ris k, Neyman-Pearson andMinimax

Decision rules,asusedincreditanalysis,categorizepatternsof descriptive variables,such

asleverage andearningsmeasures, thatwould then placeailobservation(e.g.,afirm) into a

group(e.g.,ahigh-risk-or alow-risk-of-default group)

Minimum error is adecision rulediatusesBayes’dieorem to determineaprobability

It formsaconditional probabilityofafirmbeingin onegrouporanothergiven its

characteristics,denoted C, anddie highest condidonal probability determines thegroup

towhich thefirm isassigned.Thedecision basically becomesonewhere theuserwould

compute the probabilitiesin thefollowingexpression:

p(Cgivendefault) x p(default) > or < p(C givennotdefault) x p(not default)

If die leftis greaterthan the right, then Cwould indicate that thefirm shouldbe indielikely-to-default group.Iftheinequalityis reversed, then thecharacteristicswouldindicatechat diefirm shouldhein thenot-likely-to-default group

Minimum riskrefersto a classof rules thattry toeitherminimizetheprobabilityof

misclassification (incorrecdylendingto riskyfirm) or minimize the lossassociated widichat error.

Neyman-Pearson is adecisionrulechat uses diestatistical conceptofTypeIandType

IIerrors.AType I error islendingto arisky firm becauseitwasincorrecdy accepted as a

non-ri.skyfirm,ATypeIIerror is notlendingto anon-risky firm becauseit wasincorrectly

rejectedas beingrisky.The procedure first requires that the user select afixed valuefor

the probability ofaType IIerrorandplacesit in aLagrangiau multiplier equation that

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Topic 19

Cross Reference to GARP AssignedReading—de Servigny & Renault, Chapter 3

determinesathreshold value For any givensecoffirm “characteristics,13 the decision is to

not extend a loan to the firm if thefollowing holds:

p("conditions'f givendefault)

> thresholdvalue

p("conditions"notgivendefault)

Minimax is adecision ruleof minimizing themaximum error orrisk UsingTypeland

TypeIIerrors asexamples, Lhegoal is m minimizediemaximumof the two.Ina casesuch

asthis where thereareonly two typesoferrors, theminimum isobtained bydetermininga

setofcriteriawhere diecutoffmakes the probabilityof the two typesoferrorsequal toeach

other

In summary, theminimum error rule makesadecision basedoncalculated probabilides

The other three methodsuseoptimization techniques todetermineaclassificationsystem

that reducestheprobability oferrorand/or loss

AJM19.6: Identify theproblemsand tradeoffs between classification and

predictionmodelsofperformance

AIM 19-7:Describeimportantfactorsin the choiceofaparticular classof model

Thereceiveroperatingcharacteristic (ROC)evaluatesacreditdecision ruleby computing

(1) the proportion ofcorrecdypredicteddefaultsand (2) the proportion of firms thatwere

predicted todefaultanddid not:

numberof defaults correcdy predicted

dimensionalgraph.The graphicalrepresentation wouldhavea maximum value ofunity

(i.e., 1) for both the X- and Y-axes TheX-axiscorrespondsto the propertion ofincorrecdy

predicted defaults,andthe Y-axiscorresponds to theproportionof correcdy predicted

defaults Theslopeof the ray from the originto the point represendng the plotof the two

valuesistheperformancemeasure. Ideally, the ray should haveaninfiniteslope;thisoccurs

if alldefaultswerecorrectlypredictedanddierewere noprediedonsofdefaultthat did

not occur Ifthe ray hasa45-degreeslope, then therewereequal proportions oftypesof

mistakes

Thecumulativeaccuracy profile,orGAP (alsocalledGINIcurve),comparesthe

probabilities ofdefaultcomputedby the classificationsystem tothe rankingof observed

defaults.It usesa graphicalsystemsimilartothat of theROC.The vertical axis represents

the fraction of firms that actuallydefaulted,and thehorizontalaxis representsthe

probabilities computed bythe classificationsystem.Theshapeof the lineonthegraph

indicates the successof the classificationsystem.