SCHWESERNOTES™ FOR THE FRMS EXAM FRM 2013 Part II Book # i v Credit Risk Measurement and Management KAPLAN SCHWESER FRM PART II BOOK 2: CREDIT RISK MEASUREMENT AND MANAGEMENT READING ASSIGNMENTS AND AIM STATEMENTS CREDIT RISK MEASUREMENT AND MANAGEMENT IS: Credit and Counterparty Risk 11 19: Default Risk: Quantitative Methodologies 32 20: Credit Risks and Credit Derivatives 45 21: Credit Derivatives and Credit-Linked Notes 70 22: The Structuring Process 82 23: Cash Collateralized Debt Obligations 24: Spread Risk and Default Intensity Models 25: Portfolio Credit Risk 91 26: Structured Credit Risk 27: Securitization 28: Understanding the Securitization of Subprime Mortgage Credit 29: Defining Counterparty Credit Risk 30: Mitigating Counterparty Credit Risk 31: Quantifying Counterparty Credit Exposure, I 32: Quantifying Counterparty Credit Exposure, II: The Impact of Collateral 33: Pricing Counterpart}' Credit Risk, I 104 120 136 157 167 177 191 207 224 236 SELF-TEST: CREDIT RISK MEASUREMENT AND MANAGEMENT 247 PAST FRM EXAM QUESTIONS 252 FORMULAS 275 AERENDIX 279 INDEX 282 ©2013 Kaplan, Inc Page FRM TART n BOOK 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 1-4277-44A7-X PPN: 3200-3240 Required Disclaimer: GARP® does not endorse, promote, review, or warrant die accuracy of the products or information, nor does it endorse any pass rates claimed services offered by Kaplan Schweser of FRM by the provider Further, GARP® is not responsible for any fees or costs paid by die nser to Kaplan Schweser, nor is GARP® responsible for any fees or costs of any person or entity providing any services to Kaplan Schweser, FRM®, GARP®, and Global Association of Risk Professionals™ are trademarks owned by die Global Association of Risk Professionals, Inc GARP FRM Practice Exam Questions are reprinted with permission, Copyright 2012, Global Association of Risk Professionals All rights reserved These materials may not be copied without written permission from die author The unauthorized duplication of these notes is a violation of global copyright laws Your assistance in pursuing potential violators of this law is greatly appreciated 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 Page ©2013 Kaplan, Inc READING ASSIGNMENTS AND AIM STATEMENTS Thefollowing material is a review of the Credit Risk Measurement and Management principles designed to address the AIM statements setforth by the Global Association of Risk Professionals READING ASSIGNMENTS Allan MaLz FinancialRisk Management: Models, History; and Institutions Hoboken, NJ: John Wiley & Sons, 2011 IS “Credit and Counterparty Risk,” Chapter (page 11) Arnaud tie Servigny and Oliyier Renault Measuring and Managing Credit Risk New York; McGraw-Hill, 2004 19 "‘Default Risk: Quantitative Mediodnlogies,” Chapter (page 32) Rene Stulz Risk Management & Derivatives Florence, KY: Thomson South-Western, 2002 20 “Credit Risks and Credit Derivatives,” Chapter IS (page 45) Christopher Culp Structured Finance and Insurance: The Art ofManaging Capital and Risk Hoboken, NJ: John Wiley & Sons, 2006 21 “Credit Derivatives and Credit-Linked Notes,* Chapter 12 (page 70) 22 “The Structuring Process,” Chapter 13 (page 82) 23 “Cash Collateralized Debt Obligations,” Chapter 17 (page 91) Allan Malz FinancialRisk Management: Models, History, and Institutions Hoboken, NJ: John Wiley & Sons, 2011 24 “Spread Risk and Default Intensity Models,” Chapter (page 104) 25 “Portfolio Credit Risk,” Chapter (page 120) 26 “Structured Credit Risk,” Chapter (page 136) Christopher Culp Structured Finance and Insurance: The Art ofManaging Capital and Risk Hoboken, NJ: John Wiley & Sons, 2006 27 “Securitization,” Chapter 16 (page 157) ©2013 Kaplan, Inc Page Book Reading Assignments and AIM Statements 28 Adam Ashcroft and Til Schuermann “Understanding the Securitization of Subprime Mortgage Credit.” Federal Reserve Bank of New York StaffReports, No 3M (March 2008) (page 167) Jon Gregory Counterparty Credit Risk: The New Challengefor Global FinancialMarkets West Susses, UK; John Wiley & Sons, 2010 29- “Defining Counterparty Credit Risk/ Chapter (page 177) 30 “Mitigating Counterparty Credit Risk,” Chapter (page 191) 31 “Quantifying Counterparty Credit Exposure, I,’ Chapter (page 207) 32 “Quantifying Counterparty Credit Exposure, II: The Impact of Collateral,” Chapter (page 224) 33 “Pricing Counterparty Credit Risk, 1/ Chapter Page ©2013 Kaplan, Inc, (page 236) Boole Statements and AIM Reading Assignments AIM STATEMENTS 1a Credit and Counterparty Risk Candidates, after completing this reading, should he able to: Descrihe securities with different types of credit risks, such as corporate debt, sovereign debt, credit derivatives, and structured products, (page 11) Differentiate between book and market values for a firm's capital structure, (page 12) Identify and describe different delu seniorities and dieir respective collateral structure, (page 12) Describe common frictions that arise during the creation of credit contracts (page 13) Define the following terms related to default and recovery: default events, probability of default, credit exposure, and loss given default, (page 4) Calculate expected loss from recovery rates, die loss given default, and the probability of default, (page 6) Differentiate he tween a credit risk event and a market risk event for marketable securities, (page 17} Summarize credit assessment techniques such as credit ratings and rating migrations, internal ratings, and risk models, (page 17) Define counterparty risk, describe its different aspects and explain how it is mitigated, (page 18) 10 Describe bow counterparty risk is different from credit risk* (page 18) 11 Describe the Merton Model, and use it to calculate the value of a firm, the values of a firm’s debt and equity, and default probabilities, (page 21) 12 Explain the drawbacks and assess possible improvements to the Merton Model, and identify proprietary models of rating agencies that attempt to address these issues (page 24) Describe credit factor models and evaluate an example of a single-factor model 13 (page 24) 14 Define Credit VaR (Value-at-Risk) (page 25) 19 Default Risk: Quantitative Methodologies Candidates, after completing this reading, should be able to: Describe the Merton model for corporate security pricing, including its assumptions, strengths and weaknesses: • Illustrate and interpret security-holder payoffs based on the Merton model Using the Merton model, calculate the value of a firm's debt and equity and the * volatility of firm value Describe the results and practical implications of empirical studies that use the * Merton model to value debt, (page 32) Describe the Moody’s KMV Credit Monitor Model to estimate probability of default using equity prices, and compare the Moody s KMV equity model with die Merton model, (page 34) Describe credit scoring models and the requisite qualifies of accuracy, parsimony, non-triviality, feasibility, transparency and inrerpretability, (page 37) ©2013 Kaplan, Inc, Page Bank Reading Assignments and AIM Statements Define and differentiate among die following quantitative methodologies for credit analysis and scoring: * * Linear discriminant analysis Parametric discrimination K nearest neighbor approach * Support vector machines (page 37) Define and differentiate the following decision rules: minimum error, minimum risk, Neyman-Pfearson and Minimal (page 3£) Identify the problems and tradeoffs between classification and prediction models of * performance, (page 39) Describe important factors in the choice of a particular class of model, (page 39) 20 Credit Risks and Credit Derivatives Candidates, after completing tills reading, should he able to: Explain the relationship of credit spreads, time to maturity, and interest rates (page 50) Explain die differences between valuing senior and subordinated debt using a contingent claim approach, (page 52) Explain, from a contingent claim perspective, the impact stochastic interest rates have on die valuation of risky bonds, equity, and die risk of default, (page 52) Assess the credit risks of derivatives, (page 61) Describe die fundamental differences between CreditRisk+, CreditMetrics and KMV credit portfolio models, (page 56) Define and describe a credit derivative, credit default swap, and total return swap (page 61) Define a vulnerable option, and explain how credit risk can be incorporated in determining the option’s value, (page 63) Explain how to account for credit risk exposure in valuing a swap, (pagje 64) 21 Credit Derivatives and Credit-Linked Notes Candidates, after completing this reading, should he able to: Describe the mechanics of a single named credit default swap (CDS), and describe particular aspects of CDSs such as settlement methods, payments to the protection seller, reference name, ownership, recovery rights, trigger events, accrued interest and liquidity, (pagie 70) Describe portfolio credit default swaps, including basket CDS, Ndi to Default CDS, Senior and Subordinated Basket CDS (page 72) Describe the composition and use of iTraxx CDS indices, (page 74) Explain the mechanics of asset default swaps, equity default swaps, total return swaps and credit linked notes, (page 75) 22 The Structuring Process Candidates, after completing diis reading, should he able to: Describe the objectives of structured finance and explain the motivations for asset securitization, (page 82) Describe die process and benefits of ring-fencing assets, (page S3) Describe the role of structured finance in venture capital formation, risk transfer, agency cost reduction, and satisfaction of specific investor demands, (page 84) Page ©2013 Kaplan, Inc Book Reading Assignments and AIM Statements Explain die steps involved and die various players in a structuring process (page 85) Define and describe the process of Lranching and subordination, and describe die role of loss distributions and credit racings, (page 86) 23 Gish Collateralized Debt Obligations Candidates, afcer completing this reading, should be able to; Define collateralized debt obligations (CDOs) and describe die motivations of CDO buyers and sellers, (page 91) Describe the types of collateral used in CDOs (page 91) Define and explain die structure of balance sheet CDOs and arbitrage CDOs (page 93) Describe die benefits of and motivations for balance sheet CDOs and arbitrage CDOs (page 94) Describe cash flow vs market value CDOs (page 94) Describe static vs managed portfolios of CDOs* (page 95) 24 Spread Risk and Default Intensity Models Candidates, after completing diis reading, should be able to; I Define the different ways of represen dng spreads Compare and differentiate between the different spread conventions and compute one spread given odiers when possible, (page 104) Define and compute the Spread ‘01 (page 105) Explain how default risk for a single company can be modeled as a Bernoulli trial 10 11 (page 106) Explain die relationship between exponential and Poisson distributions, (page 107) Define the hazard rate and use it to define probability functions for default time and conditional default probabilities, (page 107) Calculate risk-neutral default races from spreads, (page 109) Describe advantages of using the CDS market to estimate hazard rates, (page 110) Explain how a CDS spread can be used to derive a hazard rate curve, (page 111) Construct a hazard rate curve him a CDS spread curve, (page 12) Construct a default distribution curve from a hazard rate curve, (page 112) Explain how the default distribution is affected by the sloping of the spread curve (page 113) 12 Define spread risk and its measurement using the mark-to-market and spread volatility, (page 114) 25 Portfolio Credit Risk Candidates, after completing diis reading, should be able to; Define default correlation for credit portfolios, (page 120) Identify drawbacks in using the correlation-based credit portfolio framework (page 121) the effects of correlation on a credit portfolio and its Credit VaR (page 122) Assess Describe how a single factor model can be used to measure conditional default probabilities given economic health, (page 124) Compute the variance of the conditional default distribution and die conditional probability of default using a single-factor model, (page 125) Explain the relationship between the default correlation among firms and their single-factor model beta parameters Apply this relationship to compute one parameter from the other, (page 26) ©2013 Kaplan, Inc Page Book Reading Assignments and AIM Statements Explain how Credit VaR of a portfolio is calculated using the single-factor model, and how correlation affects the distribution ofloss severity for intermediate values between and {page 127) Describe how Credit VaR can he calculated using a simulation of joint defaults with a copula, (page 129} 26 Structured Credit Risk: Candidates, after completing diis reading, should be able to: Identify common types of s truer ured products and the various dimensions that are important to their value and structure, (page 136) Describe the role of capital structure and credit losses in a securitization, (page 137) Evaluate a waterfall example in a securitization with multiple tranches, (page 138) Identify the key participants in a securitization, and describe some conflicts of interest that can arise in the process, (page 141) Evaluate one or two iterations of interim cashflows in a three tiered securitization structure including the final cashflows to each tranche holder, (page 142) Describe a simulation approach to calculating credit losses for different tranches in a securitization of a portfolio of loans, (page 145) Explain how the probability of default and default correlation among the underlying assets of a securitization affects the value, losses and Credit VaR of equity, junior, and senior tranches, (page 146) Define and describe how default sensitivities for tranches are measured, (page 148) Summarize some of the different types of risks that play a role in structured products, (page 148) 10 Define implied correlation and describe how it can he measured, (page 149) 11 Identify die motivations for using structured credit products, (page 149) 27 Securitization Candidates, after completing this reading, should he able to: Define securitization and describe the process and the role the participants play (page 157) Analyze die differences in the mechanics of issuing securitized products using a trust vs special purpose entity, (page 158) Describe the various types of internal and external credit enhancements and interpret a simple numerical example, (page 159) Explain the impact liquidity, interest rate and currency risk has on a securitized structure, and list securities that hedge these exposures, (page 161) Describe the securitization process for mortgage backed securities and asset hacked commercial paper, (page 163) 28 Understanding the Securitization of Subprime Mortgage Credit Candidates, after completing this reading, should be able to: Explain the subprime mortgage credit securitization process in the United States (page 167) Identify and describe key frictions in subprime mortgage securitization, and assess the relative contribution of each factor to the subprime mortgage problems (page 167) Describe the characteristics of die subprime mortgage market, including the creditworthiness of die typical borrower and the features and performance of a subprime Joan, (page 170) Page ©2013 Kaplan, Inc, Book Reading Assignments and AIM Statements Explain the structure of the securitization process of the subprime mortgage loans (page 170) Describe the credit ratings process with respect to subprime mortgage backed securities, {page 171} Explain die implications of credit ratings on die emergence of subprime related mortgage backed securities, (page 171) Describe die reladonship between die credit ratings cyde and the housing cycle (page 171) Explain die implications of the subprime mortgage meltdown on the management of portfolios, (page 172) Compare die difference between predatory lending and borrowing, (page 172) 29 Defining Counterparty Credit Risk Candidates, after completing this reading* should be able to; Define counterparty risk and explain how it differs from lending risk, (page 177) Identify types of transactions that carry counterparty risk, (page 177) Explain some ways in which counterparty risk can be mitigated, (page 178) Define the following terminology related to counterparty risk; credit exposure* credit migration, recovery, mark-to-market, replacement cost, asymmetric exposure, and potential future exposure, (page 179) Describe the different ways institutions can manage counterparty risk, (page 181) Describe the drawbacks of relying on triple-A rated* “too-big-to-fail” institutions as a method of managing counterparty risk, (page 1S2) Summarize how counterparty risk is quantified and briefly descrihe credit value adjustment (CVA) (page 182) Summarize how counterparty risk is hedged and explain important factors in assessing capital requirements for counterparty risk, (page 183) Define the following metrics for credit exposure; expected mark-to-market, expected exposure, potential future exposure, expected positive exposure, effective exposure* and maximum exposure, (page 184) 30 Mitigating Counterparty Credit Risk Candidates, after completing diis reading, should he ahle to; Differentiate between a two-way and one-way agreement, and explain the purpose of an ISDA master agreement and credit support annex (CSA) (page 191) Identify types of default-remote endues and describe problems associated with the assumption that they are in fact default remote, (page 192) Describe how terminadon and walkaway features work in credit contracts (page 192) Describe netting and close-out procedures (including multilateral netting)* explain their advantages and disadvantages, and describe how diey fit into the framework of the ISDA master agreement, (page 193) Describe the effectiveness of netting in reducing exposure based on correlation between contract mark-to-market values, (page 196) Describe the effect of netting on exposure metrics, (page 96) Describe collateralization and explain the mechanics of die collateralization process, including the role of a valuation agent, the types of collateral that are typically used* and reconciliation of collateral disputes, (page 197) Describe the following features of collateralization agreements; links to credit quality* margins and call frequency, thresholds* minimum transfers, rounding, haircuts, interest, and rehypo thecadon (page 200) ©2013 Kaplan, Inc Page Topic 25 Cross Reference to GASP Assigned Reading Mali, Chapter — Example: Realized market value Suppose a credit position has a correlation to the market factor of 0.25- What is the realized market value used to compute the probability of reaching a default threshold at the 99% confidence level? Answer: At the 99% confidence level, the default loss level has a default probability, TT, of 0,01 A default loss level of 0.01 corresponds to —2.33 on the standard normal distribudon The relationship between the default loss level and die given market return, m , is defined hy: p(m) = 0.01 = k -fkn CT, This is approximately equal to the probability of obtaining a realized market return of -2,33 as follows: $-1(0.01)ss-2.33 = k - 3m yjl-31 j The realized market value is computed as follows: -2.33 = —2.33 — (0.25)m V'l-0.252 -2.33(0.9682) = -2.33 - (0*25) m -2.256+2.33 = -(0.25) m 0.074= -(0*25) m -0*296 = in The probability that the default direshold is reached is die same probability diat the realized market return is -0.296 or lower The parameters play an important role in determining the uncondidonal loss distribution The probability of default, it, determines the unconditional expected default value for the credit portfolio The credit posi don’s correlation to the market, 01, determines the dispersion of die defaults based on die range of die market factor Page 128 ©2013 Kaplan, Inc Cross Reference to GARP Assigned Reading - Topic 25 Mali, Chapter CREDITOR WITH COPULAS AJM 25.8: Describe how Credit VaR can be calculated using a simulation of joint defaults with a copula Copulas provide a mathematical approach for determining how defaults are correlated with one another using simulated results The following four steps are used to compute a credit VaR under the copula methodology: Define the copula function Simulate default times Obtain market values and profit and loss data for each scenario using the simulated default times Compute portfolio distribution statisdcs by adding the simulated terminal value results Example: Computing credit VaR with a copula Suppose there is a credit portfolio with two loans (rated CCC and BB) that each has a notional value of $1,000,000 Figure illustrates four possible event outcomes over a default time horizon of one year for this credit portfolio The four event outcomes are only die BB rated loan defaults, only the CCC rated loan defaults, both loans default, or no loans default Figure 2: Event outcomes for a two credit portfolio Event BB Default CCC Default Both Default No Default Default Time f Tilb.i — 1’ TCCC,i > > ETCOC,iÿ *) C"r uij.i — Tcoc,iÿ Flow can credit VaR be estimated for diis portfolio assuming a correlation of 0.25? ©20] Kaplan, Inc Page 124 Topic 25 Cross Reference to GASP Assigned Reading — Mail, Chapter Answer; The copula approach to estimating credit VaR is applied using the following steps: The first step is to simulate 1,000 values using a copula function The most common copula used to calculate credit VaR is the normal copula The 2,000 simulated values (1,000 pair simulations results in 2,000 values) ate then mapped to their standard univariate normal quantile which results in ,000 pairs of probability values The first and second elements of each probability pair are mapped to the BB and CCC default times, respectively A terminal value is assigned to each loan for each simulation The values are added up for the two loans, and the sum of the no-default event value is subtracted to determine the loss Figure summarizes the sum of die terminal values and losses for 1,000 simulations Figure 3: Event outcomes for a two credit portfolio Event BB Default CCC Default Both Default No Default Default Time (TBB.i - 1* TCOC,i 51 > TCOCj - (TBB,i lr TCOC,i (TBB,i 51 lj TCCC.i 51 Terminal Value i,4ao,ooo 1,410,000 Loss 610,000 680,000 700,000 1,290,000 2,190,000 The loss level sums from the simulation are then used to determine the credit VaR based on the simulated distribution In this simulation, the 99% confidence level corresponds to the $1,290,000 loss where both loans default The 95% confidence level corresponds to the $680,000 value because the lower 5% of the simulated values resulted in defaults with a total loss of $680,000 Page 130 ©2013 Kaplan, Inc Cross Reference to GARP Assigned Reading - Malt, Topic 25 Chapter KEY CONCEPTS AIM 25.1 The default correlation for a two credit portfolio assuming the outcomes are Bernoullidistributed random variables is; Pl2 = ~ AfM 25.2 Drawbacks of using die default correlation-based credit portfolio framework are die number of required calculations (2n event outcomes with (n + 1) + [n(n - 1} / 2] conditions), certain characteristics of credit positions not fit well in the default correlation credit portfolio model, and the limited data for estimating defaults due to die fact that firm defaults are relatively rare events AIM 25.3 A portfolio's credit value at risk is defined as the quantile of the credit loss less the expected loss of die portfolio A default correlation equal to implies the portfolio is a binomially distributed random variable As a credit portfolio becomes more granular, the credit VaR decreases AIM 25.4 In the single-factor model, firm is individual asset return is defined as; — where yjl 0i is the firm's standard deviation of idiosyncratic risk, a5 = /?tm + j,s and the firm's idiosyncratic shock The model assumes that firm i defaults ifÿ; < AIM 25-5 The conditional cumulative default probability function for die single-factor model is stated as: p(m) =