Articles by kenli

LO 19.5: Describe the relationship between borrower rating and probability of default.
Based on the law of large numbers (i.e., a large number of trials will approximate the expected value) and the fact that with a homogeneous population, actual frequencies observed serve as strong predictors of central probabilities, default probabilities can be applied to estimate the future behavior of a population. Not surprisingly, what has been observed is that higher-rated issues have a lower probability of default. The highest-rated issues almost never default even over a period of 10 years, while the lowest-rated issues often default early on and are almost assured of default after a 10-year period.
A g e n c i e s R a t i n g s v s . E x p e r t s -B a s e d A p p r o a c h e s

LO 19.4: Describe rating agencies assignment methodologies for issue and issuer ratings.
Rating agencies have a goal of running systematic surveys on all default risk determinants. In their approach, both judgmental and model-based analyses are integrated. Whereas a small component of revenues for rating agencies comes from selling information to market participants and investors, the vast majority of their revenues comes from counterparty fees. Because rating agencies are concerned with maintaining their reputations, and because the issuers who pay the rating agencies to rate them want to demonstrate the credit quality of their issues, the investment community (investors, buyers, and traders) can rely on the work of these agencies.
An agency will have potential access to privileged information, as they have a window into managements strategies and vision. To successfully assign a rating, an agency must have access to objective, independent, and sufficient insider information. As an example of the decision-making process for assigning a rating, Standard & Poors has an eight- step process beginning with receiving a ratings request from an issuer and followed by the initial evaluation, meeting with management, analysis, a review and vote by the rating committee, a notification to the issuer, the dissemination/publication of ratings opinions, and continued monitoring of issuers and issues.
The final rating for a corporate borrower will come from two analytical areas: financial risks (accounting, cash flow, capital structure, etc.) and business risks (industry analysis, peer comparisons, company positioning relative to peers, country risk, etc.). As an example, in
2018 Kaplan, Inc.
Page 41
Topic 19 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 3
assessing financial risks, Standard & Poors focuses on coverage ratios, liquidity ratios, and profitability ratios. Higher margins equate to a safer financial structure and a higher credit rating for the borrower. This analysis is then merged with assessments of sovereign risk, the competitive environment of the issuer, and the strength of the business sector.
Along with the factors noted previously, additional analytical areas include firm strategy coherence and consistency, managements reputation and experience, profit and cash-flow^ diversity, the ability of an organization to address competitive needs, and the organizations resilience to business uncertainty and volatility. The quality of a firms internal governance; exposures to legal, political, environmental, and institutional risks; technological sustainability; and potential liabilities tied to employees are all relatively new factors addressed in ratings analyses. It is worth noting that an entity can have favorable positions in some of these analytical areas and less-favorable positions in other areas without it negatively affecting ratings.
At this point, there are only three main international ratings agencies: Moodys, Standard & Poors (S&P), and Fitch. Moodys focuses more on ratings for actual issuances themselves, as opposed to ratings for issuers. S&P focuses on ratings for issuers. Fitch provides issuer ratings based on potential defaults for publicly listed bonds (which ignore commercial and private bank borrowings). The obvious challenge is the lack of comparability among the agencies, although recent market pressures have led to agencies using more quantitative analyses that facilitate easier comparisons.
B o r r o w e r R a t i n g a n d P r o b a b i l i t y o f D e f a u l t

LO 19.3: Describe a rating migration matrix and calculate the probability o f default, cumulative probability o f default, marginal probability o f default, and annualized default rate.
A migration frequency represents how often ratings change from one class to another. A migration matrix shows relative frequencies of counterparties that move from one rating class (shown in each row) to another class (shown in each column). Figure 1 shows a one- year Moodys migration matrix across a 30-year period (19702007), with WR representing withdrawn ratings.
Figure 1: One-Year Moodys Migration Matrix
Aaa 89.1 1.0 0.1 0.0 0.0 0.0 0.0 0.0
Aaa Aa A Baa Ba B Caa Ca-C
Final Rating Class (%)
Aa 7.1 87.4 2.7 0.2 0.1 0.0 0.0 0.0
A 0.6 6.8 87.5 4.8 0.4 0.2 0.0 0.0
Baa 0.0 0.3 4.9 84.3 5.7 0.4 0.2 0.0
Ba 0.0 0.1 0.5 4.3 75.7 5.5 0.7 0.4
B 0.0 0.0 0.1 0.8 7.7 73.6 9.9 2.6
Initial Rating Class
Caa 0.0 0.0 0.0 0.2 0.5 4.9 58.1 8.5
Ca-C Default WR 3.2 0.0 0.0 4.5 4.1 0.0 0.0 5.1 8.8 0.0 0.6 10.4 12.8 3.6 19.8 38.7
0.0 0.0 0.0 0.2 1.1 4.5 14.7 30.0
It is worth noting that migrations are correlated and dependent transitions that occur over time (as opposed to being random walks). Observations over time have shown that when initial ratings are low (high), they become better (worse) than expected. However, default frequencies do have inherent limitations tied to the different applied methodologies of rating agencies. These limitations include differences in definitions, observed populations, amounts rated, and initial ratings.
Several key measures are used to assess the risk of default. The first is the probability of default (PD), which is shown in the following equation:
defaulted!^ PDk = ———-5
namest
where: PD = probability of default defaulted = number of issuer names that have defaulted in the applicable time horizon names = number of issuers k = time horizon
Page 40
2018 Kaplan, Inc.
Topic 19 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 3
A cumulative probability of default, given a sequence of default rates, can be calculated as follows:
p yj cumulative
i=t+k
defaulted j i= t____________
names t
Comparing the two previous equations, a marginal probability of default can be calculated as follows:
marginal k
p Q cumulative
t+k
cumulative t
Finally, the annualized default rate (ADR) can be computed for both discrete and continuous time intervals as follows:
discrete: ADRt = 1 j/(l PD cumulative i In 1 -P D fcumulative
continuous: ADR.
R a t i n g A g e n c i e s M e t h o d o l o g i e s

LO 19.2: Describe the experts-based approaches, statistical-based models, and numerical approaches to predicting default.
Although the consequences of default can be substantial, fortunately a default itself is a relatively rare occurrence (the default rate during deep recessions peaks in the range of 2% to 3%). A credit analyst whose job it is to assess the potential for default is typically an individual with a great deal of experience who can balance his knowledge with perception and intuition when evaluating default scenarios.
An early model for assessing default was created by Wilcox (1971)1 using what was called gamblers ruin theory. His model for predicting the probability of default was dependent on assessing the probability of gains and losses as well as the level of profits relative to a companys initial capital endowment. Another theory applied to corporate finance is the point of no return theory, which implies that business operations must produce enough cash to cover required interest and principal payments on debt. As long as the operational flow of funds exceeds interest and principal payments needed, the company will be successful. The balance needed represents the no-return point, as a company can only be sustainable as long as it can meet its debt payments.
Credit quality analysis from an experts-based approach will apply frameworks such as the four Cs of credit (Character, Capital, Coverage, Collateral) proposed by Altman/NYU, LAPS (Liquidity, Activity, Profitability, Structure) from Goldman Sachs, and CAMELS (Capital Adequacy, Asset Quality, Management, Earnings, Liquidity, Sensitivity) from JP Morgan. As Porter (1980, 1985)23 emphasized, qualitative features need to be factored into any analysis along with quantitative components.
A statistical-based classification centers on the fact that a quantitative model is essentially just a description of the real world within a controlled environment. Models are simply used to express a viewpoint of how the world will likely behave given certain criteria. A quantitative model will have a qualitative (formal) formulation that describes the basic view of the world we are trying to capture in the model; it will also have the underlying assumptions needed to build the model. The assumptions, which serve to simplify the process, should cover organizational behavior, possible economic events, and predictions on how market participants will react to these events. Statistical-based models are primarily focused on assessing the default risk associated with unlisted firms, even though they certainly can be useful in managing default risk for many other entities and organizations. Here, the model is based on quantitative and qualitative variables, as well as publicly unavailable and low-frequency data.
As will be described later in the topic, numerical approaches have the objective of deriving optimal solutions using trained algorithms and incorporating decisions based on relatively weak information in very complex environments. An example is a neural network, which is able to continuously update itself for changes to the environment.
1. Wilcox, J. W. (1971), A Gamblers Ruin Prediction of Business Failure Using Accounting Data,
Sloan Management Review, 12 (3).
2. Porter, M. (1980), Competitive Strategy, Free Press. 3. Porter, M. (1985), Competitive Advantage: Creating and Sustaining Superior Performance, Free Press.
2018 Kaplan, Inc.
Page 39
Topic 19 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 3
R a t i n g M i g r a t i o n M a t r i x

LO 19.1: Explain the key features o f a good rating system.
Ratings play a critical role in supporting credit risk management. Ratings are also used to support credit pricing and capital provisions used to cover unanticipated credit losses. Given that defaults represent a significant source of losses for lenders, ratings are used to measure the probability of a default event occurring in a specific time horizon. Ratings are also used to support decisions made at various levels of an organization, as assessments are used to support a structured internal governance system. Ratings represent the most critical instrument used in modern and quantitative credit risk management. However, ratings must be as objective as possible meaning different credit analysts using the same inputs and methodologies should reach similar ratings.
A good rating system will possess the following three features, which together will help entities measure the appropriateness of their internal rating systems:
Objectivity and Homogeneity. An objective rating system will produce judgments based
only on considerations tied to credit risk, while a homogeneous system implies that ratings are comparable among market segments, portfolios, and customer types. Specificity. A rating system is specific if it measures the distance from a default event while ignoring other financial elements that are not directly tied to potential default. Measurability and Verifiability. Ratings must provide correct expectations related to

default probabilities which are backtested on a continuous basis.
Page 38
2018 Kaplan, Inc.
Topic 19 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 3
E x p e r t s -B a s e d , S t a t i s t i c a l -B a s e d , a n d N u m e r i c a l A p p r o a c h e s

LO 18.6: Define risk-adjusted pricing and determine risk-adjusted return on risk- adjusted capital (RARORAC).
As VaR increases, so does the expectation of higher returns and economic capital. The cost of capital multiplied by VaR needs to be incorporated into lending decisions as a cost for banks that are price takers, or as a lending cost (to be included in credit spreads) for banks that are price setters.
Economic capital is important from a pricing perspective and should, therefore, be incorporated into loan pricing decisions. While, in theory, price is an external factor and banks are price takers in an integrated market, in reality, markets are segmented, so pricing decisions vary. For example, in the wholesale market, banks are typically price takers,
Page 32
2018 Kaplan, Inc.
Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
whereas in retail markets, banks are price setters (due to information asymmetries and costs). Regardless of the market, prices are an important component of credit decisions and loan pricing. For banks, risk-based pricing policy is important for (1) active portfolio management (by using credit derivatives), (2) integrating credit, market, and operational risks into risk budgeting, and (3) setting management objectives.
The risk-adjusted return on capital (RAROC) has been widely used by banks in measuring risk-adjusted performance. A common variant of RAROC is the risk-adjusted return on risk-adjusted capital (RARORAC). Both of these measures are used by business lines to assess whether returns generated exceed the market risk premium required by capital. The market risk premium should be in proportion to the credit spread. Transactions create value if RARORAC exceeds a minimum target, for example, a target return on equity (ROE):
RARORAC > ROEr
, target
Applied in the context of economic value added (EVA), which is a measure of the firms economic profit, EVA can be determined as the risk premium of economic capital, where Ke is the cost of shareholder capital:
EVA = (RARORAC – Ke) x economic capital
The pricing of credit products should include fundamental variables, including costs and potential losses. Therefore, RARORAC should incorporate funding cost, EL (to cover loan provisions), allocated economic capital, and excess return required by shareholders (with respect to the cost of funding). In simple form, RARORAC can be calculated as:
RARORAC =
spread + fees EL cost of capital cost of operations
economic capital
Firms can make certain exceptions to override credit decisions for relationship or reputational reasons. For example, a bank may decide to maintain ties with an otherwise unprofitable customer for reputational or relationship reasons. These decisions should be made at the senior management level.
In general, credit decisions and outcomes, as well as customer profitability analysis, should be communicated to senior management. The goal of such analysis is to generate a comprehensive view of customer profitability, costs, revenues, and risks by segmenting customers, with the aim of identifying profitable and unprofitable relationships. Capital currently set aside for unprofitable or marginally profitable customers could then be freed up and allocated to more profitable opportunities. The relative risk-adjusted profitability models of customers are important in optimizing the risk-return decisions regarding bank portfolios. These models have gained more traction recently because of the growth in investor sophistication, and the growth in size and complexity of banking groups, which now have a greater need for risk-adjusted performance measures.
2018 Kaplan, Inc.
Page 33
Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
K e y C o n c e p t s
LO 18.1
Credit ratings measure a borrowers creditworthiness. Ratings enable borrowers to access capital markets and properly manage risks.
LO 18.2
There are several classifications of credit risk. Risks relating to default include default risk, recovery risk, and exposure risk. Risks relating to valuation include migration risk, spread risk, and liquidity risk. Credit risk also encompasses concentration risk and can be correlated with pure financial risks.
LO 18.3
Determining default probability can be based on (1) analysis of historical default frequencies of a borrowers homogenous asset classes, (2) mathematical and statistical tools, (3) a hybrid approach that combines mathematical and judgmental analyses, and (4) implicit default probabilities from market prices of publicly listed counterparties.
Default risk is typically measured over one year. However, cumulative default rates extending beyond one year are important. Shorter exposures, such as overnight lending, are also exposed to default risk.
Recovery risk is a conditional metric assuming that default has already occurred. The amount of recovery depends on (1) the type of credit contracts used and the relevant legal system, (2) general economic conditions, and (3) covenants. Estimating the recovery rate on ex ante basis is challenging due to the difficulty in collecting recovery rate data, uniformity of information, and challenges in creating a comprehensive model.
Exposure risk is easily determined for term loans. For revolving credit facilities, exposure depends on borrower behavior and external events. In this case, exposure risk [i.e., exposure at default (EAD)] can be calculated as:
EAD = drawn amount + (limit drawn amount) x loan equivalency factor
LO 18.4
Expected loss (EL) is the average loss generated from credit facilities. EL can be calculated as:
EL = PD x LGD x EAD
Unexpected losses (ULs) result from actual losses that may be different from expectations. The risk of ULs can be mitigated by holding sufficient equity capital.
Page 34
2018 Kaplan, Inc.
Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
Value at risk (VaR) measures are more useful in measuring unexpected losses than traditional volatility measures since loss distributions are not symmetric. VaR is computed as the difference between the maximum loss at a certain confidence level and the EL at a given time horizon.
Traditional risk measures, like VaR, do not account for concentration risk, which arises when borrowers are exposed to common risk factors which could simultaneously affect their willingness and ability to repay their obligations.
Concentration was traditionally mitigated by minimizing exposure to a single borrower. Portfolio credit risk models specifically factor in a borrowers risk contribution to concentration, and allow for segmentation of portfolio risk or viewing the portfolio risk profile as a whole.
Default codependencies can be modeled with (1) asset value correlations, which look at the influence of external events on asset values, and (2) default correlations, which look at historical correlations among homogenous borrower groups.
LO 18.5
Marginal VaR calculates the incremental portfolio risk from an individual exposure. Marginal VaR is useful in calculating betas, which can be interpreted as the marginal risk contribution from a loan to average portfolio risk. A beta greater than one implies concentration risk, while a beta less than one indicates diversification.
LO 18.6
The risk-adjusted return on risk-adjusted capital (RARORAC) is an important risk- adjusted performance measure used to assess whether returns generated exceed the market risk premium required by capital. Transactions add value as long as RARORAC exceeds a minimum target (e.g., a target return on equity).
Economic value added (EVA) measures economic profit and looks at the additional return generated relative to the cost of capital:
EVA = (RARORAC – Ke) x economic capital
2018 Kaplan, Inc.
Page 35
Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
C o n c e p t C h e c k e r s
1.
2.
3.
4.
3.
Which of the following credit risks best reflects the risk that an entity may have to accept lower-than-expected values for credit exposures that must be sold? A. Recovery risk. B. Exposure risk. C. Spread risk. D. Liquidity risk.
During a conversation about credit risk, a colleague mentions that the typical measure of default risk is the probability of default (PD) over a one-year horizon, because overnight lending has a zero PD. Is your colleague correct with respect to her statements? A. She is correct with respect to both statements. B. She is correct with respect to default risk over a one-year horizon only. C. She is correct with respect to overnight lending only. D. She is not correct with respect to either statement.
A credit analyst notes that value at risk (VaR) is a more useful measure than volatility of losses, because loss distributions tend to be asymmetric. The analyst further notes that VaR does not account for portfolio concentration risk. Is the analyst correct with respect to his statements? A. The analyst is correct with respect to both statements. B. The analyst is correct with respect to VaR as a more useful measure only. C. The analyst is correct with respect to concentration risk only. D. The analyst is not correct with respect to either statement.
Which of the following risks is most likely associated with marginal value at risk (marginal VaR)? A. Recovery risk. B. Spread risk. C. Concentration risk. D. Exposure risk.
A bank estimated that its risk-adjlisted return on risk-adjusted capital (RARORAC) is 13%. The banks marginal cost of capital is 7%, and its economic capital is $100 million. What is the banks economic value added (EVA)? A. $7 million B. $8 million. C. $15 million. D. $22 million.
Page 36
2018 Kaplan, Inc.
Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
C o n c e p t C h e c k e r A n s w e r s
1. D Liquidity risk measures the risk that asset liquidity and values deteriorate during adverse
market conditions, resulting in lower market value.
2. B The colleagues statement with respect to the PD being measured over a one-year
time horizon is correct. She is incorrect with respect to her statement on overnight lending, which has a non-zero PD.
3. A The analyst is correct with respect to both of his statements. Value at risk (VaR)
is a more useful measure than the standard deviation of losses, since loss risk distributions tend to be asymmetric. VaR, however, does not account for portfolio concentration risk.
4. C Marginal VaR is a measure of concentration risk, which measures the probability of
loss arising from a borrowers exposure to common risk factors.
5. B EVA measures economic profit as the additional return generated relative to the cost
of capital. EVA is calculated as: EVA = (RARORAC – K J x economic capital EVA = (0.13 – 0.07) x $100 million = $8 million
2018 Kaplan, Inc.
Page 37
The following is a review of the Credit Risk Measurement and Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
Ra t in g A s s i g n m e n t M e t h o d o l o g i e s
Topic 19
E x a m F o c u s
The focus of this topic is on the assessment of default risk and assigning ratings as a means of quantifying this risk. For the exam, be comfortable with the relationship between default probability and ratings. Also, understand how ratings are derived for issues and issuers, how ratings migrate over time, how various default probabilities are calculated, and what defines a good ratings system. Default is predicted using many different approaches: experts-based (heuristic), reduced form (statistical and numerical), structural (the Merton model), linear discriminant analysis, logistic regression models, cluster analysis, principal component analysis, and cash-flow simulations. You should be familiar with the advantages and limitations of each of these approaches as well as the similarities and differences among them. These approaches are heavily quantitative, so it is critical to also factor qualitative information into any analysis of default probability.
R a t i n g S y s t e m s

LO 18.5: Evaluate the marginal contribution to portfolio unexpected loss.
>From a portfolio perspective, it is also important to measure how an individual exposure, or the addition of a new exposure, contributes to overall portfolio risk. One such measure is marginal VaR, which calculates the incremental portfolio risk from an individual exposure. The marginal contribution can be calculated as:
U LG
(9ULportf0lio
<9wj
w
This measure can be expressed under the Markowitz mean-variance framework as:
ULC- = 0-
i
r i,portfolio
. r
X W- X UL
i
. r 1- portfolio
where: U LC = marginal contribution of the ft loan portfolio unexpected loss Pi p0rtf0ij0 = default correlation between the f t loan and the overall portfolio w- = weight of the ft loan in the overall portfolio ULportfoiio = portfolio unexpected loss
A practical interpretation of marginal contribution comes from calculating betas. For example, the beta of the ft loan can be valued by rearranging the previous formula as follows:
U LQ / Wi ULportfoiio
We can interpret this measure as the marginal risk contribution from the ft loan relative to the average portfolio risk. A beta greater than one would imply that the marginal risk from the ft loan is greater than the average portfolio risk and would, therefore, increase portfolio concentration risk. A beta less than one would reduce portfolio risk and increase the effect from diversification. With this measure, loans can be quickly selected based on their betas in order to identify which loans would lead to portfolio concentration or diversification.
R i s k -A d j u s t e d P r i c i n g

LO 18.4: Explain expected loss, unexpected loss, VaR, and concentration risk, and describe the differences am ong them.
Expected loss (EL) calculates the average loss in the long run generated from credit facilities. The EL rate is a percentage of the EAD. EL can be determined on a financial basis, defined as a decrease in market value resulting from credit risk, or on an actuarial basis, ignoring credit risk and considering only losses from the EAD.
EL can be calculated as:
EL = PD x LGD x EAD
EL is determined based on expectations and is a cost that is incorporated into business and credit decisions. However, actual losses may be different from expectations, resulting in unexpected losses (ULs). ULs are problematic because they can jeopardize the viability of a bank as a going concern. Banks can prepare for ULs by holding sufficient equity capital to cover all risks, not just credit risks. Capital can be replenished from profits in good times, which can absorb ULs. Credit risk models and credit ratings are important in determining the overall credit contributions needed by banks.
In measuring UL, standard deviation is not an adequate measure since it assumes a symmetrical loss distribution. In practice, risks are often not symmetric, so other credit
Page 30
2018 Kaplan, Inc.
Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
measures, such as value at risk (VaR), are more useful. VaR is defined as a percentage of EAD and is calculated as the difference between the maximum loss at a certain confidence level and the EL at a given time horizon. For example, VaR at a 99% confidence level defines the capital that a bank must put aside to cover ULs in 99% of the cases. The banks insolvency (due to catastrophic losses) is therefore confined to events whose probability does not exceed 1%.
As mentioned, credit risk probability distributions are asymmetric, where events with small probabilities (e.g., insolvency) may significantly impact a banks profitability. Credit risk models can help estimate probability density functions. Loss distributions and calculating VaR measures can be done by (1) adopting a parametric closed-form distribution, (2) using numerical simulations, or (3) using discrete probability solutions.
Despite the usefulness of VaR and EL measures, these measures do not factor in portfolio concentration and typically ignore diversification between assets. Diversification reduces risk; therefore, the aggregate of individual risk measures does not equal portfolio risk. As a result, analyzing credit risk from a portfolio perspective should account for concentration risk. Concentration risk arises in credit portfolios where borrowers all face common risk factors, including interest rates, exchange rates, and changes in technology. Facing common risks is problematic since they simultaneously affect a borrowers willingness and ability to repay their obligations.
Banks traditionally avoided concentration risk by limiting their exposures to individual customers, and, thus, minimizing risk through higher granularity (i.e., a well-diversified portfolio). When analyzing with quantitative credit risk management, the need for granularity is already integrated into default correlations. Full portfolio credit risk models look at how much individual borrower risk factors contribute to concentration. They also enable segmentation of portfolio risk or viewing the entire portfolio risk profile as a whole. Portfolio credit risk models are critical in quantifying how much marginal risk can be attributed to various credit exposures. Without these models, it is not possible to properly quantify risks.
Default codependencies can be modeled through (1) asset value correlations and (2) default correlations. When modeling with asset value correlations, portfolios could be affected by external events, which influence counterparty values and could cause asset values to drop below the value of outstanding debt. Diversification is measured by considering the debt outstanding between two borrowers and by looking at the correlation among asset values.
Modeling with default correlations looks at historical correlations of data among homogenous borrower groups Since default correlations are generally not perfectly positively correlated, banks will have to separately address their potential losses in changing financial periods. This would allow banks to address risks in a more organized fashion, with less committed capital and smaller fluctuations in provisioning.
2018 Kaplan, Inc.
Page 31
Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2

LO 18.3: Define default risk, recovery risk, exposure risk and calculate exposure at default.
Default Risk
As mentioned, default risk relates to a borrowers inability to make promised payments. Determining the probability of default (PD) can be based on the following approaches:
Analyzing historical default frequencies o f a borrower’s homogenous asset classes. Historically, credit analysis was based on subjective analysis, and rating agencies assigned ratings and historical default rates on past observations on an ex post basis (i.e., after an event). Using mathematical and statistical tools. Statistical models are typically used for large portfolios with hundreds or even thousands of positions, which allows for segmentation into different risk classes, measuring risk on an ex ante basis (i.e., before an event). Using a hybrid approach that combines mathematical and judgmental analyses. The mathematical results are generated automatically, which are then corrected using qualitative analysis. Extracting implicit default probabilities from market prices o f publicly listed counterparties.

Default risk is typically measured over one year, although measuring cumulative probabilities of default beyond one year is also important. Shorter exposures are also exposed to default risk. For example, overnight lending will have a non-zero default probability due to unexpected shocks.
Recovery Risk
Recovery risk measures the risk that the amount recovered, in the event of a default, is less than the full amount that is due. The recovery rate is a conditional metric expressed as a percentage which assumes that default has already occurred. It is the complement to loss given default (LGD) such that the recovery rate equals 1 LGD. The amount of recovery depends on the following factors:
The type o f credit contracts used and the relevant legal system.
General economic conditions. Firms operating in more volatile sectors may see larger

swings in asset values. Covenants. Negative covenants restricting the sale of assets that are important to the borrower should be considered in LGD estimations.
Estimating the recovery rate on ex ante basis is complex due to the difficulty in collecting recovery rate data (including lost data) and problems with uniformity of information. Even when sophisticated techniques allow for the collection of good information, it is challenging
2018 Kaplan, Inc.
Page 29
Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
to create a comprehensive model. As a result, less sophisticated models, often using a top- down approach, are commonly used in determining LGD and recovery rates.
Exposure Risk
Exposure risk measures the amount of risk a firm is exposed to in the event of a default. For term loans, exposure is easily determined. For revolving credit facilities, determining exposure is more challenging since it depends on borrower behavior and external events. In this situation, exposure risk [i.e., exposure at default (EAD)] can be calculated as:
EAD = drawn amount + (limit – drawn amount) x LEQ
where: drawn amount = amount of the credit facility currently used limit = maximum amount granted by a bank to the borrower LEQ = loan equivalency factor (rate of usage of available limit beyond ordinary use)
Other assets (e.g., accounts receivable) pose additional challenges, including events of noncompliance in contractually obligated terms and certain conditions which could alter the amounts due from the borrower. Determining EAD for derivatives contracts is also challenging since market conditions could alter the value of these contracts. In this case, EAD is calculated using stochastic models that forecast future events.
C r e d i t R i s k M e a s u r e m e n t

LO 18.2: Describe classifications o f credit risk and their correlation with other financial risks.
The concept of credit risk encompasses a range of risk measures. Those relating to default include default risk, recovery risk, and exposure risk. Those relating to valuation include migration risk, spread risk, and liquidity risk. Additional measures include concentration risk and the correlation with pure financial risks (e.g., interest rate, exchange rate, and inflation risks).
Default risk, or counterparty risk, relates to a borrowers inability to make promised payments. Recovery risk is the risk that the recovered amount, in the event of default, is less than the full amount that is due. Exposure risk measures the risk that a credit exposure at the time of default increases relative to its current exposure.
Page 28
2018 Kaplan, Inc.
Topic 18 Cross Reference to GARP Assigned Reading – De Laurentis et al., Chapter 2
Migration risk looks at the risk that the credit quality and market value of an asset or position could deteriorate over time. To mitigate this risk, a periodic assessment of the credit quality of assets is necessary, and institutions may need to make credit provisions and record gains and losses. Spread risk is the risk that spreads may change during adverse market conditions as investors require different risk premiums, leading to gains and losses. Liquidity risk is the risk that asset liquidity and values deteriorate during adverse market conditions, lowering their market value.