Basel II Implementation: A Guide to Developing and Validating a Compliant, Internal Risk Rating System

By Bogie Ozdemir and Peter Miu

• Basel II is a global regulation, and financial institutions must prove minimum compliance by 2008



• The authors are highly sought-after speakers and among the world’s most recognized authorities on Basel II implementation



• Accompanying CD-ROM includes spreadsheet templates that will assist corporations as they implement Basel II

• Language: English
• Publisher: McGraw-Hill Education
• Release date: Jul 31, 2008
• ISBN: 9780071591317

Book preview

INTRODUCTION

Copyright © 2009 by Bogie Ozdemir and Peter Miu. Click here for terms of use.

Implementation of the Basel II Accord has been one of the major risk management initiatives during the past few years for many financial institutions globally. Although the purpose of implementing internal risk rating systems (IRRS) for many banks is Basel II compliance, it also serves to enhance risk management practices and competitiveness.

We have been actively involved in the implementation of IRRS on many fronts. On the theoretical front, we have conducted research and written a number of research papers; on the practical front, we have globally helped many financial institutions implement and validate their IRRS. We would like to share our experiences with risk management practitioners.

This IRRS implementation handbook incorporates our published research papers, supplemented with practical case examples based on our hands-on experience.

BACKGROUND

Basel II is a regulatory requirement for risk quantification for capital allocation purposes. It is the second of the Basel Accords, which are recommendations on banking laws and regulations issued by the Basel Committee on Banking Supervision (BCBS). It aims at:

1. Ensuring that capital allocation is more risk sensitive;

2. Separating operational risk from credit risk, and quantifying both;

3. Attempting to align economic and regulatory capital more closely to reduce the scope for regulatory arbitrage.

Basel II has profound implications for the financial industry as a whole, as well as for rating agencies and regulators. Basel II is implemented along its three pillars. Under Pillar I, banks are required to satisfy the minimum capital requirement, which determines the ratio of capital (Tier 1 or total) to risk-weighted assets. Pillar I describes the different approaches that may be taken to calculate the risk-weighted assets, namely the standardized approach and the foundation and advanced internal rating based (IRB) approaches. In the standardized approach, risk weights are assigned using rule-based methods supported by external rating assessments (e.g., those of Standard & Poor’s, Moody’s, and Fitch). In the IRB approach, using IRRS approved by national regulators, banks produce their own estimates of risk components [e.g., probability of default (PD), loss given default (LGD), and exposure at default (EAD)], which serve as inputs in the calculation of risk weights. Under the supervisory review process of Pillar II, national regulators ensure banks are in compliance with the minimum standards in fulfilling Pillar I. It can be achieved through examinations of the IRRS, methodology, risk oversight, internal control, monitoring, and reporting adopted by the banks in fulfilling the Basel II requirements. Finally, disclosures of the risk management process under Pillar III allow market participants (e.g., creditors, shareholders) to decide for themselves whether risks have been appropriately measured and managed by the banks.

Under the IRB approach, banks are allowed to develop, validate, and use their IRRS for the computations of minimum capital requirements and capital allocation purposes, subject to regulatory approval. Banks will have to demonstrate the soundness of their risk rating system to the regulators. It is a global initiative, and currently many banks and other financial intuitions have been very busy implementing Pillars I and II. Their motivation is threefold:

1. It is a regulatory requirement;

2. It could lead to a reduction in required capital, thus lowering the cost of capital;

3. It is perceived as a competitive advantage (banks believe that they cannot afford not to be Basel II compliant when the competitors are).

THE CONTENT, THE INTENDED AUDIENCE OF THE BOOK, AND OUR VALUE PROPOSITION

The intended audience of the book is risk management professionals, particularly those involved in Basel and the IRRS implementations. These people are the practitioners working for the financial institutions and the regulators and academicians, as all three groups are actively involved in Basel implementation. The audience is seeking practical and implementable solutions that are

1. Academically credible, and thus defendable to their regulators;

2. Practical and that can be implemented within data, resource, and time constraints.

Our purpose for this Basel implementation handbook is to cover all aspects of IRRS implementation especially with respect to Basel II, which meets both requirements above. Our papers provide the theoretical foundation, and we have incorporated our hands-on practical experience with case studies.

The following papers are incorporated into the book:

Practical and Theoretical Challenges in Validating Basel Parameters: Key Learnings from the Experience of a Canadian Bank, Peter Miu and Bogie Ozdemir, The Journal of Credit Risk, 2005.

Basel Requirement of Downturn LGD: Modeling and Estimating PD & LGD Correlations, Peter Miu and Bogie Ozdemir, The Journal of Credit Risk, 2006.

Discount Rate for Workout Recoveries: An Empirical Study, Brooks Brady, Peter Chang (S&P employee), Peter Miu, Bogie Ozdemir, and David Schwartz, working paper, 2007.

Estimating Long-run PDs with Respect to Basel II Requirements, Peter Miu and Bogie Ozdemir, Journal of Risk Model Validation, Volume 2/Number 2, Summer 2008, Page 1–39.

Conditional PDs and LGDs: Stress Testing with Macro Variables, Peter Miu and Bogie Ozdemir, working paper, 2008.

STRUCTURE OF THE BOOK

The book is structured parallel to the IRRS development under Basel II. In Chapter 1, we cover IRRS design, where designing of PD, LGD, and EAD risk rating systems is discussed. We continue in Chapter 2 with IRRS quantification, where PDs, LGDs, and EADs are assigned to the risk ratings. In Chapter 3, we discuss validation in detail. Lastly, in Chapter 4 we discuss some of the Pillar II issues. A number of Excel Spreadsheet applications of the methodologies considered throughout the book are provided in the CD which comes with the book.

BASEL II

IMPLEMENTATION

CHAPTER 1

Risk Ratings System Design

Copyright © 2009 by Bogie Ozdemir and Peter Miu. Click here for terms of use.

OVERVIEW

Pillar I of the Basel II Accord requires the development of internal risk rating systems (IRRS). The purpose of IRRS is the estimation of probability of default (PD) under foundation internal rating-based approach (F-IRB) and also loss given default (LGD) and exposure at default (EAD) under advanced internal rating-based approach (A-IRB). Pillar II requires the demonstration of capital adequacy (using IRB parameters). The very first step of implementing Basel II under the IRB approach is therefore the design of IRRS. The objective is to categorize the obligors into homogeneous risk groups to establish risk ratings so that they rank order correctly in terms of their credit risks. For example, all obligors in the first pool (i.e., risk rating 1) have the same (default, LGD, or EAD) risk. Similarly, all obligors in the second pool (i.e., risk rating 2) have the same (default, LGD, or EAD) risk among themselves, and the obligors in risk rating 2 are riskier than those in risk rating 1. As illustrated in Figure 1.1, the first step is to establish a discretized categorization (or risk ranking/scoring) of the obligors.

If we were to use a PD model, for instance, obligors would first be assigned to a continuous value of PD. This process involves both risk ranking (an obligor with a higher PD is riskier than the one with a lower PD) and risk quantification (the absolute level of PD assigned to each obligor). In a typical Basel II IRRS, risk ranking and risk quantification processes are likely to be separated. In other words, we first pool risk-homogeneous obligors into risk ratings so that they rank order, and then we assign risk measures (PDs, LGDs, EADs) to these risk ratings. As will be discussed in

Figure 1.1 Risk ranking/scoring of the obligors.

Chapter 3, the following three components of the overall design need to be validated:

1. Are the obligors assigned to each risk rating in fact risk-homogeneous?

2. Are the risk ratings rank-order?

3. Are the levels of risk measures (PDs, LGDs, EADs) assigned to the risk ratings accurate?

THE USE OF CREDIT RISK ASSESSMENT TEMPLATES IN IRRS

For low default portfolios (LDPs), it is usually impossible to build quantitative models based on (the inexistence of) historical default rate data. Many financial institutions (FIs) use expert judgment systems called credit risk assessment templates (or risk rating templates or matrices or score cards) for risk rating/scoring the obligors in LDPs. These templates score (i.e., rank order) the obligors based on fundamental credit risk factors/drivers. Figure 1.2 depicts the risk factors considered in a sample template

Figure 1.2 Examples of qualitative and quantitative risk factors used in a Credit Risk Assessment Template for insurance companies.

Figure 1.3 An example of scoring of a company.

for insurance companies. Typically, both quantitative and qualitative risk drivers are captured, and each risk driver has a preassigned weight. We score an obligor based on each of the risk drivers and then use the weights assigned to the risk factors to arrive at an overall score for the obligor. Figure 1.3 outlines an example of scoring a company.

Templates are designed differently for different industries, and the ensuing scores are mapped to internal and (typically) external risk ratings, each of which is assigned a distinct value of PD (as will be discussed in Chapter 2).

Essentially, these expert judgment methodologies have been used by external rating agencies for many years. Not surprisingly, the risk advisory arms of these agencies have been among the major providers of these templates leveraging their expertise and experience as well as historical default data and statistics. Availability of the historical default data is particularly important. At the final step, we need to assign PDs to the risk ratings. Using rating agencies’ rating methodologies directly has the important advantage that the rating agencies’ historical default rate data can be used in assigning PDs to the internal risk ratings, given that these are default rates of the obligors that were rated by consistent methodologies. In Figure 1.4, suppose the Standard & Poor’s BBB rating corresponds with internal risk rating 4. We also know the historical default rate for the Standard & Poor’s

Figure 1.4 Mapping of score to internal rating, external rating, and PD range.

BBB-rated companies. If our internal rating methodology is consistent with the Standard & Poor’s rating methodology, we can use Standard & Poor’s default history for BBB-rated companies when we assign a PD to our internal risk rating 4 (naturally, the same principal applies to all other ratings). In other words, internal and external ratings are mapped methodologically, and thus external default rates can be used robustly in assigning PDs to the internal ratings. If the internal and external methodologies are inconsistent, the use of the external default rates for internal ratings would not be robust, at least it would not have been proved historically. With the use of the external rating methodologies, internal ratings would have been effectively calibrated to external default rates. In the absence of internal default rates, especially for LDPs, use of methodologies of the rating agencies and thus the corresponding default rate time series has clear benefits over use of alternative methodologies. This is because these alternative risk rating methodologies have not been around long enough to produce sufficiently long default rate time series to allow for robust PD-risk rating mapping.

When a FI first adopts an external rating agency’s templates in developing its IRRS for Basel II implementation, its internal ratings are effectively calibrated to external default rates. The change of the rating methodology from the old one (typically not appropriate for Basel II as it is not transparent, replicable, and auditable) to the new one (used by the external rating agency) may result in a sudden shift in the internal ratings. For some FIs, this shift in risk ratings is not desirable considering the organizational change (cost). One way to resolve this concern is to calibrate the external rating agency’s templates directly to the existing internal ratings (rather than to the external default rates). In this approach, whereas external rating agency’s risk factors are still used, their weights are modified so that the new ratings under the new methodology would be as close as the ratings assigned under the existing methodology.¹ A level of consistency of as high as 95% can usually be achieved within plus and minus of two notches. This allows for the minimization of shifts in ratings despite the use of the new methodology while still making the new IRRS transparent and replicable as required by Basel II. The drawback, however, is the loss of the strong link between the resultant internal ratings and the external default rates, as the new rating methodology and the external rating agency’s rating methodology is now less consistent because of the change in the weights on the risk factors. A typical development and calibration process is illustrated in Figure 1.5.

The templates typically allow for overrides and exceptions that are (when the templates are hosted in appropriate IT platforms) electronically captured and analyzed periodically (see Chapter 3).

Figure 1.5 Typical development and calibration process.

Although these templates provide an efficient, transparent, and replicable framework for capturing quantitative and qualitative credit risk factors, it is after all a credit scoring methodology driven by expert judgment. They therefore do not replace credit analysts’ expert judgment but instead provide a transparent and replicable framework for it. The use of the templates consistently over time and among different credit analysts is essential in achieving consistent scores. The implementation of the templates must therefore include objective scoring guidelines for each material credit factor together with comprehensive training.

We have observed at times that some FIs try to reverse-engineer rating agencies’ methodologies by conducting regression analysis on the external agencies’ ratings and the financial ratios. This approach has the shortcoming that the qualitative factors and confidential information used in the external rating process, which play an important role, cannot be captured in the empirical analysis. Moreover, it is difficult to cater for the differences in the rating methodologies between the rated universe, which is typically made up of large corporate entities, and the nonrated universe of smaller companies. Even if we could reverse-engineer the methodologies for the rated universe, these methodologies would not necessarily be appropriate for the smaller companies.

THE USE OF QUANTITATIVE MODELS IN IRRS

When there are sufficient historical data, quantitative models can be developed and used in IRRS. There are a number of alternatives.

Models for Large Corporate Entities

Commercially available, off-the-shelf models can be used for publicly traded companies. The Moody’s KMV Credit Monitor generates expected default frequencies (EDFs) based on a modified Merton model where distance-to-default (DD) is mapped to historical default rates. Similarly, the Standard & Poor’s Credit Risk Tracker (CRT) Public Firm Model, originally designed to be used as a surveillance tool by its rating group but recently being made commercially available, generates one-year point-in-time (PIT) real-life PDs based on stock market information (e.g., DD) combined with macroeconomic factors as leading indicators and obligors’ financial ratios. Whereas these two represent structural models, there are also reduced-form models (e.g., Kamakura Public Firm Model) in which credit spread that contains information on risk-neutral expected loss is used to infer PDs. From our experience, the quantitative models used for large corporate portfolios within IRRS are largely limited to commercially available off-the-shelf models, due to data limitations in building quantitative models internally by the FIs. We have seen some models (typically built by consultants in a one-off basis and not otherwise commercially available) where risk-neutral PDs are inferred from credit default option (CDO) or credit default swap (CDS) spreads under some assumptions and are then converted into real-life PDs and in turn explained by financial ratios via regression analysis. If we assume the relationship between the spread-implied PDs and the financial ratios established within the calibrated sample (i.e., obligors with traded CDO/CDS) also holds for the rest of the universe (i.e., obligors without traded CDO/CDS), we can generate PDs by simply entering the financial ratios into the calibrated model. This approach has the obvious advantage that the lack of default rate history is substituted by market-implied PDs. However, in our experience, one needs to be cautious with the robustness of these models due to the large number of assumptions that would have to be made and especially the limited sample data set of the relevant traded instruments.

The commercially available models mentioned in the prior paragraph produce a continuous value of PD—in theory every obligor can have a different PD—however, the assigned PDs under IRRS are discrete. That is, every obligor in a certain risk rating has the same unique PD as per the master scale. A mapping system therefore needs to be designed where the continuous PDs obtained from the model are mapped to the internal ratings based on a prespecified PD range assigned to each risk rating (Figure 1.6). For example, any obligor whose continuous PD from the quantitative model falls into the range provided for risk rating 1 (RR1) would have the same assigned PD (i.e., PD 1), corresponding to RR1. Effectively, in this process, we convert the continuous PD output from the quantitative model to a score (or internal rating) and then back to a discrete PD value assigned to the risk rating. In our experience, if a FI chooses to use a commercially available PD model in its IRRS, typically it is within a hybrid framework where continuous PD output is blended with other risk factors, as discussed later in this chapter in the section The Use of Hybrid Models in IRRS.

Standard & Poor’s also has a credit rating estimation model called CreditModel, which generates Standard & Poor’s letter-grade rating symbology denoted in lowercase, indicating quantitatively derived estimates of Standard & Poor’s credit ratings. The model is tailored to specific industries and regions and is applicable to publicly traded and privately owned medium and large corporations in North America, Europe, and Japan.² The fact that this model’s output is a rating as opposed to PD can actually be

Figure 1.6 Mapping of continuous model-implied PD to discrete PD value.

quite useful. Many FIs use available rating agency ratings in risk rating assessment. CreditModel allows FIs to obtain comparable ratings for the unrated obligors. The model is also very useful in the validation of the mapping between external and internal ratings (i.e., we can compare the internal ratings and CreditModel ratings to examine the performance of the mapping between internal and external ratings).

Models for Small and Medium Enterprises (SME)

FIs have more choices available to them for middle-market (SME) portfolios where historical default data are much more readily available. FIs can use one of the commercially available models or they can build their own quantitative models should they have sufficient data. Sometime, they can even build a quantitative model based on a consortium of data among a group of FIs with similar SME portfolios.

Commercially available models include, for example, the Moody’s KMV RiskCalc, where financial ratios and equity market–based information (average distant to default of public firms) are used to explain PDs of private firms. The Standard & Poor’s Credit Risk Tracker (CRT) North America Private Firm Model generates forward-looking one-year PD estimates based on time series of relevant macroeconomic, financial, and industry-specific variables for middle-market (SME) firms (>$100,000 in assets). The model incorporates equity price information at the industry sector level.

An FI that wishes to use a commercially available model within its IRRS needs to be comfortable with the following factors:

Performance of the model: Performance comparison studies have been conducted on the commercially available models.³

Representativeness of the training data set: The training data set should be representative of the internal portfolio, in terms of the characteristics of the obligors and the average default rates.

Definition of default used for the training data set should be reasonably consistent with that of Basel II.

Models should be accompanied by sufficient methodology documentation and developmental evidence: This can be difficult because, most of the time, at least parts of the model methodologies and the training data are considered to be proprietary by the model vendor.

If an FI builds a quantitative model (or has it built) based on its own data or a consortium of data among a group of FIs with similar SME portfolios, all of the above factors are still relevant. The most critical issue is to ensure there is sufficient model documentation and developmental evidence. If they engage a subcontractor to build the models, they need to make sure model methodology and all developmental evidence are fully disclosed and documented.

If an internal model is built, the model output can be a continuous value of PD (like the commercially available models) or a score (i.e., discrete risk rate). If the output is continuous, this would need to be converted to risk ratings to which discrete values of PDs are assigned. The advantage of having a model in which the output is in the form of a continuous value of PD is that the continuous PDs may be used in other applications, for example in pricing, in which the ability to pinpoint the exact PD level of an obligor is important; a continuous spectrum of PD values is particularly essential for pricing deals of obligors with relatively high PD.

As there will be a calibration process among continuous PDs, risk ratings, and discrete value of PD assigned to each risk rate, we can make adjustments dynamically without recalibrating the continuous PD model.

The advantage of having discrete risk ratings as the output of the quantitative model is that no conversion of the continuous PDs to risk ratings is required. We, however, cannot obtain continuous value of PD; for example, all obligors in a certain risk rate are assigned a PD of 25%, even though individual PDs may vary considerably within the risk rate.

THE USE OF HYBRID MODELS IN IRRS

Hybrid solutions incorporating a core quantitative model together with a qualitative overlay are frequently used by FIs. Qualitative overlay considers the expert judgment–based qualitative factors (such as industry risk, competitiveness, and management quality) that are not captured by a quantitative model. To ensure the industry-specific characteristics can be captured, FIs usually use different overlays for different sectors (e.g., real estate, services, retail, manufacturing, trading). Incorporating the qualitative factors enables a more complete risk assessment in the view of many FIs. The hybrid framework also allows FIs to have some control over the risk assessment despite the use of a quantitative model. It should also enhance the accuracy and forward-looking-ness of the model. Many FIs consider the qualitative factors are forward-looking, which therefore should make the overall risk assessment more PIT, especially for SME portfolios where quantitative forward-looking factors are limited.

If the core quantitative model is a PD model, the continuous values of PDs generated by the model are converted into a discrete quantitative score, for example by means of the process described later in this chapter in the use of the quantitative models in IRRS. This score is then blended with the scores arrived at from the evaluation of the qualitative factors to come up with an overall risk rating as depicted in Figure 1.7. This approach has

Figure 1.7 Quantitative model together with qualitative overlay.

the benefit that we can separately backtest the PDs generated by the quantitative model and the PD generated by the whole hybrid model to assess the value-added of the qualitative overlay. We expect the addition of the qualitative overlay should increase the overall model performance.

The hybrid model illustrated in Figure 1.7 is quite typical where we use a commercially available PD model as the core quantitative model. When we determine the weights for the quantitative score (converted from the continuous PD generated from the PD model) and the qualitative scores (generated by assessing the qualitative risk factors), we can set our calibration objective to explain either the historical default rates or the current risk ratings. The former is analytically preferred, but it may result in significant shifts in the assigned risk rates when a new hybrid model is used. The latter avoids shifts in the assigned risk rates but makes the assumption that the current risk rates prior to the use of the new hybrid model are correct. If there are no historical data available for the calibration of the weights of the quantitative and qualitative scores, the weights are determined based on expert judgment.

In Figure 1.7, the quantitative PD model is first developed and then the qualitative overlay serves as an add-on module. If the FI has sufficient internal time series data including both quantitative and qualitative factors for both defaulted and survived obligors, an overall model can be developed in a single step by using, for example, logistic regressions incorporating both quantitative and qualitative explanatory variables. This integrated model development process is, however, not always preferred considering the subjectivity of the historical qualitative scores used in the regression analysis.

We have observed in some FIs that a continuous PD output from a core quantitative PD model is blended with not only qualitative factors but also some financial ratios. One needs to be careful with the potential of putting too much weight on the financial ratios in this approach, especially when the core quantitative PD model also directly uses financial ratios as inputs. The other overlap and thus potential double counting is in the quantitative factors, which are used as a direct input as well as implicitly within the agency ratings.⁴ Another drawback of this approach is that direct calibration of the assigned risk rates (and thus the assigned PDs) to the historical default rates is usually unavailable. In this approach, usually only the core quantitative PD model is calibrated but not the overall model. The relative weights assigned to the continuous PDs, financial ratios, and other inputs used in determination of the overall risk rates are therefore not established based on actual default experience. An example of this approach is depicted in Figure 1.8.

Figure 1.8 An example of a hybrid model.

The main advantage of adopting a framework likes the one presented in Figure 1.8 is the use of the alternative information available. However, our experience shows that this design is prone to consistency and stability issues as discussed below. The first issue is how to deal with the unavailability of some information for some of the borrowers, most notably PDs (or expected default frequencies (EDFs)) from quantitative models and/or agency ratings. The weights of the individual factors (PDs, financial ratios, agency ratings, and qualitative factors) are assigned under the assumption that all of these factors are available. If one (or more) of these factors is unavailable, then the weights of the remaining factors need to be increased accordingly. This means we are, in fact, talking about alternative models under the above design (one being if all risk factors are available, the other one being if PDs/EDFs are unavailable, another one being if agency ratings are unavailable, etc.). It is difficult to ensure these different models are consistent with each other. Some FIs using the above design have believed that the risk ratings produced under different scenarios (PDs [EDFs]/agency ratings are available or not) are not necessarily consistent, which indicates that the alternative models discussed above are not consistent with each other. In practical terms, we are in effect using two different risk rating philosophies under the same design thus the same risk rating system. For example, internal ratings assigned to the obligors will be more PIT when PIT PDs/EDFs are used than when they are not available.

One way to examine the consistency of the alternative models is the following. We examine the internal rating of a well-known borrower with both PD/EDF and agency rating available. It is desired that when we re-rate this company by ignoring the PD/EDF and agency rating, one at a time, the resultant internal rating would still be consistent with the original rating. This is a cross-calibration exercise among the alternative models where all factors are available or when one or some of them are missing. However, as discussed below, this cross-calibration is not a static one but a dynamic one as it changes over the course of the credit cycle.

The other issue is the stability of the ratings under this design over time. PDs (or EDFs) (e.g., produced from commercially available models) are more PIT than the agency ratings that are close to through-the-cycle (TTC). This creates a mismatch among the different risk factors, which can compromise the stability of the internal ratings over the course of the credit cycle (refer to Chapter 2 for a full discussion on risk rating philosophies). PIT PD/EDF is in effect conditional PD on current information.⁵ The overall PD assigned to the internal risk rating (based on the master scale), on the other hand, is intended to be an unconditional PD (see the section Long-run PDs in Chapter 2). We need to distinguish PD assigned to the risk rating from PDs assigned to the obligors. Note that although PDs assigned to the risk ratings are unconditional, FI can still adopt a more PIT risk rating philosophy for the PDs assigned to the obligors via continuous re-rating of the obligors (or remapping between internal ratings and PDs or a combination of the two).

So in Figure 1.9, we use conditional (PIT) PD/EDFs and mix them up with more TTC agency ratings to arrive at a risk rating that is mapped to an unconditional (long-run) PD assigned to the risk rating. This process is

Figure 1.9 A hybrid model using both PIT PD/EDFs and TTC agency ratings.

convoluted and prone to producing unstable results over the course of the credit cycle. Consider the following example: assume we are at a good part of the credit cycle and the PDs/EDFs are low (as they are more PIT than are agency ratings), but agency ratings, due to their more TTC nature, are presenting a more conservative picture. First of all, due to the conflicting information, it is difficult to arrive at an accurate internal risk rating mapped to an unconditional (long-run) PD. To further complicate the matter, suppose there are two otherwise identical borrowers where we have the PD/EDF for one but not for the other. For the one we have the PD/EDF; we will most likely arrive at a more favorable risk rating during a credit upturn.

We may try to correct this bias by correcting the PIT-ness of PD/EDF used as a factor (i.e., the first box on the left in Figure 1.9). To ensure stability, some FIs dynamically