Understanding capital requirements in light of Basel IV

The financial industry has used credit risk classification systems for a long time. With the advent of Basel II, those systems became the basis for banks’ capital adequacy calculations.

The Basel II risk-weighted asset (RWA) formula is intended to calculate the capital necessary to cover the unexpected loss (UL) – based on the probability of default (PD), loss given default (LGD) and exposure at default (EAD). For PD, the regulation requires a “long-run average of one-year default rates (LRADR).”

From a purely mathematical point of view of the assumptions used for deriving the Basel II RWA formulas, the arithmetic average of point-in-time (PIT) probability of defaults should be used. In other words, through-the-cycle (TTC) PD equals approximately the average PIT PD in RWA formulas. This supports our view that TTC PDs should be used for capital requirement calculations. If the probability of default used is not TTC, it will vary with the cycle, and the capital requirement will also vary.

This is the background to the discussion on procyclicality: In adverse times, capital requirements for banks may increase, forcing them to cut lending. Hence the cycle will be strengthened, which is clearly an undesired effect.

In reality, all PD models are something in between point-in-time and through-the-cycle models; in other words, they are hybrid models. The measurement of the degree to which they are point-in-time is called PIT-ness. Banks need to have a view of their PD models’ PIT-ness because it’s a Basel regulatory requirement.

The PIT-ness methodology

After the PIT-TTC probability of default methodology was published in the Journal of Risk Model Validation (JRMV)¹ and a corresponding 2012 SAS Risk Insights article “the methodology was used extensively in the banking industry, both for internal ratings-based (IRB) and IFRS 9 purposes.” The methodology appears to be quite complex in terms of getting easy regulatory approval inside the IRB scope of application. However, many banks around the world implemented the methodology for IFRS 9, which was approved by auditors. This created a robust way to build IFRS 9 PD models based on IRB PD models.

The methodology that introduced the PIT-ness concept is crucial to making a robust transformation from IRB TTC PD to IFRS 9 PIT PDs. That is why the 2012 publication attracted so much interest among bank practitioners and academic researchers. It therefore got one of the highest citation indexes in the JRMV, with several follow-up articles further developing it for different applications.

8 key ways the industry is using the methodology

Following are the main areas in which the industry is already using the 2012 methodology for IRB in light of Basel IV.

Establishing a fair dialogue with regulators about portfolio risk versus required capital levels

The PIT-ness methodology explains the change of PD through the changes of economic cycles and idiosyncratic risk, both on an obligor and portfolio level. As a bonus, you can see all expected changes over time of IRB default rates (DRs) and long-run average default rates (LRADR) for the same portfolio. This is tremendously helpful for banks and regulators in understanding and assessing whether IRB PD and capital levels for a specific portfolio are appropriate.

For example, consider a situation when PD is less than DR for three consecutive years. Should the bank increase LRADR and the corresponding capital level to cover that? The answer can be “yes” or “no.” The best way to answer that question would be to use the methodology described above.

This methodology is of interest not only for banks explaining portfolio credit risk and defending capital levels. It’s also relevant for regulators who can use it to obtain their own view and assessment of an individual bank’s portfolio risks.

Fulfilling Basel regulatory testing requirements with the predictive power of PD models

Recent regulations require extensive “exactness” around the predictive power of PD models. As a result, different testing requirements are introduced – for example, ECB guide to internal models, ECB instructions for reporting the validation results of internal models, EBA guidelines on PD estimation, LGD estimation and the treatment of defaulted exposures, etc. Typical statistical testing procedures are constructed by comparing “actual” observed values versus “expected” predicted values.

In this case, we’re attempting to compare hybrid PD or TTC PD versus observed DR. However, this would be like comparing apples to oranges: The prediction for observed DR is point-in-time PD.

Here, the 2012 methodology is valuable for creating robust and valid statistical tests. This approach produces PIT PD values and makes it possible to run classical statistical tests for PIT PD versus DR, as well as statistical tests based on an allowed range of variation of DR at a given LRADR (which is used for calibration TTC PD). Considering all this, the 2012 methodology provides a solid way to fulfill regulatory requirements around the predictive power of testing hybrid PD models.

Reconciling IRB PD values with IFRS 9 PD values

Regulators are starting to look at the reconciliation of IRB and IFRS 9 PDs and harmonization of the expected loss (EL) used in IRB and IFRS 9. As we know, many banks used the 2012 approach to build IFRS 9 PD models on top of existing IRB PD models. So, these PDs are automatically reconcilable – meaning they can be derived from each other.

Fulfilling Basel regulatory requirements for cyclicality or PIT-ness assessments for PD models

The authors of one paper² suggested a simple and effective calculation procedure for PIT-ness assessments based on the 2012 PIT-TTC probability of default framework. Also, research conducted by the IIF&GCD working group³ showed that several other proposed methods for PIT-ness estimation were not fit for the purpose, because they have many weaknesses and gaps. All of these are addressed in the 2012 PIT-TTC PD framework.

The 2012 PIT-TTC PD framework clearly defines PIT-ness as a unique property of the rating model itself. This clearly separates it from the volatility of segment default rate, so the rating model will have the same PIT-ness independently, whether it is applied to high volatility or low volatility segments.

Incorporating stress testing based on IRB PD models

Similar to IFRS 9, applying the 2012 approach allows us to run stress test scenarios using IRB PDs as an input. This is another area where the 2012 approach was used by several banks. Here, reconciliation of stressed PDs with IRB PDs is achieved in a way similar to the approach used with IFRS 9. The 2012 approach was also used for quantifying the effects of central bank and government interventions in the downturn (see this example).

Having a view on increased capital requirements in a downturn

When using procyclical hybrid PDs as an input to regulatory capital, the 2012 methodology is helpful. This approach allows us to estimate an internal capital adequacy assessment process (ICAAP) add-on for a potential Pillar 1 increase in a downturn scenario.

Using IRB-based pricing as part of a use case test

When using PIT PDs and TTC PDs as shown in the 2012 paper, it’s possible to estimate risk-adjusted return on capital (RAROC) for the lifetime of each loan.

Allowing a separate change of PD at the obligor level

Our recommended methodology estimates change of PD at the obligor level due to “common” economic cycle factors that affect all obligors, and it estimates change of PD due to the internal idiosyncratic characteristics change of the specific obligor.

The methodology also calculates change of long-term TTC PD for that obligor due to idiosyncratic risk change. This feature can be important for estimating COVID and climate risk probability of default impacts, assuming they are not part of the typical economic cycle – acknowledging that they impact only specific types of obligors who are sensitive to them. The advantage of this approach is that the corresponding increase of TTC PD and capital requirements will affect only specific obligors and not the whole portfolio.

Why the industry is still exploring the advantages of the 2012 methodology

Implementing a consistent way of estimating PIT and TTC PD via the 2012 approach brings many synergies for a bank and provides major advantages over competitors. It will stabilize the bank's capital ratios and prevent procyclical distortions of capital requirements, positively affecting stock price.

In addition, the Basel RWA formula requires TTC PD – and using hybrid PDs as input (as many banks do) brings procyclicality, creating risk for macro-financial instability. Employing different PD inputs with different “hybridity” – or PIT-ness-to RWA formula – is one of the major factors behind the unjustified difference of capital requirements for similar portfolios across banks, as recognized by the Basel committee and EBA.

In the 2021 benchmark exercise performed by EBA, when analyzing the variability of RWA at the portfolio level, the conclusion was that: “Misalignment between estimates (PDs and LGDs) and observed parameters (default rates and loss rates) could suggest that differences in RWAs between institutions might be driven by differences in estimation practices (different levels of conservatism, adjustments to reflect long-run averages, different lengths of time series of the data available and included in the calibration of the cycle, assumptions underlying recovery estimates, etc.) and not only by differences in portfolio risk.”⁴

A one-size-fits-all approach of using hybrid PD is not good for business. It results in inefficient pricing and customer selection as well as procyclical RWA. Industry associations (e.g., IIF/GCD) and regulators (e.g., EBA) have started looking into the topic and preparing recommendations. Therefore, even if implemented only for formally approved IRB models, the 2012 methodology creates great value both for banks and regulators.

Having IRB PDs as a regulatory approved cornerstone in the bank, the 2012 methodology provides a robust and effective tool for producing all other probability of defaults needed for different applications including IFRS 9, stress testing, RAROC calculations, validation and more. Furthermore, the methodology can also represent an important tool for dealing with some of the current challenges facing financial institutions like emerging geopolitical risks, the impact of COVID and of climate risk in PD estimates, while being aligned with the main goal from Basel IV, reducing RWA variability.

These areas represent some of the key ways in which the 2012 methodology can give banks a unique competitive edge.

References

1 Details of this methodology are published in the Journal of Risk Model Validation Volume 6/Number 3, Fall 2012 (1–23), “A methodology for point-in-time–through-the-cycle probability of default decomposition in risk classification systems,” by Magnus Carlehed and Alexander Petrov.

2 Oeyen, B., & Salazar Celis, O., "On probability of default and its relation to observed default frequency and a common factor." Journal of Credit Risk, 15(3), 2019.

3 IIF, Tests of 4 “PIT-ness” measures – Analytical support to the IIF working group. 2017. “Point-in-Time and Through Time and Through-the-Cycle Modeling: Measures and Approaches for Harmonization” – A report by the IIF RWA Task Force in cooperation with GCD, May 2018.

4 EBA Report – Results From the 2020 Low-Default and High-Default Portfolios Exercise, EBA/REP/2021/06, June 2021.