IRB PIT Calibration for Retail Unsecured: A Double-Edged Sword?

With the publication of its near-final UK Basel 3.1 rules in PS9/24, the PRA has clarified that “point in time (PIT) plus buffer” dynamic calibration approaches are admissible for non-mortgage retail exposures. In this article we continue our discussion around this topic, reviewing the definitions of both ratings and calibration philosophies and looking at the pros and cons of PIT calibration for unsecured retail portfolios. These were touched upon previously in our earlier article on RWA harmonisation. We also examine some of the less well known disadvantages associated with PIT calibration in important dimensions like stressed impacts, model accuracy, explainability and compliance, and global standards.

Recapping some key definitions
 

We begin with Rating Philosophy, which refers to the degree to which a rating model or scorecard inputs achieve predictions that are Point-in-Time (PIT) or Through-the-Cycle (TTC):

• PIT refers to Probability of Default (PD) estimates that are accurate over a one-year horizon. Time-variability in default risk is fully explained by changes in model or scorecard inputs, which are typically observed as rating migrations.
• TTC, meanwhile, refers to PD estimates that are stable across the economic cycle. In an idealised world where ratings only reflect static characteristics, time-variability in default risk is not reflected at all.

In practice, an LRA calibration that is “perfectly PIT” or “perfectly TTC” is seldom achievable. A 100% TTC rating model or scorecard would not be particularly useful to the business anyway, nor indeed compliant. And even the most PIT-weighted scorecards, those with access to current payment and balance information, rarely achieve greater than 70% PIT. Unmodified scorecard or model output PDs, which are often referred to as “hybrid” since they display a mix of PIT and TTC behaviours, are more typical. In another previous article we discussed a heuristic for managing the cyclicality of model or scorecards via risk driver selection and weighting.

Regardless of the balance of ratings philosophies used to establish the long-run average default rate, though, it is important to remember that the rating-level probabilities of default (PDs) used for regulatory capital purposes are required by regulation to represent the LRA default risk by grade or pool (see Section 11.12 in SS4/24). Again, this is an important topic we explored in another article looking at approaches for determining grade or pool boundaries from scorecard outputs.

The other key concept at issue here is Calibration Philosophy, which refers to the modification of rating model or scorecard outputs to achieve PD estimates that exist to determine the desired level of “PITness” between 100% TTC and 100% PIT calibration.

Within non-Retail exposure classes, the statistical properties of default frequencies' time series do support reasonably robust PIT-TTC conversion frameworks. With knowledge of an obligor’s PIT and TTC PDs, hybrid PDs that obey a given calibration philosophy can be achieved by straightforward interpolation. However, within retail lending, the statistical properties of default frequencies’ time series are seldom stable and often cannot robustly support a PIT-TTC calibration framework.

A common means of approximating 100% PIT PDs is to implement a PIT calibration philosophy with periodic (e.g. monthly or quarterly) updates to the rating-to-PD or score-to-PD mapping. In-effect a time-varying latent variable is introduced, to fully explain temporal variability in default risk across the economic cycle.

There exists widespread acceptance that 100% PIT PDs are the appropriate input for certain key applications. However, for regulatory capital purposes firms are permitted to make choices of risk drivers (and weighting) that influence rating philosophy (subject of a previous article). In the remainder of this article we explore the advantages and disadvantages of a 100% PIT calibration philosophy for non-mortgage retail exposures’ regulatory capital models.

Advantages of PIT in Retail

At first glance, a Point-in-Time (PIT) calibration framework, with its inherent emphasis on current data and reduced reliance on historical assumptions, seems like a promising option in several key respects:

• Eliminates need for subjective assumptions concerning identification of economic cycle: The need for subjective or unstable assumptions concerning calibration levels is eliminated. For UK data in particular, a clear economic cycle may not be visible and public write-off data does not cover the early 1990s stressed period. A dynamic PIT calibration would therefore benefit model development timelines, achieving submission dates with a minimum set of assumption that need to be agreed.
• Eliminates need for subjective assumptions concerning whether data is representative: Given the lack of data history into the early 1990s, historical data is often considered unrepresentative of the external environment in terms of current system-wide lending practices and monetary policies. Again, the need for subjective adjustments during data gathering and model development is minimised by a dynamic PIT calibration.
• Dynamic calibration alignment: Internal lending practices have evolved given shifts in the external environment. The use of current data under dynamic PIT re-calibration helps to ensure that the calibration is appropriate to a current risk profile, thereby providing a current reflection of existing lending strategies and account management practices.

Disadvantages of PIT in Retail 

So, the simplicity of PIT calibration may reduce delivery risk in modelling programmes, where timelines are tight and consensus assumptions may be difficult to reach. However, without understanding the potential pitfalls here we risk oversimplifying the problem. We may also be ignoring some potentially material impacts that occur “over the horizon” too, downstream of model implementation, when estimates are used in the live environment. It is therefore important to consider the following issues:

• Stress Impact 

By reflecting prevailing economic conditions, a PIT calibration introduces inherent cyclicality. During downturn economic conditions, elevated defaults lead directly to elevated PIT PD estimates. This can then translate into a need to hold more risk-weighted assets (RWAs) on the balance sheet.

Benchmarking of global Qualifying Revolving Retail Exposures (QRRE) risk weight densities (i.e., RWAs normalised by exposure value) by Deloitte reveals a proportional relationship in PD. This is perhaps surprising, given that Basel typically treats the RWA formula as highly non-linear in PD. Even with some migrations into the non-linear region, the overall effect as reported by global banks’ public disclosures is minimal, when considering portfolio-level impacts.

Having established a proportional relationship, we find relative increases in default rates translate directly into increases in PD and risk weight density. A review of historical UK data also suggests that moderate stress might increase default rates by a factor of at least two. A fourfold increase is also entirely plausible if one considers public arrears data in other markets. The table below (Table 1) summarises the PD and RW% impacts of moderate (x2) and severe (x4) stresses to current PDs, with each input aligned to UK medians. To highlight the system-wide impact, we assume the TTC risk of new originations is maintained across the cycle. For comparability with standardised firms, we have also stated balance normalised RWAs.

Table 1: Impact of increase in default rates on probability of default (PD) and risk weight density

Source: Deloitte Benchmarking of Global Qualifying Revolving Retail Exposures (QRRE) Risk Weight Densities, 2024

The table above can be interpreted as risk weights of a monoline lender with only retail unsecured exposures, under moderate and severe stresses, with like-for-like replacement of maturing and defaulting exposures.

The impacts on capital requirements (be they simulated via a stress test for Pillar 2, or an actual stress impact in Pillar 1) are plain to see in the table data. At diversified lenders, the impacts are likely to be diminished by the “diversification benefit” of different portfolios responding differently to the cycle (e.g., peaking at different time points as the scenario develops). And even should Pillar 2 capital requirements not be allocated (i.e., “held centrally”), it is still important to bear in mind that even a diversified banking group may have ring-fenced and/or monoline subsidiaries that would bear the Pillar 1 requirement directly during a period of actual stress.

• Model Accuracy

Changing economic conditions can cause fluctuations in PIT PD estimates even for borrowers with good credit scores. PIT calibrations are typically viewed or reported at the portfolio-level, with estimation error attributed to the lag between observations and outcomes (typically over 12 months, by definition) plus the implementation period. However, the portfolio-level view masks grade-level volatility that is inconsistent across grades and over time.

As an analogy, the PIT calibration is like using yesterday’s rainfall to predict tomorrow’s. Viewed across all seasons and regions, the estimation error may seem small, until one considers the following factors:

1. The estimation error is small, across the year, in regions that do not experience seasonal variations in rainfall (by analogy, customers with the worst credit scores); and

2. The estimation error is largest at the change-points between seasons (by analogy, at the turning points in the economic cycle, where default rates are moving up or down most steeply).

This variability in estimation error becomes problematic for banks then in two key respects:

1. Firstly, estimating tomorrow’s rainfall (by analogy, PIT PD) is simply a more difficult problem, requiring a more complex model than estimating the average rainfall across the year (by analogy, LRA PD). As a result, volatility in RWAs becomes an expected outcome.

2. The greatest volatility is also typically observed in the risk grades occupied by the lowest risk customers – i.e. the very cohorts where the business is likely to be focusing its efforts. As a result, the business bears an additional capital cost in precisely the cohorts where the PIT approach would seemingly be beneficial in terms of absolute PD levels.

• Model Explainability and Compliance

During periods of rising default rates, in particular, banks may choose to reduce new lending to riskier obligors and/or shift strategy towards higher quality originations. As a result, obligor-specific risk drivers may move in the opposite direction to the exogenous (calibration) factor. Whilst the PRA has clarified the admissibility in principle of “PIT plus buffer” calibrations, the body text of the accompanying near-final SS4/24 requires in paragraph 10.12 that firms “understand the characteristics and dynamics of the assignment of obligors or exposures to grades or pools”. Compliance risk notwithstanding, unexplainable models tend to be associated with volatility in RWA actuals, and can be even harder to explain in accessible terms using a simple narrative.

• Deviation from Global Standards

Finally, the text of the Basel rules and their various implementations are silent on rating philosophy, giving firms leeway to select both a rating philosophy and risk drivers that are appropriate to their business model. However, they also make clear that the only acceptable calibration philosophy is Long Run Average (“LRA”). Under an LRA calibration, PDs by obligor grade or pool reflect “long run averages of one-year default rates over a representative mix of good and bad economic periods”. To apply any other calibration philosophy would constitute a deviation from global standards. Such a deviation could lead to market inconsistent RWAs and/or Pillar 2 capital requirements, hindering competitiveness and ultimately the bank’s return on equity (ROE).

Conclusion

In this article we have dug into the pros and cons of PIT PD calibration in some detail, focusing on retail unsecured IRBs that have hitherto not been subject to widespread public discourse. Whilst the apparent simplicity of PIT calibration may seem appealing from a delivery risk perspective, significant headwinds are introduced downstream of model implementation, whose consequences may only become fully apparent in an actual stress.

To judge whether the benefits of PIT calibration ultimately outweigh the costs for individual banks requires comprehensive analysis and a cross-functional consensus. Whether this is optimal from a broader system-wide financial stability perspective would likely require supervisory investigation of individual bank and system-wide stressed impacts.

If you would like to talk to us about any of the issues raised in this article, please reach out to the authors below.