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A new spin for a new cycle

Hybrid PD cyclicality enters Pillar 2

In this article we discuss some of the challenges that firms using the Internal Ratings Based (IRB) approach face in selecting cyclicality assumptions as inputs to pillar 2 models. We explore the impact of moving from a 30% “prior belief” of mortgages PD cyclicality, to a 70% “posterior” that may or may not be inflated by trends in time series credit risk data that are not characteristic of a true economic response.

We present sensitivity analysis and suggest that the impact of moving from a 30% “prior belief” to 70% “posterior” cyclicality value could be worth around +4 percentage points on the peak stress risk weight, for a typical mortgages portfolio under the 2022 Annual Cyclical Stress (ACS) scenario. Conversely, a firm that holds capital at a 30% belief but experiences 70% in the next recession would be under-capitalised by the same amount.

We suggest that firms may wish to redevelop risk ranking models that minimise the uncertainty around cyclicality estimates, as opposed to minimising a particular point value observation.

Introduction and Context

The transition to “hybrid” probability of default (PD) models for Pillar 1 capital requirements has brought the concept of cyclicality to the fore in the retail credit risk community. The concept behind a hybrid PD calibration is intuitive, as well as reasonably familiar to the corporate modelling community. However, when applied to retail exposures the concept of cyclicality has proven considerably more challenging to implement.

Cyclicality describes the economic response of a rating system (or indeed rating grade) to movements in default rate (or, in corporate, market-implied Estimated Default Frequencies, EDFs): For a given movement in macro default rate or EDF, to what degree are PDs (and hence risk weighted assets, RWAs) likely to track these reflections of the credit cycle?

Corporate credit modelling is sometimes perceived as suffering from a paucity of default data. However, there exist copious volumes of EDF data from which a reasonably representative sample can be drawn. Once comfortable with EDF data, it is reasonably straightforward to parameterise cyclicality values at the grade-level. Typically, we find that an agency rating grade of AAA is close to 100% Through The Cycle (TTC) and a C rating is closer to 100% Point In Time (PIT).

By contrast, attempts to quantify cyclicality in retail credit data are faced with a number of challenges that we have previously discussed and include:

  • Use of longer time lags leads to cyclicality estimates being distorted by changes in portfolio composition.
  • There is little consensus or precedent for converting the mandated formula into a probability model that can be parametrised using standard techniques. Indeed, the most obvious approach (to build a distribution of empirical cyclicality values and seek the mean or mode) seems likely to return fat-tailed noise in the event of any noise in the denominator. Solutions in first differences, or limiting to periods with changes in default rate that are deemed significant, seem most appropriate in econometric terms but (at the time of writing) firms have not succeeded in gaining regulatory acceptance of such assumptions.
  • The most recent period of rising default rates (2008/9) has representativeness issues that include structural changes in the mortgages market (e.g. underwriting standards being impacted by the Mortgage Market Review) as well as the fact that interest rates were falling towards (or at) zero during that period.

Pillar 2

In parallel with the redevelopment of retail credit risk Internal Ratings Based (IRB) Pillar 1 capital models, many firms have updated (or are in the process of updating) their forecasting and stress testing models, to accommodate cyclicality as an input to the Pillar 2 calculation process. This allows firms to make forward-looking assumptions that deviate from simply describing historical actuals, and crucially allows the “pillar 2 number” to be sensitised reasonably quickly, should default rates and PDs start to rise faster than the cyclicality assumption in the capital plan.

An ongoing challenge, however, lies in the selection of cyclicality value for stress testing purposes.

A priori, at the point when the PRA’s expectation of a 30% cyclicality cap in back-casting approaches was published in 2017, a 30% cyclicality assumption would have seemed reasonable. With risk drivers selected and weighted to minimise cyclicality, cyclicality measured using econometric techniques to isolate the economic response, values significantly below 30% are readily achievable. We should, however, recognise that the historical cyclicality may not be fully representative of the future – changes. Nevertheless, even with significant prudence, it was hard to imagine a forward-looking view of cyclicality materially exceeding 30%.

A higher (e.g. 50% to 70%) cyclicality value can be observed using a longer period to measure differences in PD and observed default rate (ODR). But by using a longer period, we risk observing a drift in time series that is not associated with exogenous economic effects. We previously showed that the PD drift associated with even a relatively modest (single rating notch) improvement in lending quality can easily be mistaken for double-digit cyclicality with rating assignment 100% TTC (i.e. 0% cyclical) by-design. Indeed, some firms have gone so far as to construct 100% TTC challenger models using only origination characteristics, to confirm that the observed cyclicality is an artefact of changes in risk appetite.

SS11/13 paragraph 16.2 requires that firms “consider the possibility that the model proves more cyclical than anticipated”. Whilst this is not a requirement per se to increase the cyclicality input into stress testing beyond the reported Pillar 1 value, it is likely to discourage firms from selecting a lower number, even if doing so is needed to isolate the economic responsiveness per SS11/13 paragraph 12.3.

We were therefore curious to understand the financial impact of moving from a “prior belief” cyclicality input value of 30% to a “posterior” value of 70%.


We simulated the peak performing Risk Weight (RW%) that might be achieved using a hybrid PD model, for various cyclicality assumptions.

We started with a typical retail mortgage portfolio’s rating distribution, and solved for the size of rating migration that is needed to align the average performing PD with a given target PD. The target PD is calculated by re-arranging the PRA’s formula, for a given cyclicality value and movement in observed default rate between start-point and peak.

Previous years’ ACS and SST results pointed to (generally) the year-1 PD and CET1 shocks dominating (with LGD remaining at the 10% floor in this period). The 2022 scenario suggests a simultaneous PD and LGD shock in a later period. We therefore assumed an LGD migration from the 10% floor to a peak value of 15%. The results are broadly linear in LGD, so the choice of peak LGD doesn’t impact the results below.

The movements from start-point to peak-stress risk weight are summarised in the table below. We have normalised the results to allow for comparison between firms.

As an example, if the peak stress risk weight at 70% cyclicality were 28%, the equivalent peak stress risk weight at 30% cyclicality would be (1.18/1.37)*28%=24%, i.e. a 4 percentage point difference.


Normalised Peak RW%


















Assuming for a moment that a risk differentiation model’s true cyclicality value is 30%, then capitalising at 70% would suggest some level of opportunity cost of holding additional capital. Whilst it may be tempting to discuss methods of releasing the capital, the opposite phenomenon also holds: A firm that capitalises at 30% but experiences 70% going into the next stress, would be under-capitalised by the same amount.

To date, firms’ reported (or declared) cyclicality values have been a point value, across some assumption of the appropriate measurement period(s) and approach. Empirical experience, however, suggests that cyclicality values can be highly variable with respect to measurement period(s) and the approach. A reported overall value can easily mask variability in 12-month point values that range from below 0% to above 100%.

Risk driver selection techniques typically focus on minimising cyclicality. However, such techniques can therefore easily overlook the variability. Uncertainty naturally leads to prudence. Key to selecting the “right” cyclicality value for forecasting peak stress RWAs, is to minimise not the point-value itself, but the uncertainty around the point-value.

As IRB firms look towards their next redevelopment (typically retail unsecured products), users of model outputs should consider articulating business requirements to minimise or eliminate the uncertainty in cyclicality.

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