Prudential Regulation Authority Rulebook

4.1

The SCR is defined as corresponding to ‘the Value-at-Risk of [the firm’s] basic own funds subject to a confidence level of 99.5% over a one-year period’.^[7] The modelled change in basic own funds will capture any change in the MA.

4.2

When considering how a stress event can impact the MA, the PRA expects firms to capture any changes in the:

• value and cash-flow profile (before and after risk adjustment) of assets held in the MA portfolio as a result of the stress event; and
• cash-flow profile of the MA liabilities as a result of the stress event.

4.3

These changes can result from either actual portfolio losses due to the stress event or from changes in valuation assumptions triggered by new data or other information emerging over the one-year period. Furthermore, new risks may emerge in stress and existing risks could become more prevalent.

4.4

Steps 1 and 2 of the PRA’s five-step framework address the first of the points in paragraph 4.2 above. The second point is relevant to Steps 3, 4 and 5 and is discussed in Chapter 5.

4.5

The PRA expects firms to determine the change in the MA asset portfolio over one year. This will include changes in asset values and, for some assets including those with HP cash flows, any changes to the cash flow profile. This is intended to capture only those assets that were already in the MA portfolio pre-stress and not any assets subsequently injected in order to rebalance the portfolio post-stress.

4.6

Any firm that does not explicitly model a change in the value of the assets and, where applicable, a change in asset cash flows is unlikely to be able to demonstrate that it can continue to meet the MA eligibility conditions in stress conditions. In particular, this includes assessing whether the appropriate level of cash flow matching has been achieved and whether the value of assets in the MA portfolio covers the best estimate value of the MA liabilities.

4.7

The methodology used to calculate the asset values under stress should also determine the credit quality (eg credit rating) of a firm’s assets under the modelled stresses at a suitable level of granularity, considering whether it should reflect differences in credit quality by rating notch. This is a key input into the MA in stress calculation.

4.8

Many of the considerations in modelling asset-side credit risk are common to the modelling of the stressed FS. The remaining paragraphs in this chapter refer only to the FS. However, the PRA encourages firms to consider their wider applicability.

4.9

In determining the level of stressed MA, the PRA expects firms to take appropriate account of the risks they retain in stress conditions including:

• downgrade and default risk (discussed below under ‘Modelling considerations in respect of downgrade and default risk’);
• basis risk;
• concentration risk; and
• any additional risks associated with assets with HP cash flows (discussed below under ‘Modelling considerations for assets with HP cash flows’).

4.10

The PRA expects the range of risks is likely to be broader for assets other than corporate bonds such as direct lending, reflecting their more bespoke nature.

4.11

Possible sources of basis risk that the PRA expects firms to allow for in respect of their MA portfolios include:

• the use of historical data to inform a firm’s calibrations or assumptions, where the dataset(s) used may not be reflective of the actual holdings and/or risk profile of the MA portfolio. A firm should consider whether any basis risk arises from the distribution of the firm’s asset holdings by rating notch compared to that assumed in the data and judgements used to calibrate its model. Also, even if historical data does perfectly reflect a firm’s asset holdings, the past may not be a good guide to the future and so an element of basis risk should be assumed to be present;^[8]
• when firms choose to implement hedging strategies that are imperfect hedges; and
• if the risk profile of some of a firm’s assets differs materially from the assumptions used by the PRA or the firm to calibrate the FS for the purposes of calculating the TPs.

4.12

Where firms allow for basis risk when determining the stressed values of their asset holdings, they should consider how this affects the calculation of the FS in stress and whether basis risk has been appropriately reflected in the stressed FS.

4.13

Concentration risk can arise from a firm being disproportionately exposed to, for example, a given issuer or sector.

4.14

In assessing the extent to which a firm is exposed to concentration risks in its MA portfolio, the PRA expects a firm to use a number of different approaches including potentially:

• analysing the composition of its current MA portfolio(s) and the associated investment mandates and policies to identify potential areas of concentration, for example, large single name exposures, sector exposures, exposures to sub-investment grade assets or simply concentration arising from having relatively few different asset holdings comprising the total portfolio;
• including quantitative measurements where possible (eg using the Herfindahl index^[9]); and
• conducting stress and/or scenario testing to assess to what degree concentration risk in the MA portfolio could crystallise in a severe credit event, for example increased concentration of exposure to sub-investment grade assets.

4.15

Concentration risk on non-corporate bond assets is likely to be more complex and could arise from a wider range of sources. Where a firm has material exposure to assets other than corporate bonds in its MA portfolio, any analysis of concentration risk exposure should reflect the nature of these assets and the types of concentration risks to which they give rise.

4.16

If a firm considers it does not have material exposure to concentration risk, it should be able to justify this conclusion through analysis of its own portfolio and should show how any potential concentration risks are mitigated (eg through exposure limits in the investment mandates).

4.17

If, through its own analysis, a firm considers its exposure to concentration risk to be material, it should make an allowance in the model calibration for the additional variability in losses that might be incurred in an economic stress. If this allowance is based on an approximation, the firm should be able to show that this approximation is reasonable given the risk exposure it is intended to capture.

4.18

The PRA does not have a preference or expectation as to the methodological approach used by firms to model the stressed FS, as long as the chosen approach meets the internal model requirements.

4.19

The PRA expects firms to justify the granularity of the underlying modelling performed to determine the stressed FS (eg by asset class, credit quality, sector, term).

4.20

As a starting point, the PRA expects firms to consider modelling the FS at the same level of granularity as is used for the purposes of calculating TPs. However, a different level of granularity can also be justified. This is likely to be particularly pertinent where the firm’s MA portfolio includes a material proportion of assets other than corporate bonds or where using the same level of granularity would cause the model to become unduly complex.

4.21

A firm should strike a balance between modelling to a level of granularity that reflects its risk profile and ensuring sufficient credible evidence, supported by expert judgement, to develop calibrations reliably at this level of granularity.

4.21A

The PRA expects a firm to justify any differences in the granularity at which credit quality is reflected in its internal model compared to that used for the purposes of calculating TPs. This should include consideration of the following factors:

• the composition of the MA portfolio by rating notch relative to the indices used to calibrate the transition and spread stresses (basis risk). For example, the PRA would expect a firm with a bias or concentration towards the lowest or highest notch in each CQS to make an appropriate allowance for this in its SCR calculation and, all else being equal (including the distribution of assets by CQS), for it to impact the quantification of the firm’s SCR;
• the pattern of variation in spread and transition stresses by rating notch;
• the consistency between the granularity at which spreads and transitions are modelled;
• the availability and credibility of relevant data;
• the materiality of the impact of the adjustment to the FS to allow for variation in credit quality by rating notch for the purposes of calculating the TPs (Matching Adjustment 6);
• the consistency with the granularity at which the firm uses the model in accordance with Solvency Capital Requirement - Internal Models 10.3;
• the rebalancing assumptions made within the internal model and the granularity of risk modelling required to support those assumptions; and
• the type of modelling approach used. For example, a model that quantifies the SCR by determining the total stressed FS might reverse out any impacts from notching in the TPs and hence the firm may require a more granular modelling approach to address this.

4.21B

A firm may consider that its risk profile requires it to increase the granularity at which credit quality is reflected in its internal model, for example to model the FS by rating notch, but that developing its model may not be straightforward and may take some time. In this circumstance, the PRA expects the firm to consider other possible remedies until it has completed the necessary development, including potentially increasing the capital requirement calculated by the internal model, in order to ensure that the SCR complies with the core calibration standards at all times.^[10]

4.22

In the case of firms that have material exposure to less liquid assets (eg illiquid, direct investments) within the MA portfolio, the PRA expects a separate approach to be developed to model the FS for these assets. While an approach similar to that used for corporate bonds may be possible, the level of adaptation from the core corporate bond methodology and calibration should depend on the similarity of the assets in question to corporate bonds. In some cases a more bespoke methodology may be necessary. Where firms do not distinguish between asset classes in their modelling, then the appropriateness of the model for each asset class should be clearly justified.

4.23

The PRA is open to firms applying proportionate modelling approaches (likely to contain limitations and approximations) where they have only small exposures to certain asset classes, but the PRA does not expect firms to make material investment decisions using a model that does not appropriately reflect the risk profile of such investments.

4.24

Firms may seek to use their models to determine the change in FS in stress conditions or the total FS in stress conditions. While the PRA does not have a preference for either metric, firms are expected to acknowledge, when determining their preferred approach, that these metrics imply two markedly different modelling philosophies that will have a direct impact on the extent to which the SCR behaves in a cyclical manner. The PRA expects a firm to understand and justify the approach it has chosen and its limitations. Where a firm has identified scenarios where the approach operates in a way it considers inappropriate (eg produces counter-intuitive results relative to the change in risk profile), the firm should identify the actions it could potentially take in response, for example increasing the capital requirement calculated by the internal model, in order to ensure that the SCR complies with the core calibration standards at all times.

4.25

When firms use historical data they should consider whether the data is:

• of sufficient length and quality to contribute towards a credible calibration for the risk in question;
• likely to contain a sufficiently extreme event or events to be useful for calibration purposes; and
• useful in determining how potential future credit events may manifest themselves.

4.26

In particular, firms should analyse whether actual migration and default rates over the future holding period of their assets could be more onerous than those observed in historical stress events, and make adjustments accordingly. The PRA also expects firms to set out clearly any judgements made around potential future crisis events that may differ in nature, magnitude and duration to crises seen previously.

4.27

Firms may model stressed FS by modifying the approach and inputs used to produce the FS for determining the TPs. The following paragraphs are of particular relevance for firms using this approach.

4.28

Chapter 4 of the Matching Adjustment Part of the PRA rulebook (restating as rules the relevant provisions of the IRPR regulations) sets out how the MA and FS should be calculated for the purpose of determining TPs. While the PRA considers that the MA calculation method should not change in stress conditions, firms should consider if the assumptions used to calculate the MA and FS for the TP calculation, including any additions to the FS (either for assets with HP cash flows as per Matching Adjustment 4.16 or for other reasons as per Matching Adjustment 4.17), remain appropriate in stress conditions.

4.29

Firms should ensure that the MA on sub-investment grade assets, including on assets that downgrade to sub-investment grade as a result of the stress, remains appropriate post-stress, taking account of the increased risks associated with such assets and the need to comply with the Prudent Person Principle (PPP) at all times. As a continuation of (or for consistency with) existing modelling approaches, some firms may choose to assume that the MA on sub-investment grade assets does not exceed that on assets of investment grade quality of the same duration and asset class. Some firms may instead choose to cap the MA on sub-investment grade assets in a different way in order to reflect the additional risks and PPP implications of sub-investment grade exposures. The PRA considers that such approaches could potentially be a way for firms to demonstrate compliance with the internal model calibration standards. Regardless of the approach taken, firms should ensure that the resulting stresses applied to sub-investment grade assets are appropriately calibrated having regard to:

• the availability of data;
• the extent to which these assets are assumed to default in stress conditions, including the assumptions and judgements about recoveries and the associated workout processes;
• the greater breadth of risks associated with sub-investment grade assets; and
• the potential concentration of risks both pre-stress and post-stress, recognising that over-exposure to speculative investments is unlikely to be compatible with the prudent management of the portfolio as required by the PPP. This presents a risk of forced sales of such assets in stress scenarios in order to ensure continued compliance with risk management requirements, including a firm’s own risk limits and investment mandates.

4.30

The PRA expects firms to maintain a floor (ie a minimum level of FS at the appropriate point of the calculation) based on long-term average spreads as part of their modelling of the stressed FS. As a minimum, the PRA expects firms to reapply the methodology and calibration of the floor as set out in Matching Adjustment 4.11 to 4.15. If any changes are made to the floor, the PRA expects these changes to be justified. They should not result in a calibration below that which would have been obtained by re-applying the methodology and calibration used to calculate the TPs.

4.31

For all approaches, firms may also wish to apply other limits to the stressed FS. Often these will be grounded in historical experience or expressed as a percentage of total spread widening. While such limits can be helpful, they should not be an essential feature of firms’ models or overshadow the importance of any more detailed modelling work undertaken.

4.32

Notwithstanding the above points, the PRA expects the methods used to determine the stressed FS calibrations to be grounded in the requirement that the stressed FS reflects the risks retained by the firm in stress conditions. However, within their internal models, firms may need to develop approaches that use different models and/or assumptions to those used to calibrate the FS for the purposes of determining the TPs calculation, in order for the SCR to take account of all quantifiable risks to which the firm is exposed. Firms are nonetheless expected to ensure that as a starting point they use, where available, the FS information published by the PRA, adjusted as required to allow the FS to vary by rating notch^[11], for the purpose of calculating TPs.

4.33

Specifically for corporate bonds, a firm is expected to ensure that if it is using an approach to model the stressed FS that cannot closely replicate the FS used to calculate the TPs (in basis points or £ millions), consideration should be given to:

• how the FS or MA used to determine the TPs would compare to a proxy calculation based on the firm’s own assumptions, and what the key reasons are for any difference; and
• how the firm has chosen to express the stressed FS (ie as the total FS or as the change in FS) and whether the difference between its assumptions at the 50th percentile compared to the assumptions used to calculate the TPs could give rise to the SCR being potentially under- or over-stated.

4.34

The matrix format of historical transition data potentially makes it difficult to model and/or compare transition data over time. When using transition data, the PRA expects firms to:

• consider different approaches to comparing transition matrices and assessing their relative strength. The PRA’s preferred approach is for firms to consider the whole matrix rather than just a single cell or small selection of cells. However, a firm could also use an approach that considers only a selection of cells provided it has a procedure to translate the output of this alternative approach into a whole matrix;
• compare its modelled 1-in-200 year transition matrix and matrices at other extreme percentiles against key historical transition events, notably the 1930s Great Depression (and 1932 and 1933 experience in particular). This should include considering how the matrices themselves compare as well as relevant outputs; and
• justify any shortfall between its 1-in-200 year transitions scenario and the actual transitions experience implied by these events (and the impact of this on the level of capital held). The firm should explain how it has validated that the level of stress it is applying is capturing all quantifiable risks to which it is exposed in this context.

4.35

In relation to transitions data for corporate bond assets, withdrawn ratings are a specific feature of the data that should be allowed for. A rating is withdrawn where an entity or financial instrument is no longer rated by the ratings agency concerned. Reasons for withdrawals of rating can be varied and are not necessarily indicative of impending downgrade or default. Firms should be able to justify the reasonableness of the approach used to allocate withdrawn ratings across the transition matrix as well as provide sensitivity analysis that quantifies the impact of using different allocations.

4.35A

The PRA expects firms to consider the implications of any difference in granularity between the available historical transition data and the set of assumptions required for modelling, particularly if attempting to model transitions for notched ratings. Even if there is no difference, firms should consider whether low volumes of historical data for some categories of transitions could result in adjustments being required to the data when constructing estimates of future transition probabilities.

4.36

In order to ensure that the stressed FS calibration fully captures the risks retained on a forward-looking basis, a firm should consider whether its chosen methodology would allow the stressed experience (for one or more of the metrics modelled) to revert to more normal levels over a given period rather than instantaneously. This can be achieved through an explicit incorporation of a reversionary period (a ‘glide path’) within the model but other approaches are also possible.

4.37

In calibrating a glide path, the PRA expects consideration to be given to historical data and events as well as the theoretical justification.

4.38

Where a glide path is being modelled in respect of more than one element of the model (eg transitions and spreads) then the length and severity of the stressed period for different elements would not automatically be considered independent. The relationship between different glide paths should therefore be considered and any inconsistency should be justified.

4.39

Allowing stressed experience to revert to ‘normal’ over an extended period should not be seen as a correction for limitations elsewhere in the model.

4.40

The PRA considers that a distinction can usefully be drawn between assets with HP cash flows with economic variability and those with event-driven variability. Firms should consider how the cash flows and FS addition will change under stress for both types of assets.

4.41

For assets with economic variability, the cash flow profile under stress should be consistent with the modelled economic conditions. Where any optionality is ‘in the money’ the projection should reflect the increased likelihood of take-up by a rational counterparty. Firms should also consider the level of uncertainty around the stressed cash flows and the implications this has for any FS addition.

4.42

A lack of reliable data may make it challenging to model the stressed cash flows of assets that are exposed to event-driven variability. The PRA considers that a possible approach is to allow for the increased uncertainty via a change to the FS addition or a cap on the MA. In deciding on an approach, firms should carefully consider:

• the potential for the cash flow profile to change materially;
• any liquidity or reinvestment costs; and
• correlations with the wider economic environment.