Impact of a one-year stress on the matching adjustment


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’.6 The modelled change in basic own funds will capture any change in the MA.


  • 6. PRA Rulebook: SII Firms – Solvency Capital Requirement – General Provisions 3.4.


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.


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.


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.

Asset side stress to MA portfolio assets


The PRA expects firms to determine the change in the MA asset portfolio value over one year. This is intended to capture only those assets that were already in the MA portfolio prestress and not any assets subsequently injected in order to rebalance the portfolio post-stress.


Any firm that does not explicitly model a change in the value of the assets is unlikely to be able to demonstrate that it can continue to meet the MA requirements in stress, and in particular to determine whether the value of assets in the MA portfolio covers the best estimate value of the MA liabilities.


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. This is a key input into the MA in stress calculation.


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.

Risks retained in stress


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

  • downgrade and default risk (discussed below under ‘Modelling considerations in respect of downgrade and default risk’);
  • basis risk; and
  • concentration risk.


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.

Basis risk


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

  • if firms make use of historical data to inform their calibrations or assumptions, the dataset(s) used may not be reflective of the actual holdings and/or risk profile of the MA portfolio. Even if historical data does perfectly reflect firms’ 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;7
  • when firms choose to implement hedging strategies that are imperfect hedges; and
  • if the risk profile of some of the firm’s assets differs materially from the assumptions used by EIOPA to calibrate the FS for the purposes of calculating the TPs.


  • 7. It may also be the case that calibrating statistics based on historical data does not fully capture the statistical qualities of the forward-looking distribution.


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.

Concentration risk


Concentration risk can arise from a firm being disproportionately exposed to, for example, a given issuer or sector. If concentration risk is not captured in the FS used in the calculation of TPs, for example if the FS calibration implicitly assumes the portfolio is well diversified, then firms may be exposed to additional concentration risk.


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, or simply concentration arising from having relatively few different asset holdings comprising the total portfolio;
  • including quantitative measurements where possible (eg using the Herfindahl index8); 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.


  • 8. The Herfindahl index is a simple measure of concentration risk, defined as the sum of the squares of the ‘market shares’ of each asset, where the ‘market share’ is the ratio of an asset’s value to the total asset value in the MA portfolio.


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, then any analysis of concentration risk exposure should reflect the nature of these assets and the types of concentration risks to which they give rise.


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).


If through the firm’s analysis it 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.

General modelling considerations when determining the FS calibration post stress


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 required tests and standards.


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


As a starting point the PRA expects firms to consider modelling the FS at the same level of granularity as in the calibration provided by EIOPA 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.


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


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.


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.


Firms may seek to use their models to determine the change in FS in stress or the total FS in stress. 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 firms to understand and justify the approach they have 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 introducing an overlay using expert judgement.


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.


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.

Modelling considerations when determining an updated forward-looking view of the FS post stress


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


Article 77c of the Solvency II Directive and Article 54 of the Delegated Regulation set out the calculation method for the MA, the assumptions which underpin the MA and the approach which EIOPA should use to derive the technical information used to calculate the MA in accordance with Technical Provisions 7. While the PRA considers that the MA calculation method should not change in stress, the MA assumptions in the Solvency II Directive and Delegated Regulation are specifically set out in the context of the TPs calculation and firms should therefore consider whether they remain appropriate in stress.


Firms should ensure that the MA on sub-investment grade assets remains appropriate. Unless there are strongly justified arguments for moving away from the requirement in Technical Provisions 7.2(3) that (for the purposes of determining TPs) the MA on subinvestment grade assets does not exceed that on assets of investment grade credit quality of the same duration and asset class, then the PRA expects firms to continue to apply this restriction in stress conditions.


The PRA expects firms to maintain a floor (ie a minimum level of FS) 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 Article 77c of the Solvency II Directive. 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.


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.


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. 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 they use the EIOPA calibration to determine the FS for purposes of calculating TPs.


Specifically for corporate bonds, firms are expected to ensure that if they are 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 EIOPA assumptions could give rise to the SCR being potentially under- or over-stated.

Modelling considerations in respect of downgrade and default risk


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 their modelled 1 in 200 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 their 1 in 200 transitions scenario and the actual transitions experience implied by these events (and the impact of this on the level of capital held). Firms should explain how they have validated that the level of stress they are applying is capturing all quantifiable risks to which they are exposed in this context.


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.


In order to ensure that the stressed FS calibration fully captures the risks retained on a forward-looking basis, firms should consider whether their 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.


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


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.


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