​​The matching adjustment attestation and portfolio concentration risk​

Attesting to high confidence in the asset portfolio earning the MA requires consideration of the construction of the portfolio. Most notably, a highly concentrated asset portfolio could plausibly be constructed with assets that each have a sufficient FS, but that has portfolio concentration risks that reduces confidence in the portfolio earning the MA.  

Asset portfolio concentration risk is not explicitly mentioned in the PRA Rulebook’s MA Instrument 2024 or in the relevant MA legislation², but there are two key references to concentration risk in the MA attestation section of SS7/18: 

• Paragraph 5.35’s description of stage 1 of the attestation process states: “Firms should consider whether there is any concentration of exposure (e.g. to any asset or sector) relative to the portfolio of assets underlying the FS calibration data…” 
• The first sentence of paragraph 5.36A: “When assessing the portfolio as a whole, the PRA expects firms to consider the degree to which there may be reduced diversification and increased risk to the MA due to concentration from a particular risk type or within a given asset class or sector.” 

The first of the above references to concentration risk is relevant to the attestation that the fundamental spreads include compensation for all retained risk. The second of the above references is relevant to the second element of the attestation: that the MA can be earned with a high degree of confidence from the assets held in the relevant portfolio of assets. And, in particular, to what the extent this confidence may be reduced by the MA portfolio’s concentration risks. This is the question we explore further below. 

Viewing the two-pronged MA attestation statement in the context of paragraph 5.36A suggests the attestation should address the following question: If we take it as given that every individual MA asset has a sufficient FS, is there anything about the MA portfolio construction that means we do not have a high degree of confidence in the MA being earned by the MA portfolio? 

A quantitative definition of ‘a high degree of confidence’ is not explicitly developed by the MA rules and regulations. It may be argued that there is a high degree of confidence in the MA being earned by any individual asset that has a sufficient FS, as the basic FS definition and calculation includes various elements of prudence. In particular, the inclusion of the Cost of Downgrade (CoD) element in the FS definition means that it is only the credit risk premium that is expected from a buy-and-annually-rebalance strategy that is included in the MA discount rate, whereas MA asset strategies for corporate bonds will usually be closer to a buy-and-maintain strategy that generates more credit risk – and hence more credit risk premium – over the lifetime run-off of the portfolio.

Furthermore, the method used in the basic FS for the calculation of the CoD parameter attaches zero probability to any rating upgrades, which is another clear source of prudence. And, of course, there is also the Long-Term Average Spread (LTAS) component of the FS. Nonetheless, there are arguably also sources of ‘imprudence’ in the basic FS’s calculation. For example, the market price differentials used in the CoD calibration are materially narrower than current or long-term average market spread differentials.  

Overall, it is therefore not unambiguously clear that we should inevitably have a high degree of confidence in the MA being earned by every individual asset with a sufficient FS. However, the PRA has set the expectation that the MA attestation should not generally prompt firms to hold FS additions over the basic FS for vanilla corporate bonds.

This implies that an appropriately constructed portfolio of vanilla corporate bonds (i.e. a portfolio that is managed in a manner consistent with the Prudent Person Principle) will meet the attestation’s standard for ‘a high degree of confidence in the MA being earned by the MA portfolio’ when the basic FSs are applied to those bonds.  

Given this, an effective approach to supporting the attestation that there is a high degree of confidence in the MA being earned by the MA portfolio, with due allowance for its concentration risks, involves the following steps: 

1. Analyse the risk profile of a portfolio of fully diversified vanilla corporate bonds. Consider the risks to the MA being earned over the long-term run-off of this portfolio. For example, what is the probability that the portfolio does not earn the MA? This provides a benchmark or ‘baseline’. 
2. Next, consider how the MA risk profile is impacted by the composition of the actual MA portfolio. In particular, show how the MA risk profile is impacted by the portfolio risk concentrations that are present in the portfolio. For example, has the portfolio’s concentration risks resulted in a material increase in the probability that the portfolio does not earn the MA, relative to the fully diversified case? 
3. If this impact is not material, this suggests portfolio concentration risks do not have a material impact on the high degree of confidence in the MA being earned by the portfolio, and we can be satisfied that we meet 5.36A’s requirement to ‘consider the degree to which there may be reduced diversification and increased risk to the MA due to concentration from a particular risk type or within a given asset class or sector’. 

The case study below demonstrates an analytical approach to implementing each of the above three steps.

Suppose we have a single fixed MA liability cashflow that is due in ten years. This liability cashflow is backed by a portfolio of vanilla ten-year zero-coupon non-financial corporate bonds.  

We wish to consider the probability distribution of the realised rate of return of the bond portfolio over the ten-year liability cashflow horizon. In this example, we assume that the bonds are held to maturity, that the recoverable from any default that occurs within the ten-year projection is equal to the price of a risk-free bond that pays 30% of the bond’s contractual cashflow in year ten, and that the recoverable is invested in the matching zero-coupon government bond.  

Note that, in this setting, the realised rate of return of the portfolio is not a function of the changes in the levels of credit spreads or risk-free yields that occur over the ten-year projection. The probability distribution of the realised rate of return will be a function of the joint default experience of the corporate bonds.  

To analyse this, our illustrative example uses a relatively simple stochastic credit default model. In particular, we use a one-factor stochastic credit risk model with the following key assumptions: 

• Corporate bond credit rating transitions and defaults follow S&P’s average multiyear global corporate transition matrix (1981 to 2023)³. The transition matrix is assumed to be static over the ten-year projection. 
• Credit rating transitions of individual issuers are subject to a systematic risk factor that affects all issuers, and an idiosyncratic risk factor that affects each bond issuer individually. The correlation parameter used to drive the common exposure to the systematic risk is ρ = 0.30. This is a standard basic approach to the joint modelling of credit rating transitions.⁴ 

If the model’s correlation parameter was zero, then we could entirely diversify away the uncertainty in credit default rates. By holding enough bonds, we could ensure every year’s experience was equal to the assumed credit transition matrix and the ten-year realised portfolio return would be a fixed value that is knowable in advance. However, the use of a positive correlation parameter introduces non-diversifiable credit default risk – no matter how many bonds we hold, the positive correlation between credit quality changes of different bond issuers means that we cannot completely diversify away the default risk, and we will therefore experience some ‘good’ and some ‘bad’ portfolio default outcomes, even when the portfolio is diversified as fully as possible. The model structure and calibration used in this analysis produces a 99.5th percentile one-year credit rating transition matrix - this has similar levels of downgrades and defaults to the 1932 US corporate credit rating transition experience that is often used as a benchmark for credit risk internal models. 

We consider a corporate bond portfolio with equally weighted holdings (by market value) in 1000 bonds with the following credit ratings: 

We use the following assumptions that are based on UK bond index prices and PRA MA parameters as at 30 November 2024: 

The MA attestation requires that the MA discount rate (#2) can be earned by the MA portfolio with a high degree of confidence. We assess this by applying the above stochastic credit model to the bond portfolio and analysing the probability distribution of the annualised realised return. And to gain further insight into the characteristics of the realised return distribution, we also show how it compares with the MA discount rate before applying the LTAS (#3) and before applying both the Cost of Downgrade (CoD) and the LTAS (#4). 

The chart below shows the probability distribution of the ten-year annualised realised portfolio return as produced by 15,000 simulations, together with the various MA discount rate components discussed above.

Chart one: Cumulative probability distribution of the portfolio annualised realised return and the MA discount rate

Chart one shows that our stochastic model implies that the probability of the realised portfolio return being less than the MA discount rate is only 6%. To the authors, this is a surprisingly low probability – after all, this is before any use is made of the capital held outside the MA portfolio to support the credit risk in the portfolio. It is also materially lower than the 15% probability that is referred to in the PRA’s calibration of Fundamental Spread additions for non-fixed highly predictable cashflows in SS7/18. Analysis of the incremental impacts of the components of the FS on the probability of exceeding the discount rate can provide some further insight into the characteristics of this realised return distribution. 

Firstly, we can see that the probability of the realised portfolio return being lower than the yield less the probability of default (PD) component of the FS is 40%. This is an intuitive result: the portfolio is buy-and-hold, and so it does not incur a downgrade rebalancing cost. On average, the portfolio losses should be equal to the expected default loss. Given the FS PD calibration uses similar empirical data to that used to calibrate our stochastic model, we would expect the portfolio realised return to exceed the yield less PD around half the time. The negative skew in credit return outcomes means that the median return exceeds the mean return, and so the portfolio does better than the yield less PD a bit more than half the time. 

The chart shows that including the CoD allowance in the FS reduces the probability that the portfolio realised return does not exceed the discount rate from 40% to 19%. This is around the level of probability that we anticipated would be achieved by this portfolio. It is the inclusion of the LTAS that has the effect of reducing the MA discount rate to the level that is exceeded by the portfolio realised return with a probability of approximately 94%.   

The above analysis is quite striking but we should not rush to infer that LTASs or MA FSs in general are necessarily too high. In reality, MA portfolios will almost always use some form of credit re-balancing strategy that will generate a CoD component in their realised returns. Moreover, the stochastic model used in this analysis is a relatively simple one that may understate some form of risks. Most notably, the assumption that the credit rating transition matrix is static and does not vary with market conditions may understate long-term credit default tail risk (and this is arguably the risk that MA credit risk SCR is intended to capture). The key purpose of this analysis is to provide a baseline from which we can analyse the incremental effects of portfolio concentration risks. This is the focus of the next section. 

There are a number of ways in which credit concentration risks can arise in an MA portfolio. Most simply, a portfolio can have a concentrated exposure to a single counterparty through its direct holdings in bonds or loans issued by that counterparty. A more nuanced form of concentration risk can arise from indirect exposures, for example, where credit-risky assets issued by different counterparties, perhaps even in different sectors, have credit rating methodologies that depend on a common factor, such as the credit rating or financial strength of a third entity.  

We expect that credit concentration risks in MA portfolios will most commonly arise from indirect forms of exposure. In particular, a number of significant MA asset classes may use credit rating methodologies that reference the financial strength of the UK government. So, whilst UK gilts are considered credit risk-free for the purposes of Solvency II and the MA, a significant number of assets in an MA portfolio could nonetheless have a credit quality that is a function of the credit rating of the UK government. The impact of the gilt downgrade of 2016 on the credit ratings of assets in some important investment sectors for MA portfolios provides a good illustration of this effect. 

Let’s now re-visit our portfolio return analysis. Our previous results assumed the portfolio consisted of 1,000 issuers whose credit ratings were correlated through a single systematic risk factor. We’ll now consider the cases where either 100 or 200 of the portfolio’s 450 A-rated bonds have an indirect exposure to a single third entity’s credit rating. We will assume that this third entity currently has a credit rating of A; and that any change in the credit rating of the third entity is immediately transmitted to the credit ratings of the corporate bonds with this form of exposure.  

Chart two shows the portfolio realised annualised return distribution for the 100 and 200 bond concentrations along with the 1,000 diversified bonds case that we discussed earlier. 

Chart two: Cumulative probability distribution of the portfolio annualised realised return and the MA discount rate

Chart three shows the cumulative probability distribution of the portfolio annualised realised return (with concentrations) and the MA discount rate (left-hand tail zoom) 

Chart three: Cumulative probability distribution of the portfolio annualised realised return (with concentrations) and the MA discount rate (left-hand tail zoom)

Charts two and three show that these portfolio concentration levels have minimal impact on the portfolio realised return distribution, except in the extreme left-hand tail – in particular, in the most severe 3% of outcomes. The probability that the MA portfolio earns the MA discount rate remains at 94%, even in the case where 20% of the portfolio is similarly exposed to changes in the single credit rating. This may be considered a surprising result: having 20% of a bond portfolio effectively exposed to a single counterparty sounds like an unnecessarily imprudent strategy. Why does our model not suggest it is impairing the level of confidence in the MA being earned? Part of the reason is that we are assuming here that the portfolio has a ‘pure’ buy-and-hold strategy. So, in this example we only care about downgrades over time to the extent they result in a default within our ten-year projection horizon. This strategy means the portfolio outcomes are often left unscathed by the increased downgrade tail that occurs with higher concentration levels (the A-rated third entity only defaults with 1.3% probability over the ten-year period).  

However, this strategy also means that when the concentration risk does crystallize, its impact is substantial. This can be seen by considering the notable left-hand tail of the realised return distribution, as highlighted in chart three. For example, the first percentile realised returns for the three cases are 4.5% (fully diversified portfolio); 4.3% (with 100 bonds with the same indirect exposure) and 3.6% (with 200 bonds with the same indirect exposure. And note that, as these are ten-year annualised returns, a 1% p.a. difference is approximately equivalent to a 10% ‘present value’ impact. 

Firms should undertake adequate assurance activities for their solvent exit preparations. These assurance activities can be performed internally, or externally if the firm would like to do so.

There are many ways a firm could look to achieve this assurance. Regulatory compliance checklists, industry benchmarking, desktop scenarios and war-gaming all offering different tests of the SEA. 

Clearly, it is important to test if the SEA reflects how things will work in practice and ensure that the necessary actions can adapt to changing circumstances.