Default risk charge and residual risk add-on · RiskAtoms Academy

By the end you will be able to

1Compute a position's jump-to-default from LGD, notional and P&L, and scale it by maturity.
2Net JTD by obligor, apply the hedge benefit ratio and the default risk weights, and sum the buckets.
3Decide whether an instrument attracts the residual risk add-on, at 1.0% or 0.1% of notional.
4Complete the bank's standardised capital: £33.41m of SBM plus £6.14m of DRC and £0.105m of RRAO.

Why it matters

RiskAtoms Bank's credit desk holds £80m of BBB corporate bonds. The SBM charges their credit spreads: what they lose if spreads widen. It says nothing about the day an issuer simply defaults and a bond worth £10m is suddenly worth £2.5m. Credit spread sensitivities are small numbers; default is a jump. The default risk charge is there for the jump, and the residual risk add-on for the risks no sensitivity can see. Together they take the bank's market risk RWA from £417.7m to £495.7m.

Core explanation

Default, and what is left over

Illustrative dataRiskAtoms Bank plc's capital book

The same made-up UK bank as Level 3: £67bn of assets and £4bn of equity at 31 December 2025, in £ millions. Module 4.1 adds its regulatory layer: own funds, deductions, risk-weighted assets by risk type, buffers, the leverage exposure and MREL, computed from the Level 3 credit, trading, derivatives and operational risk books. Every figure is illustrative, not any bank's data.

Pro forma. The book applies Basel 3.1, the 2017 finalisation of Basel III, to the 31 December 2025 balance sheet. On that date the bank still reported under the old UK CRR. The UK applies Basel 3.1 from 1 January 2027, and the internal model approach for market risk from 1 January 2028 (PRA PS1/26, paras 1.23 and 1.24). So the book shows the bank as it would look under the new rules.

Market risk in Module 4.3. The positions are the Level 3 trading desk (M3.2: Market risk): eight positions in four books, Equities, Rates, FX and commodities, and Credit, valued by full revaluation on eight risk factors. The client derivatives are the four netting sets of M3.4: Counterparty credit risk. The £417.7m of market risk RWA in L4.1.04: Risk-weighted assets is the sensitivities-based method only: it leaves out the default risk charge and the residual risk add-on, which this module adds. No position has been changed; where a lesson adds one to teach a rule, it is labelled illustrative.

Added in this lesson. To apply the DRC, the data splits the corporate bonds into eight BBB issuers of £10m each, the US basket into five names and the UK index into ten equal names, all rated A (the desk has no constituent data). The gilt is rated AA. A CDS hedge and two residual-risk positions are illustrative and labelled so.

Jump-to-default

The DRC starts from each exposure's jump-to-default: what the bank would lose if the issuer defaulted now (MAR22.9–22.11). A long exposure is one that loses money on default (MAR22.10): a bond held, a share held, protection sold. A short exposure gains: protection bought, a short sale, or a put on an index. For a long,

JTD_{\text{long}} = \max\big(LGD \times \text{Notional} + P\&L,\ 0\big), \qquad P\&L = \text{market value} - \text{notional}

The LGD is not estimated; the rule fixes it by seniority (MAR22.12):

Exposure	LGD
Equity, and non-senior debt	100%
Senior debt	75%
Covered bonds	25%

Shares default too, with nothing recovered: that is the default charge on equities that L3.2.03: Equity risk promised. Each of the bank's eight bond issuers gives 0.75 × £10m + 0 = £7.5m. The gilt, bought below par, gives 0.75 × £100m + (98.797 − 100) = £73.797m.

One year, scaled

The DRC looks one year ahead. A position that ends sooner is scaled by its maturity as a fraction of a year, floored at three months (MAR22.15, 22.18): weight = min(max(T, ¼), 1), a floor and a cap (M-A11: Min, max, floors and caps). Cash equities may be given either one year or three months, at the bank's choice (MAR22.16); RiskAtoms Bank uses one year for its US shares. The UK index futures and puts have three months to run, so their JTD counts at a quarter.

Net by name, then by bucket

Longs and shorts on the same obligor net, provided the short is no more senior than the long (MAR22.19). On the UK index, each of the ten names has £1.50m of long JTD from the futures and £0.9543m of short JTD from the puts, which gain if a constituent defaults: net £0.5457m a name. The nets then go into three buckets, corporates, sovereigns and local governments (MAR22.22). Within a bucket, shorts on other names can offset longs, but only through the hedge benefit ratio (MAR22.23). Between buckets, nothing offsets (MAR22.26).

Risk weights by rating

Each net JTD is weighted by the issuer's rating (MAR22.24, Table 2). The weights are percentages of JTD (M-A01: Percentages), and read like one-year default rates with a margin:

Rating	Default risk weight
AAA	0.5%
AA	2.0%
A	3.0%
BBB	6.0%
BB	15.0%
B	30.0%
CCC	50.0%
Unrated	15.0%
Defaulted	100.0%

The residual risk add-on

Some risks fall through every net. The residual risk add-on (MAR23) is a blunt charge on gross notional, with no offsetting: 1.0% for instruments with an exotic underlying such as weather or longevity (MAR23.3), and 0.1% for other residual risks such as gap, correlation and behavioural risk: barriers, digitals, best-of options and retail prepayment (MAR23.4–23.5). It is added on top of the SBM and the DRC (MAR23.8).

Sort itExotic, other residual risk, or no RRAO?

Sort each instrument, then check.

A swap paying on UK heating degree days, sold to an energy client
A longevity swap with a pension fund
A digital put on the UK index
An over-the-counter best-of option on two indices
The bank's own plain vanilla European puts on the UK index
A bond future with cheapest-to-deliver risk
A barrier option bought from a dealer as an exact back-to-back of one sold to a client

None of the bank's 8 positions attracts it: they are linear, or plain vanilla European puts, which MAR23.6 leaves out. To show the add-on at work, the data adds two small positions, labelled illustrative below.

The formal version

For a bucket b with net JTD by obligor and default risk weights $RW_i$ (MAR22.9–22.26; the formulas are images in MAR22, and the JTD and bucket formulas were read as text in the 2019 version of the CRR's Articles 325w and 325y):

\begin{aligned} JTD_{\text{long}} &= \max\big(LGD \cdot N + P\&L,\ 0\big), \qquad JTD_{\text{short}} = \min\big(LGD \cdot N + P\&L,\ 0\big) \\ \text{scaled } JTD &= JTD \times \min\big(\max(T, 0.25),\ 1\big) \\ HBR &= \frac{\sum \text{net } JTD_{\text{long}}}{\sum \text{net } JTD_{\text{long}} + \sum \lvert \text{net } JTD_{\text{short}} \rvert} \\ DRC_b &= \max\Big(\sum_{i \in \text{long}} RW_i\, \text{net } JTD_i - HBR \sum_{i \in \text{short}} RW_i\, \lvert \text{net } JTD_i \rvert,\ 0\Big), \qquad DRC = \sum_b DRC_b \\ RRAO &= 1.0\% \times \sum \text{notional}_{\text{exotic}} + 0.1\% \times \sum \text{notional}_{\text{other}} \end{aligned}

N is the notional, signed (negative for protection bought or a short bond), and P&L is market value minus notional. T is in years.
The HBR uses unweighted JTD; the bucket charge uses weighted JTD. With no shorts, HBR = 1 and the bucket is just $\sum RW_i \cdot \text{net } JTD_i$ .
Supervisors may give a zero default risk weight to sovereigns that get 0% under the credit risk standardised approach (MAR22.7).

Try it

Buy protection on a name the desk does not hold and watch the hedge benefit ratio fall below 1. Set the notional to £40m on another BBB name: that is the illustration in the worked example. Then switch the reference name to an issuer the desk holds: the same CDS nets that name first, at full weight, until it overshoots. Shorten the maturity below three months and see the floor hold. Last, put the same £40m on another BB name: the corporate charge comes out lower than on another BBB name, because the short is weighted at its own rating's 15% rather than 6% before the hedge benefit ratio scales it, so protection on a riskier name takes more off.

Try itHedge the corporate DRC bucket

CDS protection bought (£m notional)£0m

Reference name

Reference obligation

CDS maturity (years)5.00 → weight 1.00

Weight the gilt at 0% (the MAR22.7 national discretion) instead of 2%

CDS short JTD, scaled0.000

Σ net long JTD95.457

Σ |net short JTD|0.000

Hedge benefit ratio1.0000

Σ RW × long4.664

Σ RW × |short|0.000

Corporate bucket DRC£4.664m

Sovereign bucket DRC£1.476m

Total DRC (no offset between buckets)£6.140m

Change from the book£0.000m

No hedge: every corporate name is long, so the hedge benefit ratio is 1 and the bucket is Σ RW × JTD.

The bucket holds the bank's eight bond issuers, five US basket names and ten UK index names. The CDS's own P&L is taken as zero. Illustrative, £ millions; the book itself has no CDS.

Worked example

Completing the bank's standardised capital

£ millions, on the Level 3 trading desk at its valuation date.

From positions to £39.66m

Step 1 of 8

1

Gross JTD

Position	Names	LGD	JTD per name	Maturity weight	Scaled
Corporate bonds	8	75%	7.500	1.00	7.500
10-year gilt	1	75%	73.797	1.00	73.797
US equity basket	5	100%	6.000	1.00	6.000
UK index futures	10	100%	6.000	0.25	1.500
UK index puts (short JTD)	10	100%	−3.817	0.25	−0.954

Regulatory lens

The DRC is MAR22 and the RRAO MAR23. Statements on jurisdictions are as at 3 November 2026 as at 3 Nov 2026.

In the UK

The PRA's Market Risk: Advanced Standardised Approach (CRR) Part, which applies from 1 January 2027, has the DRC in its Section 5 (Article 325c(2)). We could not open that section of the rule, so the UK's sovereign weight is unconfirmed here. The version of Article 325y that the EU added to the CRR in 2019 (omitted from UK law on 1 January 2022) gave a 0% default risk weight to “exposures which would receive a 0% risk-weight under the Standardised Approach for credit risk”, and Article 114(4) gives UK central government exposures denominated and funded in sterling 0%. If the PRA kept that treatment, the gilt's £1.476m falls away and the DRC is £4.664m. The data here keeps the Basel 2%.

In the EU

Delegated Regulation (EU) 2026/1221, applying from 1 January 2027 to 31 December 2029, sets the RRAO to zero (a multiplier of 0) for some instruments where nothing else triggers it, including instruments referencing future realised volatility and options on the spread between two constant maturity swap rates in the same currency (Article 495p). For banks with internal models it sets a zero default probability for obligors whose exposures would get a 0% risk weight (Article 495l). See L4.3.11: Market risk and CVA capital: what changes from 2027.

In the US

The US proposals of 19 March 2026 would introduce a standardised approach for market risk (Federal Reserve fact sheet); as far as we could find, no final rule had been published by 3 November 2026.

Spark Atoms

Spark AtomFrom the IRC to the DRC

In July 2009 the Basel Committee added an incremental risk charge for default and migration risk in the trading book, at 99.9% over one year, because the losses of 2007–08 came from downgrades, wider spreads and illiquidity, which value-at-risk had largely missed (bcbs159). The standardised DRC is for the jump to default “that may not be captured by credit spread shocks” (MAR22.1): a downgrade widens the bond's spread, which the CSR delta charge of L4.3.02: The sensitivities-based method: delta and vega already sees.

Spark AtomOne AA sovereign, one quarter of the charge

The gilt alone is £1.476m of the bank's £6.140m: 24%. Whether a national supervisor uses the 0% discretion for its own government's debt matters more to this desk than the eight corporate issuers' seniority.

Spark AtomWhy notional, not risk?

The RRAO ignores how much risk a position carries: a deep out-of-the-money digital and an at-the-money one pay the same 0.1%. It is meant as a simple backstop for what the sensitivities cannot measure, and a supervisor that finds it too light can add more under Pillar 2 (MAR23.8).

Key takeaways

JTD = max(LGD × notional + P&L, 0) for a long, with LGD fixed by the rule: 100% equity and non-senior, 75% senior, 25% covered bonds.
Positions under a year are scaled by maturity, floored at three months; longs and shorts net by obligor.
Within a bucket, shorts on other names offset longs only through the hedge benefit ratio; buckets simply add up.
The RRAO is 1.0% of notional for exotic underlyings and 0.1% for other residual risks, with no offsetting.
The bank's DRC is £6.140m (RWA £76.75m); with an illustrative RRAO of £0.105m, the full SA is £39.657m, RWA £495.71m.

Reaction

Check what stuck

Before the questions: long or short JTD?

Question 1 · objective 1

A desk holds a senior bond with face value £20m and market value £19m. What is its gross jump-to-default, in £m?

£m

Question 2 · objective 1

An equity future with three months to run has a gross JTD of £8m. What JTD goes into the bucket after maturity scaling, in £m?

£m

Question 3 · objective 2

After netting by obligor, a bucket has £60m of net long JTD and £20m of net short JTD (absolute). What is its hedge benefit ratio?

Question 4 · objective 3

A desk has £50m notional of over-the-counter barrier options and a £10m longevity swap. What is its residual risk add-on, in £m?

£m

Question 5 · objective 4

Why is the market risk RWA of £417.7m in L4.1.04: Risk-weighted assets not the bank's full standardised figure?

AIt is the sensitivities-based method only; the default risk charge and residual risk add-on come on topBIt is before the 1.06 scaling factorCIt leaves out the curvature chargeDIt is an internal model figure

Glossary

Default risk charge (DRC): Default risk charge (DRC): the part of the standardised approach for the loss if an issuer of a bond or share in the trading book defaults suddenly.
Jump-to-default (JTD): Jump-to-default (JTD): the loss, or gain, on a position if its issuer defaulted now: LGD × notional plus the P&L already in the price.
Loss given default (LGD): Loss given default (LGD): the share of the notional lost on default, set by the rule by seniority: 100% for equity and non-senior debt, 75% for senior debt, 25% for covered bonds.
Hedge benefit ratio (HBR): Hedge benefit ratio (HBR): in a DRC bucket, net long JTD divided by net long JTD plus the absolute net short JTD. It scales down how far shorts on other names can offset longs.
Residual risk add-on (RRAO): Residual risk add-on (RRAO): a simple charge on the gross notional of instruments whose risks the SBM and DRC do not capture: 1.0% for exotic underlyings, 0.1% for other residual risks.
Exotic underlying: Exotic underlying: an underlying outside the delta, vega, curvature and default risk charges, such as longevity, weather or natural disasters (MAR23.3).

Deep Dives & Origins

Deep Dives

L4.3.05: Internal models: expected shortfall: the internal models approach, and its own default risk model. Advanced.
L3.2.07: Credit spread risk: the credit desk's spread risk, which the SBM charges alongside the DRC. Intermediate.

Origins

Basel Committee on Banking Supervision, MAR22: Standardised approach: default risk capital requirement, paras 22.7–22.26, bis.org.
Basel Committee on Banking Supervision, MAR23: Standardised approach: residual risk add-on, paras 23.3–23.8, bis.org.
Basel Committee on Banking Supervision, Guidelines for computing capital for incremental risk in the trading book, July 2009.
Regulation (EU) No 575/2013, Articles 325w and 325y, version of 27 June 2019, and Article 114, legislation.gov.uk.
Prudential Regulation Authority, PRA Rulebook: CRR Firms: Overseas Prudential Recognition Regime Instrument 2026 (PRA2026/19; Annex I, amending Article 325v of the Market Risk: Advanced Standardised Approach (CRR) Part), made 2 July 2026 (PS16/26, Appendix 1).
Commission Delegated Regulation (EU) 2026/1221, Articles 495l and 495p, Official Journal of the European Union, 2026.
Board of Governors of the Federal Reserve System, Fact sheet on the capital proposals, 19 March 2026.

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