How it works
Illustrative dataElmthwaite Bank plc, a new bank for the Lab Test
The lessons use RiskAtoms Bank plc's netting sets, loss data and Tier 1. These problems apply the same rules to a new, smaller UK bank: Elmthwaite Bank plc, invented, with £20,000m of assets at 31 December 2025. Its trades, collateral, income, losses and counterparties are all made up and kept hand-sized; amounts in £ millions. Counterparties are labelled by letter. Rules are the Basel Framework's (CRE22, CRE52 to CRE54, OPE25, LEX), as the lessons cite them, with the UK rules that start on 1 January 2027 where they change a number: α = 1 for non-financial counterparties and pension schemes, and an ILM of 1 for operational risk. Problem 4's internal model figures are illustrative: Elmthwaite has no IMM permission. L4.1.08: Basel 3.1 from 2027: UK, EU and US sets out the UK, EU and US dates.
Problem 1Replacement cost and the multiplier
L4.4.01Counterparty credit risk, SA-CCR
Elmthwaite Bank plc (invented) is a UK bank with £20,000m of assets. It computes counterparty credit risk with SA-CCR at 31 December 2025, α = 1.4. Two of its netting sets are margined under CSAs with daily variation margin and a ten-day margin period of risk. In £ millions:
| C2: a UK bank | C3: a hedge fund | |
|---|---|---|
| Value of the trades to Elmthwaite, V | −1.0 | 4.0 |
| Variation margin held (+) or posted (−) | −1.0 | 0.0 |
| Initial margin held, segregated | 3.0 | 0.0 |
| Threshold, TH | 0.0 | 8.0 |
| Minimum transfer amount, MTA | 0.5 | 1.0 |
| Aggregate add-on (margined) | 4.0 | Problem 3 |
C3 has not yet called any variation margin: its exposure is under the threshold. No collateral has been posted by Elmthwaite other than the variation margin to C2.
Lessons: L4.4.01: SA-CCR: replacement cost and the multiplier
(a)What is the multiplier for C2? Answer in %.
%(b)What is the EAD for C2? Answer in £m.
£m(c)However much more initial margin C2 posts, what is the lowest EAD this netting set can reach? Answer in £m.
£m(d)What is the margined replacement cost for C3? Answer in £m.
£m
Problem 2Sterling swaps for a food manufacturer
L4.4.02 · L4.4.01Counterparty credit risk, SA-CCR
C1 is a UK food manufacturer, a non-financial counterparty with no CSA, so the netting set is unmargined. Its three sterling swaps with Elmthwaite have all started (S = 0):
| Trade | Elmthwaite | Notional, £m | Years left |
|---|---|---|---|
| T1 | receives fixed | 60 | 7.0 |
| T2 | pays fixed | 40 | 3.0 |
| T3 | pays fixed | 50 | 0.5 |
The trades are worth £5.0m to Elmthwaite. At inception C1 posted £1.5m of cash as an independent amount, which Elmthwaite still holds. Supervisory duration discounts at 5% a year; the interest rate supervisory factor is 0.5%.
Lessons: L4.4.02: SA-CCR: the add-ons · L4.4.01: SA-CCR: replacement cost and the multiplier
(a)What is T1's adjusted notional? Answer in £m.
£m(b)What is T3's effective notional δ × d × MF? Answer in £m.
£m(c)What is the interest rate add-on for the netting set? Answer in £m.
£m(d)C1 is a non-financial counterparty. What is the netting set's EAD under the PRA's rules from 1 January 2027? Answer in £m.
£m
Problem 3An option, a swap and a forward under a CSA
L4.4.02 · L4.4.01Counterparty credit risk, SA-CCR
C3, the hedge fund of Problem 1, has three trades with Elmthwaite, margined under its CSA with a 10-business-day MPoR (V = £4.0m, TH £8m, MTA £1m, no initial margin, no variation margin yet):
| Trade | Elmthwaite's position | Size, £m | Years left |
|---|---|---|---|
| T4 | Sold a FTSE 100 call, strike 8,400, index at 8,000 | 30 | 1 |
| T5 | Receives the FTSE 100 return on a total return swap | 10 | 1 |
| T6 | Long US dollars against sterling, forward | 40 | 2 |
The sizes are the adjusted notionals: units times the index level for T4 and T5, the dollar leg in pounds for T6. Supervisory parameters (CRE52.72, Table 2): equity index factor 20%, correlation 80%, option volatility 75%; FX factor 4%.
Lessons: L4.4.02: SA-CCR: the add-ons · L4.4.01: SA-CCR: replacement cost and the multiplier
(a)What is T4's supervisory delta? Answer as a decimal (negative if it is negative).
(b)What is the aggregate add-on with the margined maturity factor? Answer in £m.
£m(c)What is the aggregate add-on if the set is treated as unmargined? Answer in £m.
£m(d)What is C3's EAD? Answer in £m.
£m
Problem 4A model's exposure and a repo in euros
L4.4.03Counterparty credit risk, IMM (illustrative) and SFTs
The model. Elmthwaite is weighing an application to use the internal model method. This is illustrative: it has no permission. For its only candidate netting set, which runs well past a year, the model gives expected exposure on a quarterly grid over the first year, current calibration, in £ millions:
| Time, years | 0.25 | 0.50 | 0.75 | 1.00 |
|---|---|---|---|---|
| EE | 4.0 | 6.0 | 5.0 | 7.0 |
On the stressed calibration the model gives effective EPE of £6.20m for the same set.
The repo. Separately, Elmthwaite's treasury lends £80m of cash to a European bank for a week under a reverse repo, with daily remargining, and takes euro government bonds (rated AA, 1–3 years) worth £84m as collateral. The ten-day supervisory haircuts are 2% for the bonds and 8% for the currency mismatch; repo-style trades use a five-business-day holding period.
(a)What is the effective EPE on the current calibration? Answer in £m.
£m(b)What would the IMM EAD be? Answer in £m.
£m(c)What is E* for the reverse repo? Answer in £m.
£m(d)What market value of the euro bonds would bring E* to zero? Answer in £m.
£m
Problem 5Clearing through a qualifying CCP
L4.4.04Counterparty credit risk, CCPs
Elmthwaite is a clearing member of a qualifying CCP and clears its own interest rate swaps there. In £ millions:
| Item | £m |
|---|---|
| SA-CCR EAD of Elmthwaite's trades with the CCP (ten-day MPoR) | 45.0 |
| The CCP's SA-CCR exposure to all its member accounts, net of the margin and contributions it holds | 150.0 |
| Elmthwaite's prefunded default fund contribution | 6.0 |
| All members' prefunded default fund contributions | 200.0 |
| The CCP's own prefunded resources ranking with or ahead of them | 40.0 |
Initial margin Elmthwaite posts is held by a custodian and is bankruptcy remote. If the CCP were not qualifying, its standardised risk weight as an ordinary counterparty would be 100%.
(a)What are the RWA for Elmthwaite's trade exposures to the CCP? Answer in £m.
£m(b)What is the CCP's hypothetical capital K_CCP? Answer in £m.
£m(c)What are the RWA for Elmthwaite's default fund contribution? Answer in £m.
£m(d)What would the RWA for trade exposures and default fund together be if the CCP were not qualifying? Answer in £m.
£m
Problem 6The business indicator and the multiplier
L4.4.05Operational risk capital
Elmthwaite's income statement items for the business indicator, in £ millions (trading and banking book lines are net P&L):
| Item | 2023 | 2024 | 2025 |
|---|---|---|---|
| Interest income | 1,050 | 1,180 | 1,300 |
| Interest expense | 500 | 590 | 660 |
| Interest-earning assets | 19,000 | 20,000 | 21,000 |
| Dividend income | 6 | 8 | 10 |
| Fee and commission income | 380 | 400 | 420 |
| Fee and commission expense | 120 | 130 | 140 |
| Other operating income | 30 | 40 | 50 |
| Other operating expense | 50 | 60 | 70 |
| Trading book P&L | 80 | −60 | 100 |
| Banking book P&L | 20 | −10 | 15 |
Its operational losses of £20,000 or more, net of recoveries, by accounting year, in £ millions: 2016 6.2, 2017 7.4, 2018 5.9, 2019 8.8, 2020 9.6, 2021 31.5, 2022 7.1, 2023 8.3, 2024 6.7, 2025 8.5. Use the PRA's sterling buckets (£880m and £26bn, coefficients 12%, 15% and 18%).
Lessons: L4.4.05: Operational risk: the standardised approach
(a)What is the interest, leases and dividend component (ILDC)? Answer in £m.
£m(b)What is the business indicator? Answer in £m.
£m(c)What is the business indicator component (BIC)? Answer in £m.
£m(d)What would Basel's internal loss multiplier be for Elmthwaite? Answer as a decimal.
×(e)From 1 January 2027 the PRA sets the ILM to 1. How much higher would Elmthwaite's operational risk RWA be with Basel's ILM? Answer in £m.
£m
Problem 7Exclusions, thresholds and a sale
L4.4.06Operational risk capital
The operational risk team tests three changes to Problem 6's figures, each on its own. The first two change the loss component, so they are measured on Basel's ILM, as L4.4.06: Operational risk capital in practice does; in the UK and EU, where the ILM is 1, they change no Pillar 1 capital.
- Exclusions. Four losses are candidates for exclusion from the loss data set, listed in part (a). The 2021 figure of £31.5m includes a £24m settlement.
- The threshold. Elmthwaite is in bucket 2, so its supervisor could raise the loss data threshold to €100,000 (£86,957 at €1.15 per £). Events with net losses from £20,000 up to that amount total £9.0m over the ten years.
- A sale. On 31 December 2025 Elmthwaite sold its pensions administration business, with the PRA's permission to remove it from the BI. It earned fee income of £60m, £62m, £64m in 2023 to 2025 and paid fee expense of £10m a year. It had no interest-earning assets and no other income or expense.
(a)Which loss can Elmthwaite ask its supervisor to exclude?
(b)With the £24m settlement excluded, what is Basel's ILM? Answer as a decimal.
×(c)With the €100,000 threshold, what is the loss component? Answer in £m.
£m(d)After the sale, what are Elmthwaite's UK operational risk RWA? Answer in £m.
£m
Problem 8Large exposures
L4.4.07Credit risk, large exposures
Elmthwaite's Tier 1 capital is £1,200m. Its largest exposures at 31 December 2025, in £ millions:
- P, a property company: a loan of £180m, against which P has pledged £30m of cash on deposit with Elmthwaite.
- P2, owned 70% by P: a loan of £90m and an undrawn committed facility of £100m (standardised CCF 40%).
- S, a building contractor that earns 60% of its gross receipts from P2 and could not replace that work quickly: a loan of £25m.
- Q, a UK bank (not a G-SIB): money market placements of £250m and a reverse repo lending £150m of cash against gilts, E* = 0.
- V, a retailer: a loan of £140m, £60m of it guaranteed by the UK government.
- The UK government and the Bank of England: gilts and reserves of £1,500m.
- A bond fund: Elmthwaite holds £60m of units in a £400m fund that holds bonds issued by q (£100m), bonds of r, a utility (£40m), bonds of 26 other issuers, £10m each (£260m).
All the protection is eligible under the standardised approach. Q, P, P2, S and V are not connected in any other way.
Lessons: L4.4.07: Large exposures
(a)Which counterparties must Elmthwaite treat as one with P?
(b)What is Elmthwaite's exposure to that group after CRM? Answer in £m.
£m(c)What is the exposure to Q after CRM, including the fund, as a share of Tier 1? Answer in %.
%(d)Which exposures breach the 25% limit before CRM, and which after?
(e)Which must Elmthwaite report as large exposures?
Back · L4.4.07
Large exposures
Next module · L4.5.01 · coming soon
The LCR: high-quality liquid assets