Operational risk: the standardised approach · RiskAtoms Academy

Know these first

L3.7.03: Loss data
L3.7.07: Measuring frequency and severity
L4.1.04: Risk-weighted assets

Math Atoms

By the end you will be able to

1Build the business indicator from its three components, with three-year averages, absolute values and the 2.25% cap.
2Turn the BI into the business indicator component with marginal coefficients, on Basel's and the UK's buckets.
3Compute the loss component and the internal loss multiplier, and say what the ILM does at LC = BIC and at LC = 0.
4Reproduce the bank's operational risk RWA: £3,322.7m in the UK (ILM = 1) and £3,631.1m under Basel.

Why it matters

In L4.1.04: Risk-weighted assets, RiskAtoms Bank's operational risk RWA of £3,322.7m is one line, 15% of its £22,807.7m total. It comes from one formula: how big the bank is, measured from its income statement, and, under the Basel standard, how much it has lost. Change where a fee is booked or which ten years of losses count, and the line moves by tens of millions. The UK and the EU have switched the loss part off; Basel has not, and on this bank the difference is £308.5m.

Core explanation

Size, scaled by losses

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.

Operational risk in Module 4.4. The data is the Level 3 operational risk book (M3.7: Operational and non-financial risk): three years of business indicator items (2023 to 2025, with 2025 tied to the bank's net interest income in Module 3.6) and ten years of internal loss events (2016 to 2025), every one invented. L4.1.04: Risk-weighted assets uses the UK rule, where the internal loss multiplier is 1, so operational risk RWA is £3,322.7m. Under the Basel standard the same book gives £3,631.1m. Nothing in the book has been changed; anything a lesson adds to it, such as a disposal, is labelled as an assumption.

L3.7.07: Measuring frequency and severity ran the standardised approach once, on the same book, to set it beside a loss distribution model. It is sometimes called the standardised measurement approach, or SMA, the name the Basel Committee used when it consulted on it in March 2016. Here we take each piece apart. There are three (OPE25.1): a business indicator that measures size from the income statement, a business indicator component that turns size into capital, and an internal loss multiplier that scales it by the bank's own losses.

The business indicator

The BI adds three components (OPE25.3–25.5), each an average over the last three years. The detailed items are in OPE10.2, Table 1, and the exclusions in OPE10.3.

Component	What goes in	How it is combined
ILDC	Interest income and expense, operating lease income and expense, dividend income	\|interest income − expense\|, capped at 2.25% of interest-earning assets; plus dividends
SC	Fee and commission income and expense; other operating income and expense, including losses and provisions for operational loss events	The larger of fee income and fee expense, plus the larger of other operating income and expense
FC	Net P&L on the trading book; realised gains and losses and hedge results on the banking book	\|trading book P&L\| + \|banking book P&L\|

Three choices in the table matter. Services take the larger of income and expense, not the net, so a bank that pays out as much in fees as it earns is not treated as having no fee business. The financial component takes absolute values year by year and then averages them (OPE25.5, footnote): a desk that made £55m, lost £10m and made £62m counts as £42.33m, not the £35.67m that averaging first would give (M-A08: Summation notation). And the interest component is capped at 2.25% of interest-earning assets, so a lender with a wide margin is not charged for its margin. Staff costs, premises, depreciation, impairments, insurance and tax are left out altogether (OPE10.3).

Sort itWhich component, if any?

Sort each income statement item into the business indicator component it belongs to, then check.

Interest received on the bank's mortgages
Dividends on a stake in a company the bank does not consolidate
Card and account fees charged to customers
A provision set up for customer redress after mis-selling
Net gain on the trading book for the year
A realised gain on selling a banking book bond
Salaries of the bank's staff
Loan impairment charges
An insurance payout received after a flood at an office

The BIC: marginal coefficients

The BIC charges each slice of the BI at its own rate (OPE25.7, Table 1), like an income tax. The rates rise with size, so a larger bank pays a higher average rate:

Bucket	Basel (OPE25.7)	UK (PRA 5.8)	Marginal coefficient
1	up to €1bn	up to £0.88bn	12%
2	€1bn to €30bn	£0.88bn to £26bn	15%
3	above €30bn	above £26bn	18%

A bank in bucket 2 pays 15% only on the part of its BI above the first threshold (marginal, M-A01: Percentages), so its average rate climbs slowly from 12%. RiskAtoms Bank's BI of £1,948.1m gives a BIC of £265.81m: an average rate of 13.64%. The PRA wrote its thresholds in sterling; they match Basel's at about €1.14 and €1.15 per pound.

The loss component and the multiplier

The loss component is 15 times the bank's average annual operational losses over the last ten years (OPE25.8). The multiplier compares it with the BIC through a logarithm (M-A04: Logarithms): when LC equals BIC the bracket is e, and ln e = 1, so the bank pays exactly its BIC (OPE25.9). Above that, losses add capital, but slowly: the power 0.8 and the log both bend the curve down. Below it they take capital off, never further than ln(e − 1) = 0.541 at no losses at all.

Two exits switch the losses off. Banks in bucket 1 have an ILM of 1, and supervisors may set the ILM to 1 for all banks in their jurisdiction (OPE25.11). Banks whose loss data fail the standards must hold at least the BIC, whatever their losses (OPE25.13). The standards themselves are the next lesson's subject, L4.4.06: Operational risk capital in practice.

The formal version

For a bank with three years of income statement data (t = 1, 2, 3) and ten years of losses (OPE25.2–25.8; the formulas are images on bis.org: the components were read as text in the PRA's Operational Risk Part, 5.3, and the ILM in the Hong Kong Monetary Authority's MA(BS)3(V) instructions):

\begin{aligned} \text{BI} &= \text{ILDC} + \text{SC} + \text{FC} \\ \text{ILDC} &= \min\Big(\tfrac13 \textstyle\sum_t \lvert II_t - IE_t \rvert,\ 2.25\% \times \tfrac13 \textstyle\sum_t IEA_t\Big) \\ &\quad + \tfrac13 \textstyle\sum_t DI_t \\ \text{SC} &= \max\big(\overline{OOI},\ \overline{OOE}\big) + \max\big(\overline{FI},\ \overline{FE}\big) \\ \text{FC} &= \tfrac13 \textstyle\sum_t \lvert \text{P\&L}_{TB,t} \rvert + \tfrac13 \textstyle\sum_t \lvert \text{P\&L}_{BB,t} \rvert \\ \text{BIC} &= 12\% \min(\text{BI}, B_1) + 15\% \big(\min(\text{BI}, B_2) - B_1\big)^{+} \\ &\quad + 18\% (\text{BI} - B_2)^{+} \\ \text{LC} &= 15 \times \tfrac{1}{10} \textstyle\sum_{y=1}^{10} \text{Loss}_y \\ \text{ILM} &= \ln\!\Big(e - 1 + \big(\tfrac{\text{LC}}{\text{BIC}}\big)^{0.8}\Big) \\ \text{ORC} &= \text{BIC} \times \text{ILM} \\ \text{RWA} &= 12.5 \times \text{ORC} \end{aligned}

II and IE are interest income and expense, IEA interest-earning assets, DI dividend income; OOI and OOE other operating income and expense; FI and FE fee income and expense; TB and BB the trading and banking book. A bar is a three-year average.
$B_1$ and $B_2$ are €1bn and €30bn (Basel) or £0.88bn and £26bn (UK); $x^{+} = \max(x, 0)$ .
$\text{Loss}_y$ is the year's operational losses net of recoveries, above the threshold, by accounting date (OPE25.18, 25.28).
Bucket 1, or a national discretion: ILM = 1 (OPE25.11). Then ORC = BIC.

Try it

Start at the bank. Switch the multiplier from 1 to “from losses” and watch capital rise by a little over 9%. Then push the average loss down to about £17.7m, where LC equals the BIC: the dot sits on the line at 1. Shrink the BI below £0.88bn and the losses stop mattering at all. Last, switch to Basel's euro buckets: the bank's BIC barely moves, because the PRA's sterling thresholds are close to Basel's at the capital book's €1.15 per pound.

Try itBusiness indicator, losses and capital

Business indicator, £m£1,948m

Average annual loss over ten years, £m£23.8m

Bucket thresholds

Internal loss multiplier

The bank: BI £1,948.1m, average loss £23.76m.

BIC by bucket: BI £1,948m

Bucket 1: 12% of £880m

£106m

Bucket 2: 15% of £1,068m

£160m

Bucket 3: 18% of £0m

£0m

ILM = ln(e − 1 + (LC/BIC)^0.8). The dot is this bank; it is hollow when the ILM used is 1.

Operational risk RWA£3,322.7m

Capital (ORC = BIC × ILM)£265.8m

BIC£265.81m

Bucket, marginal coefficient2, 15%

Average coefficient, BIC / BI13.64%

LC = 15 × average loss£356.4m

LC / BIC1.341

ILM used1.0000

With the ILM set to 1, losses do not move capital. From losses it would be 1.0928.

Illustrative data, £ millions. The Basel buckets convert the BI to euros and the BIC back at the capital book's rate. The slider sets the ten-year average loss directly; which losses count is the subject of the next lesson.

Worked example

RiskAtoms Bank's operational risk capital

£ millions, years to 31 December. Every input is in the Level 3 book.

From the income statement to RWA

Step 1 of 6

Three years of items

Item	2023	2024	2025	Average
\|Interest income − expense\|	1,420.00	1,530.00	1,585.20	1,511.73
2.25% × interest-earning assets	1,406.25	1,440.00	1,476.00	1,440.75
Dividend income	12.00	14.00	16.00	14.00
Other operating income	35.00	30.00	40.00	35.00
Other operating expense	45.00	50.00	40.00	45.00
Fee income	380.00	395.00	410.00	395.00
Fee expense	95.00	100.00	105.00	100.00
\|Trading book P&L\|	55.00	10.00	62.00	42.33
\|Banking book P&L\|	8.00	20.00	5.00	11.00

Regulatory lens

The standard is OPE25 of the Basel Framework, with definitions in OPE10. Statements on jurisdictions are as at 3 November 2026 as at 3 Nov 2026; L4.1.08: Basel 3.1 from 2027: UK, EU and US has the overview of what starts when.

In the UK

The PRA's Operational Risk Part applies the standardised approach from 1 January 2027: own funds are BIC × ILM (4.1), with buckets of £0.88bn and £26bn (5.8), and “the Internal Loss Multiplier is equal to one” (5.9). Firms must still collect loss data of £20,000 or more over ten years (7.1). The PRA's reasons (CP16/22, paras 8.23–8.24): the ILM is non-linear, operational loss data are fat-tailed and sparse, and ten unweighted years let old losses weigh too much; large past losses are better handled in Pillar 2A. Until 31 December 2026 UK banks use the older approaches of the UK CRR.

In the EU

CRR3 (Regulation (EU) 2024/1623) has applied the new approach since 1 January 2025. The own funds requirement for operational risk is the BIC (Article 312), on Basel's euro buckets (Article 313): the Regulation's recitals say the discretion is used “by disregarding historical operational loss data for all institutions” (recital 46). Institutions with a BI of €750m or more must still calculate their annual operational risk loss (Article 316).

In the US

The agencies' proposal of 19 March 2026 would add an explicit operational risk requirement for Category I and II banks, “calculated based on a firm's income and expenses” (Federal Reserve Board memo). Comments closed on 18 June 2026 (OCC Bulletin 2026-9); as far as we could find, no final rule had been published by 3 November 2026.

Spark Atoms

Spark AtomLosses count twice under Basel

OPE10.2 puts losses from operational loss events, and provisions for them, into other operating expense, which sits in the services component. The book keeps them out, for simplicity. Had the bank's gross losses booked in 2023 to 2025 (39.7, 12.0, 31.1) been in it, other operating expense would average £72.60m instead of £45m, the BI would be £1,975.7m and UK RWA £3,374.4m: £51.7m more. So losses reach Pillar 1 even where the ILM is 1, through size; under Basel they also come in through the loss component.

Spark AtomA bank with no losses still pays half

The ILM never falls below ln(e − 1) = 0.541: a bucket 2 bank with a spotless record still holds 54% of its BIC. RiskAtoms Bank without its redress programme would be at 0.891 (L4.4.06: Operational risk capital in practice).

Spark AtomWhy the bank's BIC is almost the same in pounds and euros

The PRA's £0.88bn and £26bn equal Basel's thresholds at €1.14 and €1.15 per pound. At €1.15, the bank's BI of £1,948.1m is €2,240.3m, and the BIC differs by only £0.31m.

Key takeaways

Operational risk capital is BIC × ILM, and RWA are 12.5 times that (OPE25.2).
The BI is ILDC + SC + FC, three-year averages; interest is capped at 2.25% of interest-earning assets, services take the larger of income and expense, and P&L enters as absolute values year by year.
The BIC charges marginal rates of 12%, 15% and 18% above €1bn and €30bn (UK £0.88bn and £26bn).
LC = 15 × average annual losses over ten years; ILM = ln(e − 1 + (LC/BIC)^0.8) is 1 at LC = BIC and never below 0.541.
RiskAtoms Bank: BI £1,948.1m, BIC £265.8m, LC £356.4m, Basel ILM 1.093. RWA £3,322.7m in the UK and EU (ILM = 1), £3,631.1m under Basel.

Reaction

Check what stuck

Question 1 · objective 2

A UK bank has a business indicator of £30bn. On the PRA's buckets (12% to £0.88bn, 15% to £26bn, 18% above), what is its BIC, in £m?

£m

Question 2 · objective 3

A bank's loss component is twice its BIC. What is its internal loss multiplier? (Three decimals.)

Question 3 · objective 1

A bank's trading book made £30m, lost £50m, then made £20m over the last three years. What does the trading book add to the financial component, in £m?

£m

Question 4 · objective 4

From 1 January 2027, RiskAtoms Bank's £120m redress programme (2018 and 2019) is in its ten-year loss data. What does it do to its UK Pillar 1 operational risk capital?

ANothing: the PRA sets the ILM to 1, so losses do not enter the formulaBIt raises the ILM above 1CIt raises the BIC through the services componentDIt is excluded automatically after five years

Question 5 · objective 4

RiskAtoms Bank's BIC is £265.81m and its Basel ILM is 1.0928. How much more RWA does Basel's rule give than the UK's, in £m?

£m

Glossary

Business indicator (BI): Business indicator (BI): a measure of a bank's size built from its income statement: ILDC + SC + FC, each averaged over three years (OPE25.3–25.5).
Interest, leases and dividend component (ILDC): Interest, leases and dividend component (ILDC): net interest income, capped at 2.25% of interest-earning assets, plus dividend income.
Services component (SC): Services component (SC): the larger of other operating income and expense, plus the larger of fee income and fee expense.
Financial component (FC): Financial component (FC): the absolute net P&L of the trading book plus the absolute net P&L of the banking book.
Business indicator component (BIC): Business indicator component (BIC): the BI times marginal coefficients of 12%, 15% and 18% that rise with size (OPE25.7).
Marginal coefficient: Marginal coefficient: the rate applied to the slice of the BI in a bucket only, as an income tax applies a higher rate only to income above a threshold.
Loss component (LC): Loss component (LC): 15 times the bank's average annual operational losses over the previous ten years (OPE25.8).
Internal loss multiplier (ILM): Internal loss multiplier (ILM): ln(e − 1 + (LC/BIC)^0.8). It is 1 when LC equals BIC, above 1 when losses are high for the bank's size and below 1 when they are low (OPE25.8–25.9).
Operational risk capital (ORC): Operational risk capital (ORC): BIC × ILM. RWA are 12.5 times ORC (OPE25.2).

Deep Dives & Origins

Deep Dives

L4.4.06: Operational risk capital in practice: the loss data standards, exclusions and the BI adjustments, and Pillar 2. Intermediate.
L3.7.07: Measuring frequency and severity: the loss distribution approach the standardised approach replaced. Intermediate.

Origins

Basel Committee on Banking Supervision, OPE25: Standardised approach, paras 25.1–25.13, version in force from 1 January 2023, bis.org; and the Swiss SIF copy of OPE25.
Basel Committee on Banking Supervision, Standardised Measurement Approach for operational risk, consultative document (d355), 4 March 2016, bis.org.
Basel Committee on Banking Supervision, OPE10: Definitions and application, paras 10.1–10.3 (Table 1, the BI items), Swiss SIF copy.
Prudential Regulation Authority, PRA Rulebook: Operational Risk Part, version in force from 1 January 2027, rules 4.1, 5.1–5.9, 7.1 and Annex 1.
Prudential Regulation Authority, CP16/22 Implementation of the Basel 3.1 standards, chapter 8 (operational risk), November 2022.
Hong Kong Monetary Authority, Completion instructions for MA(BS)3(V), March 2025 (the ILM formula as text).
Regulation (EU) 2024/1623 (CRR3), recital 46 and dates of application (EUR-Lex); Regulation (EU) No 575/2013, Articles 312, 313 and 316 (consolidated text on gesetze.legal; the Article 313 buckets, an image there, as given in Finanstilsynet's slides on operational risk in CRR3).
Board of Governors of the Federal Reserve System, Basel III proposal, GSIB surcharge proposal, and standardized approach proposal (staff memo to the Board), 19 March 2026; Office of the Comptroller of the Currency, Bulletin 2026-9, 19 March 2026.

Watch this lesson

Video version

Prefer to watch? The same lesson as a 12-minute video will sit here, made from this page's script.

Previous · L4.4.04

Exposures to central counterparties

Next · L4.4.06

Operational risk capital in practice