The standardised approach for operational risk worked line by line, from the profit and loss account to RWA, with the loss multiplier and the four errors that move the answer most.
Under Basel III, operational risk capital is the business indicator component (BIC) times an internal loss multiplier: build the business indicator from three-year averages of the interest, services and financial components, apply 12 per cent to the first 1,000 million, 15 per cent up to 30,000 million and 18 per cent above, then multiply by 12.5 to get risk-weighted assets. An illustrative bank with a business indicator of 1,843.0 million carries 246.45 million of operational risk capital, or 3,080.6 million of RWA, where the loss multiplier is set to 1 as in the EU.
Worked in full in Financial Regulation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The new standardised approach replaced the basic indicator, standardised and advanced measurement approaches with one formula. It no longer asks how much income a bank makes but how large its business is, measured from the profit and loss account. The bank below is fictional; figures are in EUR millions for its last three financial years.
| Item | Year 1 | Year 2 | Year 3 | Average |
|---|---|---|---|---|
| Interest income | 2,900 | 3,100 | 3,400 | 3,133.33 |
| Interest expense | 1,600 | 1,750 | 2,050 | 1,800.00 |
| Net interest income | 1,300 | 1,350 | 1,350 | 1,333.33 |
| Dividend income | 8 | 10 | 12 | 10.00 |
| Fee and commission income | 490 | 520 | 550 | 520.00 |
| Fee and commission expense | 130 | 140 | 150 | 140.00 |
| Other operating income | 55 | 60 | 65 | 60.00 |
| Other operating expense | 80 | 90 | 100 | 90.00 |
| Net P&L, trading book | 45 | -30 | 60 | 25.00 |
| Net P&L, banking book | 12 | 8 | -4 | 5.33 |
Average interest-earning assets over the three years are 52,000 million.
ILDC = min(|interest income − interest expense|, 2.25% × interest-earning assets) + dividend income
SC = max(other operating income, other operating expense) + max(fee income, fee expense)
FC = |net P&L trading book| + |net P&L banking book|
Each term is a three-year average. In Excel, for the financial component: =AVERAGE(ABS(B10:D10))+AVERAGE(ABS(B11:D11)), entered as an array formula in older versions.
Interest, leases and dividend component. Net interest income averages 1,333.33, but it is capped at 2.25 per cent of interest-earning assets: 2.25% × 52,000 = 1,170. The bank earns a margin of 2.56 per cent, so the cap binds. Add 10.00 of dividends and the ILDC is 1,180.00. The cap exists so that high-margin lenders are not charged for their margin as if it were size.
Services component. The larger of other operating income and expense, 90.00, plus the larger of fee income and fee expense, 520.00. The SC is 610.00. Income and expense are not netted: a bank that pays away most of what it earns in fees is still running the activity, with the operational exposure that goes with it.
Financial component. Absolute values, year by year, before averaging. The trading book gives (45 + 30 + 60) / 3 = 45.00; the banking book (12 + 8 + 4) / 3 = 8.00. The FC is 53.00. A loss year adds to the indicator; it does not offset a profitable one.
The business indicator is 1,180.00 + 610.00 + 53.00 = 1,843.00.
BIC = 12% × min(BI, 1,000) + 15% × (min(BI, 30,000) − 1,000) + 18% × (BI − 30,000), each part floored at zero
BIC = 120.00 + 15% × 843.00 = 120.00 + 126.45 = 246.45
Operational risk capital = BIC × ILM; RWA = 12.5 × capital
The coefficients are marginal, like income tax bands, so the effective rate on this bank is 13.37 per cent, not 15. With the internal loss multiplier at 1, operational risk capital is 246.45 and operational risk RWA are 3,080.6. Those RWA sit in the denominator of every capital ratio, beside credit and market risk; at a 4.5 per cent CET1 minimum alone they consume 138.63 of common equity.
Basel allows the BIC to be scaled by the bank's own loss history: ILM = ln(e − 1 + (LC / BIC)0.8), where the loss component LC is 15 times average annual operational losses over the previous 10 years. The EU, under CRR3, and the UK have set the ILM to 1 for every bank, so the business indicator alone drives the charge there. Where the multiplier is used, the arithmetic is as follows. With average annual losses of 18, LC is 270, the ratio LC / BIC is 1.0956 and the ILM is 1.0275: capital rises to 253.22 and RWA to 3,165.3, 84.66 more. The multiplier equals 1 exactly when average losses are BIC / 15, here 16.43.
| Average annual losses | ILM | Capital | RWA |
|---|---|---|---|
| 5 | 0.7440 | 183.36 | 2,292.0 |
| 10 | 0.8715 | 214.78 | 2,684.7 |
| 18 | 1.0275 | 253.22 | 3,165.3 |
| 30 | 1.2051 | 296.99 | 3,712.4 |
| 50 | 1.4241 | 350.98 | 4,387.2 |
| Business indicator | BIC | Effective rate | RWA |
|---|---|---|---|
| 600 | 72.00 | 12.00% | 900.0 |
| 1,000 | 120.00 | 12.00% | 1,500.0 |
| 1,843 | 246.45 | 13.37% | 3,080.6 |
| 5,000 | 720.00 | 14.40% | 9,000.0 |
| 30,000 | 4,470.00 | 14.90% | 55,875.0 |
| 40,000 | 6,270.00 | 15.68% | 78,375.0 |
The charge is progressive. For this bank every additional 100 of fee income, at the 15 per cent margin, adds 187.50 of RWA, whatever the activity's loss record. That is the trade-off the standard makes: comparability across banks at the cost of any sensitivity to how well a business is controlled.
Operational risk RWA are one block of the denominator; the ratio itself is built in how to calculate the CET1 ratio, and the floor that caps internal-model savings on the credit side in how to calculate the output floor.
The full RWA ladder this charge sits in, credit, market, CVA and operational risk side by side, is built in the free workbooks for this book.
It is the Basel III proxy for the size of a bank's business, the sum of three components averaged over three years: interest, leases and dividends (with net interest capped at 2.25 per cent of earning assets), services (the larger of income and expense for fees and for other operating items) and the financial component (absolute trading and banking book P&L). In the worked case it comes to 1,843.00 million.
12 per cent on the business indicator up to 1,000 million, 15 per cent from 1,000 to 30,000 million and 18 per cent above. They apply band by band, so a bank with a business indicator of 1,843 pays 120.00 plus 126.45, a BIC of 246.45 and an effective rate of 13.37 per cent, not 15.
No. CRR3 sets the ILM to 1 for all EU banks, and the UK has done the same, so capital equals the BIC. Where it applies, ILM = ln(e - 1 + (LC/BIC)^0.8) with LC at 15 times average annual losses: losses of 18 a year against a BIC of 246.45 give an ILM of 1.0275 and 84.66 more RWA.
This article is one calculation from Financial Regulation. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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