Equity of 5,180 becomes 3,511.9 of common equity tier 1. The ratio is the easy part; the deductions are where the 1,668.1 goes.
The CET1 ratio is common equity tier 1 capital divided by risk-weighted assets. The work is in the numerator: start from accounting equity, remove what is not common equity, apply the prudential filters, deduct goodwill, intangibles and the other items the rules list, then deduct whatever exceeds the 10 and 17.65 per cent thresholds. On an illustrative bank, 5,180 of equity becomes 3,511.9 of CET1, and over 27,654.7 of risk-weighted assets that is a CET1 ratio of 12.70 per cent, not the 19.9 per cent a reader of the balance sheet would compute.
Worked in full in Financial Regulation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The bank is fictional, in millions of euros, under the EU's Capital Requirements Regulation (CRR): the items are defined in Article 26, the deductions in Article 36 and the thresholds in Article 48. Basel's text has the same structure. Every balance is illustrative.
| Item | Amount |
|---|---|
| Share capital and share premium | 2,400 |
| Retained earnings | 1,900 |
| Interim profit, verified by the auditor | 300 |
| Accumulated other comprehensive income | 80 |
| of which cash flow hedge reserve | 45 |
| AT1 notes classified as equity | 500 |
| Equity per the accounts | 5,180 |
| Foreseeable dividend | 120 |
| Goodwill | 350 |
| Other intangibles, less 30 of associated deferred tax liability | 210 |
| Deferred tax assets on tax losses | 140 |
| Additional valuation adjustments (prudent valuation) | 35 |
| IRB shortfall of provisions to expected loss | 60 |
| Deferred tax assets from temporary differences | 420 |
| Significant investment in an insurance subsidiary | 480 |
| Risk-weighted assets before threshold items | 26,000 |
AT1 notes sit in accounting equity but are additional tier 1, not common equity, so the 500 leaves first. The interim profit counts only with the supervisor's permission under Article 26(2), which requires it to be verified by the auditor and taken net of any foreseeable charge or dividend. The cash flow hedge reserve is filtered out, because it reflects gains on hedges of cash flows that are not themselves on the balance sheet.
CET1 items = 2,400 + 1,900 + 300 − 120 + 80 − 45 = 4,515
Goodwill and other intangibles are deducted in full, the intangibles net of their deferred tax liability (210 less 30 is 180). Deferred tax assets that rely on future profits and do not arise from temporary differences, here the 140 on tax losses, are deducted in full. So are the prudent valuation adjustments and, for an IRB bank, any shortfall of provisions against expected loss.
Deductions = 350 + 180 + 140 + 35 + 60 = 765
CET1 before threshold deductions = 4,515 − 765 = 3,750
Two items are deducted only in part: deferred tax assets from temporary differences and significant investments in financial sector entities. Each is deducted above 10 per cent of the 3,750 base. What remains of the two together is then deducted above 17.65 per cent of the same base, which is the EU's way of writing Basel's 15 per cent of CET1 after all deductions. Whatever survives both tests is not deducted but risk-weighted at 250 per cent.
| Step | DTAs, temporary | Insurance stake | Total |
|---|---|---|---|
| Amount held | 420 | 480 | 900 |
| 10% threshold (10% x 3,750) | 375 | 375 | |
| Deducted above 10% | 45 | 105 | 150 |
| Remaining after 10% tests | 375 | 375 | 750 |
| Combined threshold (17.65% x 3,750) | 661.9 | ||
| Deducted above 17.65% | 88.1 | ||
| Total threshold deductions | 238.1 | ||
| Not deducted, weighted at 250% | 661.9 |
CET1 = 3,750 − 238.1 = 3,511.9
RWA = 26,000 + 661.9 × 250% = 26,000 + 1,654.7 = 27,654.7
CET1 ratio = 3,511.9 / 27,654.7 = 12.70 per cent
Excel: =(Items-Deductions-ThresholdDed)/(RWA+NotDeducted*2.5), with the threshold deductions in their own cells: =MAX(0,DTA-0.1*Base)+MAX(0,Stake-0.1*Base)+MAX(0,Remaining-0.1765*Base)
Against a requirement of 4.5 per cent Pillar 1, 1.125 per cent from the Pillar 2 requirement of 2.0 per cent (56.25 per cent of it in CET1) and a combined buffer of 4.0 per cent, the bank needs 9.625 per cent. It has 3.07 points of headroom, or 850 million. That headroom, and what eats into it, is the subject of how the maximum distributable amount is calculated.
| Change | CET1 | RWA | Ratio % | Change, bp |
|---|---|---|---|---|
| Base | 3,511.9 | 27,654.7 | 12.70 | 0 |
| Goodwill impaired by 100 | 3,511.9 | 27,654.7 | 12.70 | 0 |
| Loss of 200 | 3,276.6 | 27,566.4 | 11.89 | -81 |
| Temporary DTAs up 100 | 3,411.9 | 27,654.7 | 12.34 | -36 |
| Insurance stake sold at book, cash at the central bank | 3,705.0 | 26,937.5 | 13.75 | 106 |
| 100 more profit retained | 3,629.5 | 27,698.8 | 13.10 | 40 |
Three of these surprise people. A goodwill impairment, which headlines treat as a capital event, changes nothing: goodwill was already deducted, so equity and the deduction fall together. A loss of 200 costs 235.3 of CET1, 1.18 times the loss, because the thresholds are percentages of a base that has just shrunk, and more of the deferred tax and the insurance stake spills over them. And a retained 100 adds 117.7, the same effect run backwards, though the extra amount it lets in under the thresholds also adds risk-weighted assets at 250 per cent. Once a bank is over its thresholds, every euro of temporary-difference DTA is a euro of CET1 lost.
CET1 is the numerator of three constraints at once: the risk-based ratio here, the leverage ratio (as part of tier 1) and the distribution trigger. Which of them binds first is a separate calculation; the leverage side is worked in how to calculate a bank's leverage ratio.
The three capital compartments, the requirement stack and the headroom computed twice are live in the free workbooks for this book.
Shareholders' equity is an accounting figure; CET1 is what remains after regulatory filters and deductions. On the illustrative bank here, 5,180 of equity becomes 3,511.9 of CET1: 500 of AT1 classified as equity comes out, the foreseeable dividend and hedge reserve come out, and 765 of goodwill, intangibles, loss DTAs, prudent valuation and IRB shortfall are deducted before 238.1 of threshold deductions.
No. Goodwill is already deducted in full from CET1, so writing it down lowers equity and the deduction by the same amount. On the illustrative bank a 100 impairment leaves CET1 at 3,511.9 and the ratio at 12.70 per cent. An ordinary loss of 200 is different: it costs 235.3 of CET1, because the 10 and 17.65 per cent thresholds shrink with the capital base.
Under the EU's CRR, deferred tax assets from temporary differences and significant investments in financial sector entities are deducted only above 10 per cent of the CET1 base each, and then above 17.65 per cent of it combined, which is the EU expression of Basel's 15 per cent of CET1 after deductions. Here the combined excess is 88.1 and the 661.9 not deducted is risk-weighted at 250 per cent.
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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