A worked European bank: the buffer level by level, the outflows line by line, and the 51 points that separate the ratio from the figure that circulates.
The liquidity coverage ratio is the stock of unencumbered high-quality liquid assets divided by net cash outflows over 30 days of stress, and it must be at least 100 per cent. The word that matters is unencumbered: securities pledged as collateral leave the buffer. On an illustrative European bank, 5,629.8 million of pledged sovereign bonds take the ratio from the 168.84 per cent the whole portfolio suggests to 117.49 per cent.
Worked in full in Financial Regulation by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
In the EU the ratio is defined by Delegated Regulation (EU) 2015/61. Article 7 requires liquid assets to be unencumbered, meaning free of any legal, contractual or regulatory restriction that would stop the bank from selling or repoing them within the 30 days. An asset already posted in a repo, or held in a cover pool, cannot also be counted as available to meet outflows. The rule is uncontroversial. The error is in the data: the securities portfolio treasury reports is usually the whole holding, not the part that is still free.
Northbank plc holds 8,400.0 million of central bank reserves and a securities portfolio of four lines. It also has 14,260.0 million of secured funding, of which 37.6 per cent is raised against its own securities; the rest is matched-book repo, which pledges collateral the bank does not own. Every figure is illustrative and in EUR millions.
| Security | Level | Holding | Haircut | After haircut |
|---|---|---|---|---|
| Central bank reserves | 1 | 8,400.0 | 0% | 8,400.0 |
| EU sovereign bonds | 1 | 6,200.0 | 0% | 6,200.0 |
| Covered bonds, AAA | 1b | 2,100.0 | 7% | 1,953.0 |
| Corporate bonds, AA- and above | 2A | 1,600.0 | 15% | 1,360.0 |
| Listed equities | 2B | 1,200.0 | 50% | 600.0 |
| Portfolio after haircuts | 18,513.0 |
The denominator is built line by line, each balance times its 30-day run-off rate.
| Line | Balance | Run-off | Outflow |
|---|---|---|---|
| Retail deposits, stable | 18,000.0 | 5% | 900.0 |
| Retail deposits, less stable | 7,400.0 | 10% | 740.0 |
| Corporate deposits, operational | 6,200.0 | 25% | 1,550.0 |
| Corporate deposits, non-operational | 11,500.0 | 40% | 4,600.0 |
| Financial institution deposits | 5,600.0 | 100% | 5,600.0 |
| Committed credit lines to corporates | 7,200.0 | 10% | 720.0 |
| Guarantees and cancellable lines (model assumption) | 4,100.0 | 5% | 205.0 |
| Other contractual outflows | 850.0 | ||
| Gross outflows | 15,165.0 | ||
| Less contractual inflows (cap 75% of outflows: 11,373.75) | −4,200.0 | ||
| Net outflows | 10,965.0 |
Of the secured funding, 37.6 per cent is raised against Northbank's own inventory: 5,361.76 million of cash. The counterparties take 105 of paper for every 100 of cash, so the securities pledged are 5,361.76 × 1.05 = 5,629.848 million. That 5 per cent is a repo margin (the market often calls it a repo haircut), not an LCR haircut: it increases the securities that leave the buffer.
Which securities are pledged is a matter of record, and in this case it is the sovereigns: 5,629.8 of the 6,200.0 million are encumbered, leaving 570.2 million free. No covered bond, corporate bond or equity is pledged.
Level 1 = 8,400.0 + 570.2 = 8,970.2; level 1b = 1,953.0; level 2A = 1,360.0; level 2B = 600.0
Unencumbered HQLA = 12,883.2
LCR = 12,883.2 / 10,965.0 = 117.49%
Excel: =(Reserves+SUMPRODUCT(Holding-Pledged,1-Haircut))/(GrossOut-MIN(Inflows,0.75*GrossOut))
The composition caps then have to be checked on the buffer as it stands: covered bonds no more than 70 per cent, level 2 no more than 40 per cent, level 2B no more than 15 per cent. Here level 2 is 15.2 per cent and level 2B 4.7 per cent, so none binds. (The full formula in the regulation also adjusts the caps for secured transactions maturing within 30 days; on this balance sheet it changes nothing.)
Had the pledge been forgotten, the ratio would be 18,513.0 / 10,965.0 = 168.84 per cent. Both figures are arithmetically correct. Only one is the liquidity coverage ratio, and the 51.34 points between them are the difference between a surplus of 7,548.0 million and one of 1,918.2 million.
| Share against own securities | Securities pledged | Unencumbered HQLA | LCR |
|---|---|---|---|
| 0.0% | 0.0 | 18,513.0 | 168.84% |
| 20.0% | 2,994.6 | 15,518.4 | 141.53% |
| 37.6% | 5,629.8 | 12,883.2 | 117.49% |
| 50.0% | 7,486.5 | 11,116.6 | 101.38% |
| 60.0% | 8,983.8 | 9,778.8 | 89.18% |
Beyond 6,200.0 million of pledges the sovereigns are exhausted and covered bonds start to leave the buffer. The ratio reaches 100 per cent when 51.1 per cent of the secured book is raised against own securities. The reported portfolio would read 168.84 per cent on every row.
The mistake is taking the liquidity buffer from the securities ledger rather than from the collateral system. The ledger shows what the bank owns; the collateral system shows what it can still use. A second version of the same error is to apply the 5 per cent margin as if it were a haircut, which removes 5 per cent of value from the buffer instead of adding 5 per cent to the securities pledged. The fix is a monthly reconciliation of holdings, pledges and the buffer, line by line, with the imputation order written down.
The buffer before and after encumbrance, the outflows and the stable funding ratio beside them are in the free workbook for this case. The same bank's mortgage weights are worked in how to calculate a mortgage risk weight under loan splitting.
No. To count as high-quality liquid assets, securities must be unencumbered: not pledged, not used as collateral and free to be sold or repoed within the stress period. In the worked case 5,629.8 million of sovereign bonds are pledged against secured funding, and removing them takes the buffer from 18,513.0 million to 12,883.2 million and the ratio from 168.84 to 117.49 per cent.
Each liability and commitment is multiplied by its 30-day run-off rate, for example 5 per cent for stable retail deposits, 40 per cent for non-operational corporate deposits and 100 per cent for deposits from financial institutions. Contractual inflows are deducted, capped at 75 per cent of gross outflows. In the example, 15,165.0 million of gross outflows less 4,200.0 million of inflows leaves 10,965.0 million.
A haircut reduces the value at which an asset counts in the buffer: 7 per cent on high-quality covered bonds, 15 per cent on level 2A corporate bonds. A margin is the extra collateral posted in a repo: 105 of securities for 100 of cash. A margin increases the securities that leave the buffer. On 5,361.8 million of cash it pledges 5,629.8 million of bonds.
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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