A worked bank: the liquidity sources marked and haircut, the two coverage figures, and how many days each one lasts in a run.
Uninsured deposit coverage is the liquidity a bank can raise in a hurry divided by its deposits above the insurance limit. On an illustrative bank with 2,980,800 of uninsured deposits, cash, securities at market value less haircuts and unused borrowing capacity give 2,900,844, or 97.32 per cent. That is the figure that reaches the board. The coverage the bank can reach without breaching the well-capitalised threshold is 90.91 per cent, and the difference is a capital decision nobody has been asked to make.
Worked in full in Bank Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Sagebrook National Bank has 6,480,000 of deposits, 46 per cent of them above the insurance limit (in the United States, 250,000 per depositor per ownership category). Rates have risen 425 basis points over the year, so its fixed-rate securities stand well below par. Every figure is illustrative and in thousands of dollars.
| Input | Value |
|---|---|
| Total deposits | 6,480,000 |
| Share above the insurance limit | 46% |
| Cash and equivalents | 420,000 |
| Available-for-sale securities, at par (duration 4.6) | 1,180,000 |
| Held-to-maturity securities, at par (duration 7.8) | 1,640,000 |
| Federal Home Loan Bank capacity / drawn | 980,000 / 620,000 |
| Haircuts, AFS / HTM | 2% / 3% |
| Published CET1 capital / risk-weighted assets | 639,600 / 5,610,000 |
| Well-capitalised CET1 threshold | 6.5% |
First the denominator: 46 per cent of 6,480,000 is 2,980,800 of uninsured deposits. These are the balances with a reason to leave at the first rumour.
Then each source at the value a lender or a buyer would give for it today. With duration and convexity, the 425 basis point shock takes the available-for-sale book down 17.38 per cent, to 974,886, and 955,389 after a 2 per cent haircut. The held-to-maturity book falls 26.74 per cent, to 1,201,500, and 1,165,455 after a 3 per cent haircut. The accounting label does not change what the securities are worth. The unused borrowing line adds 360,000.
| Source | Par or limit | Usable value |
|---|---|---|
| Cash | 420,000 | 420,000 |
| Available for sale, at market less haircut | 1,180,000 | 955,389 |
| Held to maturity, at market less haircut | 1,640,000 | 1,165,455 |
| Unused borrowing capacity | 360,000 | 360,000 |
| Total mobilisable | 2,900,844 |
Coverage = mobilisable liquidity / uninsured deposits = 2,900,844 / 2,980,800 = 97.32%
Excel: =(Cash+AFS*(1+dAFS)*(1-hAFS)+HTM*(1+dHTM)*(1-hHTM)+(FHLBcap-FHLBdrawn))/(Deposits*UninsShare)
Sagebrook reports CET1 of 639,600 on 5,610,000 of risk-weighted assets, 11.40 per cent, without the unrealised loss on its securities. Most US banks below the largest categories may filter that loss out of regulatory capital, and the borrowing line is already counted in full. The case assumes the available-for-sale book is raised by repo against it, which realises nothing, and the held-to-maturity book by sale. A sale realises the loss.
The gross loss on the whole held-to-maturity book is 438,500, or 328,875 after 25 per cent tax. Sell all of it and the ratio falls to 5.54 per cent, below the 6.5 per cent well-capitalised threshold. The bank has 639,600 less 364,650, or 274,950, of capital above the threshold, so it can sell 274,950 / 328,875 = 83.60 per cent of the book before the published ratio breaks.
Coverage without a breach = (2,900,844 − (1 − 83.60%) × 1,165,455) / 2,980,800 = 2,709,746 / 2,980,800 = 90.91%
The 6.41 points between the two figures are 191,098 of liquidity. Using them means choosing to fall below well-capitalised in order to pay depositors. That may be the right choice on the day, but it should be a decision taken in advance by the board, not a footnote discovered by treasury during the run. Under US accounting, selling out of held to maturity also calls the classification of the rest of the book into question. And if the available-for-sale book has to be sold rather than repoed, its loss of 153,835 after tax comes out of the same headroom first: only 36.83 per cent of the held-to-maturity book could then be sold, and coverage without a breach falls to 72.62 per cent.
Coverage turns into time once an outflow rate is assumed. With outflows stated as a share of uninsured deposits per day, the days to exhaustion are simply coverage divided by the daily rate.
| Outflow per day | Outflow, $ thousands | Days, total liquidity | Days, without breach |
|---|---|---|---|
| 1% | 29,808 | 97.3 | 90.9 |
| 2% | 59,616 | 48.7 | 45.5 |
| 5% | 149,040 | 19.5 | 18.2 |
| 10% | 298,080 | 9.7 | 9.1 |
| 25% | 745,200 | 3.9 | 3.6 |
The 25 per cent row is not a fantasy: Silicon Valley Bank lost close to a quarter of its deposits in a single day in March 2023. At that speed the 191,098 between the two coverage figures last 6.15 hours. A constant rate is also the generous assumption, since real runs accelerate.
The haircut and the valuation basis matter as much as the balances. Had the held-to-maturity book been pledgeable at par with no haircut, as the Federal Reserve's Bank Term Funding Program allowed for new loans from March 2023 to March 2024, the same balance sheet would show 3,375,389 of liquidity and coverage of 113.24 per cent without selling anything.
The usual error is to count securities at par or at amortised cost because that is how the balance sheet carries them. Held-to-maturity securities on Sagebrook's books are 1,640,000; their usable value is 1,165,455. Counting par would add 474,545 of liquidity that no lender or buyer will provide. The second error is to report one coverage figure. The headline ratio assumes the bank will sell regardless of what selling does to its capital; the constrained ratio states what it can do without crossing a supervisory line. Both belong on the page, each with its days.
The rate shock that marks down the securities is the same one that drives the deposit cost, worked in how to calculate a deposit beta, and the same marks decide what a buyer would actually pay for the bank.
The sources, the two coverage figures and the days table are in the free workbook for this case, ready for your own balance sheet.
There is no regulatory minimum for this ratio, and a single threshold would hide what matters. In the worked case the headline is 97.32 per cent, but the figure reachable without breaking the 6.5 per cent well-capitalised threshold is 90.91 per cent. A bank should report both, and the days each lasts: 48.7 against 45.5 at a 2 per cent daily outflow.
Because reaching their cash value by sale crystallises the unrealised loss, which flows into earnings and common equity. In the example, the held-to-maturity book stands 26.74 per cent below par after a 425 basis point shock. Selling all of it costs 328,875 after tax and takes the capital ratio to 5.54 per cent, so only 83.60 per cent of it can be sold before the threshold breaks.
Divide coverage by the daily outflow rate, both expressed against uninsured deposits. At 97.32 per cent coverage, a 2 per cent daily outflow lasts 48.7 days and a 25 per cent outflow 3.9 days. This assumes a constant rate, which is generous: a real run accelerates, and liquidity runs out sooner than the simple division suggests.
This article is one calculation from Bank Management. 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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