The LCR asks whether the buffer covers 30 days. The survival horizon asks how many days it covers, and the answer moves fastest with the largest uninsured deposits.
A bank's liquidity survival horizon is the number of days until the cumulative net cash outflow under a stress scenario exceeds the liquidity it can raise: cash, unencumbered securities at market value less haircut, and unused secured borrowing capacity. On an illustrative bank with $1,710m of capacity facing a run concentrated in uninsured corporate deposits, cumulative outflows overtake the buffer on day 23. If those corporate deposits leave twice as fast, the horizon falls to 8 days.
Worked in full in Bank Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
The liquidity coverage ratio asks one question: does the buffer cover 30 days of stressed outflows? The survival horizon asks how many days it covers, and that is what a treasurer, a supervisor in a crisis and an analyst reading a bank after a run actually want to know. It is built from the same two ingredients, a maturity ladder of outflows and a stack of counterbalancing capacity, laid out by time bucket rather than summed into one ratio.
| Source | Market value | Haircut | Cash raised |
|---|---|---|---|
| Cash at the central bank | 250 | 0% | 250 |
| Treasuries, unencumbered | 500 | 2% | 490 |
| Agency MBS, unencumbered | 600 | 5% | 570 |
| Unused FHLB capacity on pledged loans | 400 | 0% | 400 |
| Counterbalancing capacity | 1,710 |
Three rules. Securities count at market value, not book value. Anything already pledged counts once, as capacity on the facility it secures, never again as a security. And borrowing capacity counts only if the collateral is already lodged and tested; a line that needs paperwork in a crisis is not day-one liquidity.
Each deposit class gets a run-off rate per bucket. The rates below are illustrative assumptions for an idiosyncratic stress, chosen to show the mechanism, not regulatory factors.
| Deposit class | Balance | Day 1 | Days 2 to 7 | Days 8 to 14 | Days 15 to 30 | Days 31 to 90 |
|---|---|---|---|---|---|---|
| Insured retail | 4,000 | 1% | 1% | 1% | 2% | 3% |
| Uninsured retail and small business | 2,000 | 3% | 5% | 4% | 4% | 6% |
| Uninsured corporate | 2,500 | 10% | 15% | 8% | 7% | 10% |
Add the wholesale funding that will not roll, the draws customers make on undrawn commitments when the bank is in the news, and deduct contractual loan repayments at 50 per cent, because a bank under stress keeps lending to its best customers.
| Bucket | Deposit outflow | Wholesale and draws | Inflows | Net outflow | Cumulative | Capacity left |
|---|---|---|---|---|---|---|
| Day 1 | 350 | 0 | 20 | 330 | 330 | 1,380 |
| Days 2 to 7 | 515 | 250 | 60 | 705 | 1,035 | 675 |
| Days 8 to 14 | 320 | 150 | 60 | 410 | 1,445 | 265 |
| Days 15 to 30 | 335 | 250 | 120 | 465 | 1,910 | −200 |
| Days 31 to 90 | 490 | 450 | 300 | 640 | 2,550 | −840 |
Capacity is still positive at day 14, with 265 left, and negative by day 30. Interpolate inside the bucket, assuming the 465 of net outflow leaves evenly over its 16 days, about 29 a day:
Survival horizon = 14 + 265 ÷ 465 × 16 = 14 + 9.1 = 23 days.
In Excel, with cumulative outflows in F2:F6, bucket end days in B2:B6 and capacity in H1, the bucket is =MATCH(TRUE,INDEX(F2:F6>H1,0),0), and the day is the previous bucket end plus (H1-previous cumulative)/net outflow*bucket length.
The 30-day view of the same ladder gives a coverage of 1,710 ÷ 1,910 = 90 per cent, a shortfall of 200. The survival horizon says something the ratio does not: the bank runs dry in the third week, not at the end of the month, and it needs 2,550 to survive 90 days, 840 more than it holds.
The uninsured corporate deposits are 29 per cent of the deposit base and 1,000 of the 1,910 that leaves in 30 days, 52 per cent of the stressed outflow. That is the concentration to measure first, and the subject of how to calculate a bank's uninsured deposit coverage ratio.
| Scenario | 30-day net outflow | Survival horizon, days |
|---|---|---|
| Corporate run-off at half speed | 1,410 | 65 |
| Base case | 1,910 | 23 |
| Corporate run-off 1.5 times | 2,410 | 12 |
| Corporate run-off twice as fast (80% in 30 days) | 2,910 | 8 |
| Base case, 500 more FHLB capacity | 1,910 | 58 |
| Base case, 1,000 more FHLB capacity | 1,910 | more than 90 |
The horizon is not linear. Halving the speed of one deposit class nearly triples it, because the run is front-loaded and the buffer only has to outlast the first wave. Doubling the speed takes it to 8 days, which is the speed at which a bank needs the discount window rather than a plan. In the other direction, 500 of extra pre-positioned collateral is worth 35 days, because it pushes the crossing point out of the steep part of the ladder into the slower 31 to 90 day bucket.
The usual error is to count securities at book value. If the agency MBS were carried at 706 with an unrealised loss of 106, a ladder that took them at book value with no haircut would add 136 of capacity that does not exist (706 against 570 after the haircut), and report a horizon of 28 days instead of 23. Repo raises cash only on market value less the haircut, and selling the bonds turns that unrealised loss into a realised one, which is how a liquidity problem becomes a capital problem. The related trap, counting the same collateral as both a security and borrowing capacity, is worked in how to calculate the LCR when part of the buffer is pledged.
For the ALCO pack: show the horizon under at least two speeds of the largest uninsured deposit class, and the capacity at market value. A single horizon at one run-off assumption hides the only number that moves.
Build the ladder, cumulate the net outflows, and find the day they pass counterbalancing capacity. Here: 1,710 of capacity, 23 days, 8 days if the corporate deposits leave twice as fast. Which of the bank's numbers a depositor actually reads, and how the run plays through the balance sheet, is the subject of the liquidity workbook among the free workbooks for this book.
The LCR compares the liquid asset buffer with 30 days of stressed net outflows and returns one ratio. The survival horizon lays the same outflows out by time bucket and finds the day they exhaust the buffer. An illustrative bank covering 90 per cent of its 30-day outflows survives 23 days, which the ratio alone does not say.
Cash at the central bank, unencumbered securities at market value less the repo or sale haircut, and unused borrowing capacity on collateral already pledged to the FHLB or discount window. In the illustration that is 250 of cash, 490 of Treasuries, 570 of agency MBS and 400 of FHLB capacity, 1,710 in all.
More than proportionally, because runs are front-loaded. With uninsured corporate deposits losing 40 per cent in 30 days the illustrative bank lasts 23 days; at half that speed it lasts 65, and at twice the speed, 80 per cent in 30 days, it lasts 8.
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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