Liquidity stress tests and survival horizons · RiskAtoms Academy

By the end you will be able to

1Design a liquidity stress test: name-specific, market-wide and combined scenarios, with run-off, rollover, drawdown, collateral and forced-sale assumptions.
2Build the daily path of outflows and inflows as a sequence and its running total, the cumulative net outflow.
3Compare the path with counterbalancing capacity and read off the survival horizon in days.
4Explain why a bank's own stress test can be much harsher than the LCR, and what each assumption does to survival.

Why it matters

RiskAtoms Bank's LCR is 157.4%: comfortably above the 100% minimum. Yet when its treasury runs its own combined stress, a downgrade during a market freeze, the bank runs out of cash on day 48. Both numbers are right. They answer different questions. The LCR asks whether the buffer covers a standard 30-day stress. The stress test asks how long this bank, with its own customers and its own funding, can keep paying, day by day. That number, the survival horizon, is what boards set limits on and what a contingency funding plan is built around.

Core explanation

Cash out, cash in, day by day

Illustrative dataRiskAtoms Bank plc's liquidity book

A £67bn balance sheet on one made-up reporting date, in pounds: every line's contractual maturity, its HQLA level, LCR rate and NSFR factors, the undrawn facilities and collateral triggers, and a daily 90-day stress test in three scenarios. The numbers are round illustrative values, not any bank's data, and the cash flows are principal only (no interest). The same book runs through every lesson in Module 3.5, so the figures agree.

This lesson uses the book's 90-day stress test. Maturing funding and loans fall due evenly within each maturity bucket; the gilt repo rolls throughout; no senior bond falls due within 90 days.

The contractual ladder of L3.5.04: Cash flow ladders and maturity gaps says what falls due if nobody changes their mind. A liquidity stress test asks what happens when they do. It replaces each contractual flow with a behavioural one under a severe but plausible story, and it runs day by day, because a bank fails on a particular morning, not on average over a month.

Three scenarios

Banks run at least three stories: the Basel Committee's 2008 Sound Principles ask for name-specific and market-wide scenarios, alone and in combination (Principle 10), and the LCR's own scenario is the combined one (LCR20.2). A name-specific stress hits only this bank: here a three-notch downgrade. A market-wide stress hits everyone: funding markets freeze and asset prices fall. The combined stress does both. Each scenario is a set of assumptions:

Run-off (run-off rate): the share of demand deposits withdrawn. Insured current accounts run least, instant-access savings more, corporate operational balances more again (L3.5.03: What drains liquidity).
Rollover (rollover rate): the share of maturing funding renewed. In a downgrade, banks and money market funds stop lending unsecured at once.
Drawdowns: companies draw committed lines when their own markets close.
Collateral: extra margin on a downgrade and on market moves (L3.4.05: Collateral and the CSA).
Inflows: maturing interbank lending comes back, but the bank keeps renewing part of its customer loans to protect its franchise.
Capacity: the buffer, valued at forced-sale prices (L3.2.17: Market liquidity risk), is the counterbalancing capacity.

Assumption	Name-specific	Market-wide	Combined
Stable retail run-off (30 days)	8%	2%	10%
Less stable retail run-off	25%	5%	30%
Operational deposit run-off	30%	10%	40%
Retail term deposits rolled	50%	85%	50%
Other corporate deposits rolled	20%	70%	20%
Bank and fund deposits rolled	0%	30%	0%
CP and CDs rolled	0%	25%	0%
Corporate credit lines drawn	10%	15%	20%
Corporate liquidity lines drawn	30%	50%	50%
Collateral calls	£400m	£300m	£700m
Forced-sale haircut, Level 1 / 2A / 2B	0% / 5% / 15%	2% / 10% / 30%	2% / 10% / 30%
Maturing customer loans renewed	50%	70%	50%

Deposits do not run evenly. The book's run profile takes half of each 30-day run-off in the first five days and the rest by day 30, then half as much again by day 90, as a long stress grinds on.

ExploreFrom assumptions to a survival horizon

Click a box to see what happens there.

Scenario

A downgrade, a market freeze, or both. The story fixes every rate in the table above. Treasury writes it; risk challenges it; the board approves it.

The book under three stresses

Name-specificMarket-wideCombined

Scenario	Capacity	Net outflow, day 30	Capacity ÷ day 30	Survival
Name-specific	£14.25bn	£9.89bn	144%	90+ days
Market-wide	£13.89bn	£3.14bn	442%	90+ days
Combined	£13.89bn	£12.65bn	110%	47 days

Three things stand out. Day 1 is brutal in the two downgrade scenarios, because everything overnight that can leave does. The market-wide stress alone is mild for this bank (£3.14bn by day 30): its deposits are sticky and its own name is sound. And the combined stress is not just the sum of the two: the market strain shrinks capacity through bigger haircuts at the very moment the downgrade drains cash. Its £12.65bn by day 30 is far more than the LCR's £8.71bn of net outflows, which is why its 30-day cover is 110%, not 157%.

Sort itName-specific or market-wide?

Which kind of scenario does each assumption belong to?

Rating agencies cut RiskAtoms Bank by three notches and derivative counterparties call £400m of collateral.
Money market funds stop buying CDs from every UK bank for a month.
A newspaper story about the bank's losses drives a quarter of its instant-access savers to move their money.
Corporate bond markets shut and companies draw their bank credit lines to pay maturing debt.
Prices of BBB corporate bonds fall sharply, so selling the Level 2B holdings raises 30% less.

The formal version

A stress test is a pair of sequences (M-A06: Sequences): daily outflows $O_1, O_2, \ldots$ and inflows $I_1, I_2, \ldots$ . Everything else is built from their running total.

The run profile. The cumulative share of a 30-day run-off gone by day $t$ is

r(t) = \begin{cases} 0.5\,\min(t/5,\ 1) + 0.5\,t/30 & 0 \le t \le 30 \\ 1 + 0.5\,(t - 30)/60 & 30 < t \le 90 \end{cases}

Its daily steps form a sequence that is constant on three stretches:

\begin{aligned} \Delta r_t = r(t) - r(t-1) &= \tfrac{0.5}{5} + \tfrac{0.5}{30} = \tfrac{7}{60} \approx 0.1167 && 1 \le t \le 5 \\ &= \tfrac{0.5}{30} = \tfrac{1}{60} \approx 0.0167 && 6 \le t \le 30 \\ &= \tfrac{0.5}{60} = \tfrac{1}{120} \approx 0.0083 && 31 \le t \le 90 \\ \textstyle\sum_{t=1}^{30} \Delta r_t &= 5 \times \tfrac{7}{60} + 25 \times \tfrac{1}{60} = \tfrac{35 + 25}{60} = 1 \end{aligned}

The last line checks the telescoping sum: the steps add back to $r(30) - r(0) = 1$ , the whole 30-day run-off.

Survival with steady flows. If from day $k$ on the daily net outflow is a constant $n > 0$ , the cumulative outflow is an arithmetic sequence and the headroom falls in a straight line:

\begin{aligned} H_{k+j} &= H_k - j\,n \\ H_{k+j} \ge 0 \iff j &\le H_k / n \\ T^{*} &= k + \left\lfloor H_k / n \right\rfloor \end{aligned}

In the book every bucket from day 31 to day 90 is one maturity bucket and the run profile is linear there, so the flows are constant and this short cut gives the exact answer, as the worked example shows.

Try it

Start from any of the three scenarios and change its assumptions. Watch where the cumulative net outflow crosses the capacity line: that crossing is the survival horizon. Try the combined stress with interbank and CP rollover at 50%, then with deposit run-off at × 1.5.

Try itRun the stress test yourself

Start from a scenario

Deposit run-off (× scenario)× 1.0

Interbank, CP and CD rollover0%

Facility drawdowns (× scenario)× 1.0

Maturing customer loans renewed50%

Collateral calls (downgrade and market moves)

Cumulative net outflowCounterbalancing capacity

Survival horizon47 days

Combined as set in the book47 days

Counterbalancing capacity£13.89bn

Net outflow by day 30£12.65bn

Lowest headroom−£2.96bn (day 90)

Capacity ÷ 30-day net outflow110%

The run-off lever scales the scenario's 30-day rates (capped at 100%); drawdowns too. The collateral calls scale the £400m downgrade call and the £300m market call where the scenario has them. Capacity changes only with the scenario, through its forced-sale haircuts. Illustrative book, principal flows only.

Worked example

The combined stress, day by day

Scenario: the three-notch downgrade and the market freeze together. All figures are from the book, in pounds.

From capacity to the day the cash runs out

Step 1 of 6

1
Counterbalancing capacity
Cash at par; the unencumbered securities at the combined scenario's forced-sale haircuts.
$\begin{aligned} C &= \text{£}6{,}000\text{m} + \text{£}5{,}500\text{m} \times 0.98 \\ &\quad + \text{£}2{,}000\text{m} \times 0.90 + \text{£}1{,}000\text{m} \times 0.70 \\ &= \text{£}13{,}890\text{m} \end{aligned}$

Regulatory lens

The Basel LCR fixes one 30-day scenario with standard rates and calls it a minimum: banks are expected to build their own scenarios for their own business, with longer horizons, and share the results with supervisors (LCR20.3). In the UK and the EU those internal stress tests sit in the bank's internal liquidity adequacy assessment process (ILAAP), which supervisors review. The LCR itself is in L3.5.07: LCR and NSFR in practice; the rules on ILAAP and supervisory review are in M4.5: Liquidity and IRRBB regulation; and the behavioural models that estimate run-off and drawdown rates from data are in M6.7: Liquidity, ALM and behavioural models.

Spark Atoms

Spark AtomHalf in five days is not harsh

The book takes half a month's run-off in the first five days. Real runs can be faster. On 9 March 2023 more than $40bn left Silicon Valley Bank, and management expected $100bn more to go the next day: together over 80% of the $173bn of deposits it had at the end of 2022 (Federal Reserve review of SVB, April 2023; SVB's results for 2022).

Spark AtomA straight line at the end

After day 30 the book's combined stress loses the same £69.92m every day, so the survival horizon is just 30 + ⌊1,235 ÷ 69.92⌋ = 47 days. A 90-step simulation and one line of arithmetic agree to the day.

Key takeaways

A liquidity stress test replaces contractual flows with behavioural ones under a scenario and runs day by day.
Banks run name-specific, market-wide and combined scenarios, each a set of run-off, rollover, drawdown, collateral, inflow and forced-sale assumptions.
The cumulative net outflow is a running sum of daily net flows; headroom is capacity less that sum; survival is the last day headroom stays non-negative.
On the book: name-specific and market-wide survive 90 days; the combined stress survives 47 days.
The combined stress drains £12.7bn in 30 days against the LCR's £8.7bn: the LCR is a minimum, not the bank's worst case.

Reaction

Check what stuck

Question 1 · objective 2

Under the book's run profile (half the 30-day run-off in the first five days, the rest evenly by day 30), what share of the 30-day run-off has gone by the end of day 10, in %?

%

Question 2 · objective 2

A bank has £10bn of instant-access savings and assumes 30% run off over 30 days on the same profile. What leaves on day 1, in £m?

£m

Question 3 · objective 3

Capacity is £10bn. By day 30 the cumulative net outflow is £6bn, and from then on it grows by a steady £100m a day. How many days does the bank survive?

days

Question 4 · objective 1

RiskAtoms Bank survives 90 days in the name-specific stress but only 47 in the combined one. Which change does the most damage?

ADeeper retail and operational run-off, more facilities drawn, market collateral calls and bigger forced-sale haircuts, all on top of the downgradeBFewer maturing loans renewedCSenior bonds falling due within 90 daysDRepo lenders refusing to roll the gilt repo

Question 5 · objective 4

The bank's LCR is 157.4%, yet its combined stress survives only 47 days. What does that tell you?

AThe LCR is a supervisory minimum on standard rates over 30 days; the bank's own scenario is harsher and runs longer, as the Basel text expectsBThe LCR is wrong and should be ignoredCThe stress test must contain an error, because the LCR is above 100%DSurvival in days and the LCR always agree

Glossary

Liquidity stress test: A projection of a bank's cash flows, day by day, under a severe but plausible scenario, to see how long it can keep paying.
Name-specific (idiosyncratic) stress: A stress that hits only this bank: a downgrade, a scandal or large losses, while markets work normally. Also called idiosyncratic.
Market-wide stress: A stress that hits every bank at once: funding markets freeze and asset prices fall, though this bank's own name is not in doubt.
Combined stress: Both at once: the bank's own name is in doubt while markets are also under strain.
Run-off rate: The share of a deposit balance customers withdraw over a period of stress.
Rollover rate: The share of maturing funding that lenders renew. A rollover rate of 0% means every maturing loan to the bank is repaid.
Counterbalancing capacity: Counterbalancing capacity: the cash a bank can raise during the stress from its own resources, here the unencumbered buffer at forced-sale values.
Forced-sale haircut: The fall in an asset's price when it must be sold quickly in a stressed market.
Headroom: Capacity left on a given day: counterbalancing capacity less the cumulative net outflow so far.
Survival horizon: The number of days a bank can meet all its outflows in a stress before it runs out of capacity.
Franchise lending: Lending a bank keeps doing in a stress, such as renewing customer loans as they mature, to protect its business and reputation.

Deep Dives & Origins

Deep Dives

Basel Committee on Banking Supervision, Principles for Sound Liquidity Risk Management and Supervision, BIS, September 2008: the principles on stress testing and the liquidity cushion (Principles 10 and 12). Intermediate.
Basel Committee on Banking Supervision, Basel Framework, LCR20 Calculation (the LCR's own stress scenario), BIS. Intermediate.

Origins

Basel Committee on Banking Supervision, Basel Framework, LCR20 Calculation, paragraphs 20.1 to 20.3, BIS, version effective 15 December 2019.
Basel Committee on Banking Supervision, Principles for Sound Liquidity Risk Management and Supervision, BIS, September 2008, Principle 10.
Prudential Regulation Authority, SS24/15 The PRA's approach to supervising liquidity and funding risks, Bank of England; European Central Bank, ECB Guide to the internal liquidity adequacy assessment process (ILAAP), November 2018.
Board of Governors of the Federal Reserve System, Review of the Federal Reserve's Supervision and Regulation of Silicon Valley Bank, April 2023.
SVB Financial Group, fourth-quarter 2022 financial results (Form 8-K, exhibit 99.1), 19 January 2023.

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