Core Path · L3.5.04

Cash flow ladders and maturity gaps

12 minLiquidity riskCash flow ladderMaturity gapBehavioural assumptions

Know these first

By the end you will be able to

  1. 1Build a contractual cash flow ladder from a balance sheet, bucket by bucket.
  2. 2Compute marginal and cumulative gaps with summation notation, add the buffer, and find the liquidity position and the funding need.
  3. 3Contrast the contractual view with the behavioural view, in which most demand deposits stay, and explain why both are needed.
  4. 4Read the book's ladder: where the gaps are, why the last cumulative figure is what it is, and when term funding must be refinanced.

Why it matters

On contract, RiskAtoms Bank owes £42.3bn tomorrow and is owed £1.5bn. Read literally, it is £40.8bn short overnight, three times its buffer. Yet the bank is sound, and its depositors will still be there next week. Both statements are true. The cash flow ladder is the tool that shows them side by side, and the gap between the two views is the bank's whole business.

Core explanation

Sorting every pound by when it moves

Illustrative dataRiskAtoms Bank plc's liquidity book

A made-up UK bank's £67bn balance sheet on one made-up reporting date, in pounds, seen through its cash flows: every line's contractual maturity in ten buckets from overnight to over five years, its undrawn commitments and collateral triggers, and a 90-day stress test. The figures are round illustrative values, not any bank's data. The same book runs through every lesson in Module 3.5, so the figures agree.

Simplifications this lesson relies on: principal only, no interest; HQLA securities and cash are held as a stock (the buffer) rather than by maturity; no new business; off-balance-sheet commitments are left out of the ladder (they are in L3.5.03 and the stress test). The behavioural profile of demand deposits is an extra, made up for teaching.

A cash flow ladder takes every asset and liability and places its cash flows in time buckets: inflows from assets that mature, outflows to liabilities that fall due. For each bucket it records the marginal gap, inflows less outflows, and the cumulative gap, the running total. A negative cumulative gap is cash the bank must find from somewhere: its buffer, new funding or asset sales.

The first ladder is contractual: every flow on the earliest date its contract allows, no rollovers, no new loans. It is mechanical and objective. Here is the book's:

RiskAtoms Bank's contractual ladder, £bn (HQLA held as a stock and left out)
BucketInflowsOutflowsGapCumulative
Overnight£1.50bn£42.30bn−£40.80bn−£40.80bn
2–7 days£1.20bn£1.50bn−£0.30bn−£41.10bn
8–30 days£1.65bn£2.30bn−£0.65bn−£41.75bn
1–3 months£1.95bn£2.40bn−£0.45bn−£42.20bn
3–6 months£1.85bn£2.50bn−£0.65bn−£42.85bn
6–12 months£3.00bn£2.10bn£0.90bn−£41.95bn
1–2 years£4.50bn£3.90bn£0.60bn−£41.35bn
2–5 years£11.05bn£4.00bn£7.05bn−£34.30bn
Over 5 years£22.30bn£2.00bn£20.30bn−£14.00bn
No maturity£2.00bn£0.00bn£2.00bn−£12.00bn
−£40bn−£30bn−£20bn−£10bn£0bn£10bn£20bnO/N2–7d8–30d1–3m3–6m6–12m1–2y2–5y>5yNoneGap, O/N: −£41bnGap, 2–7d: −£0.3bnGap, 8–30d: −£0.7bnGap, 1–3m: −£0.5bnGap, 3–6m: −£0.7bnGap, 6–12m: £0.9bnGap, 1–2y: £0.6bnGap, 2–5y: £7bnGap, >5y: £20bnGap, None: £2bnCumulative gap, O/N: −£41bnCumulative gap, 2–7d: −£41bnCumulative gap, 8–30d: −£42bnCumulative gap, 1–3m: −£42bnCumulative gap, 3–6m: −£43bnCumulative gap, 6–12m: −£42bnCumulative gap, 1–2y: −£41bnCumulative gap, 2–5y: −£34bnCumulative gap, >5y: −£14bnCumulative gap, None: −£12bnCumulative gap + buffer, O/N: −£27bnCumulative gap + buffer, 2–7d: −£27bnCumulative gap + buffer, 8–30d: −£28bnCumulative gap + buffer, 1–3m: −£29bnCumulative gap + buffer, 3–6m: −£29bnCumulative gap + buffer, 6–12m: −£28bnCumulative gap + buffer, 1–2y: −£28bnCumulative gap + buffer, 2–5y: −£21bnCumulative gap + buffer, >5y: −£0.3bnCumulative gap + buffer, None: £2bnMaturity bucket
Gap in the bucket: red when more goes out than comes in, green otherwiseCumulative gapCumulative gap + buffer

The shape is maturity transformation drawn as a picture (L1.8.02: A bank’s balance sheet): a huge hole at the short end, where deposits fall due, filled slowly at the long end as mortgages and loans repay. Even with the £13.7bn buffer counted as cash on day one, the position stays negative until the last bucket.

The behavioural view

Nobody runs a bank on the assumption that £37.0bn of current accounts and savings vanish tomorrow. Experience says most demand deposits stay for years: salaries keep arriving, bills keep being paid, balances churn but the total holds. The behavioural view places each flow where the bank expects it. The long-lived part is called core. The book's illustrative profile:

Share of each demand deposit line expected to leave in each bucket in normal times (extra, illustrative)
LineO/N2–7d8–30d1–3m3–6m6–12m1–2y2–5y>5y
Insured current accounts0.5%0.5%1.0%2.0%2.0%4.0%5.0%15.0%70.0%
Instant-access savings1.0%1.0%3.0%5.0%5.0%10.0%15.0%30.0%30.0%
Operational corporate2.0%2.0%6.0%5.0%5.0%10.0%15.0%25.0%30.0%

With that profile the overnight outflow drops from £42.3bn to £5.6bn, and with the buffer the position stays positive through the first year, at its lowest £2.55bn at twelve months. It then dips to −£0.20bn in the 1–2 year bucket, when £3.9bn of term funding falls due: senior and covered bonds, central bank funding and retail term deposits. That is not a crisis; it is the refinancing the funding plan must schedule.

Contractual or behavioural? Which view answers each question?

The formal version

Gaps in summation notation

Number the buckets k=1,…,Kk = 1, \dots, K (here K=10K = 10). With IkI_k and OkO_k the inflows and outflows in bucket kk and BB the buffer, build the position step by step (M-A08: Summation notation).

Each bucket's inflow is itself a sum over the lines ℓ\ell that mature in it: Ik=∑ℓ∈assetsaℓkI_k = \sum_{\ell \in \text{assets}} a_{\ell k} and Ok=∑ℓ∈liabilitiesbℓkO_k = \sum_{\ell \in \text{liabilities}} b_{\ell k}. Swapping the order of the two sums explains the last cumulative figure:

GK=∑k=1K(Ik−Ok)=∑k=1K∑ℓaℓk−∑k=1K∑ℓbℓk=∑ℓ(∑k=1Kaℓk)−∑ℓ(∑k=1Kbℓk)=assets outside the buffer−liabilities=£51,000m−£63,000m=−£12,000m=equity−HQLA at face=£4,000m−£16,000m\begin{aligned} G_K = \sum_{k=1}^{K} \left(I_k - O_k\right) &= \sum_{k=1}^{K} \sum_{\ell} a_{\ell k} - \sum_{k=1}^{K} \sum_{\ell} b_{\ell k} \\ &= \sum_{\ell} \Bigl(\sum_{k=1}^{K} a_{\ell k}\Bigr) - \sum_{\ell} \Bigl(\sum_{k=1}^{K} b_{\ell k}\Bigr) \\ &= \text{assets outside the buffer} - \text{liabilities} \\ &= \text{£}51{,}000\text{m} - \text{£}63{,}000\text{m} = -\text{£}12{,}000\text{m} \\ &= \text{equity} - \text{HQLA at face} = \text{£}4{,}000\text{m} - \text{£}16{,}000\text{m} \end{aligned}

The second line holds because each line's flows across all the buckets add up to its balance. Moving demand deposits between buckets changes every GkG_k before the last but never GKG_K: timing assumptions move the gap through time, they do not create money. Put the HQLA securities back in the flows at their maturities and the ladder ends at £4.0bn, the equity: assets less liabilities.

Try it

Slide the demand deposits from their contractual date to their behavioural profile and watch the overnight hole fill. Then switch the buffer off to see the bare gap, and find where the position first turns negative in each view.

Try itFrom contractual to behavioural

−£40bn−£30bn−£20bn−£10bn£0bn£10bn£20bnO/N2–7d8–30d1–3m3–6m6–12m1–2y2–5y>5yNoneGap, O/N: −£41bnGap, 2–7d: −£0.3bnGap, 8–30d: −£0.7bnGap, 1–3m: −£0.5bnGap, 3–6m: −£0.7bnGap, 6–12m: £0.9bnGap, 1–2y: £0.6bnGap, 2–5y: £7bnGap, >5y: £20bnGap, None: £2bnCumulative gap, O/N: −£41bnCumulative gap, 2–7d: −£41bnCumulative gap, 8–30d: −£42bnCumulative gap, 1–3m: −£42bnCumulative gap, 3–6m: −£43bnCumulative gap, 6–12m: −£42bnCumulative gap, 1–2y: −£41bnCumulative gap, 2–5y: −£34bnCumulative gap, >5y: −£14bnCumulative gap, None: −£12bnCumulative gap + buffer, O/N: −£27bnCumulative gap + buffer, 2–7d: −£27bnCumulative gap + buffer, 8–30d: −£28bnCumulative gap + buffer, 1–3m: −£29bnCumulative gap + buffer, 3–6m: −£29bnCumulative gap + buffer, 6–12m: −£28bnCumulative gap + buffer, 1–2y: −£28bnCumulative gap + buffer, 2–5y: −£21bnCumulative gap + buffer, >5y: −£0.3bnCumulative gap + buffer, None: £2bnMaturity bucket
Gap in the bucket: red when more goes out than comes in, green otherwiseCumulative gapCumulative gap + buffer
Overnight gap−£40.8bn
First bucket below zeroOvernight
Position at 30 days−£28.1bn
Position at one year−£28.3bn
Lowest point−£29.1bn (3–6 months)
Cumulative gap at the end−£12.0bn

Illustrative. Principal only. HQLA securities are held as a stock (the buffer), not by maturity. Only the demand deposits move; every other line keeps its contractual dates. The behavioural profile is an extra made up for teaching.

Worked example

Building the book's ladder

From the balance sheet to the position

Step 1 of 6
  1. 1

    The overnight inflows

    I1=£1,200m+£300m=£1,500m(reverse repos, interbank placements)I_1 = \text{£}1{,}200\text{m} + \text{£}300\text{m} = \text{£}1{,}500\text{m} \quad \text{(reverse repos, interbank placements)}

Where the truth lies

The contractual ladder says the bank needs £27.1bn more than its buffer overnight; the behavioural one says it never runs short in the first year. In normal times £1,440m of demand deposits leave in a month; the book's combined stress assumes £7,200m. The stress test in L3.5.05: Liquidity stress tests and survival horizons sits between the two views, and that is where the buffer is sized.

Regulatory lens

The Basel liquidity monitoring tools (Basel Framework, SRP50) start with the contractual maturity mismatch: contractual cash and security flows from all on- and off-balance-sheet items, mapped to time bands from overnight to beyond five years, assuming no rollover of existing liabilities and no new assets. Supervisors collect it raw, without behavioural assumptions, and expect banks to run their own behavioural, going-concern analyses alongside. The Basel Committee's 2008 Principles ask for cash flow projections over an appropriate set of time horizons (Principle 5). The regulatory returns are in M4.5: Liquidity and IRRBB regulation, and modelling behavioural deposit profiles from data is in M6.7: Liquidity, ALM and behavioural models.

Spark Atoms

Spark AtomThe ladder that cannot lie at the end
However a treasurer reshuffles the buckets, the last cumulative gap of the book's ladder is fixed at −£12.0bn: assets outside the buffer less liabilities. Behavioural assumptions only decide when the gap appears, which is exactly why they matter so much and why supervisors want the raw contractual version too.
Spark AtomGap analysis, then and now
The 2008 Principles call cash flow projections, and the cash flow mismatch or liquidity gap analysis they produce, a critical tool, and the Basel monitoring metrics suggest overnight, 7-day, 14-day and 1, 2, 3, 6 and 9-month bands, then 1, 2, 3, 5 years and beyond, leaving each supervisor to set its own. The book uses ten coarser buckets; a real treasury runs daily buckets for the first weeks, because a run is measured in days.

Key takeaways

  • A cash flow ladder sorts inflows and outflows into time buckets; the marginal gap is gₖ = Iₖ − Oₖ and the cumulative gap Gₖ = Σ gⱼ.
  • Adding the buffer gives the liquidity position Pₖ = B + Gₖ; its lowest negative value is the funding the bank must find.
  • On contract the book is £40.8bn short overnight, because £37.0bn of demand deposits fall due at once.
  • Behaviourally, most demand deposits stay: the overnight outflow falls to £5.6bn and, with the buffer, the position stays positive for a year.
  • Timing assumptions move gaps between buckets but never change the last one: −£12.0bn = equity less HQLA at face.
  • Supervisors collect the contractual ladder raw; banks plan on the behavioural one; stress tests sit between them.

Reaction

Check what stuck

Question 1 · objective 2

A ladder has marginal gaps of −£5bn, +£2bn and −£1bn in its first three buckets. What is the cumulative gap at the end of the third bucket, in £bn?

£bn

Question 2 · objective 2

The book's contractual cumulative gap at 30 days is −£41.75bn and its buffer is £13.7bn. What is the liquidity position at 30 days, in £bn?

£bn

Question 3 · objective 3

Why does the contractual ladder put all £37bn of demand deposits in the overnight bucket?

Question 4 · objective 3

In the behavioural view (all demand deposits on their behavioural profile, buffer included), what is the liquidity position at the end of the first year, in £bn?

£bn

Question 5 · objective 4

A treasurer shows the board the behavioural ladder only. What is the main risk in that?

Glossary

Cash flow ladder
Cash flow ladder (maturity ladder): a table of a bank's cash inflows and outflows sorted into time buckets, from overnight to over five years.
Time bucket
Time bucket: one band of the ladder, such as 2 to 7 days or 1 to 3 months.
Marginal gap
Marginal gap: inflows less outflows within one bucket.
Cumulative gap
Cumulative gap: the sum of the marginal gaps from the first bucket to the current one.
Contractual view
Contractual view: every flow on the earliest date its contract allows, with no renewals and no new business.
Behavioural view
Behavioural view: flows on the dates the bank expects from experience, such as demand deposits that stay for years.
Core deposits
Core deposits: the part of non-maturity deposits expected to stay with the bank over a long horizon in normal times.
Liquidity position
Liquidity position: the cumulative gap plus the buffer the bank can turn into cash on day one.
Maturity transformation
Maturity transformation: funding long-term assets with short-term liabilities.

Deep Dives & Origins

Deep Dives

  • Basel Committee on Banking Supervision, Basel Framework, SRP50 Liquidity monitoring metrics, BIS. Intermediate.
  • Basel Committee on Banking Supervision, Principles for Sound Liquidity Risk Management and Supervision, BIS, September 2008. Intermediate.

Origins

  • Basel Committee on Banking Supervision, Basel Framework, SRP50 Liquidity monitoring metrics, paragraphs 50.6 to 50.12 (contractual maturity mismatch), BIS.
  • Basel Committee on Banking Supervision, Principles for Sound Liquidity Risk Management and Supervision, BIS, 2008, Principle 5 and paragraph 48.

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