Repricing gap analysis · RiskAtoms Academy

By the end you will be able to

1Build a bank's repricing gap band by band, in contractual and behavioural views.
2Compute band and cumulative gaps with summation notation and read what they say about earnings.
3Estimate the change in net interest income as gap × Δr, crudely and with time weights.
4Explain where the gap estimate fails: administered rates, options and floors, curve shape and value.

Why it matters

Sort RiskAtoms Bank's balance sheet by when each rate can change, add up the first year, and you get −£16.6bn: far more liabilities than assets reprice. The textbook reading is that NII falls when rates rise. The bank's full model says the opposite: up £91.7m for a 1% rise. The repricing gap is the oldest tool in ALM and still the first table in every ALCO pack. Used well it gives the right answer in one line. Used carelessly it gives the wrong sign.

Core explanation

Sorting the balance sheet by repricing date

Illustrative dataRiskAtoms Bank plc's banking book

The same £67bn balance sheet as Module 3.5, on one made-up reporting date, in pounds, now with how each line reprices: fixed, floating or administered, its customer rate, a SONIA curve with Bank Rate at 4.00%, a macro hedge and a structural hedge. The figures are round illustrative values, not any bank's data. Every lesson in Module 3.6 uses this book, so the figures agree.

This lesson relies on: fixed items placed at the mid-point of their Module 3.5 maturity buckets ("over five years" at seven years); floating items at their next reset; equity, shares and other assets left out as rate-insensitive; and, in the behavioural view, core deposits slotted in equal monthly cohorts and mortgages prepaying at 8% a year.

A cash flow ladder (L3.5.04: Cash flow ladders and maturity gaps) sorts cash by when it moves. A repricing gap table sorts it by when its rate moves. A two-year fixed mortgage goes in the band where its fix ends; a floating corporate loan goes in the band of its next reset, even if it runs for five more years. In each band:

rate-sensitive assets (RSA) less rate-sensitive liabilities (RSL), plus the hedges' net position, is the band's gap;
the running total is the cumulative gap;
a positive gap means more assets than liabilities reprice: NII tends to rise with rates. A negative gap means the opposite.

The contractual gap

First, contract dates only: every one of the £40bn of current and savings accounts can reprice tomorrow, so all of it sits in the first band, and nobody prepays.

Contractual repricing gap, £bn. Hedges: receive legs less pay legs.
Band	RSA	RSL	Hedges	Gap	Cumulative
Up to 1 month	£13.23bn	£47.10bn	£1.33bn	−£32.53bn	−£32.53bn
1–3 months	£16.79bn	£2.40bn	£0.80bn	£15.19bn	−£17.34bn
3–6 months	£2.92bn	£2.50bn	−£1.00bn	−£0.57bn	−£17.91bn
6–12 months	£5.20bn	£2.10bn	−£1.79bn	£1.31bn	−£16.61bn
1–2 years	£10.10bn	£2.90bn	−£2.85bn	£4.35bn	−£12.26bn
2–3 years	£3.00bn	£0.00bn	£0.84bn	£3.84bn	−£8.41bn
3–5 years	£11.30bn	£4.00bn	£2.66bn	£9.96bn	£1.55bn
5–10 years	£3.05bn	£2.00bn	£0.00bn	£1.05bn	£2.60bn
Over 10 years	£0.00bn	£0.00bn	£0.00bn	£0.00bn	£2.60bn

A gap of −£32.5bn in the first month, slowly made back as fixed loans reprice. The cumulative gap ends at £2.6bn: every rate-sensitive pound is somewhere, so the final figure is what is left out, the £4bn of equity less £1.4bn of assets with no rate. In the hedges column, the swaps' SONIA legs sit in the first three months, where they reset, and their fixed legs sit where each swap's fixed rate ends.

The behavioural gap

Contract dates overstate how fast deposits reprice. The behavioural view slots the £23.62bn of core deposits evenly over up to five years (non-core, £16.38bn, stays overnight) and lets mortgages prepay. L3.6.09: Non-maturity deposits explains how the core is found.

Behavioural repricing gap, £bn
Band	RSA	RSL	Hedges	Gap	Cumulative
Up to 1 month	£13.40bn	£23.94bn	£1.33bn	−£9.21bn	−£9.21bn
1–3 months	£17.08bn	£3.32bn	£0.80bn	£14.56bn	£5.35bn
3–6 months	£3.30bn	£3.89bn	−£1.00bn	−£1.59bn	£3.76bn
6–12 months	£5.69bn	£4.87bn	−£1.79bn	−£0.98bn	£2.79bn
1–2 years	£10.16bn	£8.45bn	−£2.85bn	−£1.13bn	£1.65bn
2–3 years	£2.95bn	£5.40bn	£0.84bn	−£1.61bn	£0.04bn
3–5 years	£9.97bn	£11.13bn	£2.66bn	£1.51bn	£1.55bn
5–10 years	£3.05bn	£2.00bn	£0.00bn	£1.05bn	£2.60bn
Over 10 years	£0.00bn	£0.00bn	£0.00bn	£0.00bn	£2.60bn

Positive gap: more assets than liabilities repriceNegative gap: more liabilities repriceCumulative gap

Read the cumulative line. It is £5.3bn at three months: floating loans and the macro hedge's SONIA legs reset fast. By one year it is £2.8bn, and by three years £0.04bn: almost exactly matched. That is the hedges at work, mostly beyond the first year: without them the cumulative gap would be £3.4bn at one year and £2.71bn at three years.

From gap to earnings

If a band's gap reprices by $\Delta r$ , the bank earns (or pays) $g \times \Delta r$ a year more from then on. Add the bands within a year and you have the oldest estimate in ALM; the Basel 2004 principles describe exactly this: the gap "can be multiplied by an assumed change in interest rates" to approximate the change in NII (Annex 1). On the book, for +1%:

View	One-year cumulative gap	Estimate of ΔNII	Full model
Contractual	−£16.61bn	−£185.5m	+£91.7m
Behavioural	£2.79bn	+£20.7m	+£91.7m
Beta-weighted	£11.81bn	+£97.9m	+£91.7m

The contractual gap gets the sign wrong. The behavioural gap gets it right but far too small: slotting is about how long deposits stay, which matters for value (L3.6.05: Economic value of equity sensitivity), not how much of a rate move the bank passes on, which matters for income. The fix for earnings is a beta-weighted gap: count each administered balance at its beta, a month out. The £22bn of current accounts (beta 10%) count as £2.2bn; the £10bn of savings (beta 60%) as £6.0bn. The one-year gap becomes £11.8bn and the estimate lands within £6.2m of the model.

Where the gap fails

Five blind spots. Guess each before you open it.

The formal version

Take bands $j = 1, \ldots, 9$ , the first $J = 4$ of which end within a year, with mid-points $m_j$ . The gap and the estimate use summation notation (M-A08: Summation notation).

Written out in full:

\begin{aligned} g_j &= \text{RSA}_j - \text{RSL}_j + H_j \\ G_k &= \sum_{j=1}^{k} g_j, \qquad G_9 = \text{equity} - \text{assets with no rate} = \text{£}4.0\text{bn} - \text{£}1.4\text{bn} = \text{£}2.6\text{bn} \\ \Delta\text{NII} &\approx G_4\,\Delta r \qquad \text{(crude)} \\ \Delta\text{NII} &\approx \sum_{j=1}^{4} g_j\,\Delta r\,(1 - m_j), \qquad m = \left(\tfrac{1}{24},\ \tfrac{1}{6},\ \tfrac{3}{8},\ \tfrac{3}{4}\right) \end{aligned}

In the beta-weighted view an administered balance $A$ with beta $\beta$ enters the 1–3 month band as $\beta A$ ; the rest, $(1 - \beta)A$ , is treated as insensitive. Both estimates are linear in $\Delta r$ : doubling the move doubles the answer, and $-\Delta r$ gives exactly minus the answer.

Try it

Switch between the three views, take the hedges out, and move rates. Watch the gap estimate against the full model. Find the view in which the two agree, then try a move of −275bp and a move of +275bp.

Try itGap, estimate and model

View

Parallel move in all rates+100bp

Positive gap: more assets than liabilities repriceNegative gap: more liabilities repriceCumulative gap

Gap estimate, Σ g × Δr × (1 − m)+£20.7m

Full NII model, year 1+£91.7m

Cumulative gap at one year£2.79bn

Crude estimate, G(1y) × Δr+£27.9m

Estimate less model−£71.0m

Insensitive liabilities and equity£4.0bn

Illustrative book. Contractual: every deposit reprices overnight, no prepayment. Behavioural: core deposits slotted over up to five years, mortgages prepay at 8% a year. Beta-weighted: deposits and other administered rates count at beta × balance, a month out, as the NII model treats them. The model adds floors, prepayment that responds to rates and exact timing.

Worked example

The beta-weighted estimate, band by band

Rates rise by 1% today. ALM estimates next year's NII change from the beta-weighted gap.

From the gap to ΔNII

Step 1 of 4

1

The bands inside a year

Band	Gap gⱼ	Mid-point mⱼ	1 − mⱼ	gⱼ × 1% × (1 − mⱼ)
Up to 1 month	£7.63bn	0.042	0.958	£73.15m
1–3 months	£2.58bn	0.167	0.833	£21.53m
3–6 months	−£0.20bn	0.375	0.625	−£1.26m
6–12 months	£1.80bn	0.750	0.250	£4.50m
Total	£11.81bn			£97.92m

Regulatory lens

The Basel 2004 principles described repricing schedules and the gap × Δr estimate as the simplest measures, and listed their weaknesses (Annex 1). The 2016 standard keeps time bands at its core: its standardised framework slots every cash flow into 19 time buckets, with caps on how long non-maturity deposits can be slotted, before computing EVE (L3.6.06: The standard shock scenarios). Supervisory reporting of repricing schedules and the details for UK and EU banks are in M4.5: Liquidity and IRRBB regulation.

Spark Atoms

Spark AtomOne table, two answers

On contract RiskAtoms Bank looks liability-sensitive (−£185.5m for +1%). Weighted by how much of a rate move it actually passes on, it is asset-sensitive (+£97.9m). The only thing that changed was one assumption about £40bn of deposits. That is why ALCOs spend so long on deposit betas.

Spark AtomThe final number is always the same

Whatever the view, the cumulative gap ends at £2.6bn: equity less assets with no rate. Every rate-sensitive pound reprices somewhere, so the bands can only move it in time. A gap table that does not end at that figure has lost a position.

Key takeaways

A repricing gap table places each rate-sensitive position, hedges included, in the band where its rate next changes; the cumulative gap is the running sum.
On contract RiskAtoms Bank's first-month gap is −£32.5bn; slotting core deposits shrinks it to −£9.2bn, and the hedges bring the three-year cumulative gap close to zero.
ΔNII ≈ Σ gⱼ × Δr × (1 − mⱼ) over the bands within a year; the crude version uses the one-year cumulative gap alone.
For income, administered rates must enter at beta × balance: the beta-weighted estimate (+£97.9m) is close to the model (+£91.7m); the contractual one has the wrong sign.
The gap is linear and one-dimensional: it misses options, floors, curve shape, timing inside bands, and value.

Reaction

Check what stuck

Question 1 · objective 2

A bank's band gaps are +£3bn, −£5bn and +£1bn in its first three bands. What is the cumulative gap at the end of the third band, in £bn?

£bn

Question 2 · objective 3

The one-year cumulative gap is +£4bn. Using the crude rule, by how much does next year's NII change if all rates rise by 0.5%, in £m?

£m

Question 3 · objective 3

A band from 3 to 6 months has a gap of +£6bn. Rates rise by 1% today. Using the band's mid-point, how much does that band add to next year's NII, in £m?

£m

Question 4 · objective 2

RiskAtoms Bank's contractual one-year gap is −£16.6bn, which says NII falls when rates rise. The full model says it rises. Why is the contractual gap wrong here?

AIt reprices all £40bn of current and savings accounts overnight at the full rate move, but the bank passes on only part of a move, and lateBIt leaves out the hedgesCIt uses the wrong interest rate curveDContractual gaps always have the wrong sign

Question 5 · objective 4

Which of these can the gap × Δr estimate not capture, even with perfect bands?

AThat a 275bp cut costs a different amount from a 275bp rise, because of floors and prepaymentBThat more assets than liabilities reprice within three monthsCThat the hedges change the gapDThat a bigger rate move gives a bigger NII change

Glossary

Repricing gap table: Repricing gap table: every rate-sensitive asset, liability and hedge placed in the time band in which its rate next changes.
Rate-sensitive assets (RSA): Rate-sensitive assets (RSA): assets whose rate changes, or that mature and are replaced, within a given band.
Rate-sensitive liabilities (RSL): Rate-sensitive liabilities (RSL): liabilities whose rate changes, or that mature and are replaced, within a given band.
Repricing gap: Repricing gap: rate-sensitive assets less rate-sensitive liabilities (plus hedges) in one band.
Cumulative gap: Cumulative gap: the sum of the band gaps from today to the end of a given band.
Positive (asset-sensitive) gap: Positive (asset-sensitive) gap: more assets than liabilities reprice; NII tends to rise when rates rise.
Negative (liability-sensitive) gap: Negative (liability-sensitive) gap: more liabilities than assets reprice; NII tends to fall when rates rise.
Slotting: Slotting: placing non-maturity deposits in time bands by how long they are expected to stay, instead of overnight.
Beta-weighted gap: Beta-weighted gap: a gap in which administered rates count at beta × balance, the part of a market move the bank actually passes on.

Deep Dives & Origins

Deep Dives

Basel Committee on Banking Supervision, Principles for the Management and Supervision of Interest Rate Risk, BIS, July 2004, Annex 1: repricing schedules, the gap estimate and its weaknesses. Introductory.
A. Saunders, M. M. Cornett and O. Erhemjamts, Financial Institutions Management: A Risk Management Approach, 11th edition, McGraw-Hill, 2023: chapter 8, Interest Rate Risk I, on the repricing model. Introductory.

Origins

Basel Committee on Banking Supervision, Principles for the Management and Supervision of Interest Rate Risk, BIS, July 2004, Annex 1, paragraphs 3 to 7.
Basel Committee on Banking Supervision, Basel Framework, SRP31 Interest rate risk in the banking book, BIS, version in force from 1 January 2026.
Basel Committee on Banking Supervision, Standards: Interest rate risk in the banking book, BIS, April 2016, paragraph 101 and Table 2 (the 19 time buckets and the caps on non-maturity deposits).

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