The subtraction is trivial. Where the current accounts and savings go decides the sign of the answer.
A repricing gap is the rate-sensitive assets minus the rate-sensitive liabilities that reset within each time bucket, and the change in net interest income is roughly the gap times the rate move, weighted by how much of the year is left after each reset. The answer depends on where the deposits go. On an illustrative $5,000m bank the contractual one-year gap is −$1,800m, predicting a $15.75m fall in net interest income for +100 bp; placed by behaviour, with a 40 per cent savings beta, the gap is +$280m and the same shock adds $2.45m.
Worked in full in Bank Management by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
Same balance sheet, opposite sign. The gap report is the oldest interest rate risk tool a bank has, and it is still the first page of most asset-liability committee packs. The arithmetic is trivial. The decision about which bucket a current account belongs in is not, and it decides the answer.
| Assets | 0 to 3m | 3 to 12m | 1 to 5y | Over 5y | Not sensitive |
|---|---|---|---|---|---|
| Cash and short-term placements | 300 | 0 | 0 | 0 | 0 |
| Floating-rate loans | 1,200 | 0 | 0 | 0 | 0 |
| Fixed-rate loans (repayments and maturities) | 150 | 350 | 1,000 | 500 | 0 |
| Securities | 50 | 150 | 500 | 500 | 0 |
| Other assets | 0 | 0 | 0 | 0 | 300 |
| Rate-sensitive assets | 1,700 | 500 | 1,500 | 1,000 | 300 |
On the other side: $1,000m of non-interest-bearing current accounts, $1,800m of savings and money market accounts, $1,000m of time deposits maturing $300m, $500m and $200m across the first three buckets, $400m of short-term borrowings, $300m of long-term debt in the one-to-five-year bucket, and $500m of other liabilities and equity. Total assets are $5,000m and net interest income is $150m a year.
Gap in bucket i = RSAi − RSLi
ΔNII over one year ≈ Σ gapi × Δr × (1 − midpointi), for the buckets inside the year
The weight is the share of the year left after the average reset: 0.875 for the 0 to 3 month bucket (midpoint 1.5 months), 0.375 for 3 to 12 months (midpoint 7.5 months). In Excel: =SUMPRODUCT(Gap0_12,1-Mid0_12)*Shock.
Step 1: the contractual gap. Current accounts and savings can be withdrawn or repriced tomorrow, so contractually all $2,800m go in the first bucket, beside $300m of time deposits and $400m of borrowings. Rate-sensitive liabilities in 0 to 3 months are $3,500m against $1,700m of assets: a gap of −$1,800m. The 3 to 12 month bucket balances at $500m each side. The one-year cumulative gap is −$1,800m, 36.0 per cent of assets, and the ratio of sensitive assets to liabilities is 0.55.
Step 2: the behavioural gap. Current accounts pay nothing whatever the market does: their beta is zero, so they move to "not sensitive". Savings accounts follow market rates only partially: with a 40 per cent beta, $720m of the $1,800m behaves as if it repriced, and $1,080m does not. Liabilities in 0 to 3 months fall to $1,420m. The gap becomes +$280m, 5.6 per cent of assets, and the ratio 1.15.
Step 3: from gap to earnings. Contractual: −1,800 × 1% × 0.875 = −$15.75m, 10.5 per cent of net interest income. Behavioural: 280 × 1% × 0.875 = +$2.45m, 1.6 per cent. Without the timing weight the figures would be −$18.00m and +$2.80m: a gap that resets in month eleven earns the new rate for one month, not twelve.
| Bucket | RSA | RSL contractual | Gap contractual | RSL behavioural | Gap behavioural |
|---|---|---|---|---|---|
| 0 to 3 months | 1,700 | 3,500 | −1,800 | 1,420 | 280 |
| 3 to 12 months | 500 | 500 | 0 | 500 | 0 |
| Cumulative to one year | 2,200 | 4,000 | −1,800 | 1,920 | 280 |
| 1 to 5 years | 1,500 | 500 | 1,000 | 500 | 1,000 |
| Over 5 years | 1,000 | 0 | 1,000 | 0 | 1,000 |
Contractually the bank looks heavily liability-sensitive: a rate rise costs it $15.75m and a cut of 100 bp adds $15.75m. By behaviour it is mildly asset-sensitive: +100 bp adds $2.45m, +200 bp $4.90m, and a cut costs it. The $18.20m between the two readings comes entirely from where $2,800m of non-maturity deposits were placed. The longer buckets carry the other half of the story, a $1,000m positive gap in each, which is fixed-rate assets funded by stable deposits: that is value risk, measured by EVE sensitivity, not by this one-year gap.
| Savings beta | Savings repricing | One-year gap | ΔNII per +100 bp | Share of NII |
|---|---|---|---|---|
| 0% | 0 | 1,000 | 8.75 | 5.8% |
| 20% | 360 | 640 | 5.60 | 3.7% |
| 40% | 720 | 280 | 2.45 | 1.6% |
| 60% | 1,080 | −80 | −0.70 | −0.5% |
| 80% | 1,440 | −440 | −3.85 | −2.6% |
| 100% | 1,800 | −800 | −7.00 | −4.7% |
The gap changes sign at a savings beta of 55.6 per cent. Below it the bank gains from rising rates, above it it loses. That is the number to put in front of the committee, because the beta is an assumption, measured on past cycles and on a denominator that is often unstated: see how to calculate a deposit beta, and on which deposits. Even the 100 per cent column is far from the contractual reading, because current accounts stay out of it.
Betas are not constant through a cycle. They start low and rise as rates stay high and depositors notice, so a gap measured early in a hiking cycle tends to overstate the gain from the later steps.
Build the gap by bucket, weight each by the time left in the year, and present it twice: contractually and by behaviour, with the beta at which the sign flips. Here −$1,800m becomes +$280m, and a predicted loss of $15.75m becomes a gain of $2.45m. Bank Management weights its own bank's repricing gap by behaviour rather than by contract, and the free workbook for this case computes the gap, the margin it predicts and the beta that erases the year.
The contractual gap puts each balance at the earliest date it could reprice, so current accounts and savings go in the first bucket. The behavioural gap places them by how they actually respond, using betas. On an illustrative $5,000m bank the one-year gap is -$1,800m contractually and +$280m by behaviour, with a 40 per cent savings beta and current accounts treated as not sensitive.
Multiply each bucket's gap by the rate change and by the share of the year remaining after the average reset, then add the buckets inside one year. A -$1,800m gap in the 0 to 3 month bucket, weighted 0.875, gives -$15.75m for +100 bp, against -$18.00m if the timing weight is ignored.
There is no single target; most banks set limits on the one-year gap as a share of assets and on the NII change it implies. What matters is knowing where the sign flips. On an illustrative bank with $1,800m of savings, the one-year gap moves from +$280m to negative once the savings beta passes 55.6 per cent.
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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