BANK3011 · Bank Financial Management
Interest Rate Risk I: The Repricing (GAP) Model
In BANK3011 Bank Financial Management at the University of Sydney, the repricing (GAP) model is the first, earnings-based way to measure a bank's interest-rate risk. It sorts every balance-sheet item into rate-sensitive or not over a chosen planning horizon, nets rate-sensitive assets against rate-sensitive liabilities to get the repricing (funding) gap, and reads the change in net interest income straight off ΔNII = CGAP × ΔR. It is a book-value, earnings measure — simple and heavily exaavailable — that deliberately ignores the market-value effects the duration model later supplies.
What this chapter covers
- 011. Rate sensitivity — an item is rate-sensitive if its rate resets within the planning horizon, not by its maturity
- 022. The planning horizon and repricing buckets — how the window sets RSA and RSL
- 033. The repricing (funding) gap — GAP = RSA − RSL in each bucket
- 044. Cumulative gap (CGAP) and ΔNII = CGAP × ΔR — the whole-bank earnings exposure
- 055. The CGAP effect — the sign of the gap fixes which way NII moves with rates
- 066. Refinancing risk vs reinvestment risk — the two maturity-mismatch exposures
- 077. The spread effect — why even a zero-gap bank's NII can move (unequal rate changes)
- 088. Weaknesses of the model — market-value blindness, over-aggregation, runoffs, off-balance-sheet
Repricing gap, ΔNII and the CGAP effect
- +1(a) Repricing gap: GAP = RSA − RSL = 80 − 120 = −$40m — a negative gap (more liabilities than assets reprice inside the year).
- +1(b) Rates rise 1%: ΔNII = CGAP × ΔR = (−40) × 0.01 = −$0.40m. With a negative gap, a rate rise pushes funding cost up faster than asset income, so NII falls.
- +1(c) Rates fall 0.5%: ΔNII = (−40) × (−0.005) = +$0.20m. The same negative-gap bank is helped by a rate fall — the mirror image of (b).
- +1(d) Unequal moves (spread effect): use ΔNII = RSA × ΔR(RSA) − RSL × ΔR(RSL) = 80(0.01) − 120(0.004) = 0.80 − 0.48 = +$0.32m.
- +1Why the sign flips: although the gap is still negative, liability rates rose far less than asset rates, so the widening spread lifts NII. The simple CGAP × ΔR shortcut assumes equal moves and would have given the wrong sign here.
- +1Name the risk: a negative gap funds longer assets with shorter liabilities, so the bank carries refinancing risk — it must roll its funding, possibly at a higher rate, when rates rise.
Key terms
- Rate-sensitive asset / liability (RSA / RSL)
- A balance-sheet item whose interest rate can be reset within the chosen planning horizon — either because it matures and is rolled over inside the window, or because it is a floating-rate item that reprices inside it. Maturity alone does not decide this: a long-dated loan repriced yearly is rate-sensitive over a one-year horizon.
- Repricing (funding) gap
- The dollar difference GAP = RSA − RSL in a repricing bucket. It measures a bank's earnings exposure to interest rates: a positive gap is hurt by a rate fall, a negative gap by a rate rise.
- Cumulative gap (CGAP)
- The sum of the individual bucket gaps that reprice within the planning horizon. Multiplying it by the rate shock gives the whole-bank change in net interest income, ΔNII = CGAP × ΔR.
- Net interest income (NII)
- Interest income earned on assets minus interest expense paid on liabilities. It is the earnings figure the repricing model tracks, computed from book-value rates and balances.
- Planning horizon
- The forward window (often one year) over which items are judged rate-sensitive and sorted into repricing buckets. Widen the horizon and more items become rate-sensitive; narrow it and fewer do.
- Refinancing vs reinvestment risk
- Refinancing risk arises when assets are longer than liabilities, so funding must be rolled over — possibly at a higher rate (a negative-gap exposure, hurt by rising rates). Reinvestment risk arises when liabilities are longer than assets, so returning cash must be reinvested — possibly at a lower rate (a positive-gap exposure, hurt by falling rates).
- CGAP effect vs spread effect
- The CGAP effect says the sign of the cumulative gap fixes the direction NII moves when rates change by the same amount on both sides. The spread effect says that even a zero-gap bank's NII changes if the spread between its asset and liability rates widens or narrows — captured by ΔNII = RSA × ΔR(RSA) − RSL × ΔR(RSL).
Interest Rate Risk I: The Repricing (GAP) Model FAQ
What is the repricing (GAP) model in BANK3011?
It is the first, earnings-based measure of a bank's interest-rate risk. You classify each balance-sheet item as rate-sensitive or not over a planning horizon, net rate-sensitive assets against rate-sensitive liabilities to get the repricing gap, and estimate the change in net interest income with ΔNII = CGAP × ΔR. It uses book values, so it captures earnings effects but not market-value effects.
How do I decide if an item is rate-sensitive?
Ask one question only: does its rate reset within the planning horizon? Short maturities that mature and roll over inside the window are rate-sensitive, and so are floating-rate items that reprice inside it. The stated maturity is a distractor — a 15-year loan repriced every year is rate-sensitive over a one-year horizon, while a 4-month fixed bill is too because it matures inside the year.
Does a negative gap mean rising rates are good or bad for the bank?
Bad. A negative gap means more liabilities than assets reprice inside the horizon, so when rates rise the bank's funding cost climbs faster than its asset income and net interest income falls. A positive-gap bank is the mirror image — it is hurt by a rate fall. Always compute the sign of CGAP before assuming a direction.
When do I use CGAP × ΔR versus the spread formula?
Use ΔNII = CGAP × ΔR only when asset and liability rates move by the same amount. The instant the question gives different rate changes for assets and liabilities, switch to the spread form ΔNII = RSA × ΔR(RSA) − RSL × ΔR(RSL); the shortcut silently assumes equal moves and can give the wrong sign.
What are the main weaknesses of the repricing model?
It ignores market-value effects (it is book-value, earnings-based only), it over-aggregates items into wide time buckets that hide mismatches within a bucket, it can omit runoffs (scheduled repayments that reprice inside the horizon), and it leaves out off-balance-sheet exposures. That is why the duration model, a market-value measure, is taught alongside it.
Can AI help me with the repricing (GAP) model?
Yes — ask Sia to walk through any repricing (GAP) model problem or concept step by step, the way University of Sydney tests it. Sia is an AI tutor that explains each move — classifying RSA and RSL, computing the gap, applying ΔNII = CGAP × ΔR, and switching to the spread form — so you learn how to reach the answer yourself.
Studying with AI? Sia — free AI financial modeling tutor works through BANK3011 step by step.
Exam move
Treat this chapter as two linked skills the exam always tests together. First, the classification skill: for every item, state the planning horizon and decide rate-sensitive or not on whether the rate resets inside it — never on maturity. Second, the numerical skill: lay out interest income and interest expense as separate lines to get NII, compute GAP = RSA − RSL and CGAP, then apply ΔNII = CGAP × ΔR and always cross-check the two. Drill the trap: whenever asset and liability rates move by different amounts, switch to the spread form. Keep book values here and market values in the duration chapter, and be ready to list two weaknesses of the model as a short-answer. Practise one full four-part NII/GAP question end to end, then ask Sia to check your working step by step.
