How Banks Construct Interest-Rate Hedges: Duration Gaps, Key-Rate Sensitivities, Swaps, Basis Risk and Hedge Effectiveness

Quick answer: banks construct interest-rate hedges by first measuring which cash-flow maturities and reference rates create unwanted sensitivity, then selecting instruments whose sensitivities offset those exposures. A simple hedge can match portfolio DV01 with an interest-rate swap. A more robust hedge matches several key-rate buckets, because yield curves do not move only in parallel. Natural hedges can offset assets with liabilities that reprice similarly. Options can protect nonlinear exposures. The hedge is then tested under multiple scenarios because reducing one risk can create basis risk, curve risk, optionality, liquidity risk or counterparty exposure somewhere else.

A hedge is not the opposite trade. It is a deliberately chosen sensitivity that should disagree with the loss you are trying to reduce.

Ownership boundary: measurement versus construction

The existing Bukit Timah Tutor article How Banks Measure Interest-Rate Risk: Duration, Convexity and Scenario Shocks owns the measurement job: how EVE, NII, duration, convexity and curve scenarios reveal exposure.

This article begins after that measurement. Its job is narrower:

Given an exposure we do not want, how should we construct an offsetting position—and how do we know the offset will still work when the world moves differently from the hedge assumption?

1. Start with DV01: the money value of a small rate move

DV01 (or PV01 in related conventions) measures the approximate change in present value for a one-basis-point move in yield. If a bank portfolio has DV01 = −S$250,000, then a one-basis-point upward parallel move in the relevant rate structure produces an approximate S$250,000 loss under the local linear approximation.

If an available hedge instrument has DV01 = +S$5,000 per unit, a first-order hedge ratio is:

Hedge units = − portfolio DV01 / hedge-instrument DV01 = 250,000 / 5,000 = 50 units.

At that moment and for that small parallel move, the combined DV01 is approximately zero.

This is the beginning of the hedge—not the end.

2. Duration-gap hedging at balance-sheet level

A bank often has assets with longer effective duration than liabilities. Fixed-rate mortgages or securities may retain their coupon while deposits or wholesale funding reprice sooner. Rising rates can therefore reduce the economic value of assets more than liabilities.

At a simplified level, a duration gap can be written:

DGAP = D_A − (L/A)D_L

where D_A and D_L are effective asset and liability durations, and L/A scales liability sensitivity relative to assets.

A positive duration gap generally means economic value is vulnerable to rate increases. The bank can reduce that exposure through balance-sheet changes or derivatives that add offsetting negative duration.

3. Interest-rate swaps transform cash-flow behaviour

An interest-rate swap exchanges fixed and floating cash flows on a notional amount. For interest-rate-risk management, two broad directions matter:

• Pay fixed / receive floating generally adds a position that benefits when rates rise relative to a fixed-rate asset exposure, reducing positive duration.
• Receive fixed / pay floating generally adds positive duration and can offset liabilities or assets that otherwise reprice too quickly.

ECB analysis of euro-area banks’ banking books found that derivatives have historically offset part of the interest-rate exposure arising from non-derivative positions. Banks increased use of longer-dated interest-rate swaps as they managed exposures to rising rates. See Interest rate risk exposures and hedging of euro area banks’ banking books.

4. A simple swap hedge example

Suppose a fixed-rate asset portfolio has DV01 of −S$400,000. A pay-fixed swap with the selected maturity has DV01 of +S$8,000 per S$10 million notional under the bank’s sign convention.

A first-order hedge requires approximately:

400,000 / 8,000 = 50 blocks of S$10 million, or S$500 million notional.

Now ask the questions the ratio hides:

• Does the asset cash flow really behave like the swap’s fixed leg?
• Does the yield curve move in parallel?
• Is the asset exposed to mortgage prepayment?
• Does the floating leg reference the same rate as the bank’s funding?
• What happens if deposits reprice faster than expected?
• Can the swap be collateralised through a CCP or bilateral agreement without creating unacceptable liquidity demands?

A zero-DV01 position can still contain large residual risks.

5. Key-rate duration: hedge the curve, not only the parallel shift

A single DV01 assumes all maturities move together. Real yield curves steepen, flatten and twist. Key-rate duration decomposes sensitivity into selected maturity nodes such as 2-year, 5-year, 10-year and 30-year points.

Represent the portfolio’s key-rate sensitivity vector as:

d = [DV01_2Y, DV01_5Y, DV01_10Y, DV01_30Y].

Each candidate swap or bond has its own sensitivity vector. The hedge can then solve for weights w such that:

d + Hw ≈ target

where H is a matrix of hedge-instrument key-rate sensitivities. The target may be zero or a deliberately retained risk profile.

This becomes a linear-algebra problem rather than one ratio.

6. Exact matching is often impossible, so optimisation enters

The bank may have more risk buckets than liquid hedge instruments. It may also face transaction costs, notional limits, accounting considerations and counterparty constraints.

A hedge optimiser can minimise an objective such as:

Minimise ||d + Hw||² + λ(transaction cost) + penalties for liquidity, counterparty and balance-sheet constraints.

The λ term controls how aggressively the bank pays to reduce residual sensitivity. A perfect mathematical hedge may be economically irrational if it requires illiquid instruments or constant rebalancing.

7. Natural hedging uses the balance sheet before derivatives

A bank can reduce interest-rate risk by changing the mix of assets and liabilities:

• fund fixed-rate assets with longer-term fixed-rate liabilities;
• originate more floating-rate assets against rate-sensitive funding;
• issue term debt;
• adjust deposit pricing and product mix;
• sell or securitise selected assets;
• change loan tenor or repricing frequency.

Derivatives are powerful because they can alter sensitivity quickly without changing customer contracts. Natural hedges can be operationally slower but may reduce reliance on derivative collateral and counterparty infrastructure.

8. Basis risk: two floating rates can both move and still disagree

Suppose a bank’s loans reprice from one benchmark while the swap hedge references another. If the spread between those benchmarks changes, the hedge can fail even if both are “floating rates.”

This is basis risk. The OCC interest-rate-risk handbook explicitly separates repricing, basis, yield-curve and options risk. See the OCC Interest Rate Risk handbook.

A useful hedge therefore matches not only duration but also reference-rate exposure where material.

9. Deposit beta is part of the hedge ratio

Non-maturity deposits do not have a fixed contractual repricing schedule. If a bank assumes deposit beta = 30% but actual pass-through becomes 70% in a high-rate environment, liabilities reprice much faster than the hedge design expected.

A hedge built on a stale deposit model can therefore become over- or under-sized without any error in the swap calculation.

See How Banks Model Deposit Behaviour.

10. Mortgage prepayment makes duration move against the hedge

Mortgage assets can shorten when rates fall because borrowers refinance and lengthen when rates rise because prepayment slows. This negative-convexity behaviour means the asset’s DV01 is not fixed.

A static swap hedge can therefore become wrong-way sized:

• rates fall → mortgage duration shortens → previous hedge may be too large;
• rates rise → mortgage duration extends → previous hedge may be too small.

Mortgage hedging can require dynamic rebalancing or options that protect convexity as well as first-order duration. See How Banks Model Mortgage Prepayment.

11. Options hedge nonlinear risk

Caps, floors, swaptions and other options can protect against rate movements that create nonlinear losses. An option hedge may be more expensive than a linear swap but can preserve protection in states where the exposure itself changes shape.

For example, a bank exposed to falling rates through mortgage prepayment can use options to obtain convexity that a fixed swap cannot provide. The trade-off is premium cost, volatility sensitivity, liquidity and model risk.

12. Hedge effectiveness is a scenario statement, not one correlation

An economic hedge is effective when the combined position reduces the targeted loss across the states that matter. A useful test can compare:

Residual loss(scenario) = unhedged loss(scenario) + hedge P&L(scenario).

Effectiveness should be examined under:

• small parallel shifts;
• large parallel shifts;
• steepeners and flatteners;
• key-rate shocks;
• basis changes;
• deposit-beta changes;
• prepayment changes;
• volatility shocks for options.

A hedge that works only in the scenario used to construct it is an overfit.

13. Economic hedge and hedge accounting are separate questions

A derivative can reduce economic interest-rate risk while failing to qualify for a particular accounting hedge treatment. Conversely, an accounting designation does not prove the hedge is the best economic risk reducer.

Risk management should therefore separate:

• economic exposure being managed;
• derivative valuation and collateral;
• accounting treatment;
• capital treatment;
• legal and counterparty constraints.

Those systems interact but are not interchangeable definitions of “effective.”

14. Counterparty and margin risk can make the hedge expensive under stress

An interest-rate swap that gains value as the bank’s asset portfolio loses value can protect economic value. But if the swap is centrally cleared, daily or intraday variation margin can move cash. If it is bilateral, counterparty credit and collateral terms matter.

A hedge can therefore reduce interest-rate risk while increasing liquidity usage. The bank must ask whether it can finance the hedge’s margin calls in the very rate scenario where the hedge is most valuable.

See CCP margin algorithms and counterparty credit risk.

15. Rebalancing creates a control problem

As rates, balances, deposits and prepayments change, the hedge drifts. Rebalancing too rarely leaves exposure. Rebalancing too frequently creates transaction cost, operational burden and possible procyclical trading.

A hedge policy can define bands: rebalance only when residual DV01, EVE sensitivity or key-rate mismatch leaves a permitted range. This creates a control problem similar to inventory management: how much deviation is acceptable before the cost of correction is justified?

16. The hedge-construction pipeline

1. Measure EVE, NII, DV01 and key-rate exposures.
2. Separate unwanted risk from deliberately retained risk.
3. Identify natural balance-sheet offsets.
4. Select liquid candidate hedge instruments.
5. Calculate their sensitivity vectors.
6. Solve first-order hedge ratios.
7. Optimise multiple key-rate buckets where needed.
8. Stress basis, curve and optionality mismatches.
9. Include deposit and prepayment model uncertainty.
10. Evaluate transaction cost, liquidity and counterparty effects.
11. Execute and reconcile the hedge.
12. Measure post-trade residual risk.
13. Monitor hedge drift and margin requirements.
14. Rebalance or redesign when the underlying exposure changes.

17. Failure modes

• One-DV01 hedge. Parallel sensitivity is neutral while curve-twist risk remains large.
• Basis blindness. Hedge and exposure reference different floating rates.
• Static deposit model. Liability repricing changes but hedge ratio does not.
• Static mortgage duration. Prepayment changes the asset faster than the hedge.
• Counterparty omission. The derivative introduces credit or collateral risk not included in the objective.
• Margin blindness. The hedge generates liquidity calls the bank cannot comfortably fund.
• Overhedging. The original risk falls but the hedge is not resized.
• Scenario overfit. Hedge is perfect under one prescribed shock and poor under neighbouring scenarios.

18. Diagnostics and falsifiers

• What is residual DV01 after the hedge?
• What are residual 2Y, 5Y, 10Y and long-end key-rate sensitivities?
• Which basis relationship must remain stable for the hedge to work?
• How much does the hedge ratio change if deposit beta rises?
• How much does mortgage duration extend under a rate rise?
• What variation-margin cash demand appears in the stressed scenario?
• Does the hedge reduce both EVE and NII risk, or improve one while worsening the other?
• Which curve scenario produces the largest post-hedge loss?

Suppose someone claims, “The portfolio is fully hedged because net DV01 is zero.” A falsifier is a steepening or basis scenario that creates a material loss despite zero parallel DV01. Neutralising one derivative of value is not the same thing as neutralising the full function.

19. Verification and update triggers

• independently calculate hedge sensitivities;
• reconcile derivative notionals and valuations;
• compare predicted hedge P&L with realised performance;
• stress multiple curve shapes rather than one parallel shift;
• update deposit and prepayment assumptions;
• review hedge effectiveness after large balance-sheet changes;
• include collateral and margin usage in hedge evaluation;
• retire hedges whose underlying exposure has disappeared.

Connections across the finance-and-banking algorithms lane

• Interest-rate-risk measurement — establishes the exposure this article hedges.
• Yield-curve algorithms — the curve nodes used to value and hedge cash flows.
• Deposit behaviour — liability-side model risk inside the hedge ratio.
• Mortgage prepayment — why asset duration can change with rates.

Research anchors

• ECB — Interest rate risk exposures and hedging of euro-area banks’ banking books.
• OCC — Interest Rate Risk Comptroller’s Handbook.
• Basel Framework — interest-rate risk in the banking book.
• ECB — maturity transformation and bank derivative hedging.
• OCC — interest-rate-risk resources and derivative hedging guidance.

The deeper lesson

Hedging is the mathematics of intentional disagreement. If the asset loses value when rates rise, the hedge should gain value in the same state. But no financial instrument is the exact negative of an entire bank balance sheet. Duration matches one local slope. Key-rate hedges match more of the curve. Options address curvature. Basis and behavioural assumptions remain. A strong hedge therefore does not claim risk has vanished; it identifies which sensitivity was transferred, what residuals remain and what new risks were accepted in exchange.

Educational note: This article explains public banking and derivatives mathematics. It is not trading advice, hedging advice, investment advice or institution-specific treasury guidance.