Asset-Liability Management and IRRBB

Introduction and context

Asset-liability management (ALM) is the coordinated management of a bank’s assets, liabilities, capital, liquidity and off-balance-sheet positions. Its purpose is not simply to maximise net interest income. A sound ALM process balances profitability, liquidity, solvency, market risk, customer behaviour and regulatory constraints.

Interest-rate risk in the banking book (IRRBB) is the risk that changes in interest rates adversely affect a bank’s earnings, economic value, capital adequacy or strategic position. The banking book generally contains positions intended to be held for relationship banking or longer-term investment, rather than traded actively. Typical exposures arise because assets and liabilities reprice at different times, have different maturities, respond differently to market rates, or include behavioural options.

ALM therefore links balance-sheet structure to decision-making by the asset-liability committee (ALCO). It informs pricing, funding choices, product design, investment strategy, hedging, capital planning and stress testing.

Learning objectives

By the end of this chapter, the reader should be able to:

• explain the purpose and scope of ALM and IRRBB;
• construct and interpret repricing-gap and duration-gap measures;
• estimate earnings-at-risk and economic-value sensitivity;
• incorporate deposit behaviour, prepayments and other embedded options;
• explain funds-transfer pricing and its relationship to ALCO decisions;
• evaluate hedging alternatives and governance requirements; and
• identify the limitations of simplified ALM measures and the value of scenario analysis.

1. The structure of banking-book interest-rate risk

A bank earns interest by transforming maturities, liquidity and credit risk. It may fund long-term fixed-rate loans with short-term deposits, or hold floating-rate assets against liabilities whose rates are administratively controlled. This transformation creates income opportunities but also exposes the bank to rate movements.

The main dimensions of IRRBB are:

1. Repricing risk: assets and liabilities reset at different dates or frequencies.
2. Yield-curve risk: rates at different maturities move by different amounts.
3. Basis risk: instruments linked to different reference rates do not move together.
4. Option risk: borrowers, depositors or the bank can exercise contractual or behavioural options.
5. Volume and spread risk: balances, margins and product spreads change as customers react to rates.

A useful distinction is between an earnings perspective and an economic-value perspective. The earnings perspective examines the effect of rate changes on future net interest income over a specified horizon. The economic-value perspective examines the change in the present value of expected future cash flows, often expressed as the change in economic value of equity (EVE).

2. Repricing-gap analysis

The repricing gap is a schedule-based measure of the difference between rate-sensitive assets and rate-sensitive liabilities in each time bucket.

where RSA_i is the value of rate-sensitive assets repricing in bucket i, RSL_i is the value of rate-sensitive liabilities repricing in that bucket, and GAP_i is the bucket gap. All values should be measured in the same currency and on a consistent balance basis.

The cumulative gap through bucket k is:

A positive gap means that more assets than liabilities reprice within the bucket. If rates rise, asset income will generally increase more rapidly than liability expense, improving short-run net interest income. A negative gap generally has the opposite exposure. This interpretation assumes that repricing changes are sufficiently similar, balances remain constant, and basis and option effects are immaterial.

A simplified earnings sensitivity is:

where ∆NII_i is the approximate change in interest income less interest expense, ∆r_i is the rate change expressed as a decimal, and d_i is the number of days during which the repriced position affects earnings. The formula assumes a parallel, immediate repricing of the gap and ignores compounding, fees, credit losses, new business, customer behaviour and basis differences.

Worked example: repricing gap

Suppose a bank has the following one-year repricing schedule:

Amounts are in millions of currency units. In the first bucket, the bank has a negative gap of 120 million. If rates rise immediately by 1 percentage point and the full gap remains exposed for 90 days, the approximate earnings effect is:

Thus, short-run earnings would fall by approximately 296,000 currency units, before considering behavioural and basis effects. The second bucket has a positive gap, but its benefit occurs later and does not fully offset the immediate exposure.

Limitations of repricing gaps

A repricing schedule can be misleading when it treats all balances in a bucket as repricing on the same date. It may also classify non-maturing deposits as if their contractual maturity were meaningful, even though customers may retain balances for many years. Fixed-rate loans with prepayment options, floating-rate loans with rate caps, and administered-rate deposits cannot be represented accurately by simple contractual dates. Gap analysis is therefore a screening tool, not a complete risk model.

3. Duration gap and economic-value sensitivity

Duration measures the sensitivity of a present value to a change in yield. Macaulay duration is the weighted average time of cash flows:

where CF_t is the cash flow at time t, PV(CF_t) is its present value, and P is the market value or present value of the instrument. Time must be measured consistently, such as years.

Modified duration is:

where y is the annualised yield and m is the number of compounding periods per year. For a small change in yield, the price sensitivity is approximately:

This approximation assumes a small, parallel yield change and ignores convexity. For larger changes, convexity should be included:

where C is convexity, measured consistently with the duration convention.

For a banking book, the duration gap compares the duration-weighted value of assets with liabilities. A simplified measure is:

where D_A and D_L are asset and liability durations, A is the market value of assets, and L is the market value of liabilities. If equity is E = A − L, then the approximate change in economic value of equity is:

This form assumes a parallel shift, a common yield convention and small changes. It is not appropriate without modification for strongly non-parallel movements, large rate changes or significant embedded options.

Worked example: duration gap

Assume market-value assets are 1,000 million with duration 4.0 years, and liabilities are 900 million with duration 1.5 years. Equity is 100 million. For a 1 percentage-point increase in yields, using the simple duration approximation:

The approximate economic value of equity falls by 25.24 million. The result is economically significant relative to initial equity, demonstrating why a bank can appear profitable on an accounting basis while being highly exposed in present-value terms.

4. Earnings-at-risk and economic-value measures

Earnings-at-risk (EaR) estimates the adverse change in projected net interest income under specified interest-rate scenarios and a defined horizon. A simple scenario measure is:

where NII_base is projected net interest income under the baseline scenario and NII_stress is projected income under the adverse scenario. A positive result denotes a reduction in earnings. The horizon may be one quarter, one year or another period approved by governance policy.

EaR is useful for budgeting, pricing and dividend planning. It is sensitive to assumptions about loan growth, deposit retention, margins, prepayments, credit migration and management responses. It can therefore be more realistic than a static gap, but also more model-dependent.

The economic-value perspective discounts expected cash flows. Conceptually:

A scenario sensitivity is:

EVE captures long-term value effects beyond the earnings horizon. It is particularly important for fixed-rate instruments and for assessing whether current earnings are being purchased at the cost of future value. EaR and EVE are complementary: EaR focuses on near-term performance, whereas EVE focuses on the present value of longer-term cash flows.

5. Deposits, behavioural modelling and embedded options

Contractual maturity is not always behavioural maturity. Current accounts and savings deposits may have no contractual maturity, yet balances can be stable for long periods. Their effective repricing characteristics depend on customer sensitivity, competition, product design and the level and direction of market rates.

A behavioural deposit model commonly estimates:

• the stable or core balance likely to remain in the bank;
• the decay rate of balances over time;
• the proportion that reprices when market rates change;
• the lag between market-rate movement and deposit-rate adjustment; and
• differences among retail, corporate and institutional customers.

A simplified balance-decay model is:

where B_t is the projected balance after t periods, B₀ is the initial balance and d is the periodic decay rate. This is an illustrative model, not a universal law. In practice, decay may vary by rate regime, customer segment and balance level.

Deposits often contain an implicit customer option: the depositor can withdraw funds or move them to a competitor. Loans may contain borrower prepayment options. When rates fall, borrowers may refinance, shortening asset duration; when rates rise, prepayments may slow, lengthening it. These effects create negative convexity in many mortgage portfolios and make linear duration estimates unreliable.

Robust modelling requires historical observation, segmentation, sensitivity analysis, expert judgement and independent validation. Models should not assume that past low-rate behaviour will persist in a high-rate environment.

6. Funds-transfer pricing

Funds-transfer pricing (FTP) allocates the cost and benefit of funding, liquidity, optionality and interest-rate risk to business lines. A central treasury function normally retains structural interest-rate risk, while lending and deposit businesses are evaluated on risks they control.

A matched-maturity FTP system assigns a transfer rate to each transaction according to its tenor, repricing profile, liquidity characteristics, optionality and currency. A simplified business-line margin is:

The exact sign convention depends on whether the business is an asset producer or a liability gatherer. The principle is that product managers should be assessed after the cost of funds and the value of deposits have been recognised.

Good FTP prevents a lending unit from appearing profitable merely because it receives cheap short-term funding from treasury. It also rewards stable deposits when they provide reliable funding value. FTP should be transparent, consistent, documented and aligned with the bank’s risk appetite. Arbitrary transfer rates can distort product pricing and encourage risk-taking.

7. Hedging and ALCO decisions

ALCO typically reviews rate scenarios, gap reports, EVE and EaR limits, deposit assumptions, hedge performance, capital effects, liquidity conditions and strategic balance-sheet plans. Decisions may include:

• changing the mix of fixed- and floating-rate loans;
• adjusting deposit pricing and product terms;
• issuing debt with different maturities;
• purchasing or selling securities;
• using interest-rate swaps, futures, options or swaptions;
• setting limits on duration, basis and option risk; and
• retaining or transferring risk through securitisation.

An interest-rate swap can convert fixed-rate exposure to floating-rate exposure or the reverse. For example, a bank with fixed-rate assets and short-term floating-rate liabilities may pay fixed and receive floating in a swap, depending on the desired net exposure. The hedge must be analysed together with collateral, counterparty credit risk, basis risk, accounting treatment, liquidity requirements and termination costs.

Hedging should be risk-reducing rather than an excuse for speculative positioning. A hedge that reduces EaR under a parallel shock may increase EVE sensitivity under a curve twist. Effectiveness should therefore be assessed across multiple scenarios.

8. Scenario analysis, stress testing and governance

IRRBB stress testing should include parallel increases and decreases, steepening and flattening of the yield curve, short-rate shocks, basis movements and institution-specific events. Scenarios should consider management actions but should distinguish feasible actions from actions that are merely assumed.

A sound governance framework includes:

• board-approved risk appetite and limits;
• an independent ALCO with documented responsibilities;
• independent risk measurement and model validation;
• reliable data lineage and reconciliations to the general ledger;
• regular back-testing and benchmarking;
• escalation procedures for limit breaches;
• documentation of behavioural assumptions; and
• internal audit and supervisory review.

Regulatory frameworks commonly require banks to identify, measure, monitor and control IRRBB. Exact supervisory metrics and shock sizes differ by jurisdiction, so institutions must follow applicable prudential standards rather than relying on a generic template. Governance should also address model risk, conduct risk and the possibility that hedging decisions disadvantage customers or obscure the true risk profile.

9. Illustrative case: Meridian Commercial Bank

Background. Meridian Commercial Bank has 1.2 billion currency units of assets and 1.1 billion of liabilities. Its assets include long-term fixed-rate mortgages and securities. Funding consists mainly of current accounts, savings deposits and short-term wholesale borrowing.

Problem. The bank’s one-year EaR report shows only a modest loss under a rate increase because many deposits are classified as non-rate-sensitive. However, its EVE analysis shows a substantial decline because fixed-rate assets have much longer duration than liabilities. Recent competition has also caused deposit rates to respond more rapidly than the historical model predicts.

Analysis. ALCO identifies three weaknesses. First, the deposit model treats a stable historical balance as permanently insensitive to rates. Second, the gap report ignores mortgage prepayment changes. Third, treasury’s FTP credits deposits using a long behavioural life without charging sufficiently for model uncertainty.

Approach. Meridian segments deposits by customer type and balance size, applies alternative decay assumptions and introduces a deposit-beta analysis. It re-estimates mortgage prepayments under both rising and falling rates. It then sets separate EaR and EVE limits, adds a curve-steepening scenario and uses a receive-floating/pay-fixed swap strategy to reduce the duration mismatch. The hedge is approved only after basis, collateral and counterparty effects are included.

Outcome. The revised model produces a higher but more credible rate-risk estimate. The bank shortens part of its securities portfolio, improves FTP incentives for stable deposits and establishes a trigger requiring ALCO review when actual deposit betas exceed modelled values.

Learning points. A low short-term earnings exposure does not prove that economic-value risk is low. Behavioural assumptions can dominate contractual data. ALCO decisions are effective only when measurement, pricing, hedging and governance are integrated.

10. Limitations and contemporary developments

ALM models face parameter uncertainty, structural breaks, incomplete data and non-linear customer responses. Historical relationships can fail during monetary-policy transitions, financial stress or technological changes in customer behaviour. Model outputs should therefore be presented as ranges or scenario distributions where appropriate, not as precise forecasts.

Technology can improve ALM through automated data aggregation, cloud-based scenario engines and machine-learning tools for deposit attrition or prepayment prediction. Nevertheless, artificial intelligence does not remove the need for explainability, stability testing, bias assessment, human challenge and model governance. A model that predicts customer actions accurately in normal conditions may perform poorly in a crisis.

Best practice is to combine quantitative models with expert judgement, conservative overlays, clear documentation and frequent review. The objective is not to eliminate all interest-rate exposure. Some exposure is a natural consequence of banking and may be economically valuable. The objective is to ensure that exposure is deliberate, measurable, adequately capitalised and consistent with the bank’s strategy.

Chapter Summary

Asset-liability management coordinates a bank’s balance-sheet structure, profitability, liquidity and risk. IRRBB arises from repricing, yield-curve, basis and option effects. Repricing gaps provide a simple earnings-oriented view, while duration gaps and EVE measure longer-term economic-value sensitivity. EaR and EVE are complementary and should be interpreted under clearly defined scenarios.

Deposit behaviour, loan prepayments and embedded options make contractual maturity insufficient for serious risk measurement. Behavioural models require segmentation, validation and stress testing. FTP allocates funding and risk costs so that business lines receive appropriate incentives. ALCO must integrate measurement, pricing, hedging, capital and governance. Effective IRRBB management uses multiple measures, independent challenge and conservative judgement rather than reliance on a single model.

Key Terms

Asset-liability management: Coordinated management of assets, liabilities, capital, liquidity and related risks.

IRRBB: Interest-rate risk arising from positions in the banking book.

Repricing gap: Rate-sensitive assets minus rate-sensitive liabilities in a time bucket.

Cumulative gap: Sum of repricing gaps up to a specified bucket.

Rate-sensitive asset: An asset whose interest rate or cash flow changes within the measurement period.

Rate-sensitive liability: A liability whose interest cost or cash flow changes within the measurement period.

Duration: A measure of the timing of cash flows and price sensitivity to yield changes.

Duration gap: Difference between duration-weighted asset and liability exposures.

Earnings-at-risk: Potential reduction in projected earnings under specified adverse scenarios.

Economic value of equity: Present value of assets less present value of liabilities and relevant positions.

Yield-curve risk: Risk from non-parallel changes in interest rates across maturities.

Basis risk: Risk that related reference rates move differently.

Option risk: Risk arising from contractual or behavioural rights to alter cash flows.

Deposit beta: Sensitivity of a deposit rate to a change in a market reference rate.

Balance decay: Reduction in a deposit balance over time under a behavioural assumption.

Funds-transfer pricing: Internal allocation of funding, liquidity and risk costs and benefits.

ALCO: Management committee responsible for balance-sheet and financial-risk decisions.

Convexity: Curvature in the relationship between price and yield.

Model risk: Risk of adverse decisions caused by errors or inappropriate use of models.

Review Questions

Short Answer Questions

1. What is the difference between repricing risk and basis risk?
2. Why are EaR and EVE complementary measures?
3. What does a negative repricing gap imply under a rate increase?
4. Why can contractual maturity misrepresent deposit behaviour?
5. What is the purpose of funds-transfer pricing?

Long Answer Questions

1. Explain the construction, interpretation and limitations of a repricing-gap report.
2. Derive the simplified duration-gap relationship and discuss its assumptions.
3. Compare earnings-at-risk with economic-value sensitivity for ALCO decision-making.
4. Explain how embedded options affect mortgage and deposit exposures.
5. Discuss the governance requirements for an effective IRRBB framework.

Analytical / Application Questions

1. A bank has 600 million of rate-sensitive assets and 750 million of rate-sensitive liabilities repricing for 90 days. Estimate the first-order NII effect of a 2 percentage-point rate increase and explain the assumptions.
2. Design a stress-testing programme for a bank whose deposits are predominantly non-maturing and whose assets are long-term fixed-rate loans.
3. Evaluate whether a swap that reduces one-year EaR but increases EVE sensitivity should be approved. Identify the additional information ALCO requires.

Multiple Choice Questions with Answers

Question 1

A bank has a negative repricing gap of 100 million for a 90-day bucket. Assuming immediate full repricing and a 1% rate increase, what is the approximate NII effect?

A. A gain of 246,575

B. A loss of 246,575

C. A gain of 1,000,000

D. No effect

Correct Answer: B. A loss of 246,575

Question 2

Which measure primarily captures the present-value effect of interest-rate changes on the banking book?

A. Economic value of equity

B. Deposit turnover

C. Loan-to-deposit ratio

D. Operating expense ratio

Correct Answer: A. Economic value of equity

Question 3

A positive repricing gap generally means that, under the simple gap assumptions, a rate increase will:

A. Reduce asset income relative to liability expense

B. Increase liability expense only

C. Increase short-term net interest income

D. Have no earnings effect

Correct Answer: C. Increase short-term net interest income

Question 4

Which factor is most directly associated with basis risk?

A. Different reference rates moving by different amounts

B. A borrower repaying a loan early

C. A deposit having no contractual maturity

D. A bond having a long duration

Correct Answer: A. Different reference rates moving by different amounts

Question 5

For a small increase in yield, modified duration implies that bond price will generally:

A. Increase in proportion to duration

B. Decrease approximately by duration multiplied by the yield change

C. Remain unchanged

D. Change only when credit spreads move

Correct Answer: B. Decrease approximately by duration multiplied by the yield change

Question 6

Funds-transfer pricing is primarily intended to:

A. Eliminate all market risk from the bank

B. Allocate funding and risk costs and benefits to business lines

C. Set the central bank policy rate

D. Measure loan default probability

Correct Answer: B. Allocate funding and risk costs and benefits to business lines

Question 7

Which is an example of option risk in the banking book?

A. A borrower prepaying a fixed-rate mortgage

B. A transaction being recorded in the general ledger

C. A loan being denominated in local currency

D. A bond paying a fixed coupon on schedule

Correct Answer: A. A borrower prepaying a fixed-rate mortgage

Question 8

If assets have a duration of 4 years and liabilities a duration of 1.5 years, with asset value 1,000 million and liability value 900 million, which position is indicated by the simple duration calculation?

A. A substantial positive duration mismatch for equity

B. A zero duration mismatch

C. A liability duration longer than asset duration

D. No sensitivity to rates

Correct Answer: A. A substantial positive duration mismatch for equity

Question 9

Why should ALCO use both parallel and non-parallel yield-curve scenarios?

A. Because all rates always move identically

B. To capture curve twists and maturity-specific exposures

C. To avoid measuring basis risk

D. Because duration applies only to liabilities

Correct Answer: B. To capture curve twists and maturity-specific exposures

Question 10

A deposit beta measures:

A. The probability of loan default

B. The sensitivity of a deposit rate to a market-rate change

C. The maturity of a government bond

D. The ratio of assets to equity

Correct Answer: B. The sensitivity of a deposit rate to a market-rate change