FRM Exam Part II · Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

Interest Rate Risk and Asset-Liability Management Basics

Updated 11 October 2026 · Fact-checked

Interest rate risk in the banking book is the risk that rate changes reduce a bank's earnings or economic value. Asset-liability management (ALM) measures and controls it. To solve questions, identify the perspective (earnings or economic value), find which items reprice, apply the rate shock, and interpret the sign.

Understand Interest Rate Risk and Asset-Liability Management Basics

A bank borrows money (deposits, wholesale funding) and lends or invests it. Assets and liabilities rarely reprice at the same time or by the same amount. When rates move, interest income and interest expense change by different amounts. This is interest rate risk.

There are two perspectives. The earnings perspective looks at the change in net interest income (NII) over a short horizon, usually one to three years. The economic value perspective looks at the change in the present value of all expected cash flows, often called economic value of equity (EVE). EVE = PV of assets − PV of liabilities (plus off-balance-sheet items). Earnings is short-term and accounting-based. Economic value is long-term and captures all future cash flows.

Sources of the risk include repricing risk (timing mismatch), yield curve risk (non-parallel shifts), basis risk (different reference rates move differently) and optionality (prepayable loans, withdrawable deposits, caps and floors). Basel's standards for interest rate risk in the banking book (IRRBB) expect banks to measure both perspectives under standardised rate shock scenarios.

ALM is the process of managing the balance sheet structure to keep these exposures within the risk appetite. The ALCO (asset-liability committee) sets limits, reviews gap and sensitivity reports, and decides on hedges such as swaps or changes in the asset and funding mix.

A typical bank is liability-sensitive in the short term: it funds long fixed-rate assets with short-term liabilities. Rising rates then cut NII and lower EVE. A bank with many floating-rate loans and sticky fixed-rate funding is asset-sensitive and gains when rates rise.

Key formulas to remember

Net interest income: NII = Interest income − Interest expense; The main target of the earnings perspective.
Repricing gap: Gap = Rate-sensitive assets (RSA) − Rate-sensitive liabilities (RSL); Computed per time bucket. Positive gap means asset-sensitive.
Change in NII from gap: ΔNII ≈ Gap × Δr; Applies to a one-year horizon for items repricing at the start. Use the fraction of the year remaining for later buckets.
Economic value of equity: EVE = PV(assets) − PV(liabilities) ± PV(off-balance-sheet); The economic value perspective. ΔEVE is measured under rate shocks.
Duration approximation: ΔPV ≈ −D × PV × Δr (D = modified duration); First-order estimate. Ignores convexity and non-parallel shifts.

How to solve Interest Rate Risk and Asset-Liability Management Basics questions

Use the same sequence for any interest rate risk or ALM question.

1Identify the perspective: NII (earnings, short horizon) or EVE (present value, all cash flows).
2List the balance sheet items and decide which reprice within the horizon. Fixed-rate items do not reprice until maturity.
3Note the shock: size, direction, parallel or not, and the horizon.
4Calculate: for earnings, Gap × Δr (adjusted for timing); for value, change in PV of assets minus change in PV of liabilities.
5Check the sign. Positive gap with rising rates raises NII. Longer asset duration than liability duration means value falls when rates rise.
6State the interpretation and any limit: optionality, basis risk, non-parallel shifts or behavioural assumptions on deposits.

Quickest way: Gap sign shortcut

When to use it: Use when the question asks for the direction or size of the NII effect from a rate move.

Compute RSA − RSL for the horizon bucket.
Multiply by the rate change (in decimals).
Positive gap: NII moves with rates. Negative gap: NII moves against rates.
For value questions, compare durations: the side with larger duration × value drives the EVE direction.

Common mistakes in Interest Rate Risk and Asset-Liability Management Basics

Treating NII and EVE as the same measure.
Both respond to rate changes, so they look alike.
Fix: NII is a short-horizon income flow. EVE is the present value of all future cash flows. They can move in opposite directions.
Counting fixed-rate items as rate-sensitive.
Students include every item in the horizon bucket by size.
Fix: Only items that reprice or mature within the horizon are rate-sensitive.
Getting the sign wrong for a negative gap.
Mixing up assets minus liabilities with the reverse.
Fix: Always use RSA − RSL. Negative gap and a rate rise lowers NII.
Applying the full-year shock to items repricing mid-year.
Ignoring timing within the horizon.
Fix: Multiply by the fraction of the year left after repricing, e.g. 0.5 for repricing at six months.
Ignoring optionality and basis risk.
Gap analysis looks complete.
Fix: Remember that gap is a simple measure. Prepayments, deposit behaviour and different reference rates are not captured.

Worked examples

Example 1

A bank has RSA of $800 million and RSL of $950 million in the one-year bucket. All reprice at the start of the year. Rates rise by 1% (parallel). What is the approximate change in NII?

Show the solution

Gap = 800 − 950 = −$150 million.
ΔNII ≈ Gap × Δr = −150 × 0.01 = −$1.5 million.
Negative gap means the bank is liability-sensitive, so higher rates reduce NII.

Answer: NII falls by about $1.5 million.

Example 2

A bank has assets of $1,000 million with modified duration 4 and liabilities of $900 million with modified duration 2. Rates rise by 0.5% (parallel). Estimate the change in EVE using the duration approximation.

Show the solution

ΔPV assets ≈ −4 × 1,000 × 0.005 = −$20 million.
ΔPV liabilities ≈ −2 × 900 × 0.005 = −$9 million.
ΔEVE = ΔPV assets − ΔPV liabilities = −20 − (−9) = −$11 million.
Assets lose more value than liabilities, so equity value falls.

Answer: EVE falls by about $11 million.

Exam tips

Read whether the question asks about earnings or economic value before calculating anything.
Watch the timing: items repricing part-way through the year get a fractional effect.
Expect conceptual items on basis risk, yield curve risk and optionality, not only calculations.
Link the result to ALM action: a negative gap and falling NII may call for receive-fixed swaps or shorter-duration assets.
Know that gap analysis ignores value effects and convexity, which is why EVE is used as well.

Practice questions from Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

Interest Rate Risk and Asset-Liability Management Basics in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Interest Rate Risk and Asset-Liability Management Basics: frequently asked questions

What is interest rate risk in the banking book?

It is the risk to a bank's earnings or economic value from changes in rates on banking book positions, which are generally held to maturity or not actively traded. Basel's IRRBB standards require banks to measure it under defined shock scenarios.

What is the difference between the earnings and economic value perspectives?

The earnings perspective measures the change in net interest income over a short horizon. The economic value perspective measures the change in the present value of all future cash flows, so it captures the long-term effect of rate changes.

What is asset-liability management in banks?

ALM is the coordinated management of assets, liabilities and off-balance-sheet positions to control interest rate and liquidity risk. The ALCO sets limits and decides on balance sheet changes and hedges.

Does a positive gap always mean NII rises when rates rise?

Only approximately, and only if the repricing assumptions hold. Basis risk, prepayments and deposit behaviour can change the outcome.