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FRM Part II · FRM Exam Part II

Risk Management for Changing Interest Rates: ALM and Duration Techniques

Asset-liability management (ALM) measures and controls how interest rate changes affect a bank's earnings and economic value. You solve questions by picking the right tool: repricing gap for earnings, duration gap for economic value of equity, then hedge or immunize. Always state the sign and the size of the impact.

What this chapter covers

This chapter is about one question: what happens to a bank or investor when interest rates move? You learn two lenses. The earnings lens looks at net interest income over the next year, using repricing gap and funding gap. The value lens looks at the present value of all cash flows, using duration, convexity, duration gap and economic value of equity (EVE).

You then move to action. Immunization matches the duration of assets and liabilities so equity value is protected from small parallel shifts. Hedging uses swaps, futures and options to reshape exposure. The chapter ends with limits: duration assumes small, parallel moves, so you must know what breaks when the curve twists or steepens, or when customer behaviour such as prepayment and deposit withdrawal changes cash flows.

It connects to other parts of the paper. Interest rate risk in the banking book sits next to market risk measurement. Funding gaps tie into liquidity and treasury risk. Hedging links to derivatives and to risk management in investment management. Rate shocks also feed credit losses, so the ideas return in case-style questions across topics.

Part II has 80 equally weighted multiple-choice questions in 4 hours, and many are applied. This chapter gives you calculation questions that are quick to score once the method is clear: gap numbers, duration gap, EVE change, hedge ratios. It also gives interpretation questions, where you must say who gains when rates rise and why. Both types reward a clean method, and the same concepts appear in liquidity, market risk and investment management questions. Time spent here pays back in several areas.

Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques: topics in the order to study them

  1. 1Interest Rate Risk and Asset-Liability Management BasicsStart here to learn the types of rate risk (repricing, yield curve, basis, optionality) and the two lenses, earnings and economic value, that the rest builds on.
  2. 2Repricing Gap and Funding Gap AnalysisIt is the simplest tool and needs only buckets and subtraction, so it gives you an easy first win on the earnings view.
  3. 3Duration and Convexity of Assets and LiabilitiesYou need price sensitivity for each side of the balance sheet before you can combine them into one measure.
  4. 4Duration Gap and Economic Value of EquityThis combines asset and liability duration and leverage to estimate the change in equity value, the main calculation in the chapter.
  5. 5Immunization and Hedging Interest Rate ExposureOnce you can measure the gap, you learn how to close it by matching duration or using swaps, futures and options.
  6. 6Limitations of Duration and Non-Parallel Rate ShiftsStudy this last so you understand what the earlier models assume, and can judge when their answers fail.

How to prepare Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

Treat this chapter as one method repeated with different inputs. Learn the sign logic first, then the formulas, then practise applied questions.

  1. Write a one-page map: rate risk types, earnings lens versus value lens, and which tool answers which question.
  2. Practise gap tables until you can build them without help: set the buckets, count only rate-sensitive items, subtract liabilities from assets, then multiply the gap by the rate change for the income effect.
  3. Learn duration, modified duration and convexity: ΔP ÷ P ≈ −D_mod × Δy + ½ × C × (Δy)². Check that your answer has the right sign before looking at size.
  4. Practise duration gap with leverage: DGap = D_A − (L ÷ A) × D_L, and ΔEVE ≈ −DGap × A × Δy ÷ (1 + y). Always use the same units for A, L and y.
  5. Work hedging questions in two steps: find the exposure, then size the hedge. Know what a pay-fixed swap does to a bank that is asset-sensitive or liability-sensitive.
  6. Finish with limitation questions. For each assumption of duration, write what happens when it fails: large moves, twists, prepayment, deposit behaviour.
  7. Do timed mixed sets on your phone. Review every wrong answer by naming the step where you lost the mark.

Common mistakes in Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

  • Getting the sign of the gap effect wrong

    Fix: Ask: do assets or liabilities reprice sooner? If assets, income rises with rates. Check the sign before calculating.

  • Ignoring leverage in duration gap

    Fix: Always multiply D_L by L ÷ A. Equal durations do not mean zero risk when A and L differ.

  • Mixing earnings and value measures

    Fix: Label each answer 'income' or 'value'. Match the tool to the question wording.

  • Counting non-rate-sensitive items in a gap bucket

    Fix: Include only items that reprice or mature within the bucket.

  • Treating immunization as a full hedge

    Fix: State the conditions: small, parallel moves, and rebalancing as duration drifts. Convexity and twists still matter.

  • Forgetting behavioural options

    Fix: When a question mentions prepayment, non-maturity deposits or embedded options, expect duration to be unreliable and effective duration to be needed.

Last-day revision: Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

  • Repricing gap = rate-sensitive assets − rate-sensitive liabilities in a time bucket.
  • Change in net interest income ≈ gap × change in rates, for that bucket's horizon.
  • A positive gap gains income when rates rise; a negative gap loses.
  • Modified duration = Macaulay duration ÷ (1 + y) for annual compounding.
  • ΔP ÷ P ≈ −D_mod × Δy + ½ × C × (Δy)².
  • Convexity helps the holder: gains from falling rates exceed losses from rising rates, for the same size move.
  • Duration gap = D_A − (L ÷ A) × D_L.
  • Positive duration gap: equity value falls when rates rise.
  • ΔEVE ≈ −DGap × A × Δy ÷ (1 + y).
  • Immunization matches duration, and protects only against small parallel shifts.
  • A pay-fixed swap behaves like issuing a fixed-rate bond and buying a floating-rate asset. It shortens the effective duration of assets (or lengthens that of liabilities), so it reduces a positive duration gap, as in a bank with long-dated fixed-rate assets funded by short-term liabilities. It would not help a bank whose liabilities are already longer than its assets.
  • Duration fails for large moves, non-parallel shifts and options such as prepayment.

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

Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques in other exams

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

Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques: frequently asked questions

Is repricing gap or duration gap more important for FRM Part II?

Both matter. Gap analysis answers earnings questions over a short horizon, and duration gap answers economic value questions. Learn when each fits, because questions often test that choice.

Do I need to memorise the duration gap formula?

Yes. Know DGap = D_A − (L ÷ A) × D_L and how to turn it into a change in equity value. Practise it until the leverage term is automatic.

Why does duration fail for non-parallel shifts?

Duration measures sensitivity to one uniform yield change. If short and long rates move by different amounts, assets and liabilities with different cash flow timing change value differently. Key rate durations or full revaluation handle this better.

How should I study this chapter on my phone?

Use short sessions on one topic at a time. Do the gap and duration gap calculations on paper first, then practise interpretation questions on the phone.