Risk Management in Banking and Insurance · Market Risk Management

Interest Rate Risk and Duration Gap Analysis for CMA Final

Updated 11 October 2026 · Fact-checked

Interest rate risk is the risk that changes in market rates reduce a bank's earnings or the economic value of its equity. Measure earnings impact with the repricing gap (RSA − RSL) × change in rate. Measure value impact with the duration gap: DG = D_A − (L ÷ A) × D_L, then ΔE ≈ −DG × A × Δy ÷ (1 + y).

Understand Interest Rate Risk and Duration Gap Analysis

Banks borrow short and lend long. Deposits reprice quickly, while loans and bonds may be fixed for years. When market rates move, the interest a bank earns and the interest it pays change by different amounts. This is interest rate risk. In the banking book it is called IRRBB.

There are two views. The earnings view asks how net interest income (NII) changes over the next 12 months or so. The economic value view asks how the present value of assets, liabilities and off-balance sheet items, and so the value of equity, changes. Repricing gap serves the first view. Duration gap serves the second.

Repricing gap analysis sorts rate-sensitive assets (RSA) and rate-sensitive liabilities (RSL) into time buckets by their next repricing date. A bucket gap is RSA − RSL. A negative gap means more liabilities than assets reprice, so a rate rise hurts NII. A positive gap means a rate rise helps NII. The method is simple, but it ignores the size of the price effect, basis risk and optionality.

Duration is the weighted average time to receive a bond's cash flows, with present values as the weights. It tells you how sensitive price is to yield. Modified duration converts it into a direct percentage price change per unit change in yield. Because the price-yield curve is bent, duration alone is only a first approximation. Convexity corrects for the curvature. A positive convexity means the price falls less than duration predicts when yields rise, and rises more when yields fall.

For the whole balance sheet, the duration gap compares the duration of assets with the leverage-adjusted duration of liabilities. A positive duration gap means assets are more sensitive than liabilities, so rising rates cut equity value. Bank equity is thin, so even a small percentage change in asset value can cause a large percentage change in equity.

Key rules to remember

Repricing gap: Gap = RSA − RSL; Calculate for each time bucket. Cumulative gap is the running total up to the bucket you are testing.
Change in NII: ΔNII ≈ Gap × Δi; Use the cumulative gap for the horizon (usually 1 year). Δi as a decimal, e.g. 0.5% = 0.005. Assumes a parallel shift and that all items reprice at the start of the bucket.
Gap ratio: RSA ÷ RSL; Below 1 means liability-sensitive, above 1 means asset-sensitive.
Macaulay duration: D = Σ [t × CF_t ÷ (1 + y)^t] ÷ Price; t is time in years, CF_t is the cash flow at time t, y is yield per period. The price is the sum of discounted cash flows.
Modified duration: MD = D ÷ (1 + y ÷ m); m is compounding periods per year. For annual compounding, MD = D ÷ (1 + y).
Price change with duration and convexity: ΔP ÷ P ≈ −MD × Δy + ½ × C × (Δy)²; C is convexity. Drop the second term if the question gives no convexity. Use Δy in decimals.
Convexity (annual cash flows): C = Σ [t × (t + 1) × CF_t ÷ (1 + y)^(t + 2)] ÷ Price; Use only if the question asks you to compute it. Otherwise the value is usually given.
Duration gap: DG = D_A − (L ÷ A) × D_L; A is the market value of assets, L is the market value of liabilities, D_A and D_L are the weighted durations.
Change in equity value: ΔE ≈ −DG × A × Δy ÷ (1 + y); Divide ΔE by E to get the percentage change in equity. A positive DG with rising yield gives a loss.

How to solve Interest Rate Risk and Duration Gap Analysis questions

Decide first whether the question asks about earnings (gap) or value (duration). Then follow the steps in order and show each one, because marks are given for method.

1Read what is asked: change in NII, change in value of a bond, duration gap, or change in equity value. Note the rate change and whether it is up or down.
2List the data in a small table: RSA and RSL by bucket for gap questions, or A, L, D_A, D_L and yield for duration questions.
3For gap questions, compute RSA − RSL for the bucket or the cumulative gap up to the horizon, and say whether the bank is asset-sensitive or liability-sensitive.
4Apply ΔNII = Gap × Δi. Convert basis points into decimals first (100 bps = 0.01) and keep the sign.
5For duration questions, compute MD = D ÷ (1 + y), then ΔP ÷ P = −MD × Δy. Add the convexity term if C is given.
6For a bank balance sheet, compute DG = D_A − (L ÷ A) × D_L, then ΔE = −DG × A × Δy ÷ (1 + y). Express it as a percentage of equity.
7Interpret the answer in one or two lines: who gains or loses, how large the hit is against capital, and the likely response.
8Name the hedge or fix: reprice or shorten asset duration, lengthen liability duration, or use swaps, FRAs or futures.

Quickest way: Sign-first shortcut for gap and duration gap

When to use it: Use this for MCQs and for the first line of a descriptive answer, when you need the direction and size of the impact in under a minute.

Decide the sign before the arithmetic. Negative gap with rising rates means NII falls. Positive duration gap with rising yields means equity value falls. Opposite cases give gains.
For NII, multiply the cumulative gap by the rate change in decimals. Gap in ₹ crore × 0.01 per 100 bps gives ₹ crore directly.
For bonds, price change in % ≈ −MD × Δy in %. A modified duration of 4 and a 0.5% rise gives about −2%.
For duration gap, compute L ÷ A first, then D_L × (L ÷ A), then subtract from D_A.
For equity, multiply DG × A × Δy and divide by (1 + y). Then divide by equity to get the percentage.

Common mistakes in Interest Rate Risk and Duration Gap Analysis

Using the total gap instead of the cumulative gap up to the one-year horizon (or the wrong bucket).
Students add all buckets, including long-dated ones that do not reprice within the earnings horizon.
Fix: Add buckets only up to the horizon asked. Then multiply by the rate change.
Getting the sign wrong in ΔNII or ΔE.
The formula for price and equity has a minus sign, while the gap formula does not.
Fix: Decide direction first from the sign rule. Check that your final number agrees with it.
Using Macaulay duration where modified duration is needed, or forgetting to divide by (1 + y).
The two terms look alike and some questions give D only.
Fix: For a price change, always convert: MD = D ÷ (1 + y ÷ m). Write the line even when the numbers are simple.
Writing duration gap as D_A − D_L, ignoring leverage.
Students forget that liabilities are smaller than assets, so their weight is L ÷ A.
Fix: Always scale D_L by L ÷ A. Use market values, not book values, if both are given.
Entering basis points as whole numbers, such as 50 instead of 0.005.
Rushing under time pressure.
Fix: Convert immediately: 1 bp = 0.0001. Write the decimal on the line before multiplying.
Presenting only the number and no recommendation.
Students treat it as a pure calculation question.
Fix: Add a line saying the bank is liability- or asset-sensitive, what the loss means for capital, and one or two practical hedges.

Worked examples

Example 1

A bank's balance sheet shows rate-sensitive assets of ₹6,200 crore and rate-sensitive liabilities of ₹7,500 crore repricing within one year. (a) Find the one-year gap and the RSA ÷ RSL ratio. (b) Estimate the change in NII if rates rise by 50 bps. (c) Estimate the change in NII if rates fall by 100 bps. Assume a parallel shift and that all items reprice immediately.

Show the solution

Gap = RSA − RSL = 6,200 − 7,500 = −₹1,300 crore. The bank is liability-sensitive.
Ratio = 6,200 ÷ 7,500 = 0.827, below 1, which agrees with the negative gap.
Rate rise of 50 bps: Δi = 0.005. ΔNII = −1,300 × 0.005 = −₹6.5 crore.
Rate fall of 100 bps: Δi = −0.01. ΔNII = −1,300 × (−0.01) = +₹13 crore.
Interpretation: more liabilities than assets reprice within the year, so a rise squeezes the margin and a fall widens it.

Answer: Gap = −₹1,300 crore (RSA ÷ RSL = 0.827). A 50 bps rise cuts NII by about ₹6.5 crore. A 100 bps fall raises NII by about ₹13 crore.

Example 2

A bank has assets of ₹10,000 crore with a weighted duration of 4.0 years, and liabilities of ₹9,200 crore with a weighted duration of 2.5 years. Equity is ₹800 crore. The market yield is 8%. (a) Compute the duration gap. (b) Estimate the change in the value of equity if yields rise by 1 percentage point. (c) Express this as a percentage of equity.

Show the solution

L ÷ A = 9,200 ÷ 10,000 = 0.92.
DG = D_A − (L ÷ A) × D_L = 4.0 − 0.92 × 2.5 = 4.0 − 2.3 = 1.7 years.
The gap is positive, so a rise in yields will reduce equity value.
ΔE ≈ −DG × A × Δy ÷ (1 + y) = −1.7 × 10,000 × 0.01 ÷ 1.08.
Numerator = 1.7 × 10,000 × 0.01 = 170. So ΔE = −170 ÷ 1.08 = −₹157.41 crore.
Percentage of equity = 157.41 ÷ 800 = 19.68%, about 19.7%.
Interpretation: a 1% yield rise wipes out nearly a fifth of equity. The bank should shorten asset duration, lengthen liability duration, or hedge with interest rate swaps.

Answer: Duration gap = 1.7 years. A 1 percentage point rise in yields reduces equity value by about ₹157.41 crore, roughly 19.7% of equity.

Exam tips

Section A MCQs usually test one step: a gap, a modified duration, or the sign of the effect. Decide the sign first and eliminate options of the wrong direction.
In written answers, state which view you are using (earnings or economic value) and name the formula before you substitute. This secures method marks even if arithmetic slips.
Always finish with an interpretation and a hedging suggestion. Case-based questions reward a recommendation, not just the figure.
Keep the limits of each method ready for 'discuss' questions: gap ignores price effects, basis risk and options. Duration is accurate only for small, parallel yield changes, which is why convexity is added.
Convert bps to decimals and units (₹ crore) before calculating, and write the units in the answer.

Practice questions from Market Risk Management

Interest Rate Risk and Duration Gap Analysis 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 Duration Gap Analysis: frequently asked questions

How do I calculate the duration gap of a bank?

Compute the weighted duration of assets (D_A) and of liabilities (D_L). Then use DG = D_A − (L ÷ A) × D_L with market values. A positive result means rising yields reduce equity value.

What is the difference between repricing gap and duration gap?

Repricing gap looks at the earnings effect, mainly on NII over a short horizon, using RSA and RSL in time buckets. Duration gap looks at the economic value of equity, using the price sensitivity of all assets and liabilities.

Why is convexity needed when we already have modified duration?

Modified duration is a straight-line estimate, but the price-yield relationship is curved. Convexity adds a correction, which improves the estimate for larger yield changes. For a bond with positive convexity, the duration-only estimate overstates the fall when yields rise and understates the gain when yields fall.

What is IRRBB?

IRRBB is interest rate risk in the banking book. It covers the risk to a bank's earnings and economic value from rate changes on its non-trading positions such as loans and deposits. Banks measure it with both the earnings and the economic value approaches.