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Explain the mechanics of interest-sensitive gap management and use that strategy to get the highest possible net interest margin for a bank.

FRM® Part II · Liquidity and Treasury Risk Measurement and Management · Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques · FRM2.LTR.17.b

The idea

Interest-sensitive gap management classifies assets and liabilities as rate-sensitive if they reprice within a chosen window. The gap is the difference between rate-sensitive assets (RSA) and rate-sensitive liabilities (RSL) in that window, so Gap = RSA − RSL. Here dNII is the change in net interest income and dr is the change in the interest rate. When assets and liabilities reprice by the same amount, the income effect is dNII = Gap × dr. A positive gap is asset-sensitive: rising rates raise income, falling rates cut it. A negative gap is liability-sensitive and does the reverse. Relative gap is gap divided by total assets, and the interest sensitivity ratio is RSA divided by RSL, which is above 1 for a positive gap. To raise net interest margin, hold a positive gap when you forecast rising rates and a negative gap when you forecast falling rates. The usual error is a wrong sign, or using gap when the two sides do not move by equal amounts. With asset and liability rate changes drA and drL, the income effect is then dNII = RSA × drA − RSL × drL.

Formulas

Change in net interest income from a repricing gap

ΔNII = (RSA − RSL) × Δr

RSA
assets that reprice within the period
RSL
liabilities that reprice within the period
Δr
the change in interest rates, applied to both

Holds only when both sides reprice by the same amount. Use the cumulative gap for every bucket inside the horizon, and watch the sign.

Change in net interest income when asset and liability rates move differently

ΔNII = RSA × ΔrA − RSL × ΔrL

RSA
assets that reprice within the period
RSL
liabilities that reprice within the period
ΔrA
the change in asset yields
ΔrL
the change in funding rates

Use when funding costs and asset yields move by different amounts. A positive gap can still lose income if funding costs rise faster.

Interest sensitivity ratio

ISR = RSA ÷ RSL

RSA
assets that reprice within the period
RSL
liabilities that reprice within the period

Above 1 means a positive gap and an asset-sensitive bank; below 1, liability-sensitive.

A practice question

From the question bank, with the reason each wrong option is wrong.

In interest-sensitive gap management, a bank has rate-sensitive assets that exceed rate-sensitive liabilities within the planning horizon. Which statement is correct?

  1. The gap is positive and net interest income falls if rates riseWhy not: Reverses the effect: more assets than liabilities repricing means income rises when rates rise.
  2. The gap is negative and net interest income rises if rates riseWhy not: Gap = RSA - RSL, so excess RSA gives a positive gap, not a negative one.
  3. The gap is positive and net interest income rises if rates rise - correct
  4. The gap is negative and net interest income falls if rates fallWhy not: Mislabels the gap sign. With a positive gap, income falls if rates fall, but the gap is positive.

Gap = RSA - RSL > 0 means asset-sensitive. When rates rise, interest income reprices upward more than interest expense, so net interest income rises, and it falls when rates fall.

A harder one

A bank's repricing report shows rate-sensitive assets of USD 180 million and rate-sensitive liabilities of USD 260 million in the 0 to 3 month bucket, and rate-sensitive assets of USD 240 million and liabilities of USD 300 million in the 3 to 12 month bucket. Rates rise by 2 percentage points, parallel for assets and liabilities, and every balance repricing inside the 12-month horizon is treated as repricing immediately. The estimated change in net interest income over the 12-month horizon is closest to:

  1. Increase of USD 2.8 millionWhy not: Wrong sign: the cumulative gap is negative, so income falls when rates rise.
  2. Decrease of USD 2.8 million - correct
  3. Decrease of USD 1.6 millionWhy not: Uses only the 0 to 3 month gap of -80 instead of the cumulative 12-month gap of -140.
  4. Decrease of USD 1.2 millionWhy not: Uses only the 3 to 12 month gap of -60 and ignores the first bucket.

Cumulative gap = (180 + 240) - (260 + 300) = -140 million. Change in net interest income = -140 x 2% = -2.8 million. The horizon gap includes every bucket that reprices inside it.

The hardest tier

A bank has USD 700 million of rate-sensitive assets and USD 650 million of rate-sensitive liabilities, a positive gap of USD 50 million. Over the next year, asset yields rise by 1.0 percentage point but the funding rates rise by 1.4 percentage points. The change in net interest income is closest to:

  1. Increase of USD 0.5 millionWhy not: Applies the gap to the asset-rate change only: 50 x 1.0%. Assets and liabilities do not reprice equally.
  2. Increase of USD 0.7 millionWhy not: Applies the gap to the liability-rate change: 50 x 1.4%, which treats both rates as moving by 1.4%.
  3. Decrease of USD 2.1 million - correct
  4. Increase of USD 2.8 millionWhy not: Multiplies RSA by the difference between the rate changes (0.4%) and gets both the size and the sign wrong.

Change in NII = 700 x 1.0% - 650 x 1.4% = 7.0 - 9.1 = -2.1 million. The gap formula only holds for equal rate changes; when funding costs move more (spread risk), a positive gap can still lose income.

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