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Point out the drawbacks of managing interest rate exposure through rate-sensitivity gaps and through duration gaps.

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.d

The idea

Both techniques are approximations and each has known blind spots. Gap management ignores how far inside a maturity bucket repricing falls, so a zero gap can still hide a timing mismatch. It assumes assets and liabilities reprice by the same amount, ignoring basis risk between different benchmark rates. It overlooks the market value of equity. It also treats balances as fixed, ignoring prepayments, deposit runoff and embedded options. Duration gap management assumes small parallel shifts of the yield curve, and it uses a linear approximation that ignores convexity, so large moves are misestimated. Durations drift as time passes and rates move, so the hedge needs rebalancing, and durations of prepayable loans and nonmaturity deposits are estimated. A zero duration gap stabilizes equity value, not net interest income. The exam favors knowing which limitation each method suffers from.

A practice question

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

Which is a limitation of managing interest rate risk with interest-sensitive gaps?

  1. It ignores the timing of repricing within a maturity bucket and the market value of equity - correct
  2. It relies on the assumption that the yield curve moves in a parallel shift only for durations beyond one yearWhy not: Parallel-shift reliance is typical of duration gap analysis, not a defining limitation of repricing gap.
  3. It requires estimating the convexity of every assetWhy not: Convexity corrections belong to duration analysis; the gap uses repricing buckets.
  4. It cannot be used for floating-rate assetsWhy not: Floating-rate assets are exactly what the gap measures; they are rate-sensitive.

The gap lumps items together by bucket, so two balances repricing at different dates are treated alike, and it measures net interest income rather than market value of equity.

A harder one

A bank has a one-year gap of zero, but its assets are priced off the prime rate while its deposits are priced off a money market rate. Which problem does this illustrate?

  1. Convexity risk: a zero gap overstates the value of the assetsWhy not: Convexity relates to nonlinear price changes, not different reference rates.
  2. Reinvestment risk is eliminated because the gap is zeroWhy not: A zero gap does not remove reinvestment risk, and basis risk is the issue here.
  3. Immunization is complete, since duration and gap are equivalentWhy not: Gap and duration measure different things; zero repricing gap does not give zero duration gap.
  4. Basis risk: the two rates need not change by the same amount, so net interest income can still move - correct

Gap analysis assumes the same rate change on both sides. When prime and the funding rate move differently, income changes despite a zero gap.

The hardest tier

A bank has USD 500 million of rate-sensitive assets and USD 500 million of rate-sensitive liabilities within one year, so the one-year gap is zero. All assets reprice at the end of month 2 and all liabilities at the end of month 10. Rates rise by 1 percentage point. The change in net interest income over the year is closest to:

  1. ZeroWhy not: Takes the zero gap result at face value; it ignores that the balances reprice at different times in the year.
  2. Increase of USD 3.3 million - correct
  3. Increase of USD 4.2 millionWhy not: Counts the 10 months of extra asset income but ignores the extra cost on the liabilities for the last 2 months.
  4. Decrease of USD 3.3 millionWhy not: Gets the timing reversed: the assets reprice earlier, so the bank gains, not loses.

Assets earn the extra 1% for 10 months: 500 x 1% x 10/12 = 4.17 million. Liabilities cost the extra 1% for 2 months: 500 x 1% x 2/12 = 0.83 million. Net = +3.33 million. A bucket gap hides timing differences.

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