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

A bank's assets (USD 500m) have duration 4.0 and its liabilities (USD 450m) have duration 4.0. Management claims the bank is immunized because durations match. Which is the best critique?

Equal durations do not immunize equity when leverage exists. The correct leverage-adjusted gap is 4.0 minus 4.0 times 0.9, or 0.4 years, which is positive. Asset values fall more than liability values when rates rise, so equity remains exposed.

  1. AThe duration gap is zero, so equity is fully protected
  2. BLeverage-adjusted duration gap is 4.0 - 4.0*(450/500) = 0.4, so equity remains exposed to rate changesCorrect
  3. CThe gap is negative, so rising rates benefit equity
  4. DMatching durations is irrelevant for equity value

Explanation

Equity is protected only if D_A = D_L*(L/A). Here D_L*(L/A) = 4.0*0.9 = 3.6, so the gap is 4.0 - 3.6 = 0.4 years. Assets are more sensitive than liabilities in value terms, so rising rates reduce equity.

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