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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 liability portfolio has a market value of $400 million and a modified duration of 3.0. Its assets have a market value of $440 million. To immunize the equity value against small parallel yield shifts (ignoring convexity), what modified duration should the asset portfolio have?

The asset modified duration should be about 2.73. Equity is immunized when asset dollar duration equals liability dollar duration, so 440 times D equals 400 times 3.0. Simply matching durations at 3.0 would ignore that assets are larger than liabilities and leave the bank exposed.

  1. A2.73Correct
  2. B3.00
  3. C3.30
  4. D2.50

Explanation

Immunization requires the dollar duration of assets to equal that of liabilities: 440 x D_A = 400 x 3.0 = 1,200, so D_A = 2.727, about 2.73. Choosing 3.00 matches durations but ignores the leverage difference, leaving assets with a larger dollar duration than liabilities. Choosing 3.30 inverts the ratio.

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