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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 has assets of 1,000 with duration 3.0 and liabilities of 900 with duration 3.0. Equity is 100. A risk manager says the bank is immunized against a parallel rate rise because durations are equal. What is the best assessment?

The bank is not immunized. The leverage-adjusted duration gap is 3.0 minus 0.9 times 3.0, or 0.3, which is positive, so a rise in rates reduces equity value.

  1. ACorrect, equal durations always immunize equity
  2. BIncorrect; the duration gap is positive on a leverage-adjusted basis, so equity falls when rates riseCorrect
  3. CIncorrect; the duration gap is negative, so equity rises when rates rise
  4. DCorrect, because equity is positive

Explanation

Leverage-adjusted duration gap = D_A - (L/A) x D_L = 3.0 - 0.9 x 3.0 = 0.3 > 0. Equity change ≈ -0.3 x 1,000 x Δy, so a rate rise reduces equity. Equal durations only immunize when assets equal liabilities in value.

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