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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 total assets of $1,000 million with a modified duration of 4.0 years and total liabilities of $900 million with a modified duration of 3.0 years. Using the duration gap approach, what is the approximate change in the market value of equity if all yields rise by 100 basis points in a parallel shift?

Equity falls by about $13 million. Dollar duration of assets is 4,000 and of liabilities is 2,700, leaving a gap of 1,300. A 1% rise in yields multiplies this by 0.01, so equity value declines by roughly $13 million.

  1. A-$13 millionCorrect
  2. B-$10 million
  3. C-$1.3 million
  4. D+$13 million

Explanation

Change in equity ≈ -(D_A × A − D_L × L) × Δy = -(4.0×1,000 − 3.0×900) × 0.01 = -(4,000 − 2,700) × 0.01 = -$13 million. The option of -$10 million wrongly ignores liability duration weighting by using only the leverage-free difference in durations on assets (1.0 × 1,000 × 0.01). A rise in rates lowers equity because the dollar duration of assets exceeds that of liabilities.

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