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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 USD 1,000 million with a modified duration of 4.0 and liabilities of USD 900 million with a modified duration of 3.5. Using the duration approach, what is the approximate change in the market value of equity if all yields rise by 50 basis points?

Equity value falls by about USD 4.25 million. Assets lose 20.0 million (4.0 × 0.5% × 1,000) while liabilities fall by 15.75 million (3.5 × 0.5% × 900), so the net change to equity is negative 4.25 million.

  1. ADecrease by USD 4.25 millionCorrect
  2. BDecrease by USD 2.50 million
  3. CDecrease by USD 0.50 million
  4. DIncrease by USD 4.25 million

Explanation

Asset change = -4.0 × 0.005 × 1000 = -20.0 million. Liability change = -3.5 × 0.005 × 900 = -15.75 million. Equity change = -20.0 - (-15.75) = -4.25 million. The -2.50 option wrongly uses the duration gap times asset value without scaling liabilities by leverage (…0.5 × 1000 × 0.005).

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