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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 treasury wants to immunize equity against parallel rate shifts. Assets are USD 800 million with a modified duration of 3.0. Liabilities are USD 700 million. To make the market value of equity approximately insensitive to rates, what must the modified duration of liabilities be?

Liability duration must be about 3.43. Equity is immunized when asset dollar duration equals liability dollar duration: 3.0 × 800 = D × 700, so D = 2,400 / 700 ≈ 3.43. Matching durations alone would leave equity exposed because assets exceed liabilities.

  1. A3.43Correct
  2. B2.63
  3. C3.00
  4. D3.86

Explanation

Zero equity sensitivity requires D_A × A = D_L × L, so D_L = 3.0 × 800 / 700 = 3.43. The 3.00 option equates durations without adjusting for leverage. The 2.63 option reverses the ratio (3.0 × 700/800). The 3.86 option is not derived from the duration-dollar balance.

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