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FRM Part II · FRM Exam Part II · Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

Using the data of a bank with assets of USD 1,000 million, duration gap of 1.70 years, and equity of USD 80 million, the yield level of 5% (annual compounding) rises by 100 basis points. Using the approximation change in equity = -DGap x A x dy/(1+y), what is the approximate change in the bank's equity value?

Equity falls by about USD 16.2 million. With a positive duration gap of 1.70, a 1% rise in yields reduces net worth by 1.70 x 1,000 x 0.01 divided by 1.05, which equals roughly 16.2 million.

  1. ADecrease of USD 17.0 million
  2. BDecrease of USD 16.2 millionCorrect
  3. CDecrease of USD 13.0 million
  4. DIncrease of USD 16.2 million

Explanation

Change = -1.70 x 1,000 x 0.01/1.05 = -USD 16.19 million, about 16.2 million. Omitting the 1.05 divisor gives 17.0. Equity falls because the duration gap is positive and rates rise.

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