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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 holds assets with a market value of $800 million and a modified duration of 4.0 years. Its liabilities have a market value of $720 million and a modified duration of 2.5 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 $14.0 million. Assets lose 4.0 x 1% x $800m = $32.0m, while liabilities lose 2.5 x 1% x $720m = $18.0m. Equity absorbs the difference because the asset decline exceeds the liability decline.

  1. A-$14.0 millionCorrect
  2. B-$32.0 million
  3. C+$14.0 million
  4. D-$18.0 million

Explanation

Change in assets = -4.0 x 0.01 x 800 = -32.0 million. Change in liabilities = -2.5 x 0.01 x 720 = -18.0 million. Change in equity = -32.0 - (-18.0) = -14.0 million. The -$32.0 million option ignores the offsetting fall in liability value, and -$18.0 million reflects only the liability move.

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