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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. Interest rates are expected to rise by 50 basis points in a parallel shift. Using the duration approximation, what is the approximate change in the market value of equity?

The equity value falls by about $6.5 million. Assets lose $20 million (4.0 x 0.5% x $1,000m) while liabilities fall by $13.5 million (3.0 x 0.5% x $900m), so the net effect on equity is a loss of $6.5 million.

  1. A-$6.5 millionCorrect
  2. B-$5.0 million
  3. C+$6.5 million
  4. D-$13.0 million

Explanation

Change in assets = -4.0 x 0.005 x 1,000 = -$20.0 million. Change in liabilities = -3.0 x 0.005 x 900 = -$13.5 million. Change in equity = -20.0 - (-13.5) = -$6.5 million. Ignoring the liability offset gives a larger loss, and using the wrong sign gives a gain.

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