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FRM Part II · FRM Exam Part II · The Investment Function in Financial Services Management

A bank's investment portfolio has market value $400 million and modified duration 4.0. Management expects a parallel yield rise of 50 bp and wants to cut the expected loss by half by selling long bonds and buying short-term securities, keeping market value constant. Ignoring convexity, what is the required new portfolio modified duration, and what is the loss at the current duration?

The current loss is $8 million, computed as 400 million times modified duration 4.0 times 0.5 percent. Halving the loss to $4 million requires reducing modified duration to 2.0, because the price change is proportional to duration when market value is held constant and convexity is ignored.

  1. ADuration 2.0; current loss $8 millionCorrect
  2. BDuration 2.0; current loss $4 million
  3. CDuration 3.0; current loss $8 million
  4. DDuration 1.0; current loss $2 million

Explanation

Current loss is 400 × 4.0 × 0.005 = $8 million. Halving it to $4 million requires duration 2.0, since 400 × 2.0 × 0.005 = $4 million. Answer $4 million as current loss confuses the target with the present exposure.

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