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

A bank's investment portfolio has a market value of USD 200 million and a modified duration of 4.0. Management expects rates to rise and wants to cut the portfolio's modified duration to 2.5 by selling some bonds and buying zero-yield cash equivalents with zero duration. Assuming the remaining bonds keep a modified duration of 4.0, how much of the bonds must be switched into cash?

USD 75.0 million must be moved into cash. To reach a duration of 2.5 with bonds at 4.0, the bond weight must be 2.5/4.0 = 62.5%, or USD 125 million. The remaining 200 − 125 = USD 75 million goes into zero-duration cash equivalents.

  1. AUSD 75.0 millionCorrect
  2. BUSD 120.0 million
  3. CUSD 37.5 million
  4. DUSD 125.0 million

Explanation

Portfolio duration = weight in bonds × 4.0 = 2.5, so bond weight = 0.625, i.e. USD 125 million kept in bonds. The amount switched to cash is 200 − 125 = USD 75 million. USD 125 million is the amount retained, not switched; USD 37.5 million is 200 × 2.5/4 × 0.30 misapplied.

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