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CFA Level I · CFA Level I Exam · Yield-Based Bond Convexity and Portfolio Properties

A portfolio has a market value of EUR 50 million and a modified duration of 6.0. A manager wants to reduce duration to 4.5 by selling some of the portfolio and buying a cash-like instrument with duration 0.5, with no change in total value. The amount of bonds sold and replaced by the cash-like instrument is closest to:

About EUR 13.6 million must be shifted into the cash-like instrument. Each euro moved lowers duration by 5.5 (6.0 minus 0.5) times its weight, and the required drop is 1.5, so x equals 1.5 × 50 divided by 5.5, or roughly 13.6 million.

  1. AEUR 8.2 million
  2. BEUR 13.6 millionCorrect
  3. CEUR 15.0 million

Explanation

Let x be the amount moved from duration 6.0 into duration 0.5. Duration falls by x/50 × (6.0 - 0.5) = 1.5, so x = 1.5×50/5.5 = 13.64 million. Using 1.5/6.0 × 50 = 12.5 or ignoring the cash duration is wrong.

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