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FRM Part I · FRM Exam Part I · Modeling Non-Parallel Term Structure Shifts and Hedging

A manager builds a barbell from Bond A (modified duration 3, convexity 12) and Bond B (modified duration 12, convexity 200) to match a target portfolio duration of 7, with the weights summing to 100%. What is the convexity of the barbell?

The barbell convexity is 95.56. Matching a duration of 7 requires 4/9 in the long bond and 5/9 in the short bond, and convexity is the weighted average: (5/9)(12) + (4/9)(200) = 95.56.

  1. A95.56Correct
  2. B106.00
  3. C116.44
  4. D70.00

Explanation

Weight in B = (7 - 3)/(12 - 3) = 4/9, and weight in A = 5/9. Convexity = (5/9)(12) + (4/9)(200) = 60/9 + 800/9 = 95.56. Equal weights give 106 but a duration of 7.5, and reversed weights give 116.44 with a duration of 7.67.

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