Skip to content

FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01

A portfolio holds 40 million of Bond A (modified duration 2, convexity 6) and 60 million of Bond B (modified duration 12, convexity 200). A manager compares it with a single bullet bond of the same total value, with duration equal to the portfolio's duration and convexity of 70. For a parallel yield shift of 150 basis points, what is the approximate difference in percentage price change due to convexity, favoring the portfolio?

The portfolio gains about 0.59% relative to the bullet. Market-value weighting gives portfolio convexity of 122.4 against 70 for the bullet, a gap of 52.4. Multiplying by one-half and the squared 1.5% yield change gives roughly 0.59%, with durations already matched.

  1. A0.37%
  2. B0.59%Correct
  3. C1.18%
  4. D0.06%

Explanation

Portfolio duration = 0.4×2 + 0.6×12 = 8.0, matching the bullet. Portfolio convexity, weighted by market value, = 0.4×6 + 0.6×200 = 122.4. The difference is 52.4, and 0.5×52.4×0.015² = 0.005895, or about 0.59%. Using a simple unweighted average convexity of 103 gives 0.37%, 1.18% omits the one-half factor, and 0.06% mis-scales the yield change.

Did you get it right without looking?

One question tells you little. A timed set on Applying Duration, Convexity, and DV01 shows your real accuracy, how long you take and where you lose marks.

Practise Applying Duration, Convexity, and DV01Free diagnostic mock

More Applying Duration, Convexity, and DV01 questions