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

A portfolio of option-free bonds has a modified duration of 5.0 and a convexity of 50. Which statement about a large parallel yield change is most accurate?

With positive convexity, duration alone understates the price increase when yields fall and overstates the price decrease when yields rise. The true price-yield curve lies above the tangent line, so the convexity adjustment is positive in both directions and matters for large yield changes.

  1. AThe duration estimate understates the price gain from a yield fall and overstates the loss from a yield riseCorrect
  2. BThe duration estimate overstates the price gain from a yield fall and understates the loss from a yield rise
  3. CThe duration estimate is accurate for large changes because convexity is small

Explanation

Positive convexity means the actual price-yield curve lies above the duration tangent line. So actual price gains are larger and losses smaller than the linear estimate. The convexity term corrects this and matters for large moves.

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