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

Bond A and Bond B have the same price, yield and modified duration, but Bond A has higher convexity. Which statement about their prices after a large parallel shift in yields is most accurate?

Bond A, the higher-convexity bond, outperforms in both directions. With equal duration the linear effects match, and the convexity term is positive and scales with the squared yield change, so it adds value whether yields rise or fall.

  1. ABond B outperforms Bond A whether yields rise or fall
  2. BBond A outperforms Bond B only if yields fall
  3. CBond A outperforms Bond B only if yields rise
  4. DBond A outperforms Bond B whether yields rise or fallCorrect

Explanation

With equal duration, the first-order effect is the same. The convexity term 0.5*C*(Δy)^2 is always positive for positive convexity and grows with the square of the move, so the higher-convexity bond gains more or loses less in either direction. The other options wrongly make the benefit depend on the direction of the move.

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