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FRM Part I · FRM Exam Part I · Interest Rates

Bond X and Bond Y have the same price, yield and modified duration, but Bond X has higher convexity. Which statement is correct for a large parallel shift in yields?

Bond X, with higher convexity, gains more when yields fall and loses less when yields rise. Equal durations give the same first-order price change, but the convexity term is positive for a yield move in either direction, so the higher-convexity bond outperforms in both cases.

  1. ABond X will gain more if yields fall and lose less if yields rise than Bond YCorrect
  2. BBond X outperforms Bond Y only if yields fall
  3. CBond X outperforms Bond Y only if yields rise
  4. DBond X and Bond Y change in price by the same amount because their durations are equal

Explanation

With equal duration, the first-order price change is the same. The convexity term 0.5×C×Δy² is positive for any yield move, so the higher-convexity bond gets a larger price increase when yields fall and a smaller decline when yields rise. Equal duration only matches small-move sensitivity, not large moves.

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