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FRM Part II · FRM Exam Part II · Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

Two bonds have the same market value and the same modified duration, but Bond X has higher convexity than Bond Y. For a large parallel yield shift in either direction, which statement is correct?

The higher-convexity bond outperforms in both directions. With equal duration the linear effect is the same, and the convexity term is proportional to the squared yield change, so it adds value regardless of the shift's sign, and it is larger for Bond X.

  1. ABond X will outperform Bond Y in both rising and falling yield scenariosCorrect
  2. BBond X will outperform Bond Y only if yields fall
  3. CBond X will outperform Bond Y only if yields rise
  4. DBond X and Bond Y will have identical price changes

Explanation

With equal duration, the first-order effect is identical; the convexity term 0.5×C×Δy² is positive for both directions of shift and larger for X. So X gains more when yields fall and loses less when they rise. Equal price change would hold only for very small shifts.

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