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

A treasurer compares two asset portfolios with identical market value and modified duration. Portfolio X has higher convexity than Portfolio Y. Which statement best describes the expected outcome for a large parallel yield move, in either direction?

The higher-convexity portfolio X outperforms in both rising and falling yield scenarios. With equal duration, the convexity adjustment, half of convexity times yield change squared, is always positive and larger for X, cushioning losses when yields rise and boosting gains when they fall.

  1. AX outperforms Y in both rising and falling yield scenarios, all else equalCorrect
  2. BX outperforms Y only when yields fall
  3. CY outperforms X when yields rise because it has lower convexity
  4. DX and Y have identical price changes because duration is equal

Explanation

With equal duration, the convexity term adds a positive amount to price change, 0.5 × convexity × (Δy)², for any yield move. Higher convexity adds more in both directions. Equal duration only matches the first-order effect, so large moves differ.

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