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FRM Part II · FRM Exam Part II · The Investment Function in Financial Services Management

A bank is comparing two portfolios of equal market value and equal average duration of 5 years. Portfolio X holds only 5-year bonds. Portfolio Y holds half in 1-year bonds and half in 9-year bonds. Which statement best describes the relative behaviour of the two portfolios?

The barbell portfolio has higher convexity than the bullet at equal duration. Its cash flows are dispersed across short and long maturities, which adds curvature to the price-yield relationship. Matching duration equalises only first-order sensitivity, so price changes differ for larger rate moves.

  1. AY, the barbell, has higher convexity than X, the bullet, at equal durationCorrect
  2. BX, the bullet, has higher convexity than Y at equal duration
  3. CBoth have identical price changes for any size rate move because durations match
  4. DY has lower yield sensitivity because its short bonds dominate

Explanation

With equal duration, the barbell spreads cash flows over a wider range of times, producing higher convexity than the bullet. Duration matching only equates first-order sensitivity. For large rate moves the barbell's extra convexity gives it better price performance, so the statement that price changes are identical is wrong.

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