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CFA Level I · CFA Level I Exam · Yield-Based Bond Convexity and Portfolio Properties

Bonds X and Y have the same price, yield-to-maturity and modified duration. Bond X has a convexity of 90 and Bond Y has a convexity of 40. If yields shift in parallel by a large amount, Bond X will most likely:

Bond X will outperform Bond Y whether yields rise or fall. With equal duration, the convexity term, one-half times convexity times yield change squared, is always positive and larger for X, so X gains more when yields fall and loses less when yields rise.

  1. Aoutperform Y only if yields fall.
  2. Boutperform Y whether yields rise or fall.Correct
  3. Cunderperform Y if yields rise.

Explanation

With equal duration, the price change differs only through the convexity term, 0.5 x convexity x (Δy)^2, which is positive for either direction of yield change. Higher convexity therefore adds more to the price of X in both cases. The benefit is larger for bigger yield moves.

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