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FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01

Which statement about a callable bond that exhibits negative convexity at current yields is correct?

With negative convexity, a yield decline produces a smaller price gain than the loss from an equal yield rise. The second-order term is negative regardless of direction, and the embedded call caps price appreciation as yields fall, so the price-yield curve bends below its tangent line.

  1. AFor equal-sized yield moves, the price gain from a yield decline is smaller than the price loss from a yield increase.Correct
  2. BThe convexity-adjusted estimate of price change is always lower than the duration-only estimate when yields fall.
  3. CConvexity affects the price estimate only when yields rise, because the second-order term is negative for yield declines.
  4. DNegative convexity arises because the bond's cash flows are more spread out than those of a comparable option-free bond.

Explanation

With negative convexity, the second-order term subtracts value for large yield moves in both directions. Price appreciation as yields fall is therefore compressed (the call limits upside) while losses from rising yields are magnified relative to a duration-only estimate. The other statements misstate the sign or the source of convexity: the second-order term is symmetric in Δy², and negative convexity comes from the embedded call option.

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