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

A callable bond trades close to its call price, and market yields fall by 50 basis points. Which statement best describes why a standard duration-based estimate is unreliable here?

The callable bond exhibits negative convexity near its call price. Because the issuer can call the bond, price appreciation is capped as yields fall, so the actual price rise is smaller than the duration-based estimate suggests. Effective duration also shortens as yields decline.

  1. AThe bond has negative convexity, so its price rises by less than the duration estimate impliesCorrect
  2. BThe bond has positive convexity, so its price rises by more than the duration estimate implies
  3. CDuration is zero for callable bonds, so no price change is expected
  4. DThe price change is identical to a comparable non-callable bond because the call is out of the money

Explanation

Near the call price, the issuer's call option caps price appreciation, so the price-yield curve flattens and the bond shows negative convexity. The actual gain is smaller than a duration estimate predicts. Duration is not zero, and the call option, being near the money, makes the bond behave unlike a non-callable bond.

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