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

A callable bond is trading close to its call price. If market yields fall sharply, which statement best describes the behavior of its effective duration and why this limits the use of a fixed duration figure?

Effective duration falls. When yields drop, the issuer's call option becomes more valuable and exercise more likely, so expected cash flows shorten and price gains are capped. This negative convexity means one duration figure holds only for small yield changes and misleads for large moves.

  1. AEffective duration rises because the bond's cash flows become longer-dated as yields fall
  2. BEffective duration falls because the call option becomes more likely to be exercised, shortening expected cash flowsCorrect
  3. CEffective duration stays constant because a callable bond's coupons are fixed
  4. DEffective duration becomes negative because price falls as yields fall

Explanation

As yields fall, the issuer is more likely to call, so expected life shortens and price appreciation is capped, which reduces effective duration (negative convexity). A single duration number is therefore only valid locally. Fixed coupons do not make the duration constant when the cash flows are yield-dependent.

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