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

A callable bond's yield falls sharply so that its price approaches the call price. Compared with an otherwise identical non-callable bond, which statement about the callable bond's effective duration is correct?

The callable bond's effective duration is lower than that of a comparable non-callable bond. When yields drop, the call option caps price gains near the call price, reducing price sensitivity and producing negative convexity. Macaulay duration cannot capture this because it ignores option-driven changes in cash flows.

  1. AIt is lower, because the call option limits price appreciation as yields fallCorrect
  2. BIt is higher, because the issuer is likely to call and extend maturity
  3. CIt equals the Macaulay duration to the maturity date
  4. DIt is unchanged, because the embedded option does not affect cash flows

Explanation

As yields fall toward the level where calling is attractive, the callable bond's price is capped near the call price, so it is less sensitive to yield changes. Effective duration therefore falls below that of the non-callable bond, reflecting negative convexity. The option does change expected cash flows, which is why effective duration, not Macaulay or modified duration, is used.

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