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LOS 36.j: Compare effective durations of READING 36: VALUATION AND ANALYSIS: BONDS WITH EMBEDDED OPTIONS
callable, putable, and straight bonds.

Both call and put options have the potential to reduce the life of a bond, so the MODULE 36.5: DURATION
duration of callable and putable bonds will be less than or equal to the duration of
their straight counterparts.

• Effective duration (callable) ≤ effective duration (straight). Effective duration (straight bonds) is relatively
• Effective duration (putable) ≤ effective duration (straight). unaffected by changes in interest rates; but:
• Effective duration (zero-coupon) ≈ maturity of the bond. • an increase (decrease) in rates would decrease the
• Effective duration of fixed-rate coupon bond < maturity of the bond. effective duration of a putable (callable) bond.
• Effective duration of floater ≈ time (in years) to next reset.

LOS 36.k: Describe the use of one-sided durations and key rate durations to evaluate the interest rate sensitivity
of bonds with embedded options.

But value of a callable bond is capped by its call
In a normal yield curve: price: it will not increase beyond the call price
• value of call option falls (and rises (irrespective of how low interest rates fall).
when yields drop)
• value of a put option increases Similarly, the value of a putable bond is more
(and falls when yields increase) sensitive to downward movements in yield curve than
upward movements.

One-sided durations—only apply when interest rates rise (or, only when rates fall)—they are better at capturing interest rate
sensitivity than simple effective duration:
• Callable bonds: when at-the-money (or near-the-money): (the price change of a callable when rates fall is smaller
• One-sided down-duration < one-sided up-duration than the price change for an equal increase in rates).

• Putable bond: when near-the-money:
• larger one-sided down-duration > one-sided up-duration.