Answer: less than the effective duration of an option-free bond.

## Explanation When interest rates are increasing, the effective duration of a bond with an embedded put option is **less than** the effective duration of an option-free bond. ### Key Concepts: 1. **Effective Duration**: Measures the sensitivity of a bond's price to changes in interest rates, accounting for embedded options. 2. **Put Option**: Gives the bondholder the right to sell the bond back to the issuer at a predetermined price (usually par) before maturity. 3. **Impact of Rising Interest Rates**: - When interest rates rise, bond prices fall - For a putable bond, as rates rise, the likelihood of the bondholder exercising the put option increases - The put option effectively limits the price decline because the bondholder can sell the bond back to the issuer at the put price - This creates a price floor, reducing the bond's sensitivity to interest rate changes 4. **Comparison with Option-Free Bond**: - An option-free bond has no such price floor protection - Its price will decline more significantly as interest rates rise - Therefore, its effective duration (price sensitivity) is higher ### Mathematical Perspective: Effective duration = (Price when rates fall - Price when rates rise) / (2 × Initial price × Change in yield) For a putable bond, the price when rates rise is limited by the put price, making the numerator smaller and thus the effective duration lower. **Correct Answer: A** - The put option provides downside protection, reducing the bond's sensitivity to rising interest rates compared to an option-free bond.

Author: LeetQuiz .