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.