Explanation

Effective duration is the most appropriate duration measure for a callable bond because:

1. Accounts for embedded options: Effective duration measures the sensitivity of a bond's price to changes in interest rates while considering the impact of embedded options (like call features).

2. Considers option-adjusted cash flows: Unlike modified duration or Macaulay duration, effective duration accounts for how cash flows may change when interest rates change due to the call option being exercised.

3. Why the other options are incorrect:

   • Modified duration: Assumes cash flows are fixed and doesn't account for embedded options. It's appropriate for option-free bonds.
   • Macaulay duration: Measures the weighted average time to receive cash flows, but also doesn't account for embedded options.

4. Key concept: For bonds with embedded options, effective duration provides a more accurate measure of interest rate risk because it reflects how the bond's cash flows may change with interest rate movements.

Example: When interest rates fall, a callable bond is more likely to be called by the issuer, which changes the bond's cash flow pattern and duration. Effective duration captures this dynamic relationship.