Explanation

This question involves callable bonds and their behavior when yields decrease sharply.

Key Factors:

• Callable bonds: XYZ bonds are callable at par value and currently trade close to par
• Current position: Bonds are trading near their call price
• Scenario: Yields on comparable bonds decrease sharply

Analysis:

1. Callable Bond Characteristics: When yields decrease significantly, callable bonds approach their call price and exhibit negative convexity

2. Why Negative Convexity?:

   • As yields fall, the bond's price approaches the call price
   • The issuer is likely to call the bond when it becomes advantageous
   • This creates a price ceiling at the call price
   • The bond's price appreciation is limited compared to non-callable bonds

3. Duration Behavior:

   • Modified duration would decrease as yields fall (opposite of option B)
   • Effective duration would also decrease as the bond approaches call (opposite of option C)

4. Convexity Impact:

   • Positive convexity would mean unlimited price appreciation potential
   • Negative convexity means price appreciation is capped at the call price
   • This is exactly what happens with callable bonds trading near par when yields fall

Conclusion:

The XYZ bonds will most likely exhibit negative convexity because as yields decrease sharply, the bonds approach their call price, limiting further price appreciation and creating the characteristic negative convexity profile of callable bonds trading near par.