Explanation

Callable bonds have lower convexity compared to putable bonds, especially when the embedded options are near the money:

• Convexity comparison:

  • Callable bonds: Exhibit negative or low convexity due to the call option limiting price appreciation
  • Putable bonds: Exhibit positive convexity due to the put option providing price protection

• Downside risk: Callable bonds actually have more downside risk when rates rise because they lack the put protection

• Upside potential: Callable bonds have less upside potential when rates decline due to the call option

When the call option is near the money, the callable bond's convexity is particularly low (or negative) because small decreases in yields make the call option more likely to be exercised, limiting price appreciation.