Explanation

In a rising interest rate environment:

1. Callable bonds have negative convexity - as interest rates rise, the probability of the bond being called decreases, making the callable bond behave more like a non-callable bond.

2. Effective duration measures the sensitivity of a bond's price to changes in interest rates.

3. When interest rates rise:

   • The call option becomes less valuable (out-of-the-money)
   • The callable bond's effective duration increases (becomes more sensitive to interest rate changes)
   • The non-callable bond's duration remains relatively stable
   • Therefore, the difference in effective duration between callable and non-callable bonds decreases

4. Conversely, in a falling interest rate environment, the call option becomes more valuable (in-the-money), causing the callable bond's effective duration to decrease significantly as the probability of being called increases, widening the difference with non-callable bonds.

Key Concept: Callable bonds exhibit negative convexity - their duration decreases when interest rates fall (due to increased call risk) and increases when interest rates rise (due to decreased call risk). This causes the duration difference with non-callable bonds to narrow in rising rate environments.