Answer: rise less.

## Explanation When interest rates fall, the price of a callable bond will **rise less** compared to an otherwise identical option-free bond. Here's why: ### Key Concepts: 1. **Callable Bond**: A bond that gives the issuer the right to redeem (call) the bond before maturity at a predetermined price. 2. **Option-Free Bond**: A bond with no embedded options (neither callable nor putable). 3. **Interest Rate Movements**: When interest rates fall, bond prices generally rise. ### Analysis: - **For option-free bonds**: When interest rates fall, the bond price rises significantly because the fixed coupon payments become more valuable relative to new bonds issued at lower rates. - **For callable bonds**: When interest rates fall significantly, the issuer is more likely to exercise the call option and refinance the debt at lower rates. - **Price Ceiling Effect**: The callable bond's price is limited by the call price (the price at which the issuer can call the bond). As interest rates fall, the bond price approaches but cannot exceed the call price. - **Negative Convexity**: Callable bonds exhibit negative convexity at lower interest rates - their price appreciation is limited compared to option-free bonds. ### Example: - Option-free bond: Price rises from 100 to 120 when rates fall - Callable bond (with call price of 105): Price rises from 100 to 105 (or slightly less) when rates fall The callable bond's price rises less because investors face the risk of the bond being called away at the call price, limiting upside potential.

Author: LeetQuiz .