Assume a bond with a 4% coupon. If interest rates move up, which type of bond would have the greatest sensitivity to the change in interest rates?

The bond with the greatest sensitivity to changes in interest rates is the one with the longest duration, which in this case is the 30-year bond. Longer-term bonds have a higher duration because they have a greater number of future cash flows (coupon payments and the principal repayment) that are sensitive to interest rate fluctuations. When interest rates rise, the present value of those cash flows decreases significantly.

For a 30-year bond, the longer time horizon means that any rise in interest rates will have a more pronounced impact on its price compared to shorter-term bonds. The cash flows of the 10-year and 15-year bonds, while still sensitive, will be discounted over a shorter time frame, thus resulting in a smaller drop in their market prices when interest rates increase. The 1-year bond, being the shortest in duration, will have the least sensitivity to interest rate changes since it matures quickly, meaning its price will not be impacted as much by fluctuations in interest rates.

Therefore, the 30-year bond’s extended timeframe significantly contributes to its higher sensitivity to interest rate changes, leading to a larger decrease in its priced value when rates rise.