Final answer:
The percent change in a bond's price with a longer maturity is greater due to duration and interest rate risk. Longer-term bonds have more future cash flows affected by rate changes, causing greater price fluctuations in response to interest rate shifts.
Step-by-step explanation:
The percent change in a bond's price with a longer maturity is greater than the change in a bond's price with a shorter maturity due to the concept of duration and interest rate risk. When interest rates change, the present value of the bond's future cash flows also changes. The longer the maturity, the more future cash payments are affected by a change in interest rates. Longer-term bonds have more future cash payments that need to be discounted back to the present value. If interest rates rise, the present value of these future payments decreases more significantly than those of shorter-term bonds, leading to a steeper decline in price. Conversely, if interest rates fall, longer-term bonds' prices increase more because there are more future cash payments that have become more valuable.
Consider a bond with no risk that pays $80 per year and is set to be repaid in full at maturity. If prevailing interest rates rise well above the bond’s coupon rate, its price will drop, as investors would demand a discount for the lower relative interest payments. The closer a bond is to its maturity date, the less the price is impacted by interest rate changes because there are fewer future payments to be discounted. Hence, long-term bonds are more sensitive to interest rate changes and exhibit greater price fluctuation.