Final answer:
The duration of a bond with a high coupon rate is generally shorter because higher coupon payments reduce its sensitivity to interest rate changes. Bond prices are always determined by the present value of expected future cash flows, with bond prices and market interest rates having an inverse relationship.
Step-by-step explanation:
All other things equal, a bond's duration is usually shorter when the coupon rate is high. High coupon rates mean more cash is being returned to the bondholder early in the bond's life, which reduces the bond's sensitivity to changes in market interest rates. This is due to the fact that duration, which measures the average time it takes to receive all cash flows from a bond, is heavily influenced by the coupon rate. Meanwhile, if the coupon rate is lower, the duration extends because smaller payments are spread over a longer period. This makes low coupon bonds more sensitive to interest rate changes.
For instance, consider a bond with no risk. It would likely sell for its face value when initially issued, paying the investor periodic coupon payments until maturity. If interest rates rise significantly, this previously issued bond would become less attractive compared to new bonds which offer higher rates. Hence, to entice an investor to buy the older bond, which has a lower interest rate than the current market rate, the price would fall below its face value.
The price of a bond always equals the present value of its expected future cash flows, considering market interest rates and inherent risks. This demonstrates the inverse relationship between bond prices and prevailing interest rates in the market.