Final answer:
The statement is true as bonds with lower coupon rates pay out less interest over time, meaning more of the cash flows are received later on, leading to a longer duration, meaning higher sensitivity to interest rate changes.
Step-by-step explanation:
Bonds are debt securities under which the issuer owes the holders a debt and is obligated to pay them interest (the coupon), and to repay the debt at a later date (the maturity date). When it comes to bonds with the same maturity, risk rating, and face value, but different coupon rates, the bond with the lower coupon rate will generally have a longer duration.
Duration is a measure of the sensitivity of the price of a bond to changes in interest rates and it incorporates the bond’s yield, coupon, final maturity, and call features. A lower coupon rate implies a smaller interest payment, and thus, a larger proportion of the cash flows are received further in the future. This results in greater interest rate risk or higher duration because the investor would have to wait longer to receive the majority of the cash flows that would compensate for the bond's price sensitivity to interest rates.
This means that the statement that a bond with a lower coupon rate will have a longer duration is True.