Which of these statements is false?
A) Bond duration is higher for bond’s with longer maturity
B) Bond duration is higher for bonds with higher coupons
C) Bond duration lower for bonds with higher yield to maturity
D) Bond duration is equal to its maturity for zero-coupon bonds
The correct answer and explanation is :
The false statement is:
B) Bond duration is higher for bonds with higher coupons
Explanation (approx. 300 words):
Bond duration is a measure of a bond’s sensitivity to changes in interest rates, often used as a gauge of interest rate risk. It estimates how much the price of a bond will change with a 1% change in interest rates. Several factors affect a bond’s duration, including maturity, coupon rate, and yield to maturity.
Let’s break down the statements:
A) Bond duration is higher for bonds with longer maturity – TRUE
Duration generally increases with maturity because the longer the bond’s life, the more time it takes to recover the investment, making it more sensitive to interest rate changes.
B) Bond duration is higher for bonds with higher coupons – FALSE
Higher coupon payments lead to lower duration, not higher. This is because a bond with higher coupons returns more of the investor’s money earlier through periodic payments, reducing the bond’s sensitivity to interest rate changes. More cash flow earlier means less time for interest rate changes to impact the bond’s value.
C) Bond duration is lower for bonds with higher yield to maturity – TRUE
When yield to maturity increases, future cash flows are discounted more heavily, meaning their present value is lower. This effectively shortens the weighted average time to receive those cash flows, which lowers duration.
D) Bond duration is equal to its maturity for zero-coupon bonds – TRUE
Zero-coupon bonds do not pay periodic interest. They only pay a lump sum at maturity. Hence, all the bond’s value is received at one point in time—the maturity date—making duration equal to maturity.
Summary:
- Duration rises with maturity.
- Duration falls with higher coupons.
- Duration falls with higher yield.
- For zero-coupon bonds, duration equals maturity.
Therefore, the false statement is B.
