Which of the following statements is false?A.The higher the convexity of a bond (in absolute terms) the more inaccurate its duration is as a measure of interest rate sensitivity. B.Bonds with shorter maturities, all else being equal, have higher durations. C.A zero coupon bond with a longer maturity is more sensitive to changes in the interest rate than a shorter maturity zero coupon bond. D.Bonds with higher coupon rates, all else being equal, have lower durations.
Question
Which of the following statements is false?A.The higher the convexity of a bond (in absolute terms) the more inaccurate its duration is as a measure of interest rate sensitivity. B.Bonds with shorter maturities, all else being equal, have higher durations. C.A zero coupon bond with a longer maturity is more sensitive to changes in the interest rate than a shorter maturity zero coupon bond. D.Bonds with higher coupon rates, all else being equal, have lower durations.
Solution
A. The higher the convexity of a bond (in absolute terms) the more inaccurate its duration is as a measure of interest rate sensitivity: This statement is true. Convexity is a measure of the curvature in the relationship between bond prices and bond yields. Higher convexity means that the bond's price is more sensitive to changes in interest rates, which makes duration (a linear measure of interest rate sensitivity) less accurate.
B. Bonds with shorter maturities, all else being equal, have higher durations: This statement is false. Duration is a measure of a bond's sensitivity to changes in interest rates. All else being equal, bonds with longer maturities have higher durations because they are more sensitive to changes in interest rates.
C. A zero coupon bond with a longer maturity is more sensitive to changes in the interest rate than a shorter maturity zero coupon bond: This statement is true. Zero coupon bonds pay no interest until maturity, so their price is entirely dependent on the discount rate (interest rate). Therefore, they are more sensitive to changes in interest rates, and this sensitivity increases with the bond's maturity.
D. Bonds with higher coupon rates, all else being equal, have lower durations: This statement is true. Higher coupon rates mean that a larger portion of the bond's total cash flow is received earlier, which reduces the bond's duration (sensitivity to changes in interest rates).
Therefore, the answer is B. Bonds with shorter maturities, all else being equal, have higher durations. This statement is false.
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