Which of the following statements is false? A. Bonds with shorter maturities, all else being equal, have higher durations. B. A zero coupon bond with a longer maturity is more sensitive to changes in the interest rate than a shorter maturity zero coupon bond. C. Bonds with higher coupon rates, all else being equal, have lower durations. D. The higher the convexity of a bond (in absolute terms) the more inaccurate its duration is as a measure of interest rate sensitivity.
Question
Which of the following statements is false?
A. Bonds with shorter maturities, all else being equal, have higher durations.
B. A zero coupon bond with a longer maturity is more sensitive to changes in the interest rate than a shorter maturity zero coupon bond.
C. Bonds with higher coupon rates, all else being equal, have lower durations.
D. The higher the convexity of a bond (in absolute terms) the more inaccurate its duration is as a measure of interest rate sensitivity.
Solution
A. 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.
B. 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 coupons and their entire value comes from the difference between purchase price and face value. Therefore, they are more sensitive to interest rate changes, and this sensitivity increases with maturity.
C. 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 flows are received earlier, reducing the bond's sensitivity to interest rate changes and thus its duration.
D. 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 of the price-yield relationship of a bond. When convexity is high, the price-yield relationship is more curved and thus changes in yield have a non-linear effect on price, making duration (which assumes a linear relationship) a less accurate measure of interest rate sensitivity.
So, the answer is A. Bonds with shorter maturities, all else being equal, have higher durations.
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