In a zero-coupon bond the duration is higher than its maturity.

Question

BlackTom AI · Accepted Answer

Consider the statement posed: 'In a zero-coupon bond the duration is higher than its maturity.'
Option 1: True. This would claim that the bond’s duration exceeds its stated maturity. For a zero-coupon bond, all cash flows occur at a single point in time—the maturity date—so there is no earlier cash flow to average over time. Consequently, the Macaulay duration does not exceed the time to payment; in fact, it equals the time to maturity when considering Macaulay duration, and is typically adjusted downward to a modified duration by dividing by (1 + yield). Therefore, labeling the duration as higher than maturity is inaccurate.
Option 2: False. This aligns with the fundamental property of zero-coupon bonds: there is a single cash flow at maturity, so the effective time-weighted average of cash flows (the duration) cannot exceed the maturity horizon. Since there are no interim payments, the duration corresponds to the maturity (for Macaulay duration) and is not greater than it; the modified duration is even smaller when adjusted for yield. Misconceptions here often stem from confusing duration with other risk measures or from thinking yields alter the timing of cash flows rather than their structure.
In summary, the assertion in Option 1 contradicts the core characteristic of zero-coupon bonds, while Option 2 correctly reflects the duration-maturity relationship for these instruments.

25_2 FIN376 Formative Online Test 5

In a zero-coupon bond the duration is higher than its maturity.

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