Archive / Investment Adviser (Level 1) / Investing in Fixed Income Securities

nism-series-xa-macaulay-duration-zero-coupon-bond[ INVESTMENT ADVISER (LEVEL 1) ]

What is the exact Macaulay Duration of a 7-year Zero-Coupon Sovereign Bond?

[ A ]14.0 years (double of maturity).

[ B ]Zero years.

[ C ]3.5 years (half of maturity).

[ D ]Exactly 7.0 years (for any zero-coupon bond, Macaulay Duration equals its maturity exactly).[ CORRECT ]

Takeaway

For any zero-coupon bond, Macaulay Duration exactly equals its time to maturity — here, precisely 7.0 years — because a zero-coupon bond has only one cash flow, occurring at maturity.

Derivation

Macaulay Duration is the weighted-average time until an investor receives a bond's cash flows, with weights based on the present value of each cash flow. A coupon-paying bond has multiple cash flows scattered through its life, so its duration is pulled below maturity by the earlier coupon payments. A zero-coupon bond pays no interim coupons — its entire present value sits in a single cash flow at maturity — so 100% of the weight falls on that one date, making the weighted-average time trivially equal to maturity itself. This special case is tested because it's the cleanest illustration of what duration actually measures, and it anchors the intuition that duration always lies between 0 and maturity for coupon bonds.

Why the others fail

A — 14.0 years (double of maturity).

Duration is a weighted-average time to cash flow and by definition cannot exceed a bond's actual final maturity — 14 years for a 7-year bond is mathematically impossible.

B — Zero years.

Zero duration would mean zero interest-rate sensitivity, but a 7-year zero-coupon bond is highly rate-sensitive since its entire value is a single long-dated discounted cash flow.

C — 3.5 years (half of maturity).

Duration equaling half of maturity is not a general rule for zero-coupon bonds — with only one cash flow at the very end, the weighted-average time is exactly the full maturity, not half of it.