Lesson 4 of 5 · 11 min
Duration of zero-coupon, perpetual and floating-rate bonds
A zero's Macaulay duration equals its maturity, a perpetual's is (1 + r)/r however long it lives, and a floater's is only the fraction of a period left until its next reset.
In short
- Zero-coupon bond: one cash flow with weight 1, so MacDur = time to maturity and ModDur = maturity ÷ (1 + r).
- Perpetual bond: MacDur = (1 + r)/r, a finite number even though the bond never matures.
- Floating-rate note: MacDur = (T − t)/T, the fraction of the current coupon period still to run.
- Floaters have very low duration, so investors use them to cut a portfolio's duration.
- A coupon bond's MacDur is always below that of a zero with the same maturity.
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