Duration
A bond’s price sensitivity to rates: in years, the price drop for a one-point rise.
duration 10
10-year zero coupon
about -20%
+1 point, duration 20
Rate sensitivity, in years
Macaulay duration is the average life of a bond’s cash flows, weighted by their present value. Modified duration, derived from it, gives the price sensitivity directly: a modified duration of 7 means the price falls about 7% if rates rise one point.
First-order approximation, without convexity.
What lengthens duration
The longer the maturity and the lower the coupon, the longer the duration. A zero-coupon bond has a duration equal to its maturity. Managers lengthen duration when they expect rates to fall and shorten it when they fear hikes.
Formula
Variation du prix ≈ - duration modifiée x variation du taux
- Modified duration = Macaulay duration / (1 + yield)
- Valid for small moves; convexity corrects for large ones
Worked example
A bond fund with duration 6
- The fund has a modified duration of 6.
- Rates rise 0.75 point.
- Estimated change: -6 x 0.75 = -4.5%.
The fund loses about 4.5%, partly offset by the year’s coupons.
Common mistakes
- Confusing maturity and duration: a 10-year bond with a large coupon has a duration well below 10.
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