Lesson 4 of 6 · All lessons in this module
- From Macaulay duration to modified durationVideo lesson
- Approximate modified durationVideo lesson
- Money duration and the price value of a basis pointVideo lesson
- Integrated cases: duration of a bond bought mid-period
- Duration of zero-coupon, perpetual and floating-rate bonds
- How maturity, coupon and yield drive duration
Lesson 4 of 6 · 16 min
Integrated cases: duration of a bond bought mid-period
When settlement falls between coupon dates, every duration statistic is built on the full price: the cash-flow weights are unchanged, each time to receipt is shortened by t/T, and money duration and PVBP follow from the full market value of the position.
In short
- Start with t/T (days since the last coupon over days in the period) and the full price = PV at the last coupon date × (1 + r)^(t/T). The flat price is full price minus accrued interest.
- Weights are each cash flow's PV divided by the full price; times are measured from settlement, so each is shortened by t/T.
- Shortcut: Macaulay duration at settlement = Macaulay duration at the last coupon date − t/T (in periods). Annualise, then divide by (1 + r) per period for modified duration.
- Money duration = AnnModDur × full market value of the position; PVBP = money duration × 0.0001.
- The linear estimate understates the price after a fall in yield and overstates the loss after a rise: compare it with a full repricing.
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