Yield-Based Bond Duration Measures and Properties

How to turn a bond's cash flows into one number for its interest rate risk: Macaulay and modified duration, the approximate (price-based) modified duration, money duration and the PVBP, the special cases of zero-coupon, perpetual and floating-rate bonds, and how maturity, coupon and yield push duration up or down.

1. 1. From Macaulay duration to modified durationModified duration is Macaulay duration divided by one plus the yield per period, and it tells you roughly what percentage of its full price a bond loses or gains when its yield moves.Video · 7 minFree14 min
2. 2. Approximate modified durationReprice the bond a few basis points above and below its yield, and the price difference divided by twice the yield change and the starting price gives an accurate estimate of modified duration.Video · 6 min12 min
3. 3. Money duration and the price value of a basis pointMoney duration turns modified duration into a currency amount for a whole position, and the PVBP gives the price change for a single basis point.Video · 7 min12 min
4. 4. Integrated cases: duration of a bond bought mid-periodWhen 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.16 min
5. 5. Duration of zero-coupon, perpetual and floating-rate bondsA 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.11 min
6. 6. How maturity, coupon and yield drive durationAll else equal, a longer maturity, a lower coupon or a lower yield means a higher duration and more interest rate risk, with one curious exception for long deep-discount bonds.13 min