9.25 “Dollar Duration” and Modified Duration/Price Sensitivity
Definition:
Dollar Duration can be used to calculate the amount by which a security’s (or portfolio’s) price will change for a given change in yield. Further, the percentage change in a bond’s price is proportional to its modified duration (“D” here), given a change in YTM.
- Two different bonds that have the same modified duration will exhibit the same price sensitivity.
- Dollar Duration is a linear estimate of price change.
Let’s see how Dollar Duration operates mathematically.
| Approximate Dollar Price Change = (Initial Price) ( – D) (Yield Change) |
| Where “Dollar Duration” = (Initial Price) ( – D) |
- You must note that there is a minus sign attached to D, Duration. This is because price and yield are inverse.
Given:
D = 8.05 (That’s Mod. D here!)
Initial Price = 90.5
Yield changes by ± 50 b.p.s (“beeps”)
Solution:
(90.5) (-8.05) (± 0.0050) = ± 3.64 (that’s plus OR minus)
If yield goes up by 50 b.p.s, the bond’s price = 90.5 – 3.64 = 86.86
If yield goes down by 50 b.p.s, the bond’s price = 90.5 + 3.64 = 94.14
For a one b.p. move:
(90.5) (-8.05) (± 0.0001) = ± 0.0728
Some refer to this as the “dollar duration of a basis point,” similar to the “DV–01” idea. Dollar duration can be used to estimate price in a different rate environment.
