Transparent method
The formula
Worked example
Example inputs
How to interpret the result
DV01 translates an abstract duration figure into a concrete dollar amount, what a single basis point of yield movement is actually worth on a specific position, which is the number that matters when sizing a hedge or comparing risk across bonds of different sizes and durations that would otherwise be hard to compare directly.
Before you rely on it
What to check
Confirm the position size used in the calculation matches your actual holding, since DV01 scales directly with position size in a way that a percentage-based duration figure does not show on its own.
The common error
Where people go wrong with DV01 calculator
Comparing raw duration figures across bonds of very different sizes and calling the larger-duration one the greater dollar risk. DV01, not duration alone, accounts for position size and gives an actual dollar comparison.
Sensitivity evidence
How yield to maturity changes the modified duration
| Yield to maturity | Modified duration | DV01 per bond |
|---|---|---|
| 4.0% | 7.9 years | $0.86 |
| 5.0% | 7.8 years | $0.78 |
| 6.0%worked example | 7.7 years | $0.71 |
| 7.0% | 7.5 years | $0.65 |
| 8.0% | 7.4 years | $0.59 |
Every input, tested
Which input moves the modified duration most
| Input | Tested from | To | Modified duration at each end | Swing |
|---|---|---|---|---|
| Years to maturity | 7.0 years | 13.0 years | 5.8 years to 9.3 years | 3.5 years (45%) |
| Annual coupon rate | 4.0% | 6.0% | 7.9 years to 7.4 years | 0.5 years (6.4%) |
| Yield to maturity | 5.0% | 7.0% | 7.8 years to 7.5 years | 0.3 years (3.4%) |
| Payments per year | 1 | 3 | 7.6 years to 7.7 years | 0.1 years (1.7%) |
| Face value | $900 | $1,100 | 7.7 years to 7.7 years | none |
Two variables at once
Modified duration by yield to maturity and annual coupon rate
| Yield to maturity \ Annual coupon rate | 3.0% | 5.0% | 7.0% |
|---|---|---|---|
| 4.0% | 8.5 years | 7.9 years | 7.5 years |
| 5.0% | 8.4 years | 7.8 years | 7.4 years |
| 6.0% | 8.2 years | 7.7 years | 7.2 years |
| 7.0% | 8.1 years | 7.5 years | 7.1 years |
| 8.0% | 8.0 years | 7.4 years | 7.0 years |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Face value | $1,000 |
| Annual coupon rate | 5.0% |
| Yield to maturity | 6.0% |
| Years to maturity | 10.0 years |
| Payments per year | 2 |
| Modified duration | 7.7 years |
| DV01 per bond | $0.71 |
Where the inputs come from
Enter the bond's face value, coupon rate, yield to maturity, years to maturity and payment frequency. DV01, the dollar value of one basis point, is derived from modified duration and the bond price. Take the yield from a current quote and use the face amount you hold: DV01 scales with the size of the position, so multiply by the number of bonds. Use the same yield basis as the market convention.
When the result stops applying
DV01 is a first-order measure: it stays accurate only for small yield changes and changes as yields and time pass. It does not include convexity, credit spread changes or changes in the shape of the yield curve. Bonds with embedded options have unstable DV01. It is the same for a rise and a fall only approximately.
What to compare it with
See the duration behind it on the bond duration calculator, and the larger-move correction on the convexity page. The bond portfolio duration calculator scales it up to a portfolio. The bond price calculator shows exact prices at different yields.
People also ask
Frequently asked questions
What is a basis point?
One hundredth of a percentage point, 0.01%. A move from 5.00% to 5.25% is 25 basis points.
How do I scale DV01 to my position?
Multiply by the number of $1,000 face value bonds you hold, or by the total face amount divided by 1,000.
Why is DV01 used for hedging?
It gives the dollar exposure to a small yield change, so you can offset it with an opposite position that has the same DV01.