Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Modified duration approximates how much a bond's price moves for a given change in yield, and it's a linear approximation of something that actually curves. It stays accurate enough for a small rate move, and grows increasingly imprecise as the assumed yield change gets larger, which is exactly the gap convexity exists to correct.
Before you rely on it
What to check
Use duration for a quick, small-move estimate, and pair it with convexity whenever the yield-change scenario being modeled gets larger.
The common error
Where people go wrong with bond duration calculator
Applying modified duration to a large assumed rate change and expecting a precise price answer. The approximation holds well for small moves and drifts further from the bond's actual price behavior as the move gets bigger.
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
Face value, coupon rate, yield to maturity, years to maturity and payments per year define the bond. Duration is a weighted average time to receive the bond's cash flows, and modified duration converts it to price sensitivity. Take the yield from the bond's current quote, and use the coupon frequency of the actual bond. Longer maturities and lower coupons produce longer durations.
When the result stops applying
Duration is a linear approximation and is accurate only for small yield moves: for larger changes convexity matters. It assumes parallel shifts of the yield curve and no change in the cash flows, so callable bonds and mortgage securities behave differently. It measures interest-rate risk, not credit risk. Duration also assumes the yield curve moves in parallel, so a bond fund holding different maturities can behave differently from its average duration suggests.
Check the effective duration figure that fund companies publish, and remember that a longer duration is a bet on falling rates, not a safer or riskier bond in itself.
What to compare it with
Refine the estimate for larger moves on the bond convexity calculator, and see the dollar effect on the DV01 page. The bond portfolio duration calculator combines several bonds, and the bond price page shows the price at each yield. Compare with the time horizon of your goal.
People also ask
Frequently asked questions
What does a duration of 7.67 mean?
The bond's price should fall about 7.67% if yields rise by 1 percentage point, and rise by about the same if yields fall by 1 point.
What is DV01 in bonds?
The dollar value of a basis point: how much the bond's price changes for a one basis point, or 0.01%, change in yield.
Which bonds have the longest duration?
Long maturity, low coupon and low yield bonds, since more of their value comes far in the future and is more sensitive to rates.