How do modified duration and DV01 measure bond risk?
One yield move, two units of price sensitivity, and a callable bond whose horizon changes.
Updated · Reviewed by Juan Otero
The direct answer
Modified duration estimates how much a bond's dirty price changes after a small yield move. Modified duration = Macaulay duration ÷ (1 + semi-annual yield ÷ 2). Multiply it by dirty price and 0.0001 to get DV01 for a one-basis-point move at the stated face amount.
Worked example: América Móvil 6.375% 2035
América Móvil 6.375% 2035 (ISIN US02364WAJ45) is a USD fixed-coupon bullet without a call schedule. Its terms come from the offering documents in the bond catalog. Figures as of Sep 24, 2026, settlement Sep 28, 2026 (T+2), BondTerminal engine; clean price 102.30 per 100 face. The official US Treasury par curve of the pricing date supplies the spread benchmark, while duration comes from discounted contractual cash flows.
| Measure | Value |
|---|---|
| Yield to maturity | 6.02% S.A. |
| Macaulay duration | 6.64 years |
| Modified duration | 6.45 years |
| Dirty price per 100 face | 102.7781 |
| DV01 per 100 face | $0.0663 |
| DV01 per USD 1,000,000 face | $662.87 |
How these numbers were made
Figures as of Sep 24, 2026, settlement Sep 28, 2026, using a closing indicative clean price of 102.30. Bond terms come from offering documents in our catalog. Yields are semi-annual (S.A.) over ACT/365 time. The spread uses that date's official US Treasury par curve at average life. How we calculate →
Educational example, not investment advice.
What is the DV01 formula?
At 6.02% S.A., the weighted timing of this bond's payments is 6.64 years. Divide by the semi-annual compounding factor to get 6.45 years of modified duration. Multiply the dirty price by that duration and one basis point of yield to estimate a 0.0663 price-point change per 100 face. For USD 1,000,000 face, that is about $662.87.
The dollar amount scales with position size. The quote is per 100 face, while the catalog bond has a USD 1,000 face value, so its DV01 is first converted to the chosen face amount. Confusing a 100-point quote with a 1,000-dollar bond overstates or understates the result by a factor of ten.
Does a one-basis-point reprice match DV01?
Repricing the same scheduled cash flows at a yield 1bp higher gives a clean price of 102.2337, down 0.0663 points from 102.30. The DV01 estimate per 100 face is 0.0663 points. They match at the displayed precision; the small unrounded difference is curvature, summarized by convexity (51.34).
Duration is a first-order slope around today's yield. It is most useful for small parallel yield changes. For larger changes, cash-flow discounting curves away from the tangent, so reprice the bond rather than multiplying duration by an arbitrarily large move. A bond's credit spread and Treasury rate can also move separately.
Macaulay versus modified duration
Macaulay duration measures the present-value-weighted time to receive the promised cash flows. Modified duration rescales that time for the yield convention and estimates percentage price sensitivity. They share units of years, but they answer different questions: when cash arrives versus how fast price changes near a given yield.
The denominator depends on compounding. BondTerminal quotes yield on a semi-annual basis so duration, spread and yield use consistent conventions across bonds with different payment frequencies. See the semi-annual versus effective annual guide and yield methodology.
Why does callable-bond duration change?
At the stored quote, LATAM Airlines 7.625% 2031 has a worst-call yield of 7.24% S.A. and 2.43 years of modified duration to that call. Its maturity outcome has 3.54 years. The same bond therefore has different risk horizons depending on which cash-flow outcome leads.
When the price moves enough that maturity becomes the worst outcome, the lead yield and duration switch to maturity. A generic maturity-only calculation would miss that switch. The yield-to-worst guide lists every call candidate; callable-bond methodology specifies when the call leads.