What is modified duration?

Modified duration measures a bond's price sensitivity to interest rate changes. It estimates the percentage change in price for a 1% change in yield. For example, a bond with modified duration of 5.0 would fall approximately 5% if yields rise by 1%.

How is DV01 calculated?

DV01 (dollar value of a basis point) is the dollar change in a bond's price for a 1 basis point (0.01%) change in yield. It equals modified duration multiplied by the bond price divided by 10,000. For a $100 par bond with 5 years of modified duration, DV01 is approximately $0.05.

Convexity measures the curvature in the relationship between bond prices and yields. It captures the second-order price sensitivity that duration misses. Positive convexity means a bond gains more from falling yields than it loses from rising yields by the same amount.

Duration & DV01 Calculator

Compute the key risk metrics for any US Treasury bond: modified duration, Macaulay duration, DV01 (dollar value of a basis point), and convexity. All calculations use semiannual compounding per US Treasury convention.

Instructions

select a Maturity from the dropdown (1 Mo through 30 Yr)
enter a Coupon rate and YTM (yield to maturity) as percentages — defaults are the current par yields
optionally change the Face Value (default $100)
click GO to compute all metrics

Results

Price — the clean price given the coupon rate and YTM
Modified Duration — the percentage price change per 1% yield change; the primary interest rate risk measure
Macaulay Duration — the weighted-average time to receive all cash flows, in years
DV01 — the dollar price change for a 1 basis point move in yield
Convexity — the second-order curvature of the price-yield relationship; higher convexity benefits the bondholder in both directions
ΔP (+100bp) — estimated dollar price change for a 100bp rate increase using the duration + convexity approximation

The chart shows the modified duration profile across all standard US Treasury maturities at current par yields.

Use Cases

quickly estimate how much a bond's price will move for a given rate change
compare DV01 across maturities for hedge ratio construction
understand why longer-maturity bonds have more interest rate risk
verify duration and convexity values from Bloomberg or other systems

Formulas

For a bond with semiannual coupons, where $t$ indexes semiannual periods, $PV(CF_t)$ is the present value of each cash flow discounted at $y/2$, $P$ is the bond price, and $y$ is the yield to maturity as a decimal:

Macaulay Duration

$$D_{mac} = \frac{\sum_t t \cdot PV(CF_t)}{P}$$

$t$ is in semiannual periods; divide by 2 to convert to years.

Modified Duration

$$D_{mod} = \frac{D_{mac}}{1 + y/2}$$

DV01

$$DV01 = \frac{D_{mod} \cdot P}{10{,}000}$$

Convexity

$$C = \frac{\sum_t t(t+1) \cdot PV(CF_t)}{P \cdot (1 + y)^2}$$

Divide by 4 to convert from semiannual to annual units.

Price Approximation

$$\Delta P \approx -D_{mod} \cdot \Delta y \cdot P + \frac{1}{2} \cdot C \cdot (\Delta y)^2 \cdot P$$

Per-tenor pages (e.g. /duration/10-year) show live metrics at current par yields for each standard Treasury maturity.

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Duration