# Duration

Source: https://www.yieldcurve.pro/duration

Compute the key risk metrics for any US Treasury bond: **[modified
duration](https://www.yieldcurve.pro/learn/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; used to size hedges
* **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:

* **Macaulay Duration** = Σ(t × PV(CF_t)) / Price, converted to years
* **Modified Duration** = Macaulay Duration / (1 + y/2)
* **DV01** = Modified Duration × Price / 10,000
* **Convexity** = Σ(t(t+1) × PV(CF_t)) / (Price × (1+y)²), converted to annual
* **ΔP** ≈ −ModDur × ΔY × P + ½ × Convexity × (ΔY)² × P

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