Bond duration is a measure, quoted in years, of how strongly a bond's price responds when interest rates change. The original version, Macaulay duration, is the average time you wait to receive the bond's cash, with each coupon and the final repayment weighted by its present value. Modified duration turns that average into a working rule: for every 1 percentage point that yields rise, the price falls by roughly the duration in percent, and it gains about as much when yields fall. Maturity says when the last payment arrives; duration says how far the value can swing before then. The idea applies to anything that pays fixed amounts on fixed dates, from Treasury bills to corporate bonds and the funds that hold them. For how the different Treasury securities fit together, start at the US Treasuries hub.
How is Macaulay duration calculated?
Discount every payment at the bond's yield, multiply each present value by its payment date in years, add the results and divide by the bond's price.
Here t is the time in years until each payment. Present values use the yield per period, which for a Treasury is half the annual yield, because notes and bonds pay coupons every six months. The present values add up to the price, so each one is a weight, and the result is an average payment date. That date sits close to maturity on short bonds because the face value dwarfs any single coupon.
Worked example: Macaulay duration of a $1,000 2-year note at 4.56%
A new 2-year Treasury note bought at par on October 30, 2026, when the 2-year par yield was 4.56%, pays $22.80 every six months and $1,000 at the end. Each payment is discounted at 2.28% per half-year.
| Paid after | Cash flow | Present value | Share of price | Years × share |
|---|---|---|---|---|
| 0.5 year | $22.80 | $22.29 | 2.23% | 0.011 |
| 1 year | $22.80 | $21.79 | 2.18% | 0.022 |
| 1.5 years | $22.80 | $21.31 | 2.13% | 0.032 |
| 2 years | $1,022.80 | $934.60 | 93.46% | 1.869 |
| Total | $1,091.20 | $1,000.00 | 100% | 1.934 |
- Macaulay duration: 1.934 years, just under the 2-year maturity, because 6.54% of the value arrives early as coupons.
- Modified duration: 1.934 ÷ 1.0228 = 1.89, so a 1-point rise in yield would cut the price by about 1.89%.
What is modified duration, and how does it estimate price changes?
Modified duration is Macaulay duration divided by one plus the yield per period, and multiplying it by a yield change gives the approximate percentage price change.
The first term is the straight-line estimate. FINRA's investor guide states it the same way: a bond with a duration of 10 should lose about 10% if rates rise 1 point and gain about 10% if they fall 1 point. The second term corrects for convexity, the curve in the price-yield relationship; it is tiny for small moves and short bonds. Yield changes go in as decimals, so 1 point is 0.01. Why bond prices fall when rates rise shows how large the correction becomes on 2-point moves and long bonds.
Dealers often quote the same sensitivity in dollars as DV01, the dollar value of a 0.01-point move, which is one basis point:
Worked example: A $10,000 10-year note when yields rise 1 point
On October 30, 2026 the 10-year par yield was 4.94%, which means a 10-year note with a 4.94% coupon would have been priced at exactly par that day. The examples use that note, which pays $247 every six months on $10,000. A real new note's coupon is set in steps of one-eighth of a point, so one auctioned at that yield would carry 4.875% and sell slightly below par, with almost the same duration.
- Macaulay duration: 8.01 years. Modified duration: 8.01 ÷ 1.0247 = 7.82.
- Duration estimate for a 1-point rise: −7.82 × 0.01 = −7.82%, a loss of $781.67.
- Convexity of 73.93 adds back ½ × 73.93 × 0.01² = +0.37%, or $36.97.
- Estimate with convexity: −7.45%, a loss of $744.71.
- Actual price at a 5.94% yield: $9,254.06, a loss of $745.94, or −7.46%.
- DV01: 7.82 × $10,000 × 0.0001 = about $7.82 for each basis point.
How does duration differ for bills, notes and long bonds?
A bill's duration equals its time to maturity, at most one year; a coupon bond's duration falls further below its maturity the longer the bond runs.
A bill pays nothing until it matures, so all of its value sits on one date and its Macaulay duration is simply its term. The same holds for a zero-coupon STRIPS of any length, which is why Treasury STRIPS swing far more than coupon bonds with the same maturity. Coupons pull duration forward. The table uses Treasury's par yields for October 30, 2026, with each note and bond priced at par.
| Security | Par yield, Oct 30, 2026 | Macaulay duration, years | Duration as a share of maturity | Modified duration |
|---|---|---|---|---|
| 3-month bill | 4.16% | 0.25 | 100% | 0.25 |
| 6-month bill | 4.25% | 0.50 | 100% | 0.49 |
| 1-year bill | 4.36% | 1.00 | 100% | 0.98 |
| 2-year note | 4.56% | 1.93 | 97% | 1.89 |
| 5-year note | 4.71% | 4.51 | 90% | 4.41 |
| 10-year note | 4.94% | 8.01 | 80% | 7.82 |
| 20-year bond | 5.34% | 12.53 | 63% | 12.20 |
| 30-year bond | 5.31% | 15.32 | 51% | 14.92 |
Read across, a 1-point jump in yields moves a 3-month bill's price by about a quarter of 1%, and a 30-year bond's by roughly 15% before the convexity correction. Short duration does not remove rate risk from bills; it swaps price risk for reinvestment risk, because the cash comes back within months and has to be reinvested at whatever rate then applies. Short-term vs long-term Treasuries weighs that trade. Treasury floating rate notes are a third case: a 2-year maturity whose rate resets weekly, which leaves almost no interest-rate duration. The yields behind these figures update daily on the Treasury yield curve page.
Where do you see duration quoted?
You meet it most often on bond fund and ETF pages, which list effective duration next to average maturity; for single bonds, FINRA suggests asking your brokerage firm.
FINRA points readers to the Bond Holding Statistics, Key Facts or Portfolio Data section of a fund's fact sheet. Effective duration is the version these fund pages report. Instead of applying a formula to fixed cash flows, it reprices the holdings after shifting yields up and down, which also captures bonds whose payments change with rates, such as callable bonds. Three Treasury funds from one issuer show the same pattern as the table above.
| iShares fund, as of October 29, 2026 | Effective duration | Weighted average maturity |
|---|---|---|
| 0-3 Month Treasury Bond ETF (SGOV) | 0.11 years | 0.11 years |
| 7-10 Year Treasury Bond ETF (IEF) | 6.82 years | 8.39 years |
| 20+ Year Treasury Bond ETF (TLT) | 14.90 years | 26.01 years |
The long fund's bonds average 26 years to maturity, yet its price reacts to rates about as much as a single payment due in roughly 15 years would. A fund's duration also stays fairly constant, because it keeps selling aging bonds and buying new ones, whereas a single bond's duration shrinks every year. How that plays out for bill funds against bills held directly is covered in T-bill ETFs vs buying T-bills.
How is duration different from maturity, convexity and DV01?
Maturity is a date, duration is a sensitivity, convexity measures how that sensitivity changes, and DV01 expresses it in dollars per basis point.
| Term | What it measures | Unit | 10-year note at par, $10,000 at 4.94% |
|---|---|---|---|
| Maturity | When the face value is repaid | Years | 10 |
| Macaulay duration | Present-value-weighted average time to the payments | Years | 8.01 |
| Modified duration | Percentage price change per 1-point yield move | Percent per point | 7.82 |
| Effective duration | The same, measured by repricing after yield shifts | Percent per point | 7.83 with 1-point shifts |
| Convexity | How fast duration changes as yields move | Years squared | 73.9 |
| DV01 | Dollar price change per basis point | Dollars | $7.82 |
| Yield to maturity | Annual return if held to the end and coupons are reinvested at the same yield | Percent | 4.94% |
Two pairs get swapped most often. Maturity and duration match only for bills and zero-coupon securities; for every coupon bond, duration is shorter. And yield to maturity is a return, not a risk measure: two notes can share the same yield and still differ in duration if their coupons differ, because a lower coupon rate means a longer duration.
What do people get wrong about duration?
The usual errors are reading duration as a holding period, applying it to large moves without convexity, and assuming it stays fixed.
- Treating it as a payback period. Duration is a sensitivity first. The 20+ year fund above has a duration of 14.90 years, but nothing about its price is protected after 14.90 years, because a fund never matures.
- Using Macaulay duration for price changes. Macaulay duration is a time; modified duration is the price-sensitivity figure. The gap is small at October 2026 yields, 8.01 against 7.82 for the 10-year note, and it widens as yields rise.
- Stretching the rule to big moves. Duration is a straight line laid against a curve. On the 10-year note it missed a 1-point move by $35.73 per $10,000, and the error grows quickly with longer bonds and bigger moves.
- Assuming duration stays put. It shortens as a bond ages: with yields unchanged at 4.94%, the 10-year note's modified duration would be about 7.20 a year later. Rising yields shorten it further and falling yields lengthen it.
- Assuming the whole curve moves together. The rule assumes every yield shifts by the same amount, while short and long yields often move by different amounts for different reasons, as what moves Treasury yields explains.
- Equating low duration with low risk. FINRA warns that a low duration does not make a bond or fund low risk, since credit, inflation and call risk remain. Even for Treasuries, the government stands behind the payments and the face value at maturity, not the market price before then, which is the point of the SEC bulletin; selling Treasuries before maturity shows what that means for a sale.