Last updated: October 24, 2026. Added exact-repricing convexity table, DV01 and barbell examples, dated case studies (2022 bond bear market, SVB, UK gilts) and an FAQ. Yield data as of May 14, 2026 unless noted.
TL;DR. Duration is the single most useful number for thinking about how much a bond’s price will move when interest rates change. The rule of thumb: for a small yield change, a bond’s price moves by roughly minus duration times the change in yield. That is why a 30-year Treasury can lose 15% of its value when long yields rise one percentage point, while a 2-year note barely flinches. Convexity is the small adjustment that captures the curvature in that relationship.
What duration actually is
The intuition is older than the math. In 1938 the Canadian economist Frederick Macaulay asked a simple question: when you hold a coupon bond, how long do you really wait on average to get your money back? A bond that pays a coupon every six months returns cash to you steadily; a zero-coupon bond returns everything in one lump at maturity. Duration is the present-value-weighted average time to those cash flows. By construction, a zero-coupon bond’s Macaulay duration equals its maturity, and a coupon bond’s duration is always shorter than its maturity.
Why does that average matter for price? Because a bond’s price is just the present value of its future cash flows discounted at the prevailing yield. Push the yield up and every future dollar is worth a little less. The further out in time a cash flow sits, the more punishing the discount, so the bonds with the longest weighted-average wait fall the most. Duration is the unit-free way of summarising that sensitivity. It is measured in years, but it is really an elasticity in disguise.
The formula and the rule of thumb
Macaulay duration is the present-value-weighted average time to cash flow:
DMac = Σ ( ti × PVi ) / Price
Where ti is the time to each cash flow and PVi is its present value. Modified duration is the small adjustment that turns this time-weighted average into a clean price sensitivity:
Dmod = DMac / ( 1 + y / m )
Where y is the nominal yield and m is the number of compounding periods per year (2 for a standard U.S. Treasury). And then the rule that every fixed-income desk lives by:
ΔPrice / Price ≈ − Dmod × Δy
Translation: a bond with modified duration of 8 will lose about 8% of its price if its yield rises by 1 percentage point, and gain about 8% if its yield falls by 1 percentage point. The minus sign is the most important part of all of fixed income: price and yield move in opposite directions.
A worked example with current Treasury yields
The Federal Reserve publishes Treasury constant-maturity yields daily in the H.15 release. As of May 14, 2026, the curve looked like this:
| Treasury | Yield (May 14, 2026) | Approx. Modified Duration* | Price impact of +100 bps |
|---|---|---|---|
| 3-month T-bill | 3.69% | 0.25 | −0.25% |
| 2-year note | 4.00% | 1.90 | −1.9% |
| 5-year note | 4.13% | 4.47 | −4.5% |
| 10-year note | 4.47% | 7.96 | −8.0% |
| 30-year bond | 5.02% | 15.42 | −15.4% |
Notice how non-linear the table is. Tripling maturity from 10 to 30 years does not triple the price impact; it nearly doubles it, because the longer bond’s coupons stretch much further into the future. This is the single most important thing to internalise about duration: it grows with maturity, but it grows slowly, because each additional coupon payment pulls the present-value-weighted average back toward the present.
Picture the price-yield curve
The relationship between a bond’s price and its yield is not a straight line. It curves, and the curvature itself has a name: convexity. The chart below shows the price-yield curve for the 30-year Treasury in our example, with duration as the slope of the tangent line at today’s yield.
Two things to notice. First, the curve slopes down: higher yield, lower price. Duration is the slope. Second, the curve bends. The straight line is duration’s estimate of price at every yield; the real price is the curve. They agree only at the single point where the line is tangent to the curve – today’s yield.
Convexity: the small but important correction
Whenever the line and the curve disagree, the curve sits above the line. That is positive convexity. For an option-free bond it is mathematically guaranteed: if yields fall, your bond gains a little more than duration alone would predict; if yields rise, it loses a little less. The convexity term is the second-order Taylor adjustment to the duration approximation:
ΔPrice / Price ≈ − Dmod × Δy + ½ × C × (Δy)2
Where C is the bond’s convexity. For small yield moves the squared term is negligible. For big moves – the 1.5 percentage-point shifts that have actually happened in the long bond over the past two years – it can be worth more than a percentage point of bond price.
A few rules of thumb on convexity:
- Longer-maturity bonds have more convexity, because the price curve has more room to bend.
- Lower-coupon bonds have more convexity, because the cash flows are more back-loaded. A zero-coupon bond has the most convexity of any plain-vanilla bond of the same maturity.
- Callable bonds can have negative convexity, because the issuer’s option to refinance caps the upside when yields fall. Mortgage-backed securities behave this way – prepayments accelerate exactly when bondholders would otherwise be enjoying rate-fall gains.
Why long bonds are different
The chart below shows the estimated price hit for the same +100 basis-point move across the Treasury curve, using the durations from our table. The non-linearity in maturity is exactly what makes the 30-year bond the most rate-sensitive asset on the curve – and why long-duration funds tend to be the first place that bond-market stress shows up.
This is exactly why the long bond has been the most volatile part of the U.S. Treasury curve. When investors decide the term premium needs to be higher – or when foreign demand for long-dated paper softens – a 30 basis-point move in the 30-year drops about 5% off the price of a long-bond ETF. The same move in the 2-year barely registers.
How much does convexity really add? A worked comparison
The table above uses duration alone, which is a first-order estimate. Here is the same exercise priced exactly, by discounting every cash flow at the new yield, next to the duration-only and duration-plus-convexity estimates. The bonds are par bonds paying semi-annual coupons equal to their May 14, 2026 yields.
| Bond / yield shock | Exact repricing | Duration only | Duration + convexity |
|---|---|---|---|
| 2-year (Dmod 1.90), +100 bps | −1.88% | −1.90% | −1.88% |
| 10-year (Dmod 7.99, C ≈ 76), +100 bps | −7.62% | −7.99% | −7.61% |
| 10-year, −100 bps | +8.39% | +7.99% | +8.38% |
| 30-year (Dmod 15.42, C ≈ 351), +100 bps | −13.81% | −15.42% | −13.66% |
| 30-year, −100 bps | +17.34% | +15.42% | +17.17% |
| 30-year, +200 bps | −24.89% | −30.84% | −23.82% |
| 30-year, −200 bps | +39.28% | +30.84% | +37.86% |
Three takeaways. First, for the 2-year note convexity is a rounding error, so duration alone is fine. Second, for the 30-year bond, a 100 bp rise costs about 13.8%, not the 15.4% that duration alone implies, and a 100 bp fall earns about 17.3%. That asymmetry, losing less than duration predicts and gaining more, is what positive convexity means in practice. Third, at 200 bp the duration-only estimate is off by six percentage points, which is why risk desks never quote a long-bond scenario without the convexity term.
DV01: turning duration into dollars
Traders rarely talk about percentages. They talk about DV01 (dollar value of one basis point): how many dollars a position gains or loses when its yield moves by 0.01 percentage point.
DV01 ≈ Dmod × Market value × 0.0001
A $1,000,000 position in the par 10-year note above has a DV01 of about 7.99 × $1,000,000 × 0.0001 = $799. The same $1,000,000 in the 30-year bond has a DV01 of about $1,542. To hedge the 30-year position with 10-year notes you would need roughly $1,542 / $799 ≈ 1.93 times as much face value in 10s. This is how the “duration-neutral” trades you read about in Treasury market coverage are sized.
Barbell vs. bullet: same duration, different risk
Portfolio duration is the market-value-weighted average of the holdings’ durations. Put 47% in the 2-year note (1.90) and 53% in the 30-year bond (15.42) and the portfolio’s duration is about 0.47 × 1.90 + 0.53 × 15.42 ≈ 9.07, a bit more than a single 10-year note. But the barbell has far more convexity, because convexity rises roughly with the square of maturity. A barbell (short plus long) beats a bullet (everything in the middle) when yields make big parallel moves. It loses when the curve steepens, because the long leg sells off more than the short leg rallies. That is why the curve-shape moves in our guide to bull and bear steepeners and flatteners matter as much as the level of rates.
Duration in the real world: three dated case studies
1. The 2022 bond bear market
The 10-year Treasury yield closed 2021 at 1.52% and ended 2022 at 3.88% (Fed H.15 / FRED DGS10), a rise of about 2.4 percentage points in twelve months as the FOMC raised the fed funds target from near zero to 4.25%–4.50%. The Bloomberg U.S. Aggregate Bond Index, with a duration of roughly six years, returned about −13% for the year, its worst calendar year since the index began in 1976. Long-duration funds did far worse: the iShares 20+ Year Treasury Bond ETF (TLT), with an effective duration in the high teens, lost roughly 31% on a total-return basis. That is the duration rule playing out at scale: the longer the duration, the bigger the drawdown for the same macro shock.
2. Silicon Valley Bank, March 2023
SVB had invested a large share of its deposit inflows from 2020–2021 in long-dated Treasuries and agency mortgage-backed securities. When rates rose, the market value of those securities fell well below their book value. On March 8, 2023 the bank said it had sold about $21 billion of available-for-sale securities at an after-tax loss of about $1.8 billion; depositors ran, and regulators closed the bank on March 10. The Federal Reserve’s own post-mortem, released April 28, 2023, put it bluntly: “Silicon Valley Bank’s failure is a textbook case of mismanagement,” wrote Vice Chair for Supervision Michael S. Barr, citing in particular the bank’s interest rate risk management (Federal Reserve, Review of the Supervision and Regulation of SVB). Duration risk that is ignored on the way in still arrives on the way out. See our explainer on bank capital ratios for how those losses interact with regulatory capital.
3. UK gilts and LDI, September 2022
After the UK government’s September 23, 2022 fiscal statement, long-dated gilt yields jumped by more than a percentage point in a few sessions. Pension funds running leveraged liability-driven investment (LDI) strategies faced collateral calls on their long-duration hedges and were forced to sell gilts, which pushed yields higher still. On September 28, 2022 the Bank of England announced temporary purchases of long-dated gilts, warning that “were dysfunction in this market to continue or worsen, there would be a material risk to UK financial stability” (Bank of England, Sept. 28, 2022). A 30-year bond’s large duration means a 100 bp move is a double-digit price shock, and on leverage that can become a liquidity crisis.
How to check the duration of a bond fund you own
- Look for “effective duration” on the fund fact sheet. Every major bond ETF and mutual fund publishes it, usually monthly. Effective duration accounts for embedded options such as mortgage prepayments and is the number to use.
- Multiply it by a yield move you care about. A fund with an effective duration of 6 will lose roughly 6% if its yields rise 1 percentage point, before coupon income.
- Compare duration to your time horizon. If you will need the money in two years, a fund with a 17-year duration is a rate bet, not a savings vehicle. Short options are covered in our guide to T-bills, T-notes and T-bonds.
- Remember yield helps over time. A rough rule says that if you hold a bond fund for about its duration, the higher reinvestment income from a rate rise roughly offsets the initial price loss.
Where the rule of thumb breaks down
Duration is a linear approximation, so it stops working well in three situations:
- Big yield moves. For a parallel shift of 200 basis points or more, the convexity term in the formula starts to matter. The duration estimate will overstate losses and understate gains.
- Non-parallel curve shifts. Real markets do not move every maturity by the same amount on the same day. If the long end sells off but the short end holds, a barbell portfolio with the same duration as a bullet portfolio can behave very differently.
- Embedded options. Callable bonds, putable bonds, and mortgage-backed securities have cash flows that depend on the path of rates. Use effective duration, which is calculated by repricing the bond under small up and down yield scenarios, not Macaulay or modified duration.
Common mistakes
- Confusing duration with maturity. A 10-year Treasury has a duration of about 8 years, not 10. The two only coincide for a zero-coupon bond held to maturity.
- Adding up durations naively. A portfolio’s duration is the dollar-weighted average of its holdings’ durations – not a simple average.
- Assuming duration captures all risk. Duration is a measure of interest rate risk only. Credit risk, liquidity risk, and convexity risk live in different statistics.
- Forgetting the sign. Duration is always reported as a positive number, but the price-yield relationship is always negative. When yields rise, prices fall.
Frequently asked questions
What is the difference between Macaulay and modified duration?
Macaulay duration is the present-value-weighted average time to a bond’s cash flows, measured in years. Modified duration divides Macaulay duration by (1 + yield per period) and gives the approximate percentage price change for a 1 percentage-point change in yield. For price sensitivity, use modified duration (or effective duration for bonds with embedded options).
Why do long-term bonds fall more than short-term bonds when rates rise?
A long bond’s cash flows sit further in the future, so a higher discount rate cuts their present value more. That shows up as a higher duration: about 15.4 for a 30-year par Treasury at 5% versus about 1.9 for a 2-year note, so a 1-point rise in yields costs the 30-year bond roughly 14% and the 2-year about 2%.
Is convexity good or bad for investors?
For ordinary option-free bonds, positive convexity is good: prices rise more when yields fall than they drop when yields rise by the same amount. Callable bonds and mortgage-backed securities can have negative convexity, which works against the holder because prepayments or calls cap the upside when rates fall.
What does a duration of 7 mean for my bond fund?
It means the fund’s price would fall about 7% if the yields on its holdings rose by 1 percentage point, and rise about 7% if they fell by 1 point, before counting interest income. It is an estimate for small, parallel moves.
Does duration matter if I hold a bond to maturity?
If the issuer pays in full, a bond held to maturity returns its face value regardless of interim price swings, so duration matters less for that single bond. It still matters for opportunity cost, for funds (which have no single maturity), and for anyone who might need to sell early, as SVB’s 2023 failure showed.
What is DV01?
DV01 is the dollar value of a one-basis-point (0.01%) change in yield. It equals roughly modified duration times market value times 0.0001. A $1 million 10-year Treasury position has a DV01 of about $800.
Related ECMSource guides
- The 4 Yield Curve Shifts — why barbells and bullets behave differently
- Fed Funds vs. the 10-Year Treasury — why long yields can rise even when the Fed cuts
- T-Bills vs T-Notes vs T-Bonds — the instruments behind every duration number
- CPI vs Core CPI vs PCE — the inflation data that moves long yields
- High-Yield Bonds vs Leveraged Loans — floating-rate loans have near-zero duration
- How the Fed Sets Interest Rates — the short end of the curve
What to learn next
Once duration and convexity click, the rest of fixed income gets much easier. Useful follow-ons: the difference between nominal and real yields (look at TIPS yields on FRED), how the shape of the yield curve compresses or expands duration risk across maturities, and the role of credit spreads in fixed-income returns. For the practitioner’s view of how callable mortgages get their negative convexity, the SIFMA primer on agency MBS is the standard reference.
Sources
- Federal Reserve, H.15 Selected Interest Rates – Treasury constant maturity yields as of May 14, 2026.
- Federal Reserve Bank of St. Louis (FRED), 30-Year Treasury Constant Maturity Rate (DGS30) and 10-Year Treasury Constant Maturity Rate (DGS10).
- CFA Institute, Introduction to Fixed Income Valuation – duration, convexity, and price-yield relationships.
- Federal Reserve, Review of the Federal Reserve’s Supervision and Regulation of Silicon Valley Bank (April 28, 2023).
- Bank of England, Bank of England announces gilt market operation (Sept. 28, 2022).
- SEC Office of Investor Education and Advocacy, Investor Bulletins on bond market basics and interest rate risk.
- U.S. Department of the Treasury, Daily Treasury Yield Curve Rates.
Disclosure: It is for informational purposes only and is not investment advice.