TL;DR. Duration tells you, in years, how sensitive a bond’s price is to a change in yield. As a quick rule of thumb, a bond with a modified duration of 8 will fall about 8% in price if yields rise 1 percentage point. Convexity is the correction term: it captures the fact that the price-yield relationship is curved, not straight, so duration alone overstates losses when yields rise and understates gains when yields fall.
Why duration exists
Bond prices and yields move in opposite directions. When the U.S. Treasury auctions a new 10-year note at a higher yield, the price of an older 10-year note with a lower coupon has to fall — otherwise no one would buy the older bond instead of the new one. The Securities and Exchange Commission summarizes this in its investor primer on bonds: rising rates make newly issued bonds more attractive, pushing the prices of existing bonds down.
But how much do existing bond prices move? That depends on the bond’s cash flows — specifically, when those cash flows arrive. A 30-year zero-coupon bond is far more exposed to a yield change than a 2-year coupon bond, because almost all of its value sits in a single payment three decades away. Duration is the single number that compresses that exposure into one figure.
The two flavors of duration
Macaulay duration is the weighted average time, in years, until you receive a bond’s cash flows, where each weight is the present value of that cash flow divided by the bond’s price. It is the answer to the question, “On average, when is my money coming back?”
Modified duration is the percentage price change a bond will experience for a 1 percentage point change in yield. The conversion is simple:
Modified Duration = Macaulay Duration / (1 + y/k)
where y is the bond’s yield and k is the number of coupon periods per year. For investment-grade bonds yielding a few percent, the two numbers are usually within half a year of each other, which is why traders often speak of “duration” without specifying which one.
A worked example with real numbers
Imagine a 10-year U.S. Treasury note with a 4.5% coupon, paying semiannually, trading at par (a price of 100). With a yield-to-maturity of 4.5%, this bond has a Macaulay duration of about 8.18 years and a modified duration of about 8.00 years.
Now suppose yields jump by 50 basis points — from 4.5% to 5.0%. Modified duration predicts the price drop:
ΔP/P ≈ − Modified Duration × Δy = −8.00 × 0.005 = −4.00%
So the bond should fall from 100 to about 96.00. The actual full-precision price at a 5% yield is closer to 96.11 — eleven cents better than duration alone predicts. That eleven-cent gap is convexity at work.
Where duration fails: convexity
Duration draws a straight line tangent to the price-yield curve at today’s yield. The real curve bends. For a standard option-free bond, the price-yield curve is convex — it falls more slowly than the tangent line as yields rise, and rises faster than the tangent line as yields fall.
The second-order correction is convexity. The combined estimate is:
ΔP/P ≈ − Modified Duration × Δy + ½ × Convexity × (Δy)2
For the par 10-year note above, convexity is roughly 75. Plugging in:
ΔP/P ≈ −8.00 × 0.005 + ½ × 75 × (0.005)2 = −4.00% + 0.094% = −3.91%
That −3.91% matches the actual price move within a rounding error. Convexity always helps the bondholder: it reduces predicted losses when yields rise and amplifies predicted gains when yields fall, which is why long-duration bonds with high convexity are sometimes prized as a portfolio hedge.
Duration grows with maturity — but not linearly
For Treasury bonds, modified duration rises sharply with maturity but slows down at the long end. A 2-year note has a duration of about 1.9; a 10-year is about 8.7; a 30-year is closer to 18. Most of the curvature in the duration-maturity relationship comes from the fact that longer bonds discount their distant cash flows more heavily, so the marginal contribution of an extra year of maturity shrinks.
Duration snapshot: where common bonds sit today
Duration is not just a Treasury concept — every fixed-income product has it. Below is a snapshot of typical modified durations across major bond categories. The figures are approximations for the asset class as a whole; individual funds and indices will vary.
| Bond category | Typical modified duration (yrs) | Typical yield (%) |
|---|---|---|
| 3-month T-bill | ~0.25 | ~4.3 |
| 2-year U.S. Treasury | ~1.9 | ~4.0 |
| 10-year U.S. Treasury | ~8.7 | ~4.5 |
| 30-year U.S. Treasury | ~18.4 | ~4.7 |
| Bloomberg U.S. Aggregate (broad IG index) | ~6.0 | ~4.8 |
| Investment-grade corporates | ~7.0 | ~5.3 |
| U.S. high-yield bonds | ~4.0 | ~7.5 |
| TIPS (real duration) | ~6.5 | ~2.1 (real) |
Common mistakes
Confusing maturity with duration
A 10-year Treasury has a duration of about 8.7 years, not 10. The gap exists because intermediate coupon payments shorten the average time to cash. For a zero-coupon bond, however, duration equals maturity exactly. Many investors equate “long-dated” with “high duration,” which is roughly right within a single category but misleading across categories: a 10-year zero has much higher duration than a 10-year coupon bond.
Forgetting that duration changes
Modified duration is a snapshot. As yields move, duration moves with them, generally falling as yields rise. That is why convexity matters: a single-number duration hedge that worked yesterday will be slightly off today even with no calendar passing.
Applying duration outside its valid range
The first-and-second-order formula is a Taylor expansion. It is excellent for small yield moves — say, under 100 basis points. For large moves, especially in callable bonds and mortgages where embedded options reshape cash flows, the price curve changes shape and you need an option-adjusted framework rather than plain modified duration.
Treating high-yield bonds like Treasuries
For high-yield (junk) bonds, spread changes often dominate Treasury-yield changes. A high-yield bond’s price reacts to credit risk repricing, not just to risk-free rates, so duration-based estimates miss the bigger driver during stress.
Related concepts and what to learn next
- Key-rate duration. Instead of a single duration number, decompose price sensitivity to specific points on the yield curve (2y, 5y, 10y, 30y). Useful for portfolios that mix maturities.
- Spread duration. Sensitivity to changes in credit spread rather than the risk-free yield. The right tool for corporate and high-yield positions.
- Option-adjusted duration (OAD). Adjusts modified duration for embedded options in callable bonds and mortgages. Bloomberg, the index providers, and most analytics platforms publish OAD as the default.
- Effective duration. Computed by repricing the bond under small parallel shifts in the yield curve. Standard for bonds with embedded options.
- Yield curve mechanics. If you want to understand why yields are moving in the first place, the next step is the yield curve itself.
Sources
- U.S. Securities and Exchange Commission — Bonds (Investor.gov)
- Federal Reserve Statistical Release H.15 — Selected Interest Rates
- U.S. TreasuryDirect — Treasury Notes (cash-flow structure)
- FRED — 10-Year Treasury Constant Maturity Rate (DGS10)
- SEC Office of Investor Education — Interest Rate Risk
Disclosure: This article was produced with AI assistance and reviewed before publication. It is for informational purposes only and is not investment advice.