This guide explains bond convexity in plain language, shows the math with two worked bonds, and then checks it against live data from three large bond ETFs captured on 18 October 2026. You will see why two funds with almost the same duration can behave very differently when rates swing, and how to use that knowledge before you buy.
Here is the road map: what convexity is, why it matters, a four-step framework for using it, real fund examples, the mistakes that trip up experienced investors, and a short FAQ.
AGG, a broad bond index fund: duration 5.70 years, convexity 0.51. Source: iShares, 18 October 2026.
What Is Bond Convexity?
Bond prices and yields move in opposite directions. Duration tells you how sensitive a price is to a small change in yield. Convexity tells you how that sensitivity itself changes as yields move. In other words, duration is the slope of the price curve at one point, and convexity is how much the curve bends.
A bond with positive convexity has a curve that bends upward. When yields fall, the price rises by more than duration predicts. When yields rise, the price falls by less than duration predicts. You gain more than you lose for the same size of move, which is why investors generally like convexity and are willing to give up a little yield to own it.
The standard estimate combines both measures: percentage price change is roughly negative duration times the yield change, plus one half times convexity times the yield change squared. The second term is small for tiny moves and grows quickly because the yield change is squared.
Negative convexity is the opposite case. The price curve flattens or bends the wrong way, so gains are capped when yields fall while losses keep growing when yields rise. Callable bonds and mortgage-backed securities are the usual suspects, because borrowers refinance or issuers call debt exactly when it would be most valuable to you.
Why Bond Convexity Matters for Your Portfolio
Duration is the number most people check, and it is a fine first filter. The trouble starts when yields move a lot. Over the last few years investors have seen long Treasury funds swing hard, and the loss was never a clean straight-line function of duration.
16.3% is the drop in the iShares 20+ Year Treasury Bond ETF (TLT) net asset value between its 52-week high of $92.05 and its low of $77.08, based on iShares data as of 16 October 2026.
Convexity matters in three practical ways. First, it shows you how much extra price protection a bond gives you when rates spike. Second, it reveals hidden risk in income funds that hold callable or prepayable debt. Third, it helps you compare funds fairly, because two funds can share a duration and still deliver very different outcomes in a rate shock.
If you want a refresher on duration itself, read our guide on how rate hikes hit bond prices. For the bigger picture of what moves yields, see our explainer on yield curve inversion.
How to Use Bond Convexity: A Four-Step Framework
You do not need a spreadsheet to use convexity well. You need a repeatable routine. Here is one.
Step 1: Start with duration
Find the effective duration of the bond or fund. Fund providers publish it on the fund page, usually next to the yield to maturity. Effective duration already accounts for call options, so it is the right version to use for funds that hold callable or mortgage debt.
Step 2: Stress test with a rate shock
Pick a shock, for example yields up 1 percentage point and down 1 percentage point. Multiply duration by the shock for a first-pass estimate. Then ask whether the true outcome is likely to be better or worse than that estimate. For a plain government bond, the answer is better in both directions, because of positive convexity.
Worked example, a 10-year bond with a 4% coupon priced at par (yield 4%): duration is 8.11 and convexity is 80.75 on the standard textbook scale. Compare the straight-line estimate with the true repricing.
The convexity term closes almost the entire gap. Notice the asymmetry: a 2-point fall adds 17.97% but a 2-point rise subtracts only 14.72%. That cushion is convexity at work.
Step 3: Scale up for long maturities
Convexity grows faster than duration as maturity lengthens. Run the same test on a 30-year, 4% coupon bond priced at par. Duration is 17.29 and convexity is 419.91.
44.79% is the true gain on that 30-year bond if yields fall 2 points, versus 34.58% from duration alone. The same convexity that cushions losses also amplifies gains, which is why long bonds feel so dramatic in both directions.
Step 4: Check for negative convexity
Look at the fund's convexity figure and its holdings. A negative or near-zero number in a fund with meaningful duration is a warning that price upside is capped. Mortgage-backed securities funds are the classic case, and the next section shows it with live data.
Real Examples: Three Bond Funds, Three Convexity Profiles
Theory is tidy. Live fund data is better. The table below uses figures published by iShares as of 15 to 16 October 2026 for three widely held funds. A note on scale: fund providers often report convexity on a different scale than the textbook figure used above, so compare funds against each other on the same page rather than against the 80.75 or 419.91 numbers earlier.
TLT portfolio characteristics: effective duration 14.85 years, convexity 3.12. Source: iShares, 18 October 2026.
$47.0 billion in net assets sits in TLT, a fund whose positive convexity is the highest of the three, which is why it can rally hard when yields fall and still hurt when they rise.
The comparison between AGG and MBB is the most instructive. Their durations are nearly identical at 5.70 and 5.75 years, so a duration-only view says they carry the same rate risk. Yet AGG shows positive convexity of 0.51 while MBB sits slightly below zero at -0.03. MBB also pays more yield, at 5.73% versus 5.39%, and that extra yield is partly compensation for the prepayment behavior that flattens its price curve.
MBB portfolio characteristics: duration 5.75 years, convexity -0.03. Source: iShares, 18 October 2026.
Where convexity helps and where it misleads
For context on shorter and safer instruments, our guide to Treasury bills shows why near-zero duration means convexity barely matters there. If inflation is your main worry, see inflation-protected bonds.
Common Mistakes With Bond Convexity
Mistake 1: Treating duration as a precise forecast
Duration is a first-order approximation. The 30-year example shows duration alone overstating a 2-point loss by more than 7 percentage points. For large rate moves, always add the convexity term or reprice the bond directly.
Mistake 2: Assuming more convexity is always free
Convexity has a price. Investors pay for it through lower yield, and two bonds with the same duration will usually offer different yields depending on how convex they are. Check whether the yield you give up is worth the cushion.
Mistake 3: Ignoring the call and prepayment features
A bond that looks safe on a yield screen can behave very differently if the issuer can redeem it early. Use effective duration, not plain maturity, and read the fund's holdings. This is the central lesson of the AGG and MBB comparison.
Mistake 4: Comparing convexity numbers across providers
Providers define and scale convexity differently. A figure of 3.12 on one site and 80 on another does not mean the bonds differ that much. Compare like with like, ideally from the same provider on the same date.
If you are drawing down a portfolio, convexity interacts with timing. Our guide to sequence of returns risk explains why the order of gains and losses matters as much as their size.
Frequently Asked Questions
What is bond convexity in simple terms?
Bond convexity measures how much the relationship between a bond's price and its yield curves. It refines the duration estimate, which assumes a straight line, by capturing the bend that appears when yields move by a large amount.
Is high convexity good or bad?
For a given duration and yield, higher convexity is better, because it means smaller losses when yields rise and larger gains when they fall. In practice you usually pay for it through a lower yield, so the real question is whether the trade is fair.
What is negative convexity and which bonds have it?
Negative convexity means price gains shrink as yields fall, because the bond can be called or prepaid. Callable bonds and mortgage-backed securities are the common examples, and the MBB fund above shows it at roughly -0.03.
How do I calculate convexity for a bond?
Reprice the bond with yields shifted up and down by a small amount, add the two prices, subtract twice the starting price, and divide by the starting price times the shift squared. A spreadsheet handles this in a few cells, and most fund pages publish the result so you can skip the math.
What to Watch Next
Convexity matters most when rates are volatile, so these are the checkpoints worth tracking.
- > Does TLT keep trading near the bottom of its 52-week range of $77.08 to $92.05, or do yields fall and test the upper half?
- > Does the 30-day SEC yield on TLT, currently 5.41%, rise or fall over the next quarter?
- > Does MBB convexity stay near zero or turn clearly negative if mortgage rates drop and prepayments accelerate?
- > Does AGG duration stay near 5.70 years as the index composition shifts?
Key Takeaways
- Duration is a ruler, convexity is the curve. Duration gives a straight-line estimate, and convexity corrects it for large yield moves.
- Positive convexity means you gain more than you lose for the same size of rate move, and longer bonds have far more of it.
- A 30-year, 4% bond gains 44.79% if yields fall 2 points but loses 27.53% if they rise 2 points, so the cushion is real.
- AGG and MBB have almost the same duration but opposite convexity, so duration alone can hide risk.
- Always use effective duration for callable and mortgage debt, and compare convexity figures only within the same provider.
- Fund pages publish duration and convexity, so you can check both in under a minute before you buy.
The next time someone quotes you a duration, remember the ruler and the curve. The ruler is useful, and the curve is where the surprises live.
This article is educational and not personalized financial advice. Bond prices can fall, and you should consider your own circumstances or speak to a licensed adviser before investing.