Duration estimates how much a bond’s price moves when yields change a little. Convexity describes the curve in that price-yield relationship. For large rate moves, a straight duration line understates how much an option-free bond’s price rises when yields fall—and understates how much the price falls less (or rises less) depending on the shape—because actual prices bend. Consumer takeaway: the “duration × rate change” rule of thumb gets less accurate as the rate shock gets bigger. Duration primer: Bond duration basics. Ranking quotes: Yield to maturity basics.
Duration line vs curved price path
| Idea | What it assumes | Where it breaks down |
|---|---|---|
| Modified / effective duration | Small, parallel yield shift; local slope | Large moves (hundreds of bp); big curve twists |
| Convexity adjustment | Adds a second-order term for curvature | Still a model; credit spreads and liquidity matter too |
| Callable bonds | Effective duration embeds optionality | Negative convexity zones when calls matter—see Callable bond risks |
For many plain Treasuries and high-grade option-free corporates, positive convexity means prices tend to rise more than duration predicts when yields drop, and fall less than a naive duration line when yields rise (all else equal). Mortgage-backed and callable structures can show negative convexity in some rate regions—homeowners refinance when rates fall, capping price upside.
Where convexity shows up for fund investors
On Vanguard, Fidelity, Schwab, or iShares bond fund factsheets you may see duration but not a full convexity number. Still, convexity is why:
- A sharp Federal Reserve hiking cycle can produce NAV losses that duration roughly flags—but the path is not perfectly linear.
- Long Treasuries can rally harder than a one-line duration estimate after a large yield drop.
- Callable agency or corporate funds may lag in bull-rate markets when issuers call bonds—pair with Callable bond risks.
Fund vs ladder context: Bond funds vs bond ladders. Premium and discount accounting on individual bonds: Bond premium amortization and Bond discount accretion.
Worked example: duration says −6%, markets move more
Sam holds an intermediate Treasury ETF with effective duration ≈ 6. A textbook 1 percentage-point parallel yield rise suggests about a 6% price drop before coupons. Yields actually jump 1.5 points in a stress month. A pure duration scale says ~9% down. Positive convexity on option-free Treasuries means the mark-to-market loss is often somewhat less severe than that straight-line 9% (illustrative—not a promise). If Sam instead held a callable corporate fund in a negative-convexity pocket, a large yield drop might deliver less price gain than duration implied because issuers call or refinance. Sam uses duration for sizing, then reads prospectus language on callables and mortgages instead of treating the ×Δy shortcut as exact.
Practical habits (no spreadsheet required)
- Treat duration as a steering wheel, not a GPS coordinate for huge shocks.
- Prefer factsheet effective duration for funds with embedded options; ask why it differs from average maturity.
- Separate rate risk (duration/convexity) from credit risk (defaults, spreads).
- For individual premium bonds, remember tax amortization rules are separate from market convexity (Bond premium amortization).
- When comparing YTMs across bonds with different coupons and calls, start with Yield to maturity basics and call features—not convexity trivia alone.
Checklist
- Know your bond fund’s effective duration before a hike or cut cycle.
- Expect the duration × Δy shortcut to drift for large moves—that drift is convexity territory.
- Read whether holdings are heavy in callables or MBS (negative convexity risk).
- Do not confuse convexity with credit spreads or liquidity discounts.
- Rebalance from an asset allocation plan, not from one month’s NAV scare.
- Verify figures on the fund factsheet and prospectus—not social-media “duration calculators.”
Educational only. Not investment advice. Duration and convexity models omit spreads, fees, and taxes; fund factsheets and prospectuses control. Past rate moves do not predict future returns.