What Is Bond Duration? Price Impact of a 1% Yield Increase
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Bond duration is both a cash-flow timing measure and a practical estimate of interest-rate sensitivity. If a bond has a modified duration of 5, a one-percentage-point rise in its yield implies an approximate 5% price decline. That is a first-order estimate, not a promise: the actual move depends on the bond’s coupon, maturity, convexity, credit spread and any embedded options.
Duration answers two different questions
A bond’s stated maturity tells you when the principal is scheduled to be repaid. It ignores the coupon payments received before that date. Macaulay duration instead takes every coupon and the principal repayment, discounts them to present value and calculates the weighted average time at which the investor receives those cash flows.
That makes duration shorter than maturity for a conventional coupon-paying bond. A zero-coupon bond, which pays no interim coupon, has a Macaulay duration equal to its maturity. A higher coupon generally shortens duration because more cash is returned earlier.
| Measure | What it represents | Best use |
|---|---|---|
| Macaulay duration | Present-value-weighted time to receive all cash flows | Understanding cash-flow timing |
| Modified duration | Macaulay duration adjusted for the bond’s yield and payment frequency | Estimating price sensitivity to a small yield change |
| Effective duration | Sensitivity measured after allowing cash flows to change with rates | Callable bonds and mortgage-backed securities |
How to estimate the price impact of a 1% yield increase
Suppose a bond or bond fund has a modified duration of 5. If its relevant market yield rises from 3% to 4%, the change in yield is 0.01. The estimate is therefore “-5 × 0.01 = -0.05,” or a 5% price decline.
On a $10,000 position, that equals an estimated $500 decline. A 25-basis-point increase would imply about $125, while a 50-basis-point increase would imply about $250. The estimate isolates the rate effect and does not include coupon income, trading costs or changes in credit spreads.
Worked example: 2-, 5- and 10-year bonds
Consider three fixed-rate bonds, each with $10,000 face value, a 3% annual coupon paid semiannually and an initial yield to maturity of 3%. Because the coupon rate equals the yield, all three initially trade at par. We then reprice every coupon and principal payment at a 4% yield.
| Remaining maturity | Modified duration | Duration estimate | Repriced value | Exact decline |
|---|---|---|---|---|
| 2 years | 1.93 | -1.93% | $9,809.61 | -1.90% |
| 5 years | 4.61 | -4.61% | $9,550.87 | -4.49% |
| 10 years | 8.58 | -8.58% | $9,182.43 | -8.18% |
Calculated from the discounted coupon and principal cash flows. Figures exclude taxes, accrued interest, trading costs and credit-spread changes.
The 2-year bond loses about 1.90%, while the 10-year bond loses about 8.18% under the same 100-basis-point yield increase. The longer bond leaves more value tied to distant payments, so raising the discount rate has a larger effect on today’s price.
Why the duration estimate is not the exact price change
Duration treats the local relationship between price and yield as a straight line. The actual relationship is curved. This curvature is called convexity, and it becomes more important as the yield move or the bond’s duration becomes larger.
| Yield increase | Duration estimate | Cash-flow repricing | Approximation gap |
|---|---|---|---|
| 25 bps | -1.15% | -1.15% | Less than 0.01 percentage point |
| 50 bps | -2.31% | -2.28% | 0.03 percentage point |
| 100 bps | -4.61% | -4.49% | 0.12 percentage point |
The linear estimate is close for a 25-basis-point move and farther away at 100 basis points. For a large rate shock, a long-duration bond or an options-heavy security, investors should incorporate convexity or fully reprice the expected cash flows rather than rely on duration alone.
Why bonds with the same maturity can have different duration
Maturity is only one input. Coupon size determines how much cash arrives before maturity, while the starting yield changes the present-value weight assigned to distant payments. Embedded call or prepayment features can change the payment schedule itself.
| Annual coupon | Modified duration | Exact price decline | What changes |
|---|---|---|---|
| 1% | 9.34 | -8.88% | More value remains in the distant principal payment |
| 3% | 8.58 | -8.18% | Middle case |
| 6% | 7.84 | -7.48% | More cash is returned through earlier coupons |
Starting prices differ because the coupon rates differ while the initial yield remains 3%. Each decline is measured against that bond’s own starting price.
Does a 1% policy-rate hike mean every bond loses duration × 1%?
No. The formula requires the change in the yield used to price the bond. A central bank can raise its policy rate by one percentage point without every Treasury, municipal or corporate yield moving by the same amount.
Different sections of the yield curve respond to inflation expectations, growth, supply, demand and term premiums. Corporate bonds also reflect changes in credit spreads. A more useful estimate therefore pairs duration with the yield change for a similar maturity and credit profile, not automatically with the policy-rate announcement.
How to read duration for an individual bond and a bond fund
An investor who holds an individual bond to maturity may avoid realizing an interim market-price decline if the issuer pays every coupon and principal as promised. Selling early exposes the investor to the prevailing yield, liquidity and dealer pricing, while default risk remains throughout the holding period.
A bond mutual fund or exchange-traded fund continually replaces holdings and does not have one maturity date for the entire portfolio. Its reported duration is a current estimate of portfolio sensitivity. The fund’s return can still differ from the simple duration estimate because it includes coupon income, security turnover, spread changes, fees and—where relevant—currency movements.
Low duration also does not mean low total risk. Duration mainly describes interest-rate exposure. Credit, liquidity, inflation, call and currency risks require separate checks.
A five-step duration check for your own bond position
- Confirm whether the quoted number is Macaulay, modified or effective duration.
- Use the yield change for a comparable maturity and credit profile rather than the policy rate by default.
- Convert basis points to decimals: 25 bps is 0.0025 and 100 bps is 0.01.
- Multiply “-duration × yield change” to obtain the first-order percentage estimate.
- For large moves, long maturities or embedded options, check convexity, spread risk and full scenario repricing.
For example, if a bond ETF reports duration of 6.2 and its relevant yield rises 40 basis points, the first-order estimate is “-6.2 × 0.004 = -0.0248,” or approximately -2.48%. That is the estimated rate effect, not a forecast of the fund’s total return.
Bottom line: duration turns rate risk into a usable estimate
There is no single answer to how far bond prices fall when yields rise one percentage point. A modified duration of 2 implies roughly -2%, duration of 5 implies roughly -5%, and duration of 8 implies roughly -8% before convexity and other market forces are considered.
Investors should compare duration—not maturity alone—and verify which yield actually moved. That makes it easier to separate a bond’s credit quality from its interest-rate sensitivity and to avoid treating every “safe” bond as price-stable.
Primary and regulatory sources
- U.S. SEC Office of Investor Education and Advocacy, Fixed Income Investments—When Interest Rates Go Up, Prices of Fixed-Rate Bonds Fall
- FINRA, Bonds: features, pricing and investment risks
- FINRA, Duration—What an Interest Rate Hike Could Do to Your Bond Portfolio, March 6, 2017
- Federal Reserve Board, The U.S. Treasury Yield Curve: 1961 to the Present, sections on duration and convexity
Sources checked:
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