Modified Duration Explained: What a 1% Yield Move Costs

What does modified duration actually tell you?

Modified duration estimates how much a bond’s price changes when its yield to maturity changes. Multiply modified duration by the yield change expressed as a decimal, reverse the sign, and you have an approximate percentage price move. It is a sensitivity measure, not a maturity date, a promised return, or a forecast that rates will move.

In our hypothetical $10,000 bond, modified duration is 7.7217. A rise in yield from 5% to 6% therefore predicts a price loss of about $772.17. Exact repricing produces a smaller $736.01 loss. That difference is the point of this guide: a useful shortcut becomes misleading when you forget what it approximates.

We build that example from its cash flows, compare the shortcut with exact prices in both directions, and then use it to investigate portfolio weights and yield-curve changes. No figure below is a live bond quote. The guide is educational, not personal investment advice; duration measures one risk, not every risk involved in owning debt.

FINRA’s duration explainer provides the practical starting point: greater duration generally means greater sensitivity to interest-rate movements. The more precise yield-based interpretation comes from CFA Institute’s duration reading. Sources and models were checked on November 1, 2026.

What is the difference between maturity, Macaulay duration and modified duration?

Maturity tells you when the bond’s final scheduled payment arrives. Macaulay duration is the average time to receive its cash flows, weighted by each payment’s present value. Modified duration adjusts that cash-flow timing measure to express sensitivity to yield. These are connected ideas, but using their names interchangeably obscures the decision you are trying to make.

A coupon bond returns some money before maturity. Those earlier payments pull its weighted cash-flow timing forward. A ten-year bond therefore need not have a ten-year Macaulay duration, and its modified duration need not equal either number. A zero-coupon bond has no intervening coupon payments: its Macaulay duration equals its remaining maturity, although its modified duration still requires the yield adjustment.

Under a nominal annual yield convention with m payments per year, modified duration equals Macaulay duration divided by (1 + yield/m). You must use consistent conventions. A result calculated with annual cash flows cannot simply be pasted into a calculation using semiannual periods without checking how the yield and time units were defined.

Our guide uses annual payments throughout to keep the arithmetic transparent. That is an illustrative convention, not a claim that real US Treasury notes or bonds pay annually. For the differences between actual Treasury instrument types, start with our Treasury bills versus bonds guide. Here the narrower question is how a yield change affects a fixed set of payments.

What assumptions sit behind our $10,000 example?

Imagine an option-free bond with $10,000 face value, ten years remaining, and a 5% annual coupon. It pays $500 at the end of each year and repays $10,000 principal with its last coupon. Its initial annual yield to maturity is also 5%. We value it immediately after a coupon payment, so there is no accrued-interest adjustment.

Assume all scheduled payments are made. Exclude trading costs, taxes, currency changes, settlement delays and embedded options. A changed yield is applied immediately to the same future payments; no calendar time passes between the before-and-after valuations. This isolates price sensitivity rather than pretending to simulate a full investment holding period.

The exact price is the sum of every cash flow discounted at the assumed annual yield. In symbols, P = Σ CF(t)/(1+y)^t. For years one through nine CF(t) is $500. For year ten it is $10,500. At a 5% yield the total is $10,000. When yield equals the coupon rate, our convention produces par pricing, consistent with TreasuryDirect’s pricing explanation.

This setup is deliberately boring. There is no forecast to distract from the measurement, no questionable current quote, and no hidden spread estimate. You can reproduce the result with a spreadsheet using ten rows. Exact cash-flow valuation is the reference answer; duration and convexity are the shortcuts being tested against it.

How do you calculate modified duration from those payments?

First calculate each payment’s present value. Then multiply that present value by the number of years until payment. Add the time-weighted present values and divide by the bond’s price. That gives Macaulay duration: Σ[t × CF(t)/(1+y)^t]/P. In this model it is 8.1078 years.

Next divide by 1.05, since the annual yield is 5% and the payment frequency is one. Modified duration is 8.1078/1.05, or 7.7217 when calculated from unrounded inputs. The coupon payments pull the weighted cash-flow timing below ten years, and the yield adjustment pulls modified duration below the Macaulay figure.

Finally apply ΔP/P ≈ −Dmod × Δy. A one-percentage-point rise is 0.01, not 1. Multiplying −7.7217 by 0.01 produces approximately −0.077217, or −7.7217%. On a $10,000 initial price that is a $772.17 estimated loss. A one-percentage-point fall reverses the sign and predicts the same-sized gain.

The formula uses a change in yield to maturity, not automatically the change in a policy rate. A central bank could adjust its overnight policy rate while a particular ten-year bond yield moves differently. The translation from macroeconomic news to the bond’s own yield is a separate assumption. Duration does not perform that translation for you.

CFA Institute describes modified duration as a yield-based price-sensitivity measure. Our implementation retains all cash flows and full numerical precision until display. That matters because rounding duration before multiplying by a large portfolio can introduce avoidable dollar errors, even when the overall method is otherwise sound.

What happens when the yield moves up or down?

The following table reprices the same bond at different annual yields. Every number is calculated from the hypothetical cash flows above. The duration estimate is made from the original 5% yield and $10,000 price, not recalculated separately at each new yield. This lets us see how far the original local estimate can travel.

New yield	Exact price	Duration-only estimate	Duration plus convexity
3%	$11,706.04	$11,544.35	$11,694.34
4%	$10,811.09	$10,772.17	$10,809.67
5%	$10,000.00	$10,000.00	$10,000.00
6%	$9,263.99	$9,227.83	$9,265.33
7%	$8,595.28	$8,455.65	$8,605.65

At 6%, exact pricing gives a 7.3601% loss. At 4%, it gives an 8.1109% gain. The price response is not symmetrical even though the yield changes are equally sized in opposite directions. That asymmetry comes from the curvature of the price-yield relationship for this option-free bond.

At the larger two-percentage-point shocks, the linear estimate is further away. The duration-only price at 3% understates the exact price by $161.69; at 7% it understates it by $139.63. The shortcut remains directionally informative here, but it should not be treated as an exact transaction price.

These are instantaneous model changes before coupon income, reinvestment, fees and taxes. Saying “duration predicts my annual return” would misuse the table. A holding-period total return requires additional information, including what happens during the period and the price at which the position is eventually sold.

Why does convexity improve the estimate?

Duration gives the first-order slope. Convexity adds a second-order correction for curvature. For this annual-payment model, convexity is Σ[t(t+1) × CF(t)/(1+y)^(t+2)]/P. At the initial yield it is 74.9977, expressed in years squared under our convention.

The combined approximation is ΔP/P ≈ −Dmod × Δy + 0.5 × convexity × (Δy)^2. For a one-percentage-point move, the second term adds approximately 0.3750% of the original price, or $37.50. Because the yield change is squared, this correction is positive in both directions for our positive-convexity example.

For a rise to 6%, the correction changes the estimated loss from $772.17 to $734.67. Exact repricing gives $736.01. For a fall to 4%, it changes the estimated gain from $772.17 to $809.67, versus an exact $811.09. This is a substantial improvement, but the residual differences show that second-order estimates are still approximations.

At 7%, even the convexity-adjusted estimate remains $10.36 above the exact price. When cash flows are known and you can discount them directly, exact repricing is preferable for a specific stress scenario. Duration and convexity are especially valuable for quick comparisons and aggregated exposures, not as substitutes for available exact calculations.

Positive convexity in this example is not a free return forecast. Market prices, yields and other risks already affect what investors pay. Nor can we generalize the same curvature to every bond: instruments with embedded options may behave differently because their cash flows can change as rates move.

What is the difference between a percentage point and a basis point?

A move from 5% to 6% is one percentage point, or 100 basis points. It is a 20% relative increase in the numerical yield, but 20% is not the input for the duration formula. The relevant decimal yield change is 0.01. This units distinction prevents an enormous calculation error.

One basis point is 0.01 percentage point, or 0.0001 in decimal yield. Multiply modified duration by price and 0.0001 to obtain the approximate dollar sensitivity to one basis point, often called money-duration-based DV01 or PVBP. For our original bond that magnitude is $7.7217 per basis point.

A one-basis-point yield rise therefore predicts roughly a $7.72 price decline. Exact repricing at 5.01% gives $9,992.28 after rounding. A one-basis-point yield fall predicts roughly a $7.72 gain; exact repricing at 4.99% gives $10,007.73. At this small scale the curvature adjustment is tiny, but not literally zero.

Always ask whether a provider displays the sensitivity as a positive magnitude or a signed derivative. Also ask whether its one-basis-point number comes from analytical duration or finite repricing. Those conventions can produce slightly different values. The important operational point is to match the units and sign before comparing figures.

Can two portfolios with similar labels have different rate risk?

Yes. Names such as “bond portfolio” or “income fund” tell you little about the size of a yield shock. Our second model combines option-free two-year and ten-year bonds, each with the same 5% annual coupon and 5% initial annual yield. Their modified durations are 1.8594 and 7.7217 respectively.

Put 60% of a hypothetical $10,000 portfolio’s current market value in the two-year exposure and 40% in the ten-year exposure. The weighted modified duration is 0.60 × 1.8594 + 0.40 × 7.7217 = 4.2043. Under an equal one-percentage-point rise in both yields, its first-order estimated loss is $420.43.

Exact repricing of both holdings gives a combined value of $9,595.59, or a $404.41 loss. As with the single bond, the straight-line estimate overstates the loss for this positive-convexity parallel shock. The portfolio calculation assumes fractional exposure is possible and ignores minimum denominations and execution costs.

Those weights must be market-value weights. Face values are not interchangeable with market values when securities trade at premiums or discounts. A security worth more dollars contributes more dollars of price sensitivity. Counting the number of bonds, or averaging their duration figures equally, can therefore misstate exposure.

Our weights happen to coincide with face-value proportions initially because both examples begin at par. That coincidence disappears after yields change. A real portfolio calculation should use current values and current risk measures, rather than a stale allocation screenshot or the amounts originally invested.

What does a nonparallel yield-curve move do to that portfolio?

A single portfolio duration assumes an appropriately common yield shift. Real yield curves can twist. Suppose, solely as a hypothetical stress, the two-year yield rises by one percentage point while the ten-year yield is unchanged. Applying each holding’s own duration predicts a loss of approximately $111.56, not $420.43.

Now leave the two-year yield unchanged and raise only the ten-year yield by one percentage point. The estimated loss is $308.87. The longer holding drives more rate sensitivity despite representing the smaller market-value allocation. Adding these two first-order losses reproduces the parallel-shock estimate.

This decomposition is more informative than announcing that “rates rose.” Which rates? At which maturities? Did the same yield change reach both holdings? A single weighted number compresses exposure efficiently, but it also hides where that exposure lives along the curve.

Key-rate duration is one way practitioners examine sensitivity at different curve points. It requires an explicit curve-shock and valuation framework; it is not simply our two bond durations renamed. We do not calculate a full key-rate risk system here. The simpler separate-shock example is enough to show why the parallel assumption matters.

Similarly, a corporate bond’s yield can rise because its credit spread widens even when a government reference yield is stable. Modified duration translates a change in the modeled yield into a price estimate, but does not explain the cause. Separate rate, spread and default analysis is necessary to understand the investment risk.

How should you interpret duration on a bond fund or ETF?

A fund’s duration is a portfolio risk measure, not a date when the fund promises to return your investment. A conventional bond fund can buy, sell and replace holdings. Its exposure can change as positions age, new securities enter, investors transact, or managers adjust the allocation.

Fidelity’s duration guide explains that interest-rate sensitivity also matters for funds and ETFs. Rising yields can lower the value of their holdings and their net asset value. Higher future income does not erase the immediate mark-to-market change.

Before using a fund’s number, check the definition, the measurement date and whether it is modified, effective or another duration measure. Then inspect the holdings, credit exposure, currency exposure and any derivatives. A headline duration figure should be the start of the examination, not its conclusion.

For an ETF, the market price can also differ from net asset value. Duration primarily describes underlying valuation sensitivity; it does not forecast a widening discount or premium, bid-ask spreads, or the price available for your particular order. Our tracking error guide explains another reason a simple headline metric is not the same as the return an investor experiences.

When comparing funds, use risk measures calculated on compatible bases. A portfolio with embedded options and an option-aware duration is not directly comparable with a simple fixed-cash-flow calculation without qualification. If the documentation is unclear, uncertainty is a reason to investigate, not permission to fill the gap with assumptions.

When is effective duration more appropriate?

Ordinary modified duration works with specified cash flows and a change in yield to maturity. A callable bond complicates that setup because the issuer may redeem it under the contract’s terms. A rate change can alter both discounting and expected cash-flow timing.

CFA Institute’s embedded-options reading identifies effective duration and effective convexity as relevant measures for callable and putable bonds. These measures use an option-aware valuation framework rather than assuming the original cash flows remain fixed regardless of the rate environment.

The intuitive distinction is important. When yields fall, an issuer’s ability to call debt can limit the investor’s participation in price gains. A simple positive-convexity fixed-payment example can therefore create the wrong expectation for callable exposure. Contract terms and valuation assumptions matter.

Effective duration is not automatically a superior universal number; it answers a different modeling problem. Its estimate depends on the rate-shock size, curve assumptions and option model used. Ask what the number measures and how it was produced, especially when comparing disclosures across providers.

Does holding an individual bond to maturity remove duration risk?

If an issuer makes every contracted payment, a fixed-payment bond’s cash flows do not change simply because its market yield changes. That does not mean market-value risk vanishes. If you must sell before maturity, the prevailing price matters. A cash need can turn an unrealized price decline into a realized loss.

There are other risks too: default, inflation, opportunity cost, taxes and the reinvestment rate available for coupons. Duration is not a complete score of safety. A low-duration instrument can still have substantial credit or liquidity risk, and a high-duration instrument can still make every scheduled payment.

Reinvestment can partly offset price effects over time, but that is a holding-period problem with assumptions about future rates and cash-flow treatment. Macaulay duration has a role in classical immunization analysis under restrictive assumptions. It is not a blanket promise that waiting a particular number of years guarantees recovery.

For money needed on a known date, matching payments to obligations can be more relevant than minimizing one sensitivity number. For money that may be needed unexpectedly, liquidity and the size of possible sale-price changes deserve explicit attention. The right measure depends on the liability you are trying to fund.

How can you use the number without pretending to forecast rates?

Start with a stress test, not a prediction. Write down an assumed yield change, calculate the estimated dollar loss, and compare it with the amount of loss you can tolerate before being forced to change plans. Keep the shock clearly labeled hypothetical and do not attach an invented probability.

For example, an investor considering $50,000 of exposure identical to our ten-year model would estimate a $3,860.87 loss for a one-percentage-point yield rise. Exact repricing scales to a $3,680.04 loss. Scaling is legitimate here because the cash-flow pattern and starting yield are identical; it would not justify copying the number to a different security.

Next change the assumptions that matter. Test a larger shock, a curve twist and, where relevant, a spread change. For option-dependent holdings use a suitable valuation model. Add costs and liquidity considerations separately. The purpose is to understand vulnerable conditions, not to produce one reassuring number.

Finally record what would invalidate the estimate. Changing cash flows, moving market-value weights, an incompatible yield convention or a nonparallel shock can each break a shortcut. A written assumption is much more useful than a duration figure remembered without its context.

What should you check before relying on a duration figure?

Use this sequence: identify the measure; confirm the date; check payment frequency and yield convention; calculate market-value exposure; specify the shock; separate immediate price change from holding-period return. If you cannot identify one of these inputs, treat the estimated loss as provisional.

Our original comparison yields a practical lesson. The ten-year maturity is not the relevant multiplier. The 8.1078-year Macaulay duration is not the final price-sensitivity multiplier either. The 7.7217 modified duration is useful, but its $772.17 estimated loss still differs from exact repricing when yield rises a full percentage point.

Adding convexity narrows that discrepancy dramatically in this model, while looking at individual portfolio exposures reveals risks hidden by one average. Neither improvement predicts the future. They make the assumptions visible and the arithmetic auditable, which is what a sound risk measure should do.

How was this guide produced?

This is an AI-assisted educational analysis for MarketsHQ’s fixed-income coverage, published under Christopher Taylor’s fixed-income byline. We checked the cited source pages on November 1, 2026 and reproduced the hypothetical calculations directly from annual cash flows. Automated calculation tests check exact prices, duration, convexity, basis-point sensitivity and portfolio shocks; they do not constitute a claim of personal financial advice or independent human sign-off.

The model contains no observed security prices, live yields, forecasts or backtested returns. All dollar scenarios exclude default, accrued interest, taxes and trading costs unless explicitly discussed as limitations. Values are rounded only for display. Its purpose is to help readers distinguish a useful sensitivity estimate from an exact price and decide what additional information their own holdings require.