Tools

Bond Fund Break-even Calculator

How long must a constant-duration bond fund be held before higher yields repay the fall in its price — and does the answer depend on whether rates rose once or keep rising?

A bond fund falls when yields rise, and then earns more than it did before. Whether the second repays the first, and when, has two published answers that differ by more than a decade — the fund's duration, and twice its duration less one period. Both are correct. They answer different questions, and sources give one or the other without saying which. This calculator asks you which happened, gives the horizon for it, and shows the other beside it.

What this tool does not decide

Whether to hold, buy or sell anything. A horizon is something to compare against your own, not a verdict on a holding.
What rates will do. No probability appears anywhere. You state what happened or what you are testing; the model says what that costs and when it is repaid.
Which fund you hold. This tool ships no fund, index, ticker or published yield, names none, and fetches none. Every figure is yours.
What happens to a bond you hold to maturity. That is a third case with a third answer, and it is described in the methodology rather than computed here — a fund that rolls and a bond that matures behave differently and the resemblance is the easiest mistake to make.
Anything outside the assumptions the underlying research states for itself, which are listed in full below rather than summarised.
Anything about tax, in any jurisdiction.

Your figures

The interactive calculation runs in your browser and needs local JavaScript, which is currently switched off. Activating the Calculate button does nothing at all: no request is sent and nothing is submitted.

Everything else on this page works without it. The model, the formulas, the timing convention, the worked example, the assumptions and the limitations are all in the methodology below, and the companion explainer covers the mechanism in full.

Your fund, and what rates did

Five figures, all yours. Nothing is sent anywhere, nothing is stored, and no fund, index, yield or rate is looked up. The first question is the one the published answers disagree about, so this page asks it rather than assuming it.

What happened to yields

A single rise that then stopped, and a rise that keeps going every period, have different break-even horizons. Published sources give one number or the other without saying which question it answers, which is why this control has no default and why the answer names the question it belongs to.

The yield before the move

The yield the fund was on before rates moved. Neither horizon depends on it — it cancels out of both — and it is entered because the period-by-period path below is built from it.

The fund’s modified duration

In the same periods your yields are quoted over: if the yields are annual, this is duration in years. It has to be longer than one period — below that the approximation this rests on inverts, and says a fund gains from a rate rise.

How far yields moved

For a single rise, the whole of the move. For a rise that repeats, the move in each period. Neither horizon depends on the size, which is the property that lets a horizon be stated without anyone forecasting a rate. Enter 0 to see that for yourself.

How long you hold

Your own holding period, in the same periods as everything above. It does not change either horizon; it decides where you currently stand against the one you chose.

Result

Enter your five figures above and select Calculate. Nothing is sent anywhere: the calculation runs in this browser, and no value is stored, shared or placed in the address bar.

A single rise, then nothing: until the fall in price is repaid: Not yet calculated
A rise every period: until the average return reaches the starting yield: Not yet calculated
Where you stand at the horizon you entered: Not yet calculated
Where that leaves you: Not yet calculated
How far apart the two horizons are: Not yet calculated

This is arithmetic on a first-order approximation of how a constant-duration fund behaves, under a set of assumptions a single academic source states for itself. It has no convexity term, so it understates the price gain on a large fall and overstates the loss on a large rise, and it describes a fund whose duration is held constant by rolling — not a fund whose duration drifts, and not a bond held to maturity.

Neither number is a promise, and neither is “the” break-even for bond funds. They are the horizons at which two different quantities reach zero, under two different assumptions about what yields did — and outside those assumptions this page says nothing. Sources that publish one of them without saying which question it answers are the reason this page publishes both.

How this is worked out

Why there are two answers, and not one

Published answers to this question disagree by more than a decade. They are not all wrong: they are answers to different questions, given without saying which.The discriminator is the shape of the rate move, and the second discriminator is whether the thing being held is a fund or a bond.

Three cases, each correct under its own assumptions. This calculator answers the first two.
Case	What is held	The question it answers	The horizon	Here?
A single rise, then nothing	A fund that holds its duration constant by rolling	How long until the higher yields repay the fall in price?	The fund’s modified duration	Answered here
A rise every period	The same fund, on a yield path that keeps moving	How long until the average return reaches the yield it started at?	Twice the duration, less one period	Answered here
One bond, held to maturity	A single bond, not a fund. Nothing rolls	How long until the return approximates the yield it was bought at?	The bond’s Macaulay duration	Not answered here

The third case is the one a reader is most likely to confuse with the first, and it is not a small difference: a bond held to maturity has a terminal price risk that disappears at maturity, and a fund that rolls has a permanent one that never does. This calculator does not answer it, and says so rather than letting the resemblance stand.

The one relationship both cases are built from

Writing Y for the yield in a period, D for modified duration andΔY for the move in that period, the fund's return over one period is approximately:

R = Y − (D − 1) × ΔY

Everything else follows from summing that along a path. For a single rise measured against the path with no rise, the cumulative gap is (t − D) × ΔY, which is zero att = D. For a rise every period, the average return's excess over the starting yield is ΔY × (t + 1 − 2D) ÷ 2, which is zero at t = 2D − 1.

Neither zero depends on ΔY. That is not a convenience — it is the property that makes a horizon publishable at all, because it means no forecast of a rate is required to state one. Enter a move of zero, then a large one, and the horizons do not move.

What the comparison is measured against

For a single rise, the gap is measured against the path the fund would have followed had the rise not happened — not against the value it started at. The distinction is not cosmetic: a fund that would have earned its yield for those periods anyway is not made whole by a rise that leaves it where it was always going to be, and measuring from a flat line would credit the holder with a yield they were always going to receive.

What you enter

The rate path: Which of the first two cases above. There is no default
Starting yield: Per period. Neither horizon depends on it
Modified duration: In the same periods, and longer than one of them
The move: Per period, and not negative. Neither horizon depends on its size
Your horizon: Whole periods. It decides where you stand, not where the break-even is

The limits the source imposes on itself

Every one of these comes from the academic paper the second horizon is taken from, and is reproduced rather than summarised. A figure published without them would be a stronger claim than the research supports.

The yield curve is flat near the fund’s duration. A sloped curve changes the roll and the result is not stated for it.
The one-period return is a first-order approximation with no convexity term, so it understates the price gain on a large fall and overstates the loss on a large rise.
The fund holds its duration constant by rolling, with bonds bought at par. A fund whose duration drifts is not this fund.
The duration is longer than one turnover period, which this calculator enforces rather than warns about.
Rolldown return is excluded.
The second horizon is for the arithmetic mean return under continuous compounding. The source states that the periodic-compounding and geometric-mean version “cannot be solved analytically” and “could not be found in advance anyway”.
The second horizon’s proposition is stated under the condition that twice the duration is a whole number. This calculator publishes the figure regardless and says when the condition does not hold.
Convexity in the yield path pushes the mean return below the initial yield at twice duration. A path that is not linear in time is not the second case.
The relationship explained forecast errors well for a set of bonds over six decades, and not over nine. That is the source’s own statement of how far its result has been shown to hold.

What is not modelled

a sloped yield curve near the fund’s duration — the result is stated for a flat one
convexity, which is why a large move is approximated rather than described
rolldown return, which sections 1–5 of the primary source exclude
a fund whose duration drifts rather than being held constant by rolling
a single bond held to maturity, which is a different case with a different answer
credit risk, default, and any difference between issuers
the fund’s own charges
how likely any rate move is, which is not a quantity anywhere on this page
tax, in any jurisdiction

A fall in price and the return that undoes it are not the same size, which is the shape of this question in a different mechanism.The explainer on why losses require larger gains covers that one, and needs no JavaScript at all.

Go deeper

The nearest published mechanism
Why Losses Require Disproportionately Larger Gains
Why a percentage loss and the same percentage gain never cancel, why getting back to the old balance is not the same as getting back to the original plan, and why the size of a loss is not a reason to keep holding.
A fall and the gain that undoes it are not the same size. Here the gain arrives as a higher yield over time rather than as a price recovery, and the asymmetry is the same one.
Read the explainer: Why Losses Require Disproportionately Larger Gains

Calculation model and corrections

Calculation model: Bond Fund Break-even v1.0
Last reviewed: 26 August 2026
The rate path: Yours, and there is no default. A single rise and a rise that repeats every period have different answers, and choosing for you is how the public corpus produced its disagreement
The counterfactual: For a single rise, the path the fund would have followed had the rise not happened — not the value it started at
The fund: Constant duration, held there by rolling, with bonds bought at par. A fund whose duration drifts is not this fund
The return: A first-order approximation: the yield in the period, less the duration minus one, times the move in that period
Periods: Whatever period your yields are quoted over. Neither horizon depends on the choice, provided the duration is stated in the same periods
The starting yield: Entered, and neither answer depends on it. It builds the path shown below and cancels out of both horizons
The size of the move: Entered, and neither horizon depends on it either. That invariance is what makes a horizon statable without forecasting a rate
The second horizon: Arithmetic mean return under continuous compounding, and the source states it under the condition that twice duration is a whole number
Excluded: Convexity, rolldown, a sloped curve, credit risk, fund charges and tax
Rounding: Display only; intermediate values remain unrounded

Correction history

Before publication, the model’s verifier refused its own first distinctness check rather than the model. The check searched each path for the first whole period at which its quantity turned non-negative and required the two to differ; at a duration of 1.5 periods the two horizons are 1.5 and 2.0 — genuinely different — but both round up into period 2, so a search over whole periods cannot see the gap. Weakening the claim to fit the instrument was available and was refused; the check now states that at every whole period between the two horizons one path is at or past level while the other is still behind.
The verifier also refused the specification for a paraphrase. It requires the document to carry every interpretation limit the primary source imposes on itself, and the condition the source’s proposition is actually stated under — that twice duration is an integer — had been paraphrased rather than quoted. The specification was corrected, not the check.