Carry, rolldown and variation: where a gilt's return came from

Portfolio and risk · 7 min read · GiltIQ

Between two dates a gilt's return is the sum of several things happening at once, and the attribution tab splits it into the four rows it names — carry, rolldown, variation and a residual it calls unexplained — so each part can be read on its own.

A return is not one thing

Over any window, the return on a gilt is the change in its dirty price plus the coupons it paid inside the window. That total is easy to state and hard to explain, because the change is several things at once: time passing, the gilt moving closer to maturity, and the market repricing its yield. The attribution tab on a gilt's page separates them into four rows it names: carry, rolldown, variation, and a residual it calls unexplained.

Read together, the four rows account for the difference between the traded dirty price at the start of the window and at the end, coupons included. Three are modelled effects; the fourth is what is left when the model has done its work. Read alone, each answers a narrower question, and keeping them apart is the whole value of the tab.

The window and the basis

The tab sits on a gilt's own page, reached from the conventional gilts list. It takes a from-date and a to-date, both stored report dates, so a window never spans a gap in the series without saying so; the default is the month before the latest stored report. Everything is quoted per £100 nominal.

The arithmetic uses one discounting form throughout: every flow divided by one plus the rate over two, raised to the half-yearly periods to that flow. It is the same form as the NPV and NPV (par curve) columns on the gilt's cash-flow page, which is why the model prices here reconcile with those columns rather than inventing a second convention. The tab covers conventional gilts only: the fitted curve is a par curve of conventional gilts, and a linker's real flows have no place on it, so the tab declines one rather than mixing two bases. The curve it reads is the one drawn on the gilt yield curve for each date.

Carry: the passage of time

Carry is what the gilt earns from time alone, at an unchanged yield. Both ends of the window are priced at the gilt's own yield on the start date, so the only thing that changes between them is the calendar: the gilt gets closer to its redemption date, and it pays any coupon that falls inside the window. Carry is the change in that own-yield model price plus the coupons received. A gilt bought below par pulls towards par as it approaches maturity, and that pull is part of carry; for a gilt bought above par it works the other way.

Holding the yield flat is the whole idea. Carry answers a single question: if nothing repriced and only time moved, what would the gilt have earned? The coupons are in carry and also in the total return, so they cancel in the residual rather than hiding inside it — a window that contains a coupon date is a total return, not a price return.

Rolldown: the same curve at a shorter maturity

Rolldown is the gain from the gilt's maturity shortening while the curve stays still. Take the start date's fitted par curve and leave it in place; the gilt, however, has moved a month closer to maturity, so it sits at a shorter term on that same curve. If the curve slopes upward, a shorter term carries a lower yield, so the gilt rolls down into a lower yield without the curve itself moving — and a lower yield means a higher price. Rolldown is that price gain: the end flows priced on the start curve minus the end flows priced at the gilt's own yield. On a rising curve rolldown is positive; on a falling or inverted one it can be negative.

Variation: the curve itself moving

Variation is the change that comes from the curve moving under the gilt. It compares the end date's fitted curve with the start date's, both evaluated at the gilt's maturity at the end of the window. A rise in yields across that part of the curve is a negative variation; a fall is positive. This is the term a reader would recognise as the yield change at the gilt's own term — the repricing of the gilt's yield, as distinct from the gilt drifting along a fixed curve. Variation answers a single question: if the gilt had not moved in maturity, what would the market's repricing alone have done?

Unexplained: the residual

The fourth row is not a modelled effect; it is what is left. The traded total return — the end dirty price plus coupons minus the start dirty price — is measured from traded prices. Carry, rolldown and variation are modelled from the fitted curves and the gilt's own yield. The unexplained row is the traded total return less those three, so it is the amount by which the market's traded prices disagreed with the model, counted at both ends: the start date's traded price against its own-yield model price, and the end date's traded price against the fitted curve's.

A large residual is not an error to be suppressed. It means the stored traded prices and the fitted curve disagreed by that much over the window, which is information about how well the model tracked the market on those two days. Because the residual is defined as whatever the three modelled parts do not explain, the four rows reconcile to the total return by construction — but that is not the same as the three modelled effects summing to it. They generally do not: the residual is the gap, and it is named for exactly that.

Worked once, and how to read it

The table below runs a decomposition through with round numbers to show how the four rows reconcile. It is illustrative and not from any gilt or report: a 4.00 per cent coupon (£2.00 per £100 in a half-year), a start dirty price of £98.50, an end dirty price of £99.10, one coupon of £2.00 paid inside the window, a start gross yield of 4.50 per cent and an end yield of 4.40 per cent, over a window of 17 September 2026 to 16 October 2026. Every figure is per £100 nominal.

RowValue per £100How it is built
Start dirty price (traded)£98.50traded, mark-to-market
End dirty price (traded)£99.10traded, mark-to-market
Coupons in the window£2.00one half-year coupon
Total return£2.60£99.10 + £2.00 − £98.50
Carry£2.10time at own yield, plus the coupon
Rolldown£0.35start curve at a shorter maturity, less own yield
Variation£0.10end curve less start curve
Unexplained£0.05£2.60 − (£2.10 + £0.35 + £0.10)

The four rows add to £2.60, the total return. The three modelled effects on their own add to £2.55, and the residual is the £0.05 by which the traded prices and the model disagreed. That is the honest reading: the modelled split explains most of the return and names the part it does not.

This explains what the attribution tab's four rows mean and how they reconcile; it is general background, not investment, tax or legal advice for any reader's circumstances. Every real figure on the tab is computed from two stored reports for the window it covers, per £100 nominal, and the numbers here are illustrative. The tab declines any window it cannot fully decompose rather than showing half a split.

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