Implied RPI is the annual inflation an index-linked gilt's real and nominal yields together imply, derived from two fitted curves at the gilt's own term, and it is a market price rather than a forecast and not the same figure as a published inflation rate.
One figure, every index-linked gilt
Every index-linked gilt in issue carries its own implied RPI. The figure appears as a column on the index-linked gilts list, beside the clean price, the index ratio and the real yield, and the same figures are plotted on a separate page against maturity. It answers a question a reader naturally asks of a linker — what inflation is the market charging for over this gilt's remaining life? — and it answers it from prices rather than from anyone's opinion.
Because it is derived rather than published, it is worth being precise about what is being derived and from what. This article is a field note to that one column: where the number comes from, what moves it, what it does not mean, and how it differs from the other inflation figure the site uses, the assumed inflation behind a projection.
How the number is built
The inputs are two yields at one term. A conventional gilt's cash yield and an index-linked gilt's real yield come from the same borrower, so the credit is identical and what remains between them is mostly inflation. The site reads both from the day's report: the report carries a fitted nominal yield curve and a fitted real yield curve, and each is interpolated at the index-linked gilt's own term to maturity. The two interpolated yields are then combined.
The combination is a ratio rather than a subtraction. One plus the nominal yield, divided by one plus the real yield, less one. Subtracting the real yield from the nominal one ignores the fact that the real return compounds alongside the inflation over the same horizon, and the subtraction overstates the answer by that cross term. Dividing rather than subtracting is the whole of the correction, and the size of it is worth seeing once.
The cross term, worked once
The table below sets the two methods against each other on an illustrative pair of yields. The inputs are chosen for round numbers and are not figures from any gilt or from any curve: a nominal yield of 4.00 per cent and a real yield of 3.00 per cent at the same term.
| Method | Working | Result |
| Subtraction | 4.00% − 3.00% | 100.00 basis points |
| Ratio | (1.0400 ÷ 1.0300) − 1 | 97.09 basis points |
| Size of the cross term | 100.00 − 97.09 | 2.91 basis points |
Three basis points on this pair, more at higher yields, and always in the same direction: the subtraction is the larger number. That is why the figure on the site is described as derived rather than read off the two columns, and why two readers using different methods can disagree about the same gilt without either of them having made an arithmetic mistake.
What makes the number move
The figure is derived from two prices, so it moves when either of them does. A repricing of conventional gilts that leaves the index-linked curve alone will move every implied RPI; so will a repricing of the linkers that leaves the nominal curve alone. It can therefore change on a day when no inflation data has been published, and it can sit still on a day when a published inflation figure has surprised everyone. Neither of those is a malfunction: it is what it means for a figure to be a price.
- It moves when the nominal curve moves, even if nothing about linkers has changed.
- It moves when the real curve moves, even if nothing about conventional gilts has changed.
- It differs between maturities, because the market prices a term structure rather than one number.
- It changes with the gilt's own term as time passes, because it is an interpolation at that term rather than a fixed property of the gilt.
- It moves when the shape of either fitted curve changes, because the interpolation is taken from the fit rather than from a single neighbour.
Reading the curve rather than the column
One gilt's implied RPI is a point. The par RPI curve turns the points into a picture: one labelled point per priced index-linked gilt at its implied RPI, with a fitted par curve drawn through them. The shape is the interesting part. A curve that slopes upward says the market prices more inflation over the long run than the short; a curve that is flat says it prices the same; a curve with a kink at one maturity says something about that maturity that a flat reading would hide.
The page is also honest about thin data. With fewer than three priced index-linked gilts carrying a figure, the curve is not drawn at all and the page says so instead of drawing a line through two points and calling it a curve. That is the right posture for a fitted statistic: a fit that cannot be supported is a picture that invites a conclusion the data does not carry.
Implied RPI is not assumed inflation
The site uses a second inflation figure, and the two are easy to confuse because both are described in per cent per year. Implied RPI is a market price derived from two curves; it is an output. The assumed inflation rate is an input: the annual inflation applied to an index-linked gilt's cash flows beyond the latest published RPI, chosen for a projection and shown on the page that uses it. A projection built on an assumed rate produces an estimate, which the site marks as such.
Keeping the two apart matters for a practical reason. An assumed inflation rate belongs to whoever set it, and a reader can change it and see what follows. Implied RPI does not belong to anyone: it is what the prices say, and it is not a dial a reader can turn. Presenting a projection as though it rested on the market's implied figure, or presenting implied RPI as though it were a planning assumption, misdescribes both.
Implied RPI: what the market is pricing, derived from two fitted curves. Assumed inflation: the rate a projection applies to cash flows beyond the last published index value. One is an output, the other an input.
Background, not advice
This article explains how the implied RPI figure is derived, what moves it and what it does not mean; it is general background, not investment, tax or legal advice for any reader's circumstances. The Retail Prices Index is published by the Office for National Statistics, the gilt's terms and indexation lag are described by the Debt Management Office, and the implied figure itself comes from the day's gilt report, which are the primary sources for each input. The worked pair of yields above is illustrative, and implied RPI is a market price rather than a forecast of inflation.