Real yield against nominal yield

Inflation and index-linked · 6 min read · GiltIQ

A conventional gilt's gross yield is a cash return and an index-linked gilt's real yield is a return after the inflation the gilt is priced for, so the two are only comparable once the inflation between them is put back explicitly.

Two yields from one borrower

The UK government issues two kinds of gilt, and each is described by a yield that is measured on a different basis. A conventional gilt's gross yield is a cash return: the annualised return from holding it to maturity, taking the coupons it pays and the price paid for it together. An index-linked gilt's real yield is a return after the inflation the gilt is priced for, because its coupons and its redemption already rise with the index. Both gilts are backed by the same issuer, so the credit is identical; what differs is what the yield is measuring.

That difference is the whole subject, and it is easy to lose. Comparing a conventional gilt's gross yield with an index-linked gilt's real yield directly is comparing a number that includes inflation with a number that excludes it. The comparison is not forbidden, and it is not meaningless — but it needs one more piece of information before it says anything, and that piece is the inflation the market is pricing between the two.

What each yield is measuring

PropertyGross yield, conventional giltReal yield, index-linked gilt
What is fixedThe cash it paysIts purchasing power
What it includesInflation as it turns outNothing: inflation is taken out
The compounding conventionOnce a year, on the site's headline columnOnce a year, on the same basis
What it pairs withA clean price on a cash basisA clean price with the uplift taken out
What it cannot tell youWhat the cash will buyWhat the cash will be

Reading across the first two rows is enough to see why the pairing matters. A gross yield has to cover a real return and the inflation expected over the gilt's life, because its cash does not grow. A real yield covers only the real return, because its cash already does. Put the two side by side at the same maturity and the difference between them is a statement about inflation.

The bridge is the inflation between them

The bridge is not a subtraction. Combining a nominal yield with a real yield calls for the ratio: one plus the nominal yield, divided by one plus the real yield, less one. Subtracting the real from the nominal ignores the fact that the real return compounds alongside the inflation over the same horizon, and it overstates the answer by that cross term. The illustration below makes the size of the error visible; the inputs are illustrative and are not figures from any gilt.

StepWorkingResult
Nominal yield, illustrativeinput4.50%
Real yield, illustrativeinput1.50%
Raw difference4.50% − 1.50%3.00%
Ratio method1.0450 ÷ 1.0150 − 12.96%

Four basis points is a small difference on this pair and a larger one at higher yields, but the direction never changes: the subtraction is always the larger number. On the site the ratio is the method used. The figure is called implied RPI, and it is derived from the fitted nominal yield curve and the fitted real yield curve, each interpolated at the index-linked gilt's own term.

Implied RPI is the inflation the two yields together imply. It is a market price derived from two curves, not a forecast, and it moves whenever either yield moves.

Why the maturities have to match

A comparison of a gross yield with a real yield only means anything at one maturity. The inflation a five-year gilt is priced for and the inflation a thirty-year gilt is priced for are different numbers in a market that prices a term structure, and pairing a short conventional gilt with a long index-linked one produces a figure that is part term premium and part inflation. Matching the term is not a refinement of the comparison; it is the comparison.

The site does the matching through fitted curves rather than by finding two gilts that happen to mature on the same day. The UK gilt yield curve plots every priced conventional gilt against a fitted line, and the report carries a fitted real curve alongside it; interpolating both at one term is what produces the implied RPI for a linker of that maturity. Because the inputs are interpolated from fitted curves, the output is an estimate of what the market is pricing rather than a quote, and it is worth reading as one.

What the comparison does not tell you

The list below collects the inferences a reader might reasonably draw from putting the two yields side by side, and says which of them the arithmetic supports.

Where to read both

The index-linked gilts in issue carries a real yield and a net real yield for every index-linked gilt, so the real side of the comparison is on one page with the clean price and index ratio behind it. The yield-curve page carries the nominal side, plotting each priced conventional gilt's gross redemption yield against its term with the fitted curve through them. Read at a matched term, the two pages give the pair of numbers this article is about.

The figure that joins them is on neither page as a single number, because it belongs to the linker: the implied RPI in that gilt's row, or the same figure plotted along the maturity axis. Putting the three together — a nominal yield, a real yield and the implied inflation between them — is what turns two unrelated columns into a comparison a reader can actually use.

Background, not advice

This article explains the difference between a conventional gilt's gross yield and an index-linked gilt's real yield and how the two can be put on one footing; it is general background, not investment, tax or legal advice for any reader's circumstances. The gilt's terms and the indexation lag are described by the Debt Management Office, the Retail Prices Index is published by the Office for National Statistics, and every figure in the ratio illustration is illustrative with its inputs stated. Neither kind of gilt is free of risk, and a real yield is not a promise of a real return.

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