Working out an index-linked gilt's coupon from the index ratio

An index-linked gilt's cash coupon is its real coupon multiplied by the index ratio, and working one payment through from two index values to pounds shows exactly where every input comes from and which of them can move.

One division, then one multiplication

The arithmetic an index-linked gilt performs on every payment is short. The index ratio is the reference RPI divided by the base RPI, and the gilt's real coupon is then multiplied by it. There are two inputs to the ratio and one to the multiplication, which is why the whole mechanism can be written on a single line and still be worth working through slowly: most of the confusion about index-linked gilts comes from mixing up which of those three numbers is fixed and which can move.

The worked example below is illustrative throughout. The base RPI of 100.0 and the reference RPI of 135.0 are round numbers chosen to make the division easy to check, not index values taken from any publication, and the real coupon of 0.125 per £100 nominal is a plausible magnitude rather than a gilt's actual terms. Everything else follows from those three inputs by arithmetic.

The worked example, step by step

Run the same gilt at a ratio of 1.40000 and nothing else changes except the two figures the ratio multiplies: the cash coupon becomes £0.175 per £100, the annual coupon on £10,000 becomes £17.50, and the redemption becomes £14,000. The real coupon stays at 0.125 through both, which is the point of calling it real. What the gilt pays is not a rate applied to a fixed amount of money; it is a fixed rate applied to a moving one.

Two of the rows are worth reading twice. The redemption is scaled by the same ratio as the coupon, so the principal a holder gets back is not the £100 per unit that a conventional gilt returns — it is whatever £100 has become in the index's terms. And the half-yearly split matters for cash timing: a holder of £10,000 nominal receives roughly £8.44 every six months at that ratio rather than £16.88 once a year.

Where each of the three inputs comes from

The real coupon and the £100 of nominal are terms of the gilt. They are set when it is issued and appear on the gilt's own record; the Debt Management Office publishes a gilt's coupon rate and its maturity, and neither changes afterwards. The base RPI is fixed at the gilt's first issue and never revised, which is what makes it an anchor: every later comparison is against the same starting point, whatever the index does in between.

The reference RPI is the one input that moves, and it moves on a schedule the gilt's terms fix rather than on any schedule a reader chooses. It is the RPI for the month the gilt's indexation lag points at — eight months before the payment under the longer lag, three months before under the shorter one. The Retail Prices Index itself is published monthly by the Office for National Statistics, so both index values in the division are published statistics rather than market prices or estimates.

The real coupon and the nominal are fixed; the reference RPI moves; the index ratio is how the moving one is applied to the fixed ones. Beyond the latest published index figure, an assumed inflation rate takes over and the resulting figure is an estimate rather than a scaled one.

The same arithmetic on the income calendar

The gilt coupon calendar applies this to a whole window of payments across every gilt in issue, conventional and index-linked together. A reader sets the window, the gilt type and a nominal holding, and the page lists each coupon and redemption in the period with the amount for that holding. An index-linked payment in that list is the arithmetic above, performed for the gilt in question at its own ratio, which is why two gilts with identical real coupons can show different cash amounts in the same month.

The calendar is also where the difference between a scaled figure and a projected one becomes visible in the ordinary course of use. A payment whose reference RPI has already been published is arithmetic on facts. A payment further out is grown at an assumed inflation rate and marked accordingly. For a short-dated gilt almost everything in the window is the first kind; for a long-dated one, much of it is the second.

What a reader can check, and what they cannot

Everything in the worked example is reproducible from its three inputs with a calculator, and the list below sets out which parts of a real gilt's payment can be checked the same way.

• The ratio can be checked against the published RPI values for the two months the gilt's terms point at, and the figures are on the index-linked gilts in issue at five decimals.
• The cash coupon can be checked by multiplying, and the result should match the gilt's cash-flow schedule to the precision that schedule states.
• The redemption cannot be checked in advance, because the reference RPI for the maturity date has not been published yet.
• A projected coupon cannot be checked against a published figure at all: it is a consequence of the assumption the projection uses, and it is marked as an income estimate for that reason.
• A future coupon cannot be assumed to exceed a past one. The RPI can fall as well as rise, and the Debt Management Office says in terms that an index-linked gilt's cash flows can therefore fall.

Background, not advice

This article works one index-linked payment through from index values to pounds; it is general background, not investment, tax or legal advice for any reader's circumstances. The index values come from the Office for National Statistics, the gilt's terms and the indexation lag from the Debt Management Office, and every figure in the worked example is illustrative with its inputs stated. An index-linked gilt does not remove risk: its cash can fall with the index and its price moves before maturity.