Primer: U.K. Index-Linked Gilts

Her Majesty's Treasury of the United Kingdom of Great Britain as well as Northern Ireland was ane of the earliest modern issuers of inflation-linked bonds, amongst issuance starting inward 1981. (There were before bonds that featured some shape of indexation, but those were less systematic inward design.) Unfortunately, the master copy pattern used is much harder to operate amongst than the construction used past times Canada ("Canadian model").

The U.K. has switched over to the Canadian model inward 2005, although some of the older structures remain. However, fifty-fifty in ane trial the former construction bonds all mature, analysts volition all the same encounter pricing information based on them inward the dorsum history. In particular, if fourth dimension serial are properly labelled, they volition convey a caption to the trial that the existent yields are based on an inflation supposition of 3% (or maybe 5%), which sounds counter-intuitive if ane is familiar amongst the Canadian model. (How tin give the sack nosotros assume a degree of inflation? Isn't that determined inward the market?) This department merely presents a high degree overview of the former construction inward instance the reader encounters that dorsum history.

(This article is an unedited draft of a department that volition move incorporated into my inflation breakeven report. I am nearing the cease of adding cloth for the outset draft version.)

The U.K. Treasury has a page describing inflation-linked gilts at http://www.dmo.gov.uk/data/gilt-market/index-linked-gilts/. There is too a document describing yield calculations available at: http://www.dmo.gov.uk/media/1955/yldeqns.pdf.

There are 2 areas that distinguish the former pattern as well as the Canadian model.

1. Cash flow calculations.
2. Yield calculations.

Cash Flows

The cash flow calculations inward the former construction convey a calculation lag of 8 months, instead of iii months nether the Canadian model. (The U.K. Treasury documents volition distinguish the issues based on this lag, but every bit discussed below, this is non the exclusively difference betwixt the issues inward practice.) The index used inward indexation calculations is the Retail Price Index (RPI), as well as non the Consumer Price Index (CPI), which is the Bank of England's target inflation index. (This creates reason risk betwixt the inflation target as well as the inflation-linked bond index. That is, if ane is comparison inflation breakevens to the inflation target, ane needs to delineate of piece of work organisation human relationship for the statistical bias betwixt the RPI relative to the CPI.)

The longer lag used agency that the side past times side coupon payment volition ever move covered past times already-released CPI data. Nominal cash flows tin give the sack as well as thence move multiplied past times the indexation constituent for the bond. This agency that prices tin give the sack move safely quoted inward nominal terms. This agency that quoted prices motility good away from the 100 par price, different the Canadian model, where quoted prices are existent as well as convey a pull-to-par every bit they evolve towards maturity.

I am unsure why they chose this structure, but it appears it has ane advantage: since everything was quoted inward nominal terms, the existing trading technical infrastructure could handgrip these bonds. 

The added calculation lag is slightly unattractive, but inward a contained inflation environment, the differences from the Canadian model for cash flows is non that significant. You merely ask to yell back that quoted prices are inward nominal terms, as well as thence increase along the RPI. 

Yield Calculation Differences

From an analytical betoken of view, the big difference betwixt the 2 bond structures lies inward how yields are calculated.

Since calculations were beingness done inward nominal terms, as well as non inward indexed terms, at that spot needed to move a way to projection futurity nominal cash flows. The way this was done was to assume a frontwards charge per unit of measurement of inflation. The electrical flow supposition is 3%. In other words, nosotros projection the RPI frontwards at an annual charge per unit of measurement of 3%, as well as thence role that to generate the index ratios for all cash flows. 

We tin give the sack as well as thence calculate the bond toll every bit a component subdivision of the existent yield r past times using a nominal discount charge per unit of measurement (1+r)(1+0.03), or the Fisher relationship, amongst the assumed inflation charge per unit of measurement of 3%. We tin give the sack invert the toll component subdivision (probably numerically) to larn the existent yield every bit a component subdivision of price.

As tin give the sack move seen, the 3% inflation supposition is arbitrary. If some simplifying assumptions were true, it would non truly matter. For example, assume that the nominal yield implied past times a 3% inflation supposition was 4%. This would hateful that the existent yield is roughly equal to 1% (=4% minus the inflation assumption). If nosotros as well as thence switched to a 4% inflation assumption, the implied nominal provide would move roughly 5%. Once nosotros subtract the 4% assumed inflation, nosotros are dorsum to a 1% existent yield.

To larn the uncomplicated breakeven inflation rate, nosotros subtract the calculated existent yield from the yield on a conventional gilt. Since at that spot is no argue that the conventional yield must equal the assumed nominal provide of the inflation-linked Au nether the 3% inflation assumption, the breakeven inflation charge per unit of measurement volition vary from the 3% inflation (as would move expected). If nosotros could assume that the existent yield is independent of the inflation supposition of the calculation, the uncomplicated breakeven volition move every bit well.

The employment is that those simplifying assumptions produce non truly apply. The existent yield is somewhat sensitive to the inflation charge per unit of measurement assumption, amongst the deviations growing every bit the economical breakeven diverges from the assumed inflation charge per unit of measurement inward calculations. In other words, if the uncomplicated inflation breakeven is close 3%, it is a proficient approximation of the truthful economical breakeven. However, if the uncomplicated inflation breakeven is non close 3%, it volition move biased relative to the truthful economical breakeven.

I am non inward a seat to gauge how pregnant this trial is inward practice. It powerfulness exclusively affair if ane wants to dig really deeply into the marketplace seat history of the inflation-linked Au market. Although that may audio similar an obscure topic, it is of some interest. This U.K. history is the exclusively bridge of inflation-linked bond marketplace seat information that hails from a menstruation without stable inflation.

Concluding Remarks

If you lot facial expression at fourth dimension serial information for U.K. linkers, you lot tin give the sack process the existent yields every bit beingness similar to the indexed yields for Canadian model linkers. We may exclusively ask to move concerned nearly the serial beingness biased if the (simple) inflation breakeven considerably departs from the inflation supposition associated amongst the series.

(c) Brian Romanchuk 2018