# Back to basics

## Education: Back to Basics

Inflation is measured as an index, where the price of a 'basket of goods' is noted on a monthly basis. The basket contains weighted amounts of all the goods and services that one would typically use or buy, for example petrol, fresh fruit and clothing. If the basket cost 100 pence in June 2004 and 105 pence in June 2005, then the equivalent index in simple terms would have moved from 100 to 105. The change in the index for that period is 5% year-on-year inflation.

An inflation-linked bond, or 'linker', is linked to the inflation index, which is an important tool in determining the eventual cashflows of an inflation-linked bond. An inflation value must be found for when the bond was issued and for each coupon payment date, so that each cashflow is fully uplifted by inflation over the elapsed period.

Take the French OATe (or inflation-linked gilt) 1.6% bond, maturing on July 25, 2015. It is linked to European inflation index HICP (harmonised index of consumer prices ex tobacco) and each inflation index value is determined as an interpolation between the second and third month preceding the specified date. The base date of the bond – July 25, 2004 – has as reference the date April 25, 2004, and therefore a value interpolated between the two inflation points given for April and May (114.7 and 115.0 respectively) of 114.93226. When applied to the most recent coupon paid on July 25, 2005, this method gives an index value of 117.13226. The 'inflated' recent coupon payment can therefore be determined:

(117.13226/114.93226)*1.6%*notional held

At maturity the bearer will receive the principal uplifted in the same fashion, as well as the last uplifted coupon. This direct link to inflation means that linkers are attractive to investors such as pension funds, seeking asset-liability matching. Linkers can serve as a better inflation hedge than equities by providing predictable real returns – even when inflation rises abruptly.

Governments issue linkers to benefit from lower borrowing costs, due to the premium investors will pay for inflation protection:

Market-traded inflation = central bank inflation target rate + inflation risk premium

There is now an actively traded secondary market in UK, US, eurozone, Swedish, Japanese, Canadian and Australian linkers, as well as other more niche markets.

Bonds, however, are not the only instrument available to the end user to hedge or take views on inflation. Banks such as RBS also trade and offer derivatives such as swaps and options based on inflation. In inflation swaps, by using a zero-coupon swap which has an agreed fixed rate on a fixed date, the fixed rate is specified as an annual rate. For example, if I were to trade a five-year Swedish CPI (SWCPI) zero-coupon swap at 2.15%, the actual fixed cashflow in five years' time would be:

(((1+2.15%)^5)–1)*notional

against a floating payment on the same date of:

((relevant SWCPI in five years' time/relevant SWCPI today)–1)*notional

Collections of swaps can be built up on varying notionals in order to suit a client and in different structures where inflation is received or paid against a fixed rate, or floating such as Euribor. The resulting risk held by a market maker is then hedged out in the market through zero-coupon swaps and interest rate swaps traded with other banks and corporates. Although the most widely traded indices for swaps tend to be those against which bonds have been issued, banks are also willing to quote structures on other more illiquid indices such as Dutch, Danish and Belgian CPI.

 Glossary Inflation-linked bond: known as a ‘linker’, an inflation-linked bond is similar to a conventional bond. It has a set of coupons and a principal. However, all the cashflows for the bond are fully uplifted by inflation from the date of issuance. Inflation swap: This can be tailored to exactly match the inflation liabilities or income of a client. The building block of this instrument is the zero-coupon swap, where at a fixed date in the future two counterparties exchange an agreed fixed rate on a particular notional for the actual inflation over that period.

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The week on Risk.net, July 7-13, 2018