Break-even inflation rate

Therefore, the inflation expectation could be assumed comparing the yield of a conventional bond to the yield of an inflation-linked bond with similar maturity. This average inflation expectation is known as break-even inflation rate and is given by Fisher s equation (6.1) ... 

The break-even inflation expectation, where average inflation expectations are estimated by comparing the return oti a conventional bond against that on an indexed bond of similar maturity, but including an appUcatimi of the compound form of the Fisher identity. This has the effect of decomposing the nominal rate of return on the bond into comprments of real yield and inflation ... 

So we have formally introduced the notion of break-even inflation, a term at the heart of inflation-linked bond analysis and trading. In principle it is the rate of inflation that will equate the returns on an inflation-linked bond and a comparator nominal bond issue of the same term. In theory, calculating it by simply subtracting a real yield from a nominal yield is a crude form of a properly compounded calculation, particularly when bond market conventions are semi-annual and what you should want is an annual measure of inflation. 

Although there is no formal break-even calculation convention, or way of selecting the best nominal comparator for that matter, historically break-even inflation in the United Kingdom has been calcnlated in a slightly more complicated way. Because UK real yields require an inflation assumption—3% is the market convention— there wonld be an inconsistency between the break-even inflation (BEI) rate and the inflation assumption used. The market tends to use the last formula above to arrive at a first cut BEI, then it uses that BEI rate as the new inflation assumption to calculate a new real yield. This is done iteratively nntil the assumed inflation rate and the BEI rate converge on a final cnt BEI. 

Figure 8.3-5 shows the discounted cumulative cash-flow as a function of elapsed years. With the assumptions contained in this qualitative discussion, we found that the discounted break-even period is 4 years when the product can be sold at 220 EUR/kg, it is 9 years when the price is 150 EUR/kg, but it is more than 20 years if the price falls to 120 EUR/kg. These results are obtained assuming an inflation rate of 3% per year. 

The drawbacks of each of these approaches are apparent. A rather more valid and sound approach is to constmct a term structure of the real interest rates, which would indicate, in exactly the same way that the conventional forward rate curve does for nominal rates, the market s expectatimis rat future inflation rates. In countries where there are liquid markets in both conventional and inflation-indexed bmids, we can observe a nominal and a real yield curve. It then becomes possible to estimate both a conventional and a real term structure using these allows us to create pairs of hypothetical conventional and indexed bonds that have identical maturity dates, for any point on the term structure. We could then apply the break-even approach to any pair of bonds... 

As Deacon and Derry (1998, page 91) states, this problem is exacerbated if the maturity of both bonds is relatively short, because the less time to an indexed bond s maturity date, the greater the impact of its nonindexed component. To overcome this flaw, the break-even rate of inflation is used. This is derived by using the Fisher identity, with the risk premium p set to an assumed figure, such as 0, to relate the yield on the conventional bond to a yield on the indexed bond derived using an assumed initial inflation rate. The result is a new estimate of the expected inflation rate i, which is then used to recalculate the indexed bond s yield. The new yield, in turn, is used to produce a new estimate of the expected inflation rate. The process is repeated until a consistent value for i is obtained. 

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