Inflation-indexed bonds Fisher identity

The simple approach, where the average expected inflation rate is calculated using the Fisher identity, so that the inflation estimate is regarded as the straight difference between the real yield on an index-linked bond, at an assumed average rate of inflation, and the yield on a conventional bond of similar maturity ... 

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 ... 

Essentially, the Fisher identity describes the relationship between nominal and real interest rates. Assuming a value for the risk premium p, the two bond price equations—one for a conventional bond and one for an indexed bond—can be linked using (12.15) and solved as a set of simultaneous equations to obtain values for the real interest rate and the expected inflation rate. 

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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