Lags and Inflation Expectations

As noted earlier, indexation lags prevent indexed bonds returns from being completely inflation-proof According to Deacon and Derry (1998), this suggests that an indexed bond can be regarded as a combination of a true indexed instrument (with no lag) and an nonindexed bond. Equation (14.13) expresses the price-yield relationship for a bond whose indexation lag is exactly one coupon period. 

If the bond has just paid the last coupon before its redemption date, (14.13) reduces to (14.14). 

In this situation, the final cash flows are not indexed, and the price-yield relationship is identical to that for a conventional bond. This, then, represents the nonindexed component of the indexed bond. Its yield can be compared with those of conventional bonds, making it possible to quantify the indexation element. This implies a true real yield measure for the indexed bond. 

To estimate the true real yield, analysts use the Fisher identity, one variant of which is shown as equation (14.15). 

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 (14.15) and solved as a set of simultaneous equations to obtain values for the real interest rate and the expected inflation rate. 

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