Inflation-linked bonds curve

Kramer, W., 2013. An introduction to inflation-linked bonds. Lazard Asset Management. McCulloch, L, 1971. Measuring the term structure of interest rates. 1. Bus. XLIV, 19-31. McCulloch, L, 1975. The tax-adjusted yield curve. 1. Financ. 30 (3), 811-830. 

So, we have argued, the economics of supply and demand make the risk premium a slippery concept. Bond mathematics now makes matters worse. This new aspect centres on the issue of convexity. We know that a forward curve of implied future short-term nominal rates can be derived from the nominal government bond curve. In principle, a forward curve of implied future short-term real rates can be similarly derived from the inflation-linked bond real yield curve. These two curves, taken together, should imply a future path of inflation, if we can set aside the risk premium for the moment. Unfortunately, that is not the case. 

Using the prices of index-linked bonds, it is possible to estimate a term structure of real interest rates. The estimation of such a curve provides a real interest counterpart to the nominal term structure that was discussed in the previous chapters. More important it enables us to derive a real forward rate curve. This enables the real yield curve to be used as a somce of information on the market s view of expected future inflation. In the United Kingdom market, there are two factors that present problems for the estimation of the real term structure the first is the 8-month lag between the indexation uplift and the cash flow date, and the second is the fact that there are fewer index-linked bonds in issue, compared to the number of conventional bonds. The indexation lag means that in the absence of a measure of expected inflation, real bond yields are dependent to some extent on the assumed rate of future inflatiOTi. The second factor presents practical problems in curve estimation in December 1999 there were only 11 index-linked gilts in existence, and this is not sufficient for most models. Neither of these factors presents an insurmountable problem however, and it is stiU possible to estimate a real term structure. 

From this average inflation curve, we can select specific inflation rates for each index-linked bond in our sample. The real yields on each indexed bond are then recalculated using these new inflation assumptions. From these yields the real forward curve is calculated, enabling us to produce a new estimate of the inflation term stmcture. This process is repeated until there is consistency between the inflation term stmcture used to estimate the real yields and that produced by Equation (6.5). 

In essence, the real yield curve can and should be used for all the purposes for which the nominal yield curve is used. Provided that there are enough liquid index-linked bonds in the market, the real term stmcture can be estimated using standard models, and the result is more valid as a measure of market inflation expectations than any of the other methods that have been used in the past. 

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