Inflation-indexed bonds term structure

Observing the trading patterns of a liquid market in inflation-indexed bonds enables analysts to draw conclusions about nominal versus real interest rates and to construct an inflation term structure. Such analysis is problematic, since conventional and indexed bonds typically differ considerably in liquidity. Nevertheless, as explained above, it is usually possible to infer market estimates of inflation expectations from the difference between the yields of the two types of bonds. 

From market observation we know that index-linked bonds can experience considerable volatility in prices, similar to conventional bonds, and therefore, there is an element of volatility in the real yield return of these bonds. Traditional economic theory states that the level of real interest rates is cmistant however, in practice they do vary over time. In addition, there are liquidity and supply and demand factors that affect the market prices of index-linked bonds. In this chapter, we present analytical techniques that can be applied to index-linked bonds, the duration and volatility of index-linked bonds and the concept of the real interest rate term structure. Moreover, we show the valuation of inflation-linked bonds with different cash flow structures and embedded options. 

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... 

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. 

Certain countries have markets in bonds whose coupon or final redemption payment, or both, are linked to their consumer price indexes. Generally, the most liquid markets in these inflation-indexed, or index-linked, debt instruments are the ones for government issues. Investors experiences with the bonds differ, since the securities were introduced at different times in different markets and so are designed differently. In some markets, for instance, only the coupon payment, and not the redemption value, is index-linked. This makes comparisons in terms of factors such as yield difficult and has in the past hindered arbitrageurs seeking to exploit real yield differences. This chapter highlights the basic concepts behind indexed bonds and how their structures may differ from market to market. 

Where a liquid market in indexed bonds exists across a reasonable maturity term structure, it is possible to construct a term structure of inflation rates. In essence, the process involves constructing the nominal and real interest rate term structures, then using them to infer an inflation term structure. This, in turn, can be used to calculate a forward expected inflation rate for any term or a forward inflation curve in the same way that a forward interest rate curve is constructed. 

Using equation 14.16, we can build a forward inflation curve provided we have the values of the index at present, as well as a set of zero-coupon bond prices of required credit quality. Following standard yield curve analysis, we may build the term structure from forward rates and therefore imply the real yield curve, or alternatively we may construct the real curve and project the forward rates. However, if we are using inflation swaps for the market price inputs, the former method is preferred because IL swaps are usually quoted in terms of a forward index value. 

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