Inflation-indexed bonds interest indexation

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. 

Index-linked bonds often pay interest semiannually. Certain long-dated investors, such as fund managers whose liabilities include inflation-indexed annuities, may be interested in indexed bonds that pay on a quarterly or even monthly basis. 

There are five basic methods of linking the cash flows from a bond to an inflation index interest indexation, capital indexation, zero-coupon indexation, annuity indexation, and current pay. Which method is chosen depends on the requirements of the issuers and of the investors they wish to attract. The principal factors considered in making this choice, according to Deacon and Derry (1998), are duration, reinvestment risk, and tax treatment. 

Current pt. Current-pay bonds have been issued in Turkey. They are similar to interest-indexed bonds in that their redemption payments at maturity are not adjusted for inflation. They differ, however, in their term cash flows. Current-pay bonds pay an inflation-adjusted coupon plus an indexed amount that is related to the principal. In effect, they are inflation-indexed floating-rate notes. 

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. 

To provide precise protection against inflation, interest payments for a given period would need to be corrected for actual inflation over the same period. Lags, however, exist between the movements in the price index and the adjustment to the bond cash flows. According to Deacon and Derry (1998), such lags are unavoidable for two reasons. First, inflation statistics for one month are usually not known until well into the following month and are published some time after that. This causes a lag of at least one month, as shown in FIGURE 12.3. Second, in some markets the size of a coupon payment must be known before the start of the coupon period in... 

Interest indexation. Interest-indexed bonds have been issued in Australia, although not since 1987. They pay a coupon fixed rate at a real—inflation-adjusted—interest rate. They also pay a principal adjustment (equal to the percentage change in the CPI from the issue date times the principal amount) every period. The inflation adjustment is thus fully paid out as it occurs, and no adjustment to the principal repayment at maturity is needed. 

Capital indexation. Capital-indexed bonds have been issued in the United States, Australia, Canada, New Zealand, and the United Kingdom. Their coupon rates are specified in real terms, meaning that the coupon paid guarantees the real amount. For example, if the coupon is stated as 2 percent, what the buyer really gets is 2 percent after adjustment for inflation. Each period, this rate is applied to the inflation-adjusted principal amount to produce the coupon payment amount. At maturity, the principal repayment is the product of the bond s nominal value times the cumulative change in the index since issuance. Compared with interest-indexed bonds of similar maturity, these bonds have longer durations and lower reinvestment risk. 

The price of a TIPS comprises its real price plus any accrued interest, both of which are adjusted for inflation by multiplying them times the index ratio for the settlement date. The bond s unadjusted accrued interest, as explained in chapter 1, is calculated using expression (12.5). 

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. 

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. 

Inflation is frequently measured by the Consumer Price Index (CPI) published periodically by the Labor Department. The CPI indicates the increase in cost of a set of products over a fixed period of time. The commercial interest rate charged by banks is regulated by the U. S. Federal Reserve as a means of controlling inflation. A decrease in this controlled interest rate moves investments toward stocks, while an increase moves investments toward bonds. 

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