Inflation-linked bonds indexing

EXHIBIT 8.1 Market Value Composition of the Barclays Capital Global Inflation-Linked Bond Index ( billion)... 

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. 

Therefore, the break-even analysis allows to determine the spread that equals the price of a conventional bond to the one of an inflation-linked bond. This approach assumes a risk-neutral pricing by which an investor treats conventional and inflation-linked bonds the same. Under break-even hypothesis, both bonds have the same nominal yield. Note if the inflation breakeven is greater than expected inflation, for an investor is favorable to buy a conventional bond. Conversely, the inflation-linked bond is more attractive. If inflation breakeven and expectations are equal, the investor bond s choice will be then indifferent. Figure 6.2 shows the trend of UKGGBEIO and UKGGBE20 Index... 

To obtain the price of an inflation-linked bond, it is necessary to determine the value of coupon payments and principal repayment. Inflation-linked bonds can be structured with a different cash flow indexation. As noted above, duration, tax treatment and reinvestment risk, are the main factors that affect the instrument design. For instance, index-aimuity bmids that give to the investor a fixed annuity payment and a variable element to compensate the inflation have the shortest duration and the highest reinvestment risk of aU inflation-linked bonds. Conversely, inflation-linked zero-coupon bonds have the highest duration of all inflation-linked bonds and do not have reinvestment risk. In addition, also the tax treatment affects the cash flow structure. In some bond markets, the inflation adjustment on the principal is treated as current income for tax purpose, while in other markets it is not. 

The first step for estimating future streams is to know the expected inflation. To do this, the procedure needs the future trend of index in which the inflation expectation is built. The inflation expectation determined by countries is based on a different basket of products and services. For instance, inflation-linked bonds issued in the United Kingdom or UK index-linked gilts, are linked to the Retail Price Index (RPI) inflation-linked bonds issued in the United States or TIPS are linked to the Consumer Price Index (CPI). Table 6.1 summarizes the key global inflation indices used by the major issuers of inflation-linked bonds. 

Inflation-Linked Bonds with Zero-Coupon Indexation Zero-coupon bonds linked to the inflation do not pay coupons. Therefore, the unique adjustment is made to the principal. These types of bonds offer no... 

Table 6.2 illustrates the cash flow structure of an inflation-linked bond with zero-coupon indexation. 

Inflation-Linked Bonds with Coupon Indexation... 

As noted above for inflation-linked bonds with zero-coupon indexation, the coupon can be adjusted in a similar way ... 

As described above, inflation-linked bonds allow to save investors from changes in the general level of prices. However, the indexation is not perfect creating a lag between the index prices and the adjustment to the bond cash flows. According to Deacon and Derry (2004) at the end of a bond s life there is no inflation protection, matched with an equal period before the issue in which the inflation compensation is paid. Figure 6.11 shows an example of indexation lag according to Deacon and Derry (2004). 

There have been many different structures of inflation-linked bonds issued over time, but the most widely used form is one where principal and income are adjusted for changes in the relevant consumer price index between issue date and cash flow payment date, subject to an indexation... 

We have sketched out a couple of reasons why governments issue index-linked bonds already. We also said how the removal of inflation risk is valuable for the borrower, as it is for the investor, and earlier we described how in some countries rampant inflation resulted in a complete loss of investor confidence in nominal government debt, requiring the creation of an inflation-linked bond market out of necessity. However, there are other arguments why governments should issue linkers, and the reasons already given need to be added to, expanded upon and broken down into different subarguments. 

In April 1999 the SNDO launched two new linkers, a new 30-year bond (3104, 3.5% 2028) and a new 16-year bond (3105, 3.5% 2015). These two bonds were issued with an inflation floor, meaning that the new bonds had a similar structure to United States and French inflation-indexed bonds. The format of issuing inflation linked bonds was changed, this time moving back to bid price auctions, every three months. The reason being that this type of auction was common at the international level, allowing clearer signals of the volume on offer. The primary dealers were permitted to switch linkers directly with the SNDO on a daily basis, in order to enhance the liquidity of the market. 

In spite of the nnderperformance of index-linked over their full life, they have nevertheless proved a useful diversifying asset in low-risk portfolios, as Exhibits 8.13 to 8.15. If we can assnme we have reached a level of inflation that central bankers regard as desirable, then the prospective future returns on inflation-linked bonds will not be disadvantaged as they were in an era of economic transformation, but linkers should retain their attractive low-risk attributes. 

Description, in the chapter on inflation-linked bonds, of inflation-indexed derivatives. 

Inflation-indexed derivatives, also known as inflation-linked derivatives or inflation derivatives, have become widely traded instruments in the capital markets in a relatively short space of time. They are traded generally by the same desks in investment banks that trade inflation-linked sovereign bonds, which use these instruments for hedging as well as to meet the requirements of clients such as hedge funds, pension funds, and corporates. They are a natural development of the inflation-linked bond market. 

Inflation-Linked Bond Swap, This is also known as a synthetic index-linked bond. It is a swap with the following two cash flow legs ... 

Bonds that have part or all of their cash flows linked to an inflation index form an important segment of several government bond markets. In the United Kingdom, the first index-linked bonds were issued in 1981 and at the end of 2012 they accounted for approximately 25% of outstanding nominal value in the gilt market. Index-linked bonds were also introduced in the United States Treasury market but are more established in Australia, Canada,... 

Index-linked or inflatiOTi-indexed bonds present additional issues in their analysis, due to the nature of their cash flows. Measuring the retimi on index-linked bonds is less straightforward than with conventional bonds, and in certain cases there are peculiar market structures that must be taken into accotmt as well. For example, in the United States market for index-linked treasuries (known as TIPS from Treasury Inflation-Indexed Securities) there is no significant lag between the inflation link and the cash flow payment date. In the United Kingdom, there is an 8-month lag between the inflation adjustment of the cash flow and the cash flow payment date itself, while in New Zealand there is a 3-month lag. The existence of a lag means that inflation protection is not available in the lag period, and that the return in this period is exposed to inflation risk it also must be taken into account when analysing the bond. 

In earlier chapters, we reviewed the basic features of index-linked bonds and their main uses. We also discussed the techniques used to measure the yield on these bonds. The largest investors in indexed bonds are long-dated institutions such as pension fund managers, who use them to match long-dated liabilities that are also index linked for example, a pension contract that has payments linked to the inflation index. It is common though for investors to hold a mixture of indexed and conventional bonds in their overall portfolio. 

One final point regarding duration is that it is possible to calculate a tax-adjusted duration for an index-linked bond in markets where there is a different tax treatment to indexed bonds compared to conventional bonds. In the United States market, the returns on indexed and conventional bonds are taxed in essentially the same manner, so that in similar fashion to Treasury strips, the inflation adjustment to the indexed bond s principal is taxable as it occurs, and not only on the maturity date. Therefore, in the US-indexed bonds do not offer protection against any impact of after-tax effects of high inflation. That is, Tips real yields reflect a premium for only pretax inflation risk. In the United Kingdom market however, index-linked gilts receive preferential tax treatment, so their yields... 

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 ... 

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. 

The price of an inflation-linked bmid is determined as the present value of future coupon payments and principal at maturity. Like a conventional bond, the valuation depends on the cash flow structure. We can have three main cash flow structures of index-linked bonds. 

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