Coupon indexation

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 ... 

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. 

Zero-coupon indexation. Zero-coupon indexed bonds have been issued in Sweden. As their name implies, they pay no coupons the entire inflation adjustment occurs at maturity, applied to their redemption value. 

In the United States, Canada, and New Zealand, indexed bonds can be stripped, allowing coupon and principal cash flows to be traded separately. This obviates the need for specific issues of zero-coupon indexed securities, since the market can create products such as deferred-payment indexed bonds in response to specific investor demand. In markets allowing stripping of indexed government bonds, a strip is simply a single cash flow with an inflation adjustment. An exception to this is in New Zealand, where the cash flows are separated into three components the principal, the principal inflation adjustment, and the inflation-linked coupons—the latter being an indexed annuity. 

Reinvestment risk. Like holders of a conventional bond, investors in a coupon indexed bond are exposed to reinvestment risk because they cannot know in advance what rates will be in effect when the bond s coupon payments are made, investors cannot be sure when they purchase their bond what yield they will earn by holding it to maturity. Bonds, such as indexed annuities, that pay more of their return in the form of coupons carry more reinvestment risk. Indexed zero-coupon bonds, like their conventional counterparts, carry none. 

Treasury inflation-protected securities (TIPs) are one of the most innovative financial products to appear in recent years. They pay a real coupon, plus the return on the Consumer Price Index (CPI). Thus, they automatically protect investors 100% against rising inflation, a property no other security possesses. Further, in a rising inflation environment, returns on TIPs are negatively correlated with those of bonds and other assets whose prices tend to decline when inflation rises. 

Finally, there are a number of structured derivative products often marketed as new asset classes. Such products are usually perturbations of existing assets. For example, enhanced index products are typictdly a weighted combination of exposure to a specific equities or bond class, augmented with exposure to a particular hedge fund strategy. Similarly, yield-enhanced cash substitutes with principal guarantee features are composed of zero coupon Treasuries with the residual cash invested in options or other derivatives. Such products are part hedge fund and part primary asset from an allocation perspective and are better viewed as implementation vehicles rather than incorporated exphcitly in the asset allocation. 

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 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. 

TABLE 6.2 The Cash Flow Structure with Zero-Coupon Bond Indexation... 

For the last point, we consider the following example. We assume to have an indexation lag of 1 year. Without indexation lag, at first payment date, the coupon should be adjusted with the inflation rate tj between the issue date and first coupon date. The adjustment is given by Equation (6.25) ... 

After the first coupon payment, Barro attributes a double weight on the periodical inflation rate before the coupon payment. For instance, in the case of perfect indexation, the second coupon payment should be adjusted in the following way ... 

The inflation rate is determined by the inflation index expectations. For instance, at first coupon date, the inflation rate is 2.1% and is given by ... 

Index duration is usually equal to the time until the next reset date, whereas spread duration is equal to a modified duration of a bond paying fixed coupon, with same coupon payments and time to maturity. Therefore, conventionally floaters have lower index duration and higher spread duration. 

An inverse floating-rate note pays coupons that increase if the reference rate decreases. Therefore, this bond gives a benefit at investors with a negative yield curve. The coupon structure of inverse floaters usually is determined as a fixed interest rate less a variable interest rate linked to a reference index. Moreover, they can include floor provisimis. 

An index-linked bond has its coupon or maturity value or sometimes both linked to a specific index. When governments issue index-linked bonds, the cash flows are linked to a price index such as consumer or commodity prices. Corporations have also issued index-linked bonds that are connected to either an inflation index or a stock market index. For example, Kredit Fuer Wiederaufbau, a special purpose bank in Denmark, issued a floating-rate note in March 2003 whose coupon rate will be linked to the Eurozone CPI (excluding tobacco) beginning in September 2004. Inflation-indexed bonds are detailed in Chapter 8. 

Inflation or purchasing power risk reflects the possibility of the erosion of the purchasing power of bond s cash flows due to inflation. Bonds whose coupon payments are fixed with long maturities are especially vulnerable to this type of risk. Floaters and inflation-indexed bonds have relatively low exposures to inflation risk. 

Two measures have been developed to estimate the sensitivity of a floater to each component of the coupon reset formula the index (i.e., reference rate)... 

For settlement amounts, real accrued interest is calculated as for ordinary OATs. Clean price and accrued are each multiplied by the Index Ratio to arrive at a cash settlement amount. For actual coupons paid, the (real) annual coupon rate is multiplied by the Index Ratio for the payment date, and likewise for the par redemption amount (with the cash value subject to a par floor). 

Real interest is accrued on a European 30/360 basis. To calculate settlement amounts, real accrued interest and clean price are multiplied by the indexation ratio for the settlement date, as for France s issues. Also, as in France, coupon and redemption amounts are calculated by multiplying the real value of the payment by the indexation ratio for the payment date. All five coupon-paying bonds pay on 1 December each year. 

However, the subtraction form is widely accepted. After all, there are other difficulties involved which have to be accepted—invariably there is a term mismatch between linker and comparator, there is reinvestment risk, and there is the fact that the real yield is not a pnre real yield (as we explained in the UK section), because of the indexation lag. A truer measure of break-even inflation would be achieved if we were lucky enough to have zero coupon linkers with no lag and a zero coupon nominal of identical term. 

Calcnlating and publishing the coupons for index-linked gilts after the publication of each month s inflation data and inflation index. 

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