Reinvestment risk

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. 

With respect to the first assumption, the risk that an investor faces is that future interest rates will be less than the yield to maturity at the time the bond is purchased. This risk is called reinvestment risk. As for the second assumption, if the bond is not held to maturity, it may have to be sold for less than its purchase price, resulting in a return that is less than the yield to maturity. This risk is called interest rate risk. 

There are two characteristics of a bond that affect the degree of reinvestment risk. First, for a given yield to maturity and a given nonzero coupon rate, the longer the maturity the more the bond s total return is dependent on reinvestment income to realize the yield to maturity at the time of purchase. The implication is that the yield to maturity measure for long-term coupon bonds tells us little about the potential return an investor may real-... 

Although it is commonly quoted by market participants, the cash flow yield suffers from limitations similar to the yield to maturity. These shortcomings include (1) the projected cash flows assume that the prepayment speed will be realized (2) the projected cash flows are assumed to be reinvested at the cash flow yield and (3) the mortgage-backed or asset-backed security is assumed to be held until the final payoff of all the loans in the pool based on some prepayment assumption. If the cash flows are reinvested at rate lower than the cash flow yield (i.e., reinvestment risk) or if actual prepayments differ from those projected, then the cash flow yield will not be realized. Mortgage-backed and asset-backed securities are particularly sensitive to reinvestment risk since payments are usually monthly and include principal repayments as well as interest. 

These matching errors are less alarming than they might appear, because all known price information is built into the real yield formula as soon as it is published. Two things really matter, in terms of the achieved real yield relative to the quoted real yield at purchase firstly, the difference between future inflation over the life of the bond and the 3% inflation assumption used in the market convention for calculating yields, and secondly (as with any coupon bond) reinvestment risk. However, we are getting ahead of ourselves—the next section handles the market s yield conventions. 

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. 

On a hold-to-maturity basis, as we ve said, inflation-linked government bonds provide as close an approximation to a guaranteed real return as is currently available. If we can assume the government is credit risk-free, then there remain only two modest reasons for us to couch the above statement with the cautionary nse of the word approximation. There will inevitably always be a small conpon reinvestment risk and also a small degree of real value uncertainty becanse of the indexation lag. 

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. 

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. 

These bonds have the longest duration of all indexed securities and no reinvestment risk. 

Annuity indexation. Indexed-annuity bonds have been issued in Australia, although not by the central government. They pay a fixed annuity payment plus a varying element that compensates for inflation. These bonds have the shortest duration and highest reinvestment risk of all index-linked debt securities. 

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. 

In a conventional sequential-pay structure, the other classes in the CMO receive some of their principal prepayments from the Z bond, which lowers their average-life volatility. Z bonds are an alternative for investors who might otherwise purchase Treasury zero-coupon bonds. Like zero coupons, these bonds have no reinvestment risk, but they have higher yields than Treasury strips with similar average lives. 

Cash flow yield calculated in this way is essentially a redemption yield calculated assuming a prepayment rate to project the cash flows. As such, it has the same drawbacks as the redemption yield for a plain vanilla bond it assumes that all the cash flows will be reinvested at the same interest rate and that the bond will be held to maturity. In fact, the potential inaccuracy is even greater for a mortgage-backed bond because the frequency of interest payments is higher, which makes the reinvestment risk greater. The final yield of a mortgage-backed bond depends on the performance of the mortgages in the pool—specifically, their prepayment pattern. 

In contrast to the situation in most strip markets. Treasury strips with very short maturities do not trade expensive relative to the curve. When the yield curve is positive, short strips are often in demand because they enable investors to match liabilities without reinvestment risk and at a higher yield than they could get on coupon bonds of the same maturity. The Treasury strip yield curve, on the other hand, has been inverted from before there was a market. In other government strip markets, such as Frances, however, short maturities of up to three years are often well bid. 

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. These bonds have the longest duration of all indexed securities and no reinvestment risk. 

Series EE savings bonds have become extremely popular due to their simplicity. Savings bonds are actually discount bonds or zero-coupon bonds, since no interest is delivered during the time the bond is held. There is no reinvestment risk on the interest payments because the interest is reinvested internally at a constant yield, automatically compounding. These bonds are also known as accrual bonds because the interest is added to the redemption value rather than being paid out. The interest is all paid out at maturity. 

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