Bonds True Return

The true yield measure derived in the previous section is not as straightforward as the one given earlier for the T-bill. Because aT-bill has only a single cash flow, its maturity value is known, so its return is easily 

It would certainly help investors if they could analyze bonds as though they had single cash flows. Investors often buy bonds against liabilities that they must discharge on known future dates. It would be a comfort if they could be sure the bonds returns would meet their liability requirements. Put very simply, this is the concept of immunization. 

The difficulty in calculating a bond s return is that its future value is not known with certainty, because it depends on the rates at which the interim cash flows can be reinvested, and these rates cannot be predicted. A number of approaches have been proposed that get around this. These are described in the following paragraphs, assuming simple interest rate environments. 

The simplest approach assumes, somewhat unrealistically, that the yield curve is flat and moves only in parallel shifts, up or down. It considers a bond to be a package of zero-coupon securities whose values are discounted and added together to give its theoretical price. The advantage of this approach is that each cash flow is discounted at the interest rate for the relevant term, rather than at a single internal rate of return, as in the conventional approach. Given the flat yield curve, however, this approach reduces to (17.3). An example of its application follows. 

A bond s return is influenced by changes in the yield curve that occur after its purchase. Say the yield curve moves in a parallel shift to a new level, rmj- In that case, the expected future value of the bond changes. Assuming s interest periods from the value date to a specified horizon date, the new value of the bond on that horizon date is given by equation (17.5). 

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Resonance is an extremely useful concept that we ll return to on numerous occasions throughout the rest of this book. We ll see in Chapter 15, for instance, that the six carbon-carbon bonds in so-called aromatic compounds, such as benzene, are equivalent and that benzene is best represented as a hybrid of two resonance forms. Although an individual resonance form seems to imply that benzene has alternating single and double bonds, neither form is correct by itself. The true benzene structure is a hybrid of the two individual forms, and all six carbon-carbon bonds are equivalent. This symmetrical distribution of electrons around the molecule is evident in an electrostatic potential map. 

All the machinery of the world composes only one body, all the parts of which are bound by means which partake of the nature of the extremes. This bond is hidden, this knot is secret but it is not the less real, and it is by mean of it that all these parts lend themselves to mutual aid, since there is a relation, and a true commerce between them. The emissary spirits of the superior natures make and maintain this communication some go away while others come some return to their source while others descend from it the last come takes their place, the others depart in their turn, still others succeed them and by this continual flux and reflux Nature is renewed and maintained. These are the wings of Mercury, by the aid of which this messenger of the gods made such frequent visits to the inhabitants of the Heavens and the Earth. 

K, to transform a set of potential reaction sites, utilizing instances (e.g., Kj,i) of ab-initio-operator. Successful applications of operators generate new instances of atom-bond-configuration. Kf, to return a Boolean value of true, when the encoded set of prespecified conditions are achieved, and false, otherwise. 

O-H bond, which implies either that the thermal vibrations are anisotropic (which is certainly true) or that the H-O-H angles deviate slightly from the tetrahedral value, an average of the possible misalignments being seen. We shall return to this later. 

The market convention is sometimes simply to double the semiannual yield to obtain the annualized yields, despite the fact that this produces an inaccurate result. It is only acceptable to do this for rough calculations. An annualized yield obtained in this manner is known as a hand equivalent yield. It was noted earlier that the one disadvantage of the YTM measure is that its calculation incorporates the unrealistic assumption that each coupon payment, as it becomes due, is reinvested at the rate rm. Another disadvantage is that it does not deal with the situation in which investors do not hold their bonds to maturity. In these cases, the redemption yield will not be as great. Investors might therefore be interested in other measures of return, such as the equivalent zero-coupon yield, considered a true yield. 

Most bonds pay a part of their total return during their lifetimes, in the form of coupon interest. Because of this, a bonds term to maturity does not reflect the true period over which its return is earned. Term to maturity also fails to give an accurate picture of the trading characteristics of a bond or to provide a basis for comparing it with other bonds having similar maturities. Clearly, a more accurate measure is needed. 

As noted earlier, indexation lags prevent indexed bonds returns from being completely inflation-proof According to Deacon and Derry (1998), this suggests that an indexed bond can be regarded as a combination of a true indexed instrument (with no lag) and an nonindexed bond. Equation (12.13) expresses the price-yield relationship for a bond whose indexation lag is exactly one coupon period. 

The true yield measure derived in the previous section is not as straightforward as the one given earlier for the T-bill. Because a T-bill has only a single cash flow, its maturity value is known, so its return is easily calculated as its increase in value from start to maturity. Investors know that money put into a 90-day T-bill with a yield of 5 percent will have grown by 5 percent, compounded semiannually, at the end of three months. No such certainty is possible with coupon-bearing bonds. Consider although the investors in the 90-day T-bill are assured of a 5 percent yield after ninety days, they don t know what their investment will be worth after, say, sixty days or at what yield they will be able to reinvest their money when the bill matures. Such uncertainties don t effect the return of the short-term bill, but they have a critical impact on the return of coupon bonds. 

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