Nominal bonds

VSEPR Number Nominal Bond Angles Hybrid Orbital Set... 

The VSEPR number for the P atom is 4, so that the nominal bond angles are 109° 28. However, the Lewis structure for POCI3 shows a double bond between P and O. (P is allowed to exceed the octet because of the availability of 3d orbitals.) The increased electron density in the P=0 bond would make the repulsion between the P=0 bond and the P—Cl bond greater than between two P—Cl bonds. The Cl—P—Cl angle is lowered and the Cl—P=0 angle increased. 

A number of types of configuration can be envisaged (1) open (X /2 = K/2+i) where the HOMO energy level is only part filled (2) pseudoclosed (K/i > /2+i > 0) where the LUMO level is nominally bonding and ready to accept more electrons (3) properly closed (K/2> 0. K/i+i 0) where the HOMO is bonding and the LUMO non- or antibonding (4) metaclosed (K/2 0- K/i n/2+1) where even the HOMO is non- or antibonding. 

People tend to regard inflation as bad for savers and good for borrowers, but this is an oversimplification. Inflation that is higher than expected results in an unanticipated transfer of real wealth from nominal bond investor to borrower, while lower-than-expected inflation results in an unanticipated transfer of real wealth from borrower to investor. Therefore, inflation uncertainty is (or should be) as much of a concern for borrowers... 

There were other, peripheral and often very intangible, arguments made in the early days. One commonly held opinion was that because a government issuing such bonds cannot debase the value of these liabilities with inflation, this demonstrated a strong anti-inflation commitment. This should, it was proposed, enhance credibility and reduce inflationary expectations, thereby enabling governments to issue nominal bonds on lower yields. 

The example of Japan, in the recent past, is one of a country that has suffered from unexpected disinflation and now deflation. This has resulted in an unanticipated real wealth transfer from issuers of nominal bonds to investors, resulting in a windfall loss to the government and windfall gains for investors. Had it issued inflation-linked JGBs, this would have tempered the escalation in Japan s public debt/GDP ratio a little. The unique economic structures and circumstances might not make Japan a particularly persuasive comparison to apply to other economies, the intention is simply to illustrate the risks of the unexpected. 

Inflation-linked bonds are a little less liquid than nominal bonds, but the possibility that this results in them trading cheaply—suffering an illiquidity discount —is contentious. We would propose that turnover is lower in linkers because they meet investor needs so well. They are natural buy-and-hold assets because they are worry-free core holdings. Thus, illiquidity, relative to nominals, is something investors in linkers understand and accept. It is not so much a penalty, more the price of success. 

No thumbnail sketch of the UK linker market s early days would be complete without a mention of the one-off innovation of an index-linked convertible gilt, nicknamed the Maggie Mays. The 2% Index-Linked 1999 was convertible into a nominal bond (10.25% 1999) at three future conversion dates. At a time when inflation remained volatile, and with the term to option expiry spanning a general election whose outcome was uncertain, seldom has so much optionality been sold so cheaply. The bonds were all (or almost all) converted. 

The presence of a risk-free real asset is of great value to the study of finance, lending itself to theoretical and behavioural analysis. In this section, we examine the relationship between inflation-linked bonds and nominal bonds, then show how this framework can be applied to the relationship with equities. 

The Fisher equation, which predated the existence of inflation-linked bond markets, states that a nominal bond yield is made up of three components—inflationary expectations, a required real yield that investors demand over and above those inflationary expectations, and a risk premium. The risk premium reflects the assumption that investors want additional compensation for accepting undesirable inflation risk when holding (therefore suboptimal) nominal bonds. 

So we have formally introduced the notion of break-even inflation, a term at the heart of inflation-linked bond analysis and trading. In principle it is the rate of inflation that will equate the returns on an inflation-linked bond and a comparator nominal bond issue of the same term. In theory, calculating it by simply subtracting a real yield from a nominal yield is a crude form of a properly compounded calculation, particularly when bond market conventions are semi-annual and what you should want is an annual measure of inflation. 

This may all seem rather convoluted, so a simple example might suffice to make the point clear. Let us assume that the average bond investor expects future long-term inflation to be 2.5%, and that the average investor is inflation risk averse, so be prepared to pay a 0.25% risk premium. On this basis alone, we would expect observed break-even inflation to be 2.75%. Now let us say that the govermnent also has inflationary expectations of 2.5%, but it prefers real liabilities to nominal liabilities, and places a 0.25% yield value on that preference. It will prefer to sell inflation-linked bonds rather than nominal bonds until break-even inflation falls to 2.25%. 

On this basis, there is a huge urge to say you can t do it, but we must try to offer something a little more constructive. Nobody ever asks what the duration of an equity is, but the question is almost equivalent—linkers, like equities, are a different asset class. There are equity duration measurements—price sensitivities with respect to changes in the earnings yield or dividend yield—and equities can be related to nominal bonds via a Fisher equation as we have shown, just as linkers are related to nominals via a Fisher equation. However, equity duration numbers are seldom calculated, and would never be used in a mixed portfolio of equities and bonds to give a total portfolio duration. 

N.B. Figures shown are for nonannualised monthly changes, and are in basis points. US and UK data since February 1997 France since September 1998. IL bonds used are TII 07, OATi 09, and UKT 2.5% 09, with appropriate nominal bond comparators. 

EXHIBIT 8.8 Monthly Changes in Real and Nominal Yields using UK IL 2009 and Nominal Bond of Similar Term (bp)... 

Investors who are long-familiar with nominal bonds should probably not even ask the question, thinking back to the Fisher equation. If they... 

An important aspect of trading these bonds is using expectations of future monthly changes in linking indices, provided by economists, to calculate expected forward real yields and expected forward break-even inflation. Making assumptions about future price index levels allows these forward aggregates to be calculated in the same way that forward nominal bond prices and yields are worked out. 

The less they shot, the more they left themselves open to media specnlation, a fact Woody Allen allnded to before production wrapped. As one of the many writers and performers who pitched in on the intermittently promising, yet ultimately un inly rebus that was finally released in the spring of 1967, Woody Allen felt obliged to place the film in a class by itself (Anoitymous, 1966) This is not only a satire. This is a crazy, for better or worse, work of art, one in which no less than an atomic blast conld stave off the flood of nominal Bonds, unleashed to fill the vacuum left by Sellers abandoned experiment... 

In [9], it is suggested to explicitly represent considered degradation phenomena in a nominal bond graph of the system once a mathematical model for them is available. However, if a mathematical model of a degradation process derived from first principles is not available, if a nominal parameter in the constitutive equation of an element is then replaced by a function of time so that measured data is fitted and can be extrapolated into the future, a bond graph representation might be a problem. If a resistance becomes time-varying as of sometime point to then this may be simply captured by a nonlinear modulated resistor. If the nominal capacitance Co in the constitutive equation q t) = Co e(t) of a capacitor is replaced by a time-dependent capacitance C t) then... 

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