Real term structure

ESTIMATING THE REAL TERM STRUCTURE OF INTEREST RATES... 

The drawbacks of each of these approaches are apparent. A rather more valid and sound approach is to constmct a term structure of the real interest rates, which would indicate, in exactly the same way that the conventional forward rate curve does for nominal rates, the market s expectatimis rat future inflation rates. In countries where there are liquid markets in both conventional and inflation-indexed bmids, we can observe a nominal and a real yield curve. It then becomes possible to estimate both a conventional and a real term structure using these allows us to create pairs of hypothetical conventional and indexed bonds that have identical maturity dates, for any point on the term structure. We could then apply the break-even approach to any pair of bonds... 

In this section, we review one method that can be used to estimate and fit a real term structure. 

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. 

FIGURE 6.5 United Kingdran market nominal and real term structure of interest rates, July 1999. (Yield source BoE)... 

Brown, R., Schaefer, S., 1996. Ten years of the real term structure 1984-1994.1. Fixed Income... 

On the other hand, the Hoar Committee s estimate for the UK did not include some significant factors, and some costs that were considered have increased in real terms since the estimates were made. Larger plants and structures are more common, and even when there is no increase in size more intensive use of equipment is demanded. As a result, the real cost of downtime or unavailability, and of dislocation to users of, for example, motorway viaducts while repairs are made, have increased appreciably. Moreover, maintenance and rectification are labour intensive activities, and hence particularly susceptible to the effects of inflation. The increases probably outweigh the savings mentioned, and the current cost of corrosion in the UK is probably around 4% of GNP. As future savings depend on the improvement being maintained despite pressures to reduce first costs, a sound economic approach to corrosion is no less important than it was in 1970. 

We use here throughout the term configurations as far as different arrangements of electrons are concerned, while by the term structure a spatial arrangement of the atomic nuclei is indicated. Contrary to the latter, the separate configuration has no real physical meaning. 

Does activation succeed in bringing the jobless into work If so, under which conditions in terms of implementation, governance structures and labour market environment does activation work best Is there a general or context-specific pattern of viable activation strategies This volume tries to give answers to these research questions by bringing together country expertise with available empirical evidence on the outcomes of activation policies in real terms. 

This is where we meet the famous double helix immortalised by many books, articles, television programmes and of course films. The DNA double helix is the key element of DNA three dimensional structure. In the 1950s, when James Watson and Francis Crick first proposed the double helix as the key piece of DNA three dimensional structure, they generated enormous scientific and popular excitement, since for the first time the inheritance of genetic information could be understood explicitly in terms of a real chemical structure In order to appreciate this structure, there is a requirement to understand more about the heterocyclic bases (see Section 1.4.1) and their unrivalled capacity for specific hydrogen bonding. All these bases are aromatic but paradoxically prefer keto/amine to enol/imine tautomeric forms... 

Exact, perfect order of a periodic or quasi-periodic crystal is never obtained by a real atomic arrangement. All real crystals are more or less disordered. We describe the disorder by the term structural defect with respect to the idealized periodic structure. Many crystal properties (e.g. electrical conductivity and mechanical properties) are strongly dependent on the defect structure. 

Amorphous rare earth alloys exhibit the same variety of magnetic effects as is found for RI compounds. In addition their resistivity often manifests a behaviour which is typical of amorphous metals such as resistivity minima and negative temperature coefficients of resistivity. It is important to note that the unifying feature of all amorphous metals is the real space structure which can be described in terms o a random close packing model of hard spheres (Cargill, 1975). The magnetic feature thus depends on the type and concentration of the... 

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. 

As we have said already, trading in nominal space has its analogue in real space. So there are directional trades, real yield curve trades, and anomaly (or relative value ) trades between issues. There are also trades between the real and nominal markets, in inflation space — buying and selling break-even inflation, and expressing views on the term structure of break-even inflation. Exhibits 8.17 and 8.18 show histories of real yields and break-even inflation, respectively, for the three main European inflation-linked markets, while Exhibit 8.19 highlights the volatility in the UK s real yield and break-even inflation curves. 

Observing the trading patterns of a liquid market in inflation-indexed bonds enables analysts to draw conclusions about nominal versus real interest rates and to construct an inflation term structure. Such analysis is problematic, since conventional and indexed bonds typically differ considerably in liquidity. Nevertheless, as explained above, it is usually possible to infer market estimates of inflation expectations from the difference between the yields of the two types of bonds. 

Where a liquid market in indexed bonds exists across a reasonable maturity term structure, it is possible to construct a term structure of inflation rates. In essence, the process involves constructing the nominal and real interest rate term structures, then using them to infer an inflation term structure. This, in turn, can be used to calculate a forward expected inflation rate for any term or a forward inflation curve in the same way that a forward interest rate curve is constructed. 

The U.S. Federal Reserve uses an iterative technique to construct a term structure of expected inflation rates. First the nominal interest rate term structure is constructed using a version of the model described in Waggoner (1997) and discussed in James and Webber (2000). An initial assumed inflation term structure is then used to infer a term structure of real interest rates. This assumed inflation curve is usually set at a flat 3 or 5 percent. The real interest rate curve is then used to calculate an implied real interest rate forward curve. Next, the Fisher identity is applied at each point along the nominal and real interest rate forward... 

Brown, R., and S. Schaefer. 1994. The Term Structure of Real Interest Rates and the Cox, IngersoU and Ross AoAA. Journal of Financial Economics 35 1, 3-42. 

This is all we need to calculate the distribution of species and the average number of HBs. The latter is sometimes referred to as the structure of the system. In real water, a larger number of HBs in the system is indeed associated with a higher degree of structure. In the 1-D model, we shall continue to use the term structure although there is clearly no such structure as it exists in liquid water. 

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