Real yields curve

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... 

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. 

Real yield curves are of some use to investors, for a number of reasons. These include applications that arise in insurance investment management and corporate finance, such as the following ... 

In essence, the real yield curve can and should be used for all the purposes for which the nominal yield curve is used. Provided that there are enough liquid index-linked bonds in the market, the real term stmcture can be estimated using standard models, and the result is more valid as a measure of market inflation expectations than any of the other methods that have been used in the past. 

So the prime obstacle to the development of a Euro-zone real yield curve was gone. And, as we have said, Greece has now joined the sector and other governments are understood to be considering entry, potentially adding points to the real yield curve and investor choice. 

EXHBir 6 UK Real Yield Curves at Different Inflation Assumptions (%)... 

So, we have argued, the economics of supply and demand make the risk premium a slippery concept. Bond mathematics now makes matters worse. This new aspect centres on the issue of convexity. We know that a forward curve of implied future short-term nominal rates can be derived from the nominal government bond curve. In principle, a forward curve of implied future short-term real rates can be similarly derived from the inflation-linked bond real yield curve. These two curves, taken together, should imply a future path of inflation, if we can set aside the risk premium for the moment. Unfortunately, that is not the case. 

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. 

Using equation 14.16, we can build a forward inflation curve provided we have the values of the index at present, as well as a set of zero-coupon bond prices of required credit quality. Following standard yield curve analysis, we may build the term structure from forward rates and therefore imply the real yield curve, or alternatively we may construct the real curve and project the forward rates. However, if we are using inflation swaps for the market price inputs, the former method is preferred because IL swaps are usually quoted in terms of a forward index value. 

In Figure 24 we have, schematically, displayed the general forms of the yield curves as computed by Franken. We note in passing that the experimental results presented in Figure 22 correspond to circumstances in which the product a is real. 

Anderson, N., Sleath, J., 1999. New estimates of the UK real and nominal yield curves. Bank of England Quarterly Bulletin, November, 39, 384—392. 

As above, assuming a constant average inflation rate, which is then used to calculate the value of the bond s coupon and redemption payments. The duration of the cash flow is then calculated by observing the effect of a parallel shift in the zero-coupon yield curve. By assuming a constant inflation rate and constant increase in the cash flow stream, a further assumption is made that the parallel shift in the yield curve is as a result of changes in real yields, not because of changes in inflation expectations. Therefore, this duration measure becomes in effect a real yield duration ... 

A repeat of the above procedure, with the additional step, after the shift in the yield curve, of recalculating the bond cash flows based on a new inflation forecast. This produces a duration measure that is a function of the level of nominal yields. This measure is in effect an inflation duration, or the sensitivity to changes in market inflation expectations, which is a different measure to the real yield duration ... 

From this average inflation curve, we can select specific inflation rates for each index-linked bond in our sample. The real yields on each indexed bond are then recalculated using these new inflation assumptions. From these yields the real forward curve is calculated, enabling us to produce a new estimate of the inflation term stmcture. This process is repeated until there is consistency between the inflation term stmcture used to estimate the real yields and that produced by Equation (6.5). 

Using the modified Waggoner method described in Chapter 5, the nominal spot yield curve for the gUt market in July 1999 is shown in Figure 6.5. The real term stmcture is also shown, which enables us to draw the implied forward inflation expectation curve, which is simply the difference between the first two curves. 

From the discussion in chapter we are aware that there are range of factors that impact on the shape and level of the yield curve. A combination of economic and non-economic factors are involved. A key factor is investor expectations, with respect to the level of inflation, and the level of real interest rates in the future. In the real world the market does not assume that either of these two factors is constant, however given that there is a high level uncertainty over anything longer than the short-term, generally there is an assumption about both inflation and interest rates to move towards some form of equilibrium in the long-term. 

It is possible to infer market expectations about the level of real interest rates going forward by observing yields in government index-linked bonds, which trade in a number of countries including the US and UK. The market s view on the future level of interest rates may also be inferred from the shape and level of the current yield curve. Again from chapter 6, we saw that the slope of the yield curve also has an information content. There is more than one way to interpret any given slope however, and this debate is still open. 

Forward real yield trades and forward BEI (inflation curve) trades. 

One argument against bootstrapping is that the theoretical zero-coupon yields obtained are too sensitive for real-world tradii. This is because the spot curve derivation requires a coupon yield for every year, even if, for example, the yield curve is constructed only fi-om 1-year, 10-year, and 30-year yields. The 30-year implied spot yield could be substantially higher... 

Real differences between the tensile and the compressive yield stresses of a material may cause the stress distribution within the test specimen to become very asymmetric at high strain levels. This cause the neutral axis to move from the center of the specimen toward the surface which is in compression. This effect, along with specimen anisotropy due to processing, may cause the shape of the stress-strain curve obtained in flexure to dif-... 

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