Inflation-linked bonds real yields

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. 

EXHBIT 8.11 Long Inflation-Linked Bond Real Yields Less Equity Dividend Yields (%)... 

Also the simple difference between the yield of conventional and inflation-linked bonds or yield spread is an indicator for expected inflation. For example, on 18 September 2014 the 10-year UK 0 1/8% inflation-linked 2024 had a money yield of 2.125% and a real yield of -0.410%, assuming an inflation of 2.571%. Differently, the 10-year benchmark, the UK T A% 2023 had a gross... 

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. 

Bond valuation with real cash flows and yields We currently illustrate the pricing of inflation-linked bonds adopting real cash flows. As noted earlier, according to Fisher s theory, the real yield is given by the following equation ... 

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. 

The presence of inflation-linked bonds allows the substitution of actual real yields for required real yields in the formula, to give... 

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%. 

However, when holding linkers in a performance-based portfolio, rather than as a passively matched investment, short-time horizons become paramount. Real yields on inflation-linked bonds do change, creating short-term volatility in their real and nominal returns. 

Indexed bonds real yields in other markets are also a factor in investors decisions. The integration of markets around the world in the past twenty years has increased global capital mobility, enabling investors to shun markets where inflation is high. Over time, therefore, expected returns should be roughly equal around the world, at least in developed and liquid markets, and so should real yields. Accordingly, index-linked bonds should have roughly similar real yields, whatever market they are traded in. 

One final point regarding duration is that it is possible to calculate a tax-adjusted duration for an index-linked bond in markets where there is a different tax treatment to indexed bonds compared to conventional bonds. In the United States market, the returns on indexed and conventional bonds are taxed in essentially the same manner, so that in similar fashion to Treasury strips, the inflation adjustment to the indexed bond s principal is taxable as it occurs, and not only on the maturity date. Therefore, in the US-indexed bonds do not offer protection against any impact of after-tax effects of high inflation. That is, Tips real yields reflect a premium for only pretax inflation risk. In the United Kingdom market however, index-linked gilts receive preferential tax treatment, so their yields... 

The simple approach, where the average expected inflation rate is calculated using the Fisher identity, so that the inflation estimate is regarded as the straight difference between the real yield on an index-linked bond, at an assumed average rate of inflation, and the yield on a conventional bond of similar maturity ... 

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. 

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). 

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. 

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. 

Duration increases as coupon and yield decrease. The lower the coupon, the greater the relative weight of the cash flows received on the maturity date, and this causes duration to rise. T ong the non—plain vanilla types of bonds are some whose coupon rate varies according to an index, usually the consumer price index. Index-linked bonds generally have much lower coupons than vanilla bonds with similar maturities. This is true because they are inflation-protected, causing the real yield required to be lower than the nominal yield, but their durations tend to be higher. 

Certain countries have markets in bonds whose coupon or final redemption payment, or both, are linked to their consumer price indexes. Generally, the most liquid markets in these inflation-indexed, or index-linked, debt instruments are the ones for government issues. Investors experiences with the bonds differ, since the securities were introduced at different times in different markets and so are designed differently. In some markets, for instance, only the coupon payment, and not the redemption value, is index-linked. This makes comparisons in terms of factors such as yield difficult and has in the past hindered arbitrageurs seeking to exploit real yield differences. This chapter highlights the basic concepts behind indexed bonds and how their structures may differ from market to market. 

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