Inflationary expectations

Prevailing interest rates probably tend to reflect an estimate of future inflation and contain a component that can be attributed loosely to inflationary expectations. However, the classical treatment is to assume that an inflation-free interest rate, r and average inflation rate, r, over the project lifetime can be identified. A discount factor (1 + r) can be modified (25) so that... 

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 relationship between inflation-linked and nominal debt provides a market-based reading of inflationary expectations, although several... 

We have already described the notion of bond trading in three dimensions, thanks to the availability of linkers. Perhaps the most important aspect of this 3D trading is the ability to implement a view with much greater precision. Often, when trades are done in nominals, they really reflect a view on inflation, bnt because nominal yields do not just represent inflationary expectations, this is an imprecise enactment of that view. With inflation-linked bonds, investors can express a much purer inflation expectation. 

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 problem is that true inflationary expectations are not observable. We cannot disaggregate break-even inflation into inflationary expectations... 

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%. 

The presence of convexity means that both our forward bond curves understate true expectations of the future paths of nominal and real short-term rates. However, the value placed on convexity is a function of volatility, which is much greater in nominals than in linkers. Therefore, an implied path of future inflation derived in this way will understate true inflationary expectations because of convexity, if there are no other influences, such as the risk premium. 

Nominal yield (y) = real yield (r) + inflationary expectations (/)... 

The only mathematically correct way to report duration for a mixed portfolio of nominals and linkers, in a way that adds some useful information, is to drop the standard duration figure and instead show two new numbers duration with respect to real yield and duration with respect to inflationary expectations. These are the two main partial derivatives of the Fisher equation. 

What the formula tells us is that, theoretically, the variance of nominal yields could actually be lower than that for linker real yields if real yields and inflationary expectations were sufficiently highly negatively correlated, i.e., the beta could exceed one. We d place heavy emphasis on the word theoretically, and we mention it only because Wesley Phoa entertains the possibility in his book. He cites analysis suggesting that there is a long-term negative correlation between GDP and inflation, then (reasonably) argues that real yields are a function of real GDP, hence real yields and break-evens should be inversely related. 

UK index-linked gilts have existed since March 1981, with the FT All Index-Linked coming into existence at the end of that year. Unsurprisingly, index-linked have underperformed conventional gilts over their full history, given the collapse in inflation and inflationary expectations since the market s inception. In March 1981, the launch month of the first linker (2% IL 1996), headline UK inflation was 12.6%. We have seen inflation fall by 10%. (See Exhibit 8.12.)... 

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