The inflation hydra

But at least in those good old days there was only one rate of inflation to worry about. When news readers and politicians talked about 'inflation' you knew - or, if you were clever, you knew - they were referring to the Retail Prices Index (RPI). In the UK, inflation was the RPI and RPI was the rate of inflation.

Today it's all so complicated and inflation, the monster, has become inflation, the hydra, a many-headed beast. Talk about the UK's general rate of inflation and you can pick from up to 10 indices, each one describing something slightly different; each one producing a different number. And, what's worse, RPI - the oldest and best-known inflation rate; the one that, in a perverse way, we have got to know and love - is under threat. It has been designated "unfit for purpose" by the National Statistician, Jil Matheson, the government’s chief adviser on statistics.

Next stop, you might think, RPI will be scrapped; calculated no longer; replaced by a new-fangled measure of inflation. That would be serious partly because RPI is used so widely. Best known is its use to protect the value of the income and capital paid out on the £380bn-worth of index-linked gilt-edged stock outstanding and on index-linked National Savings certificates, the original 'Granny bonds'. In addition, UK utilities providers, whose prices are often governed by a formula linked to RPI, have issued RPI-linked bonds as have the partnerships building so-called private finance initiative schemes, whose future revenues will be tied to inflation.

But, more important, the demise of RPI would lead to real losses for all those who own index-linked securities. That's because, compared with the other ways in which the Office for National Statistics (ONS) calculates inflation in the UK, RPI gets the highest figure. So, for holders of any assets whose returns are linked to inflation, RPI would be the index of choice. Have your returns switched to another measure of inflation and they will be lower.

Meanwhile, everyone intuitively knows that the government wants to scrap RPI as the measure that drives returns on 'linkers'. George Osborne signalled as much when he became Chancellor of the Exchequer. In his first Budget he severed the link that upgrades welfare benefits, tax credits and public sector pensions to RPI and replaced it with the Consumer Prices Index (CPI), which consistently gets a lower figure (see chart, below). Now that RPI has been downgraded and no longer gets the moniker 'National Statistic', it seems just a matter of time before it is axed from gilts and National Savings products, too; maybe the ONS won't even bother to calculate it.

Relax. RPI won't be scrapped for years. However much the government would like to do it, its hands are tied by the small print of National Savings certificates and by the Bank of England's obligation to protect investors in gilt-edged securities. Besides which, the RPI ‘brand’ remains strong. The CPI and other measures of inflation - the Tax & Price index, or the so-called RPIX, for example - simply don't have the same level of acceptance or the RPI's longevity, with its detailed price history stretching back to 1947. So the use of RPI may wither but, given that the longest-dated index linker does not mature until 2068, it will survive most readers of Investors Chronicle.

Even so, it's important to know what's happening to inflation's calculations if only because inflation is such an important factor in assessing investments. An allowance for inflation - for the loss of purchasing power - is always implicit, and sometimes explicit in the cost of capital that an investor uses to assess any proposition. So if you cannot rely on the accuracy of an inflation rate - or you don't know which one to use - then you cannot work out your own cost of capital accurately and you won't know how much to pay for an investment. Similarly, while you hold an asset, if you have to calculate its fair value, then, without the correct rate of inflation, you may not know whether you are running a profit or a loss.

Yet RPI may not be the best measure of inflation because of flaws in its underlying arithmetic. To explain, let's digress for a moment.

Investors should know the difference between the average of a series of numbers and a compound growth rate; both are vital in investment calculations. To find the average - also known as the 'mean' or the 'arithmetic mean' - we simply aggregate each number in a series then divide by the number of observations. So, if 15 observations add up to 33.3, the average is 2.22 - simple enough. When we calculate a compound growth rate, which is also known as a 'geometric mean', we are answering the question: what is the average rate of change needed to get from starting point 'A' to finishing point 'B'? Use the same set of data as above - which just happens to be the annual inflation rate from 1997 to 2012 as measured by the Consumer Prices Index - and you start at an index level of 89.7, end at 123.0 and have a compound growth rate, or geometric mean, of 2.13 per cent.

True, there is only a small difference between those two averages - 2.22 per cent versus 2.13 per cent. Small, but significant. They show that if we want to know what’s likely to be a typical annual inflation rate based on those 15 years of data, we will use the arithmetic mean and answer ‘2.22 per cent’. But if we just want to know the average pace at which prices were changing over that particular period, we’ll use the geometric mean and answer '2.13 per cent'. Neither is right or wrong, but one may be more appropriate than the other, depending on what's wanted from the statistic.

Something similar is happening in the way that the ONS calculates the UK’s inflation indices. Deep within the calculations for the RPI, the arithmetic mean is widely used for the price changes of raw data before they are aggregated into elementary indices. In contrast, within the CPI, the geometric mean - or another formula that gives the same answer - is used.

These differences have two effects. First, using the arithmetic mean makes the RPI an odd-ball inflation rate, which does not meet international standards; that's why the National Statistician decided it can no longer be a 'National Statistic'. Second, and more important, it gives rise to what statisticians label ‘the formula effect’; or, as the ONS’s technical manual on constructing the inflation indices says: using the arithmetic mean "introduces a small upward bias in the overall price index. This phenomenon is known as 'price bounce'." It is to do with the variation in the data from which the averages are generated. As long as there is some variation, then the arithmetic mean will always be higher than the geometric mean. And this is why the inflation rate as measured by RPI is always higher than inflation measured by CPI.

Still, solutions are at hand. The first is to correct RPI for its mathematical oddities. Since March, the ONS has done this by calculating RPI using geometric means at its core, rather than arithmetic means. It calls this revised inflation figure 'RPIJ' - the 'J' standing for Jevons, after William Jevons, a 19th century English statistician who formalised the calculation of the geometric mean. The effect is shown clearly in the chart. Using the Jevons formula, RPIJ (the orange line) lags RPI (the black line) for the duration of the available data.

The weights of inflation: how spending categories influence the inflation indices

An alternative solution might have been to use the CPI. After all, it is the government's inflation measure of choice; a super-duper measure of inflation that uses a wider basket of goods and services than RPI - about 700 items - and the spending of a wider sample of the population to gauge its weightings.

The trouble is that CPI contains its own substantial flaw. Since it was introduced in 1997 as the UK's Harmonised Index of Consumer Prices - to be in harmony with inflation calculations elsewhere in the EU - the CPI has excluded owner-occupiers' housing costs from its constituents. This is a glaring absence since these account for 10 per cent of household spending on average. The excuse was that there was little agreement among the EU's statistical chiefs about how home-ownership costs should be included. Their absence just happened to suit the Bank of England, which began to use CPI as its inflation-targeting measure from 2003. That's because changes in interest rates - and hence mortgage rates - have perverse effects on inflation. A rise in interest rates - aimed at slowing inflation - will cause the price level to blip upwards initially.

Yet the absence of home-ownership costs has a big effect, as shown in the table, 'The weights of inflation'. In the RPI, housing costs - including mortgage costs - are 28.3 per cent of the total, but in the CPI they are just 13.7 per cent. Sure, there are other differences, too. Most obviously, RPI puts greater importance on food, drink and tobacco and less on clothes and recreation. But the basic distortion is caused by the absence of mortgage costs from the CPI.

Since February, this has been solved by the introduction of the CPIH. As the suffix 'H' implies, it is a CPI adjusted to include home ownership costs. Specifically, it uses the idea of 'rental equivalence' to impute the costs of home ownership by answering the question: "How much would I have to pay to live in a home like mine?"

The outcome is a measure of inflation that consistently shows the lowest rate of change of the four main indices. That won't necessarily always be the case and whether that makes it better, worse or just different largely depends on the aims of the user. Still, that's one of the good things about measuring inflation in the UK. If you don't like the answer that one index provides, you can always choose another. That's something that does not look set to change in a hurry. The days of simplicity are over and the monster will remain many-headed.

Just fancy that... what's been added and removed from the RPI