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I am sure you have noticed it. But a vague feeling of optimism has been permeating the markets this year. The news on the economy has not been especially good, but many had expected worse. Germany still seems to be avoiding the worse effects of the euro crisis, the US is growing at an okay pace, and China is apparently set to avoid a hard landing – however, as yesterday’s Bull and Bear pointed out, this is far from certain. (See China hard landing still on the cards ) .Then there is the massive pile of cash sitting on corporate balance sheets, which increases the prospect of a kind of mergers and acquisition mania,  especially in the mining and commodities sector. There are even signs that inflation is falling. And then there is the little matter of bonds being so expensive these days that equities look cheap in comparison. So, yes, you can see why some people are saying the runes look good. It is just that there is another way of looking at things.

Today, my main focus is the US, but since there is usually a reasonable correlation between key stock market indices in the US and UK, I think the implications remain relevant to British investors.

First of all, take the cyclically adjusted price to earnings ratio, or CAPE. This is a measure that was popularised by the US economist Robert Shiller, who also gave his name to the Case Shiller housing index in the US. The ratio compares stock market capitalisation with average earnings over the previous ten years, and is adjusted to allow for inflation. According to Capital Economics, the value of CAPE at the end of last month was 22. The average since 1900 has been 15. Of course the ratio has been higher, much higher. For example, in 2000 it was around 45. But, then again, in the 1980s it was lower. And in 1987, just before the crash, the ratio was similar to the current level.

Secondly, take the equity Q ratio. This is measured by taking the market capitalisation of corporations, and dividing by the fundamental value, or cost of replacing assets. According to Capital Economics, the level of equity Q for all US nonfarm corporations was 0.82 at the end of Q3 last year. Markets have risen since, and Capital Economics reckons it is now around 0.96. The average since 1900 was 0.65.

Both measures would suggest equities are around 45 per cent over-priced.

Well, they may be, but there are lots of counter arguments.

Counter argument number one is a fairly obvious point. Yes, equities are expensive relative to an average since 1900, but do we really want to draw the comparison so far back. As you probably know, the yield on bonds was lower than the yield on equities during the first half of the century, so it is hardly surprising to learn that equities are still quite expensive compared to those of the first half of the last century. Much depends on whether you believe the last few decades have seen – and excuse the cliché – a new paradigm.

Secondly, the problem may not be that companies are over-priced, rather their performance in recent years has been abnormally poor. After all, the West has experienced its worse downturn in a very long time, so it is hardly surprising that valuations to performance in recent years have been so high.

But there is another point, and this relates to how accountants value companies.

In the US, R&D is typically shown in corporate accounts as an expense rather than an investment. If instead, intangible assets, such as the value of a brand name, patents, investment in staff, etc were shown as assets, the story changes. Capital Economics estimates that R&D on intangibles, as a percentage of total investment has risen 5.9 per cent in 1960 to 11.1 per cent in 2007.

Making the revised calculation of CAPE after allowing for investment in intangibles is not easy, but Capital Economics reckons that, after doing this, the difference between the current level of CAPE and the historical level since 1900 is reduced significantly. Likewise, equity Q falls too. In fact, Capital Economics reckons that at the end of Q3 last year, equity Q adjusted for R&D spending was 0.76.

Mind you, it is still saying equities are overvalued by this measure. It is merely saying that after taking into account investment into intangibles, equities are not quite so overvalued.

This is what it boils down to. CAPE suggests the S&P 500 is overvalued to the tune of 45 per cent. Factor in the effect of R&D spending, and the over valuation is nearer to 19 per cent.

These views and comments are those of the author alone and do not necessarily reflect the view of The Share Centre, its officers and employees