The Jonathan Davis Column
A few years ago, the big craze at Christmas was to make a present of a Rubik's Cube. This year, a wise present for the canny stock market investor might well be a crash course in what market aficionados know as "Tobin's q". I am grateful to Andrew Smithers, chairman of the investment consultancy firm of Smithers & Co, for a fascinating insight into this improbably named tool for evaluating the state of the world's stock markets.

If you don't know what Tobin's q ratio is, the chances are that you are not alone. But be warned - it is important; and it is not for the fainthearted. For the message that it is transmitting today is uncompromisingly one of warning about the risks in the markets at their current levels.

Tobin's q ratio is the invention of a distinguished American economist by the name of James Tobin, who won the Nobel Prize in 1981 for his pioneering work In a number of economic subjects, of which the stock market was just one. He was interested in the economic behaviour of the stock market and its relationship with the real economy.

One of his great insights was to see that you could use aggregate national income statistics to take the temperature, as it were, of the stock market at any point in time. By comparing the replacement cost value of the corporate sector's assets with the value of the stock market at the same moment, you can derive an overall sense of how far the market is deviating from its fundamental value.

This relationship is the famous q ratio. In effect, it is the reading on the stock market's thermometer. It tells us whether the market is running hot or cold at any time - and by how far. Not for nothing does the Federal Reserve in the United States use a very similar measure to try and judge whether the stock market is overheating or not.

It is, let us be clear, a theoretical construct developed by a man who described himself, openly and with pride, as "an ivory tower economist". It tells us nothing about what the market is going to do tomorrow. But what it does tell us is where the current level of the markets is in relationship to the long run historical average to which it must over time revert.

In the words of Andrew Smithers, who has done more than anyone to bring the concept to the attention of the City's fund management community, it is not strictly speaking a valuation tool at all, but a measure of the risk in the market at any time. The higher the ratio stands, the greater the risk that the markets will soon fall back to their historical average levels and beyond.

What worries the aficionados of Tobin's q is that the ratio is now standing at levels in both the United States and the UK which are as high as they have ever been in the past. The chart shows how the ratio has moved over the years since the start of the great bull market of the 1920s. (The pre-war data is the result of some outstanding historical detective work by a British economist, Stephen Wright of Cambridge University). The message is about as clear as it could be: until this month's squalls in the markets, prompted by the unfolding financial crisis in the Asian region, both the UK and US markets were standing at dangerously high levels.

Andrew Smithers himself has no doubt what message investors should read into the chart's findings. Rather like Cassandra, he has been trying to sound the alarm for more than 18 months. In September 1996, he calculated that the UK market was "dangerously overpriced" at around 1.7 to 2.0 times its long-run historical average. The US market was even more overvalued on the same measure.

Yet since then the markets have continued to be strong, demonstrating that the ratio is indeed a measure of risk, not of the market's short term direction. The q ratio now is higher still. Does the market's strength invalidate the theory that lies behind Tobin's q? No. It merely emphasises that shares are volatile and more risky than other types of asset, which is precisely why they provide higher returns over long periods of time.

But what you can say - and Mr Smithers does, to who all who will listen - is that the further you look ahead, the higher the probability that returns from equities will now be poor or negative. He has a telling table which chronicles how share prices have performed in the five years after the q ratio has peaked in the past. The simple answer is: they go down. The minimum the q ratio has fallen in the past after a peak has been 46 per cent. The average fall from peak to trough has been 63 per cent.

The implication is that the US and UK stock markets are both heading for a substantial fall at some point in the next five years. This will be a familiar message to readers of this column, but this time at least you don't have to take my word for it. "Professor Tobin received a Nobel prize for his work and the US market may thus be said to be taking a $3 trillion bet that he should return his laurels," Mr Smithers commented last year, adding, "I expect him to be justified in keeping them." The markets are still making that bet, on both sides of the Atlantic, and making lots of money as a result of defying Mr Smithers' warnings, as he himself cheerfully admits. But then Cassandra never expected to be heard either.