Analysis/Martin Wolf: The past is a foreign country. Not so very long ago, the advice given to investors in equity markets was: "Buy and hold." The more sophisticated investors were also advised to "buy on the dips".

Unfortunately, both pieces of advice made sense only as marketing devices. They have led millions of investors into disaster. So can we do better than these rules? If we can, should investors be putting their faith once more in equities? The answers- to these questions are: "yes" and "only to a limited extent".

US markets remain dangerously expensive. They are more likely than not to disappoint in the years ahead.

The sensible strategy is not "buy and hold", but "buy cheap and sell dear". Even this strategy must be modified by an appreciation of one's individual time horizon. Even if equities were reasonably priced, they would still be a risky investment for investors whose time horizon is not a couple of decades.

How then is one to decide whether shares are cheap or expensive? As Andrew Smithers and Stephen Wright argue in an important book, there are three alternatives.* These are: the "Q ratio", which is the ratio of the market value of equities to the replacement cost of underlying corporate assets; the cyclically adjusted ratio of equity prices to corporate earnings (the p/e ratio); and the dividend discount model, which relates the prospective cash flow from equities to the cost of capital. Properly calculated, these would all give the same answer.

What then do these measures tell us about the value of the US and UK markets, the two biggest western equity markets?

Long-run data on Q are available only for the US. They show that at its peak in 2000, the market was more highly valued than at any time since 1900. Astonishingly, it was over 30 per cent more highly valued than in 1929. Since then the market has fallen a long way. Nevertheless, today the market needs to fall by a further third to reach its historic mean valuation. Given the tendency of markets to overshoot, it could well fall further.

Data on cyclically-adjusted p/e ratios give much the same picture. This is the favoured measure of another analyst, Robert Shiller of Yale University.** Again, Prof Shiller shows that valuations in 2000 were higher than ever before. At their peak, cyclically adjusted p/e ratios reached 40 against a geometric mean of just above 13 since 1881. In late January of this year, the ratio was 22. Today, it must be higher still. So, the market is decidedly expensive by historical standards.

Now consider the dividend discount model. At present, the dividend yield on US stocks is a miserable 1.6 per cent. If one allows for share buy-backs, the yield might rise to 2.5 per cent. Even this is little more than half the long-run average dividend yield of 4.7 per cent.

Moreover, as Robert Arnott and Peter Bernstein have shown, dividends on existing companies tend to grow at about the rate of labour productivity or gross domestic product per head.*** Even if US trend productivity growth were now to be 2 per cent a year, this would imply a real return of only 4½ per cent on US equities. But that is only two-thirds of the long-term historic return on US equities.

US equities have, in sum, moved from being grotesquely expensive to merely expensive. They are far from fair value. But this is much less true for UK stocks. Datastream's estimate of the most recent p/e ratio on the market as a whole, of just over 15, is only slightly above its average of 14 since 1965.

The dividend yield is now 3.7 per cent, which is modestly below its average of 4.5 per cent since 1973. Yet, while these facts provide support for the UK market, one must recognise the risk of contagion from any further corrections on Wall Street.

If US equities look expensive, there are always two possible responses. One is to argue that "things are different this time". Some would argue, for example, that the real return on bonds is also exceptionally low at present. But, as Cazenove argues in its latest view of equity strategy, today's low real yields on US long-dated bonds look unsustainable. If they are not, they must imply a permanently weak economy and so weak profits and earnings. That, in turn, undermines the case for equities.

The alternative response is to admit that valuations are telling us something about the likely direction of share prices. This does not mean that one can predict future movements in these prices with any degree of certainty. But one can say something about probabilities. When valuations are high, they are more likely to fall in the years ahead, and vice versa.

Because the probability of a decline in valuations is high at extremes, buy-and-hold is a poor strategy. But if one follows the alternative of buying equities when self-evidently cheap and selling when dear, then today is not the time to bet on US equities. The prudent investor would remain very cautious.

• Valuing Wall Street: Protecting Wealth in Turbulent Markets (McGraw-Hill, 2000).
• Irrational Exuberance (Princeton University Press, 2000).
• What risk premium is normal? Financial Analysts Journal, March/ April 2002 (Association for Investment Management and Research).