Any novice investor might be forgiven for thinking that "valuation" is something the finance industry has managed to sort out by now.

When investment bankers set a price for, say, an initial public offering (IPO) - think of Eircom and C&C recently - they do this on the basis of some fairly technical valuation models. Unfortunately, the answer that they get depends partly on the model that is used and mostly on the assumptions that the bankers have to make to get the models to work.

Because of the inherent sensitivity of the results to those assumptions, the forecast price of an IPO is almost always expressed as a fairly wide range rather than a single number.

Our novice investor will probably be surprised to learn that most of the methods used to value a company usually end up with the same answer - provided they are operated by people who know what they are doing. Any business is worth the (discounted) value of future profits.

That word "discounted" is the first complication - it involves making all sorts of assumptions about interest rates. Another obvious problem arises from the need to forecast future profits.

A cynical investor often smells a rat at this stage and observes that valuation can be as much art as science. "You can come up with any number you like" is often the surprised cry of anyone who spends 10 minutes or so with a spreadsheet valuation model.

A slightly more sophisticated observation is that companies, like pretty much everything else, are merely worth what somebody else will pay for them. And people have been known to pay some rather strange prices for all kinds of assets.

Housing and art are but two contemporary example of markets that are often cited as defying rational analysis, but any analyst worth half his salt could come up with a model and a set of assumptions that could justify current prices.

For property, a popular model uses the ratio of house prices to household income as a benchmark. When this number is "high", property is expensive, and vice versa.

But what is meant by "high"? The analyst almost always plots a chart of his favourite measure, draws in the historic average and compares the current level of the valuation metric to that average. If there is a big gap then we have either expensive or cheap housing.

In exactly the same fashion, stock analysts compare the price of a company to its income. The corporate price/earnings (p/e) ratio is used in exactly the same way, for exactly the same reasons, as the house price /household income ratio.

Robert Schiller, the US academic, is famous for writing a book called Irrational Exuberance, which was published almost exactly at the same time as global stock markets peaked in March 2000. There is only one chart in that book, one that describes the long-term history of the US stock market's p/e ratio.

Mr Schiller's book is a marvellous exposition of trendy "behavioural finance" theory but is rooted in that one chart. His argument was straightforward: because the actual p/e ratio was so far above its long-term average, the US stock market was headed for big trouble. The accuracy of this forecast has turned Mr Schiller into a superstar.

Similar techniques produce similar messages. And Mr Schiller is still warning about the level of the stock market today. While it may not be as expensive as it was in early 2000, the equity market is still extremely over-valued.

Some other analysts reach exactly the same conclusion using different valuation techniques.

A well-known financial consultancy in the UK, Smithers & Co, is warning that the US market is due for a major tumble. Its analysis is slightly more sophisticated than a simple p/e ratio but the underlying principles are the same.

Smithers looks at the ratio of the worth of the company in terms of its net assets - what it would cost to buy them on the open market - relative to what the market thinks those assets are worth - the price of the company. In principle, this ratio should be equal to one - the replacement cost of a firm's assets should be equal to the value (price) of the firm.

The chart describes this ratio in terms of the implied over- /undervaluation of the US market as a whole. For example, at the start of 2000, this valuation measure suggested the US market had to fall by 50 per cent to restore equilibrium valuation. It currently says the market is roughly 47 per cent over-valued.

There are all sorts of issues that can be raised at this point.

The measure of mis-valuation assumes that the market always reverts back to the long-term average valuation level (this may or may not be true). It is clearly hopeless over quite long periods of time - several years - as a forecasting tool. Markets may be wrongly valued but they can stay that way for so long that any investor who uses this tool exclusively could end up bankrupt.

Valuation measures such as these are mute as to precisely how the market anomaly will be corrected: equity prices may fall to resolve over-valuation but earnings and net assets could also rise to do some or all of the corrective work.

But the essential point is that the US and, to a lesser extent, many other markets are expensive. In such circumstances, natural bulls of equities (such as this author) need a lot of things to go right for markets to record modest rises or even to hold existing levels.

My often-expressed belief that equities are in for a period of single-digit gains has been based on this kind of optimism: a start of a prolonged economic upswing at a time of benign inflation and moderate geopolitical risk provides precisely the conditions for markets to hold on to "stretched" valuations.

As it happens, I still believe this to be true. But those views, I suspect, are about to be sorely tested. Iraq, oil prices, inflation and interest rates are all pointing the wrong way.

An optimist might be tempted to conclude that we are about to be provided with a buying opportunity.