Objectively, it is quite true that non-American markets (with the possible exception of Japan) are better value than Wall Street. They have not been so in thrall to the irrational exuberance described by Dr Greenspan. But in the short- term this may not matter much. The fact that valuations are less stretched provides only a small degree of protection against a crash on Wall Street: if their markets go down, ours will too.
In the longer term it does matter, because on a three-to-five year view, real underlying values will determine share prices: if our values are reasonable, this is comfort indeed, on the longer-term time-scale of most investors.
There are a number of different ways of valuing share prices, but most rely on the relationship between bonds and shares: what companies earn in profits compared with the yield on bonds. The charts show two ways of presenting this. The first, on the left, comes from Charterhouse and is based on the relationship between the two elements, but graded as to safety. The higher the company sector's earnings in relation to the yield on gilts, the safer the investment in equities.
The virtue of this concept is its simplicity. Back in 1987, just before the October stock market crash, this indicator showed "red alert". The crash brought it back into the safety zone, which should have encouraged any brave investor to plunge again into the market. But the same indicator would have given sell-signals in 1993 and 1994. And, except in the very short-term, that would not have been very profitable, since any ground lost by share prices was quickly recovered.
Investors then were rescued by the generally upward trend in company earnings and downward trend in gilt yields, which brought the valuation back without any sustained weakness in the share prices.
A more complicated way of expressing the relationship is shown in the right-hand graph. Merrill Lynch takes the relationship between bond yields and the market's price/earnings ratio, and adds the market's consensus view on what will happen to profits for the next couple of years. The resulting "fair value" range for share prices is also shown here. It is a nice "fit". The level for share prices stays in the range, except before the 1987 crash when prices shot beyond it, signalling that equities should be sold. After the crash, shares quickly came back below the range, signalling that they should be bought.
Since then, there have been times when shares have been above the range, but as the range itself has been rising (except in 1994), that has not really mattered too much.
Looking forward, Merrill Lynch reckons that this year we will see higher gilt yields, offset by rising profits. Their forecast is for 15 per cent earnings per share growth in 1997, followed by 5 per cent in 1998.
The conclusion? That the range for share prices will remain steady, but other factors may encourage shares to rise within the band. Those factors include the ten- dency of directors of public firms to buy stocks in their own companies rather than sell them, and the excessive gloominess of investors, given the call/put ratio on the options market. When all are pessimistic and trading puts rather than calls, that is probably a buy signal.
So here are two professional investment advisers arguing that UK shares are not too high at the moment. While they are not cheap either, they may well go higher in the coming months. How should the rest of us regard this view in the light of Dr Greenspan's warning?
First, Dr Greenspan was talking about the euphoria in the US. Here, we do not have such a mood,partly for political reasons, partly because there has not been the same cascade of money into shares via mutual funds. Also, the economic expansion is less mature.
Then, since UK expansion is solid but only "middle-aged", the profit forecasts should also be secure. Provided profits go on rising, the basic underpinnings of the market will be sound.
So,what could go wrong here? If the UK fundamentals are sound, any fall induced by transatlantic trouble would actually create a buying opportunity. You might be a bit early; you might have to wait for other investors to overcome their knee-jerk response to US events. But on a medium-term view, a sharp "correction" would amount to good news.
From a purely UK perspective, three main things could go wrong. One is connected with politics. The next UK government could be a minority one; or there might be some seismic political change out there that we cannot yet fully see, but which would lead to an anti-business government.
The second factor is the European economy. France's low-level civil disorder might spread and start to do serious economic damage to the whole region. The present weak recovery would be aborted, and the economic downturn would do lasting damage to the concept of the European Union.
Finally, there is the R-word - recession in the US. There has been some talk across the Atlantic of a dip into recession at some stage next year. There is no real evidence of that at the moment, but unless you believe that business cycles are a thing of the past, at some stage there will be another recession.
Of course, there may be legitimate reason to think that cycles in the future will be less marked than in the past, largely because the service side of an economy always seems less prone to fluctuations of output than the manufacturing side. The more the balance of our economies shifts to services, the smaller the size of the swings.
But to push the argument - to say that there will be no recessions in the future - is surely absurd. It is not a question of whether, but rather of when.
Dr Greenspan knows that fact of life, but perhaps he thought that his fellow Americans had forgotten it. His aim, therefore, must have been to prick the balloon slowly - an almost impossible trick to pull.
Those few words in his speech can be seen as a way of stopping the great bout of US euphoria getting out of hand. If, during the next few weeks, US markets do con- tinue to come back sharply, be thankful. The bubble will indeed have been pricked, hopefully before it had the chance to become so distended that financial deflation would have lead to economic deflation, too.
But if US markets do shrug this one off, become more worried, for then there will certainly be more trouble in store.