What it means is that there are always reasons to be anxious about the current level of share prices if you want to find them - and the higher the market goes during a bull market, the more serious those worries seem to become.
The successful trader, so your friendly broker will tell you, must be bold and blithe enough to ignore the warning voices that will inevitably accompany any protracted surge in the stock market - else he will miss the best part of the fun.
Like most things that old hands say about the stock market, this always seems better advice in hindsight - when you know what subsequently happened - than it does at the time.
Of course, it seems obvious now that the Mexican debt crisis in August 1982 marked the start of the current 15-year bull market in shares: it just didn't seem that way at the time.
Likewise, any old fool can see that the 1987 crash was just a blip in the long upward march of Wall Street.
We know now that it was merely an ordinary correction to a clearly overvalued market which unexpectedly spiralled out of control thanks to a previously untested invention called portfolio insurance.
This was the technique, you will recall, invented by some American computer boffins which allowed computers to run portfolios for institutions and ordered them to sell whenever shares fell more than a certain percentage.
lt took the 1987 crash to discover it had a serious bug - once the market's fall had reached a certain point, the system merely became a recipe for auto da fe, with each wave of selling automatically creating more orders to sell.
At the time, however, most people worried that the crash was a portent of some far more serious economic setback - and for some countries, including Britain, where inflation was starting to take off after the Lawson boom, those concerns were not entirely misplaced.
Now it does not take a genius to notice that the worriers are at it all over again. The difference this time is that the wall of worry the market is climbing is not economic - the US economy, as Mr Greenspan conceded, has rarely looked healthier - but simply the value of the market itself.
lt is hard, as I said a few weeks ago, not to take seriously the many well-regarded voices which now believe that Wall Street has become a very risky place at current valuation levels.
On almost any historical valuation criterion, we have entered unprecedented territory. And since the voices now include Alan Greenspan, the chairman of the Federal Reserve, the man whose decisions can do most to stop the markets in its tracks, it is no longer simply enough merely to scoff at the worriers' concerns.
This week Mr Greenspan, giving his half-yearly account of the state of the economy to Congress, repeated his concerns about the current bull market.
He repeated his warning that the stock market was showing signs of "irrational exuberance" and suggested that higher interest rates could be needed soon to stop a resurgence of inflation. There can be no doubt that the world's most powerful central banker was going out of his way to try to dampen Wall Street's continued buoyancy.
As the market took little notice of Mr Greenspan's hint last time, why should it pay any attention now? Well, one reason is that it usually takes actions, not words, to stop a genuinely rampant bull market.
As long as Mr Greenspan goes on talking about the need for interest rate rises, but refrains from actually making them, some investors may be tempted to go on calling his bluff.
That in a way is precisely how the irrationality which the Fed chairman was warning about manifests itself.
But Mr Greenspan's problem is that he knows - and admitted again this week - that the US economy is in remarkably good shape.
What concerns him most, I suspect, is not the fact that the market has been strong, but the way that those who have been busy pushing the bull market case have now started to justify their case.
As conventional valuation criteria no longer support current share prices, the recourse of the bulls now is to the "once in a lifetime" rationale that spells particular danger.
There was a telling example the other day at the Davos economic forum, where a group of prominent academics and businessmen sat down to debate - in all earnestness - the proposition that the "business cycle" has been abolished.
The argument here is that computers and new business practices, such as "just in time" delivery of goods, are eliminating the need for companies to hold large amounts of stocks.
lt is the ups and downs of the stock cycle which some believe is the principal cause of the the business cycle itself.
Do you believe that? If you do, then this is your kind of stock market. I know that I don't - and it is clear that Mr Greenspan does not either.
History, he said, is full of "new eras" that turned out to be mirages. The four most dangerous words in investment, as another old market adage goes, are "this time it is different". It never is.Reuse content