So is it too late for investors to join the party?
The US sharemarket has already more than doubled since the dark days of 2009. Records are being set, and most indexes have risen nearly every week this year.
Nearly all strategists point out that it's much better to buy at a market bottom than to invest after a record has been set. Nonetheless, for those willing to accept the risk, there are strong arguments, based on history and on market fundamentals, for believing the bull market may still have some way to run.
Chief among them is the expansive monetary policy of the US Federal Reserve.
"The old song on Wall Street is 'Don't fight the Fed', and that certainly has been the case in this market," said Byron Wien of the Blackstone Group, a veteran of many market rallies and slumps. "The Fed and other central banks have been driving the market, and there's no sign that's going to stop."
Another critical factor is the flow of funds into the market, said Laszlo Birinyi, who runs a stock research firm in Conn.
"There is still a lot of money sitting on the sidelines - and there are a lot of people who are still jumping in, and that, in itself, is a good thing for the market," he said.
His calculations show the net inflow into stocks in the past year has totalled $US76.7 billion. Inflows amount to $US27.75 billion so far this year, he said, and barring a big shock, they are likely to continue.
"We're in the fourth and last stage of a long-running bull market," he said. "We think there's a lot more to come."
No one really knows whether history is a reliable guide, but the pattern of past bull markets also suggests this one could continue to flourish. According to the Bespoke Investment Group, the near four-year run of the US market is the eighth-longest in the past 100 years, and it is the sixth-strongest, in terms of the return of the S&P 500 index. And since 1900, when the Dow Jones Industrial Average reached a new high, as it did Tuesday, it has averaged a 7.1 per cent rise over the next year.
"We believe stock valuations are still reasonable, and that the momentum of the market will keep moving it upward," Bespoke co-founder Paul Hickey said.
Because of the intervention of the Fed, even some market bears are reluctant to bet against the rally.
"This is impressive, no doubt about it," David Rosenberg, a former chief North American economist at Merrill Lynch and now chief strategist of Gluskin Sheff in Toronto, said.
Rosenberg has a reputation for being a "permabear", and he has recently emphasised on investing in high-yield bonds and corporate credit instruments over stocks. As for the immediate future of the market, he said, "I think we're overdue for a correction."
Major problems on the horizon include a weak economy that is being hobbled further by the recent payroll tax increase and the federal budget cuts that have just been put in place. And the troubles in the eurozone, which flared last month in Italy, are far from over.
Yet Rosenberg is reluctant to predict a sustained market decline. Precisely because the economy is weak, the central banks will be forced to keep short-term rates low.
"People seeking income have been fleeing other asset classes," he said, "and they have been moving their money into the market."
Not everyone is sanguine, however.
"It's getting downright embarrassing to be bearish with all this exuberance around," said Rob Arnott, the chairman of Research Affiliates, an asset management firm in California.
"With so many people eager to buy stocks, it's a wonderful time for us to take some risk off the table."
Arnott, who manages the Pimco All Asset Fund, said the economy was weak enough that there was a reasonable chance the US was already back in an undeclared recession. An economic or financial shock could induce a sharp fall on the market, he said.
"My view is simple," he said. "Could this rally continue? Absolutely. But do I want to take a risk on a rally that will at some point certainly reverse and leave a lot of people helplessly trying to de-risk in an unliquid market decline? No. I don't want to be part of that crowd."