"The bull market would be more sustainable if investors fretted about all sorts of possible bearish problems," he said. The economy isn't all that strong, for example, and it might be much weaker if the Federal Reserve were not holding interest rates artificially low and buying bonds at a relentless pace. The Fed decided on Wednesday to continue its easy monetary policy, but it will have to tighten up eventually, perhaps causing stresses in the markets.
People aren't worrying nearly enough about such things for his taste. "That," he said, "is making me a little bit nervous."
Of course, the market is not in perpetual upward motion; it fluctuates daily. After reaching a high on Tuesday, the Standard & Poor's 500-stock index dropped on Wednesday, dipped slightly Thursday and rose on Friday. But whether the news has been good or bad, investors have remained remarkably unruffled — and stock prices have trended higher, without a major break, for a very long time.
Based on valuations like the price-to-earnings ratio, we're not in a full-blown asset bubble at the moment, in Mr. Yardeni's view. Corporate earnings have increased steadily, and he contends that they will keep doing so, providing the foundation for a rise in the stock market for some time.
But he says there is now a significant danger that excessive exuberance could threaten the market's climb.
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"I expect the market to rise," he said. "But I'm worried that it could just go through the roof. If it does that, we could have a nasty correction afterward, maybe a bear market, and that could cause serious problems for the economy."
After all, there hasn't been a significant market correction—defined as a drop in average share prices of more than 10 percent—since a 19.4 percent decline in the S& P 500 in 2011. (After stock prices drop 20 percent, a correction becomes a bear market, in Wall Street parlance.)
And since the start of 2012, the market has never been in negative territory for a calendar year. Since the market nadir in March 2009, the S&P 500 has already returned more than 180 percent, including dividends. Under conditions like that, it's been hard not to make money, if you've been wise or lucky enough to have had money in the stock market.
There are many signs that people are no longer worrying all that much about the possibility of another market meltdown, of the kind that occurred in 2008, when the S.& P. 500 returned a negative 37 percent, dividends included. A global financial crisis and recession brought the economy to a perilous state back then, but for several years now, the Fed and other central banks have been flooding the world with liquidity.
(Read more: Taper tease? Market worries Fed will end easing)
In its meeting last week, the Fed again delayed carrying out an exit strategy, or taper, from its bond-buying program known as quantitative easing. Janet L. Yellen, the Fed's current vice chairwoman, has been nominated to succeed Ben S. Bernanke at the helm, and she will have to deal with some delicate issues for the markets.
Short-term interest rates remain extraordinarily low, and with the debt-ceiling crisis and partial government shutdown already fading into the past, medium- and longer-term rates have receded, too. These ultralow rates have made equity prices a bargain, at least in comparison with bonds, according to most financial models.
As the Fed's balance sheet has swelled—it is heading toward $4 trillion, according to a new Fed study, up from $800 billion before the financial crisis—the stock market has risen, and many investors have noticed the correlation. While there is still plenty of money on the sidelines, many investors are responding enthusiastically now—excessively so, in Mr. Yardeni's view.
One widely followed gauge of market sentiment, the Investors Intelligence Bull/Bear Ratio, soared last week to 3.19 from 1.96 two weeks earlier. (The percentage of market bears fell to 16.5 percent, the lowest since May 2011.) Ratios of 3.0 or higher have often signaled the onset of corrections or bear markets.
Mr. Yardeni isn't the only longtime bull to note the possibility of a melt-up. Laszlo Birinyi, an independent strategist based in Westport, Conn., did so in his current newsletter, called Reminiscences. "Historically, bull markets of this length and strength have a period of exuberance," he said. "It doesn't have to happen but it usually does and we would certainly leave the door open for what is termed a melt-up."
Still, he reiterated his conviction that the bull market's legs are strong enough to carry it considerably further—if excesses or external shocks don't batter it too badly. And so did Mr. Yardeni, picking an easy-to-remember target of 2,014 for the S&P 500 next year. (It was nearly 1,762 on Friday.) "I just hope the market doesn't blow right past my target in the next few months," he said.