NEW YORK — The bulls weren’t bullish enough.

The stock market just had its best first quarter in 14 years. The surge has sent Wall Street analysts, some of whose forecasts seemed too sunny three months ago, scrambling to raise their estimates for the year.

“That it’s up isn’t surprising. It’s the magnitude,” said Robert Doll, chief equity investment manager at BlackRock, the world’s biggest money manager.

Doll said stocks could rise 10 percent more before the end of the year. That would be enough to push the Dow Jones industrial average to an all-time high and the Standard & Poor’s 500 close to a record.

For the first three months of the year, the Dow was up 8 percent and the S&P 12 percent, in each case the best start since the great bull market of the 1990s. The Nasdaq composite index, made up of technology stocks, has had an even more remarkable run – up 19 percent for the year, its best start since 1991.

“I don’t think anyone could have predicted this,” said Chip Cobb, a senior vice president at Bryn Mawr Trust Asset Management. For these gains, he said, “I thought it would take all year.”

The jump gives money managers like Cobb hope that ordinary folks burned by two deep bear markets in a decade will start buying again, propelling the indexes even higher.

In a remarkable act of self-restraint – or foolishness, depending on your view – they have mostly stayed out of the market. One reason they may jump in now is that fear of looming disasters, such as a full-blown debt crisis in Europe or a second recession in the United States, has faded.

Bulls say investors will turn their attention to the only thing that really matters for stock prices in the long run – corporate profits.

Another hopeful sign for gains is that those who have been buying stocks appear to be taking bigger risks than before, suggesting growing confidence.

Last year, investors put much of their money into so-called defensive stocks, such as utilities and health care companies, which make money in bad times as well as good. This year, it’s the risky fare that’s being scooped up.

Financial stocks are up 22 percent, the best among the 10 industry groups within the S&P. Technology companies are up 21 percent. Consumer discretionary stocks, such as hotels and cable companies, are up 16 percent. Utilities are down 3 percent for the quarter, the only group in the red.

Standard & Poor’s Capital IQ, a research firm, predicted at the beginning of the year that the S&P would hit 1,400 by the end of the year. By March 15, it had hit 1,403, and Friday it was at 1,408.

“We were originally accused of being too optimistic,” said Sam Stovall, chief equity strategist at S&P Capital IQ. “It doesn’t mean we can’t have a 10 percent correction, but it’s unlikely we will.”

The Dow is less than 1,000 points below its all-time high of 14,164.53, set Oct. 9, 2007. The S&P is about 150 points from its record close of 1,565.15, set the same day.

The first day of the year set the tone. On Jan. 3, the Dow rose 180 points. Later that month, the Federal Reserve said it would probably keep benchmark interest rates near zero for almost three more years. That sent stocks to their highest levels since May 2011.

It was the best January for stocks since 1997. Skeptics pointed out that profits at U.S. companies, after jumping by double-digit percentages for eight quarters in a row, seemed to be growing much more slowly. They also worried that the number of shares of stock traded each day was low, which suggested a lack of conviction by buyers.

Stocks kept climbing anyway, passing two milestones in quick succession.

On Feb. 28, the Dow rose above 13,000 for the first time since May 2008, four months before the financial crisis hit that September. Two weeks later, it was the Nasdaq’s turn. It crossed 3,000 for the first time since the dot-com frenzy a dozen years earlier.

Even a few duds got caught in the upswing. The stocks of Microsoft and Cisco have barely budged this century. This year, they have have risen 24 percent and 17 percent, respectively. Dell, which has languished for years, is up 13 percent.

Some of the big winners of 2012 are perhaps less surprising: Apple has risen 48 percent. Lions Gate Entertainment, the company behind the hit movies “The Hunger Games” and “Twilight,” is up 67 percent.

The market also impressed long-time stock investors with the way it climbed – slowly and steadily, without the wild swings that characterized the market much of last year.

The gap between the daily high and low for the S&P has averaged about 0.9 percentage points. It was three times that early last fall, when the market was obsessed with debt problems in Europe and at home, among other fears.

Investor attention turns next to corporate earnings announcements, which begin when aluminum maker Alcoa, one of the 30 stocks that make up the Dow, reports April 10.

Companies in the S&P 500 are making more money than ever, an impressive feat in a tepid economic recovery.

Those who are bullish on stocks note that the S&P 500 trades at 12.9 times expected earnings this year, somewhat cheap compared with its 10-year average of 14.6.

The so-called forward earnings multiple is generally higher than the long-term average during bull markets. If it rose to 16 or 18 this year, stocks would be significantly higher than they are now, even if corporate earnings failed to grow at all.

Some investors say the bulls are fooling themselves if they think big profits this year are assured. Indeed, first-quarter profits for the S&P 500 are expected to fall 0.1 percent from a year earlier, according to a survey of analysts by FactSet, a provider of financial data.

That would be the first time in more than two years that earnings will not have grown. For the full year, analysts are expecting profits will rise a healthy 9 percent, but those predictions depend on a surge of 16 percent in the last three months.

“The idea that we’re going to have a huge rebound at the end of the year is unrealistic,” said Barry Knapp, head U.S. equity strategist at Barclays Capital.

Knapp said he’s bullish on technology stocks but the rest of the market has “overshot the fundamentals.”