The stock rally that began in 2009 may not have received much respect from some investors, but it likely still has legs, says Laszlo Birinyi, president of Birinyi Associates.

The Standard & Poor's 500 Index has soared 153 percent from its March 2009 low.

But, "I'm not seeing many signs of excess," Birinyi told The New York Times. "We have not reached the exuberant phase of the market cycle."

Editor’s Note: Dow Predicted Will Hit 60,000 — Buy These 4 Stocks Now(Shocking)

Given their sharp rise of the past few months, stocks are due to move without direction or slide for a bit, Birinyi says. But ultimately, they're probably headed higher.

As for investors' attitude, "in some ways, it's the most detested bull market of all time," Michael Hartnett, chief global equity strategist at Bank of America told The Times.

"A big part of that comes from what preceded this market: the bursting of two large equity bubbles within a 10-year period, and the terrible trauma that caused."

But in several ways, it's been an impressive bull run. For example, the S&P 500 Index never fell below its 2012 opening level last year.

And the same is true of its opening level this year, creating the second longest winning streak since 1928, Paul Hickey, co-founder of Bespoke Investment Group told The Times.

Jeremy Siegel, a finance professor at the University of Pennsylvania who has been bullish on stocks for quite some time, probably wouldn't be surprised by that streak.

He told CNBC the Dow Jones Industrial Average will likely reach 16,000 to 17,000 by year-end. "And I think 18,000 is definitely achievable in 2014," he said.

The Dow was trading at 15,370 mid-morning Tuesday.

Editor’s Note: Dow Predicted Will Hit 60,000 — Buy These 4 Stocks Now(Shocking)