On the Republican side, Sen. Ted Cruz came in first, upsetting Donald Trump who went into the Iowa caucuses as the perceived front-runner. But both of them were followed closely by Sen. Marco Rubio, who took 23 percent to Trump's 24 and Cruz's 28 percent.
"The market basically reads a win as Trump losing, which increases the odds that the establishment will coalesce around Rubio. I think the big impact right now is you have the Republicans starting to normalize, and there's now questions being raised on the Democratic side," said Clifton.
"It's probably too early for a major market impact, but the big change is Rubio is now the favorite and Trump no longer is and that creates a more stable type of candidate. You know what he's going to do," he said, adding investors would view Rubio favorably.
It's not that the market loves Clinton, but she was viewed as a known entity and relatively moderate candidate. But Wall Street has been hoping for a more mainstream traditional candidate on the Republican side, and Rubio is more consistent with that than Trump or Cruz.
"The fact Trump came in second would probably be a positive in this marketplace but it is offset by the strong showing Bernie Sanders had. The worst-case scenario would be coming out of New Hampshire with the two leaders Donald Trump and Bernie Sanders," said Art Hogan, market strategist at Wunderlich Securities.
Sanders represents the left wing of the Democratic Party, and he has pushed ideas such as free tuition at public colleges and other programs that would increase government spending. "He's proposing huge tax increases, and he's not shy about it," Clifton said.
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Stocks were sharply lower Tuesday as oil declined 3 percent, for a two-day drop of more than 8 percent. David Kelly, chief global strategist at JPMorgan Funds, said the market Tuesday was not reacting to the election, but the outcome in Iowa was actually favorable for markets.
"Markets don't like uncertainty, and the more extreme the candidates that get nominated the greater the uncertainty. The fact that on the Democratic side, a more centrist candidate won, although narrowly, and on the Republican side, there was a swing towards a more centrist candidate. I think in both those cases, those things would be regarded as market friendly," said Kelly. He said the centrist candidates are those less likely to make big policy changes that would unsettle markets.
"I think the coalescing of the Republican voters around one candidate who could be more appealing to independent voters is probably a positive for the Republicans," said Kelly.
Clifton said Cruz, who is at the conservative end of the Republican Party, does not have the staying power to win the GOP nomination. Although he could prevail in other primaries, he would not win big important states like California or Illinois.
Rubio needs to keep the momentum going and place at least second in New Hampshire, Clifton said.
"The point is that he has the highest favorability rating in the party," said Clifton. "Usually people with high favorability ratings are the ones that can weather the storm. (Jeb) Bush put $20 million against him and he's still doing OK. ... It's all based on the idea that Rubio comes in second place in New Hampshire."
Analysts say Trump, although well-known on Wall Street, was not embraced by Wall Street because of his unpredictability.
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"I think the macro sentiment that's building right now is you have a populist revolt that's happening, and the implication of that is you're going to have less trade, possibly higher taxes," said Clifton.
But Trump is also viewed positively by some because there is a perceived lack of American leadership on the world stage, and some investors believe that's one area he could improve, Clifton said.
"There's just an uncertainty to him," said Clifton. "We have no idea what he's going to do. He's brand new. He's totally unpredictable."
If Clinton starts to look as if she will not be the winner, analysts expect the market to react, as it adjusts to the policies of the new front-runner.
"She's got a greater than 50 percent probability to be the next president. I would say that's the consensus on Wall Street and our view is that probability is going to whittle down over the next few months," said Cilfton.
He said if Sanders were to get the Democratic nod, the Democratic Party may broker a deal to run another candidate, like Vice President Joe Biden, who in October said he would not run.
Among topics investors will focus on during the election are the minimum wage, tax reform, health-care reform, financial services reform, energy and climate change, and cybersecurity, according to Barclays strategists.