"I think depending on the severity of it, we have a pullback or a correction but because of the economic indicators I'm looking at, I'm not worried a recession is around the corner, and as a result, I don't think we're heading for a bear market," Stovall said.
The bond market has been a big beneficiary of this "geopolitical" trade, with the 10-year Treasury yield breaking below a range it has been in for months. The 10-year yield, which moves opposite to prices, had been trading steadily between 2.30 and 2.60 percent since mid-November.
This week, buying took the yield to a low of 2.21 percent and strategists say it could fall even further.
Aaron Kohli, rate strategist at BMO, said the market is definitely trading on fears about North Korea and other geopolitical events, but the big change in market attitude was in March, when Republicans failed to pass a new health-care bill. That legislation was seen as a necessary step ahead of tax reform, and markets now see both as in limbo.
"It's been about reading the tea leaves of the health-care failure, and it's been slowly taking back some of the inflation and growth expectations," said Kohli. "It's been the crescendo with these [geopolitical] headlines, or tape bombs."
The worries about North Korea and Syria come at the same time global investors are already on edge about the potential for the National Front candidate Marine Le Pen to win the French presidential election. While not expected, a victory by Le Pen could lead to France leaving the euro zone. The first round vote is April 23, and the second round is May 7.
"While people are shifting some risk, there's a general belief [former French Economy Minister Emmanuel] Macron is going to be the winner," said Peter Boockvar, chief market analyst at The Lindsey Group. "The most important thing people should be focused on is are we going to get tax reform, and what the formulation is going to be. It's apparently not what people entered the year hoping for, and they should also pay attention to the fact that central banks around the world are taking away the punch bowl."
Boockvar said ultimately geopolitical fears don't last that long, but they have created important technical moves against the backdrop of a market that could be disappointed by what stimulus comes out of Washington. The bond market, he said has also been moving on concerns the Fed will keep raising rates while the economy is not growing that much.
But the fact geopolitical tensions have been running high has clearly filtered through to markets. On Wednesday, stocks cut some losses and the dollar strengthened after Russia and the U.S. showed a willingness to work on their relationship and some thorny issues like Syria and North Korea.
"On the margin, it's an easing of tension. ... The U.S. missile attack is not the beginning of a wholesale military involvement in Syria. North Korea, not clear," said Marc Chandler, Brown Brothers Harriman head of foreign exchange strategy.
U.S. Secretary of State Rex Tillerson held a news briefing with his Russian counterpart Wednesday, committed to working together despite apparent disagreement.
Shortly after the briefing, President Donald Trump was quoted in a Wall Street Journal report saying he believes the dollar was too strong and that he likes low interest rates. That sent the greenback reeling and it was still under pressure Thursday.
That in turn helped gold, which already crossed above its 200-day moving average in the spot market this week. Gold futures were at $1,286 per ounce in Thursday trading, and gold is seen as the ultimate safe hold. Gold futures were up 2.4 percent week to date.
Suki Cooper, precious metals analyst at Standard Chartered Bank, said the metal could easily go to $1,300 and trade higher above that psychological threshold in the near term. "The weakness we've seen in the dollar has certainly helped gold extend its gains," she said.
Cooper said there has not been this much investor interest since the Brexit vote last June and around the U.S. election. "This time its geopolitics that stoked the safe haven demand," she said.
"It looks like there's a good base for gold prices here, and I would expect prices to extend their gains," she said.
Watch: Another North Korea nuclear test?