But Doll told CNBC that while stocks should be higher at the end of both this year and next year, there are still many unknowns about President Trump versus candidate Trump that could send the market into a tail spin.
"The main thing is we just don't know. There will be a lot of trial balloons. For the market to have a serious problem, it's going to have to be convinced the protectionist Donald Trump is showing up more than the growth Donald Trump. We elected both Donald Trumps, but I think the growth one is going to win out," said Doll, chief equity strategist at Nuveen Asset Management.
Stocks have rallied since Trump was elected president in a surprise upset over Hillary Clinton. Trump's promise of a big stimulus package, tax cuts and less regulation has boosted the dollar and triggered a selloff in the bond market.
"That's part of the Trump rally. The markets assume we elected pro-growth Donald Trump. He was the guy who was going to cut taxes and roll back regulation, but he also talked about tariffs and tearing up trade deals — things that are anti-growth. Where did that president-elect go?" he said. "Part of the market going up is Donald Trump is not doing scorched earth on all kinds of stuff which he kind of implied he would while he was campaigning."
Doll said some of the negative side of Trump could emerge, and that would cause a selloff in stocks and buying in bonds.
"I'm not convinced it's a one-way street. We'll get some of those days. Under the surface, the trend has changed. Whatever you thought about stocks before the election, you have to like them a little more, and whatever you think about bonds, you have to like them a little less," he said.
Doll notes that the economy was already improving before the election, and rates were already moving higher. But the fact that Trump is trying to spur growth has made stocks more appealing, even in a rising interest rate environment.
"We don't know what policies are going to pass or how long it will take to enact them, or how good they will be," he said. Trump's tax overhaul would be the first big tax cut package since the Reagan era, Doll said.
Stocks should continue to gain, and the bull market could be extended particularly if there is higher growth.
"We're probably heading into a period where bonds go down and stocks are up — not tons, because the P/E rate is not going to go up if interest rates are going up," he said.
As for the market's performance next year, "the default would be we're up some more and that's my best guess, but I don't know if it's a lot or a little. There is more uncertainty ... If he shuts the borders because the anti-trade Trump comes out, we'll have a recession and the market will go down. If that side stays quiet and he cuts taxes, it could be up a lot," he said.
The is about 3 percent higher since the election, and all major indices have hit new highs. The 10-year Treasury yield has risen as high as 2.40 from 1.80 percent.
The "Trump trade" has become the reflation trade, with investors buying cyclical stocks and selling bonds. Financials have benefited as well as industrials.
"Technically, we've come a long way in a short period of time. If you've got too many bonds and not enough stocks, maybe today is not the day to do the reversal. I would say any rally in bonds, you trim them, and any pull back in stocks and cyclicals, you buy them," he said.
Doll said stocks should see a year-end rally. "With seasonality, more likely it's going to be higher than where we are. I hesitate because we've run so hard for the last couple of weeks. Maybe we take a breath and then we come on with a year-end rally. I don't know. But I can't believe it would (go) straight up to the end of the year," he said.
The stock market could see better gains with Trump as president than if Clinton had won the election, Doll said. Her policies were not so aimed at jump-starting growth, but during the election, the market did better when it was perceived Clinton was winning.
"The market was saying we like certainty, and we don't like uncertainty and Donald Trump is more uncertainty than Clinton. There are going to be more good things and more bad things and we're going to see what happens," he said. "Underneath a lot of this, the economy is dong a little better and we can't lose sight of that."
Doll said there is a chance growth could be better, and that could also feed a rally.
"For the last few years, the search for yield, perceived safety and low volatility has been an investor's dream, and billions and billions and billions have gone into those things," he said. "That is over and done and it's unwinding. That is because the economy is doing better and inflation is picking up a bit."