Reports that President Donald Trump is leaning toward Federal Reserve governor Jerome Powell to be the next chairman of the Fed sent buyers into stocks and bonds on the view that he would be a safe bet who would not veer much from current Fed policy.

Whether hawk or dove, the next Fed chair is likely to face the same dilemmas as Fed Chair Janet Yellen — low inflation but an improving economy and strong job market. But how the leading candidates would respond could be extremely varied and create significantly different reactions in financial markets.

The candidate viewed as most similar to Yellen, and one that may cause the fewest ripples in financial markets, is Powell. Politico reported that Trump, after meeting with Yellen Thursday, was favoring Powell, who is being pushed by Treasury Secretary Steven Mnuchin.

“I think he’s the best choice and from a number of perspectives. He represents good continuity. We’re pretty clear on what his views are,” said Tom Simons, money market economist at Jefferies.

Treasury yields moved lower in late trading and stocks rose just ahead of the close on the Politico report. The 2-year yield slipped to 1.54 percent, after reaching 1.57 percent earlier in the day. Yields move opposite price.

“I also think he would have a relatively easy time getting through the approval process,” said Simons.

In an impromptu survey of a half-dozen strategists and economists, CNBC found there’s an overriding sense that the policy shifts by any of the candidates would likely be slow and gradual so as not to shock markets or slow down the economy. But just the very appointment of some candidates may spark a market reaction.

The two most hawkish choices are former Fed governor Kevin Warsh and Stanford University economist John Taylor. White House economic advisor Gary Cohn is also in the mix but he is seen as having low odds of being named, and the market is having a hard time pinning down his policy views.

“I think all of the candidates initially stick with the game plan of gradual hikes and balance-sheet normalization. Warsh and Taylor would likely be less sympathetic to short-term misses in the data or weakness in financial conditions and would want to keep the hiking cycle on track,” said Michelle Meyer, chief U.S. economist at Bank of America Merrill Lynch. “In contrast, Yellen, Powell and Cohn might be more inclined to pause if faced with uncertainty about the outlook.”

As of now, the Fed is forecasting three interest rate hikes next year, and Yellen’s Fed is expected to raise rates one last time in December. The Fed has also embarked on a systematic plan to roll down its balance sheet by buying fewer Treasury and mortgage securities.

Yellen is seen as having a keen interest in moving interest rates back to normal. The wild card for her, and the other candidates, is whether inflation picks up at all. Without that, she may not be able to raise rates that much next year.

“I don’t really think they’re going to get the data that will drive them to three moves next year, so our base case is they end up with two,” said Robert Tipp, chief investment strategist and head of global bonds and foreign exchange at PGIM Fixed Income. He said the inflation data is a factor for all the candidates.

However, Diane Swonk, CEO of DS Economics, said any of the candidates could be forced into four rate hikes in 2018 because of an improving economy. “It looks like a solid three, and maybe four,” she said.

Strategists said Powell could favor raising rates slightly more than Yellen but not much.

“Powell seems more hawkish than Yellen. He’s very qualified and played a lot of roles within the Fed,” said Tipp, who said Powell’s behavior suggests that he will be more consensus-driven. “There’s a lot of momentum for the measured approach. … He could be a step much more to continuity.”

But Tipp said Powell could turn out to be like Yellen “in reverse.” He said Yellen has proven to be more hawkish than her reputation as a dove would have suggested. Powell may be the opposite.

“In the case of Powell, he may be seen as going in with a slightly more hawkish edge. … He may end up holding back against some of the most hawkish elements of the Fed.”

Michael Schumacher, director, rates strategy at Wells Fargo, said Warsh and Taylor have had the most temporary impact on the market so far. He said speculation that Warsh was the front-runner two weeks ago caused a temporary curve flattening, meaning short-end Treasury yields rose faster than those on the long end.

That’s a signal of higher interest rates, and that’s the same reaction the markets could have if Warsh is named by Trump to head the Fed. Curve flattening is also seen as a sign that the Fed is moving on short-term rates, but the more subdued rate rise at the long end could signal the market is worried about the economy or even the Fed’s impact on the economy.

“What happened in the market is you saw the curve flatten a lot, and that’s because Warsh is on record as being opposed to a big balance sheet,” said Schumacher. The market temporarily moved toward the view that Warsh, who is outspoken about quantitative easing, might try to wind down the Fed balance sheet more quickly than planned.

Schumacher said the market will likely to continue to focus on that aspect of Warsh but he might actually be a catalyst for curve steepening, meaning longer-end interest rates rise. That’s because Warsh is seen more than any other candidate as someone who would push for deregulation of the financial industry.

While Trump may have leaned toward Warsh, for instance, for his focus on deregulation, Powell is not expected to veer that much from the current Fed. “He isn’t as laissez-faire as Kevin Warsh would have been,” said Simons.

Warsh is also seen as more hawkish on interest rates than Yellen, but he’s not expected to want to raise them much quicker.

But the candidate that’s seen as most likely to move the market is Taylor, who invented a very rule by which the Fed could raise interest rates. Taylor is widely seen as someone ready to push rates higher at a faster pace than Yellen. When his name surfaced this week as a stronger-than-expected candidate, Schumacher said that created a flattening of the yield curve.

Taylor has a solid background, having been an undersecretary for international affairs at Treasury. JPMorgan economist Michael Feroli said the Taylor rule, first described in a 1993 paper, is the basis for a “rules-based framework for monetary policy which has the support of many congressional Republicans.”

“For much of the past five years the standard Taylor rule has prescribed a policy rate higher than the one set by the Fed, and the current prescription is for a policy rate of 3.5 percent, or 2.25 [percentage] points higher than its actual setting,” he wrote in a note.

However, Milken Institute chief economist William Lee said the Street has it wrong on Taylor. He said Taylor is likely to be much more flexible with his rule, and his target may not be the over 3 percent target many are chatting about on Wall Street.

Lee is a longtime acquaintance of Taylor, who was his thesis advisor at Columbia University.

Lee said Taylor may not even see much reason to raise rates if inflation and the real rate of return remain low.

“Taylor has a framework from which he formulates and implements policy, but he does it in a very flexible way by not adhering to the rules all the time. Yellen does not have such a framework for policy but is guided by models for inflation that no longer work,” said Lee.