The dollar's rally since the U.S. election is likely to run out of steam soon and the damage from its strength in the past month could be enough to put the world's largest economy into a recession, an investment chief at Saxo Bank said.

The dollar has rallied on expectations that President-elect Donald Trump will increase fiscal spending and deregulate key industries, leading to higher U.S. growth and interest rates.

The dollar index rose as much as 4.2 percent at one point against six other major currencies since Trump's Nov. 8 upset win.

"I think the (Jan. 20) inauguration of Trump is probably going to be the high point for the dollar," said Steen Jakobsen, Copenhagen-based bank's chief investment officer and chief economist.

"What people forget about Mr. Trump's program is that a lot of his spending plan will not take place until Oct. 1 next year," he continued, referring to the start of U.S. next fiscal year.

Companies are also likely to be cautious about increasing investment until they see signs that the economy is picking up, Jakobsen argued, just as they did during the first years of President Ronald Reagan.

"I think a lot of businesses in the U.S. are in wait-and-see mode: if they believe things are improving, in terms of lower taxes, they have ability to invest. But I'm pretty sure that they want to see the actual proposals first."

Jakobsen also said that historically the dollar often weakens after the U.S. Federal Reserve raises rates as investors sell the currency after buying it in anticipation of higher rates.

The Fed is widely expected to hike rates late next week and give some hints on its plans for 2017.

Despite market expectations of higher inflation and rates, Jakobsen believes the Fed will raise rates only once next year and maybe not at all.

The investment chief added it's more than 50 percent likely that the U.S. will slip into a recession in 2017.

Turning to risks in Europe, Jakobsen said Italian voters' rejection of a constitutional referendum on Sunday showed the country is not ready to reform, risking another recession after its economic slump during the European debt crisis from 2011 to 2013.

"The referendum vote today was just a confirmation that Italy is totally unprepared to reform. But I think Italy being weak is good for Europe in the long term as it will create a sense of emergency, vis-à-vis the political system."

Saxo Bank had 92 billion Danish krone ($13.2 billion) in assets under management as of June 30.