NEW YORK/SINGAPORE (Reuters) - Markets greeted Donald Trump's second inauguration with a sense of deja vu, as stocks welcomed his broad pro-business agenda but currencies were skittish after he threatened tariffs within weeks.

After sliding on relief that no tariffs were immediately imposed, the dollar jumped when Trump said he was thinking of a 25% tariff on goods from Canada and Mexico from Feb. 1.

"We're definitely headline chasing, which was very much expected," said Bart Wakabayashi, branch manager at State Street in Tokyo. "You could look at this any which way, right? Is February 1 the open question, or is it the tariffs themselves?"

The volatility served as a reminder of traders' roller-coaster ride through Trump's first term but also showed how, this time, investors seem more inclined to set aside the bluster.

The dollar hit a five-year high of 1.452 Canadian dollars before steadying around C$1.44 and it stayed below November's highs on the Mexican peso. Treasuries rallied and U.S. equity futures slid back to flat after an initial small jump.

Hong Kong stocks remained stable while the yuan held overnight gains on the lack of any immediate tariffs on China.

A gradual approach to trade talks with China was reminiscent of Trump's first time, said Naka Matsuzawa, macro strategist at Nomura in Tokyo.

"For Canada and Mexico it's a different story," he said.

"Trump doesn't really see Canada and Mexico themselves as problematic on trade, rather it's the Chinese exports through those countries that he wants to limit ... it's probably a negotiation tool."

Trump enters office with an ambitious agenda spanning trade, immigration, tax cuts and deregulation which has the potential to boost U.S. corporate profits but which could also reignite inflation and put upward pressure on interest rates.

In his inaugural speech, Trump pledged to bolster the U.S. oil, gas and power industries, to crack down on immigration and repeated his intention to collect "massive amounts" of tariffs.

"Most of what he has been talking about will help spur growth and corporate profits," said Jack Ablin, chief investment officer at Cresset Capital.

"But many will come at a cost. We will need to see a lot of earnings growth to make up for even a minor increase in interest rates that could follow higher tariffs" and other proposals, he said.

During his election campaign, Trump vowed to impose steep tariffs of 10% to 20% on global imports into the U.S. and 60% on goods from China, but investors said the signs on Monday were that the new administration would take a more measured approach.

DEREGULATION PROMISE

Elsewhere in the market, Trump's promise to ease regulation has lifted bank stocks and sent cryptocurrencies soaring.

As they reported surging profits, Wall Street CEOs told investors this month that the incoming U.S. administration would be business-friendly and good for banks.

The cryptocurrency industry expects Trump to fulfill his "crypto president" campaign promises by creating a federal bitcoin stockpile, providing crypto companies access to banking services, and creating a crypto council, Reuters previously reported.

Trump also launched a branded cryptocurrency which soared on Monday to more than $8 billion in market value, raising ethics questions.

In the aftermath of Trump's Monday speech, the price of bitcoin remained below its overnight high of $109,071, at about $102,000, amid some disappointment he had made no immediate crypto announcements.

During the first year of Trump's first administration, the S&P 500 rose 19.4%, following a 5% rally in his first 100 days in the Oval Office. During the entirety of Trump's first term, the S&P 500 rose nearly 68%, but markets saw bouts of volatility, stemming in part from a trade war Trump fought with China.

Following Trump's last inaugural address, in January 2017, the S&P 500 ended up 0.3% on the day. Due to the holiday, the trading reaction this time will not be evident until Tuesday.

Some investors said they were still in wait-and-see mode.

"The big question on investors' minds right now is going to be 'how' -- how will he cut costs and lower inflation and lower interest rates," said Josh Strange, president of Good Life Financial Advisors of NoVA, a financial advisory firm.