The Federal Reserve now needs to be on Trump watch if it wants to engineer the proper dose of monetary policy, according to Bank of America chief Brian Moynihan.

"They've got a new administration with a new set of fiscal policies, and the monetary policy has to respond to that," the BofA chair and CEO told Yahoo Finance at the World Economic Forum in Davos, Switzerland.

Moynihan added: "We are not a central bank-led economy. We're actually a private sector-led economy, of which the government supports, of which the central bank responds to, and they have to think of what stimulus they're going to respond to."

The Fed, of course, is always one to play up its independence from the White House.

What has unnerved the markets to start 2025 is the Federal Reserve not committing to aggressive rate cutting, alongside a stronger-than-expected US economy.

The consensus among Fed officials is now for two rate cuts this year, down from the four forecast in September. The monetary policy body remains concerned about inflation — San Francisco Fed president Mary Daly was non-committal on more rate cuts on Yahoo Finance's Opening Bid podcast recently.

Read more: What the Fed rate cut means for bank accounts, CDs, loans, and credit cards

Potential moves by the Trump administration, such as tariffs on China, further cloud the outlook for inflation.

Not helping matters is the renewed rise in oil prices to kick off the year. The US economy has also shown impressive resilience, including a blowout December jobs report.

"The fact that the narrative has shifted is because the economy is stronger because the labor market is stronger," BlackRock's chief investment and portfolio strategist for the Americas, Gargi Chaudhuri, said on Opening Bid. "I think one to two more rate cuts in this cycle based on the data at hand, is fair to assume with a very open mindset."

Despite the Fed uncertainty, Bank of America shares have rallied 11.5% since Donald Trump's election win in November. The S&P 500 is up 4.7% during that same stretch.

Bank industry experts say the rally reflects potential lighter regulations under Trump, particularly on the capital requirements front.

"I think what we want to see is capital [requirements] a little more rational," Moynihan said on what he'd like to see from the Trump administration. "And then secondly, you want to take a look at some liquidity and other rules, which got stacked up and actually have an adverse effect on carrying capital, which doesn't make a lot of sense because some of the other tedious things that go on banking regulation."