For the first few months after his election, Donald Trump was cast by many in the financial markets as the reincarnation of Ronald Reagan. His plans for deep and widespread tax cuts and a bonfire of regulations would, they said, spark a business renaissance akin to that credited to the stetson-wearing president who dominated the 1980s.

Stock market investors lapped up Trump’s speeches and tweets, and sent the main New York share indices to fresh highs. Last October, before the US election, the Dow Jones Industrial Average was chugging sideways below 18,000. By the first week of March, its value had topped 21,000, a rise of almost 17%.

Now the market is moving sideways again – and for the simple reason that, after watching and listening to Trump since his inauguration, it has priced in most of the gains investors believe he can make for them, which over the next few years will still be bountiful, but decidedly more modest than first predicted.

That’s why America’s central banker, Janet Yellen, the head of the Federal Reserve, made it clear last week that US interest rates would rise to at most 1.5% this year. The Federal Reserve increased its base rate range to between 0.75% and 1% at its March meeting, and Yellen said there would probably be just two more quarter-point rises this year.

She was under pressure from Republicans to signal a more rapid increase, but was clear in her view that a Trump boom is still just a twinkle in the former property developer’s eye.

A study by consultancy Oxford Economics illustrates why the markets have joined the Fed in adopting a more cautious stance. It argues that Reagan entered office in a deeper hole and therefore had more room to expand. To boost growth, Reagan could also pull levers that are beyond Trump’s grasp.

In 1981, the global economy was adjusting to the two oil price shocks of the 1970s. The US was in recession and unemployment and inflation were high. Reagan’s cabinet spent much of its time talking about tax cuts and a radical overhaul of corporate and labour laws to set business free, but, as Oxford Economics point out, they mostly switched on the public spending taps.

It was a Keynesian boost that put money in people’s pockets and invited them to spend it. “From 1982 to 1986,” says the report, “the budget deficit rose from 1.8% of GDP to around 4.5% of GDP – an overall stimulus approaching 3% of GDP, which was sustained over four years. Government investment growth hit double digits in 1984-85, including a major rise in defence spending.”

Jobs were created and imports rocketed. The budget deficit and the balance of trade worsened. The dollar soared. Paul Volker, Reagan’s Fed chief, increased interest rates to quell domestic inflation.

To emphasise how different things are now, the Fed raised rates last week, aware that, like the stock markets, the dollar had already run out of steam. It hit a 14-year high against a basket of currencies in November, but has since tracked downwards.

“The prospects for dollar gains on a similar scale to the 1980s look thin,” the report goes on. “The dollar was weak in 1980 but has seen strong gains since 2014 and may be moderately overvalued. And while we think the dollar is more sensitive to small rises in rate [differences with other economies] than previously, that sensitivity cuts both ways and quite a lot is arguably already priced into markets in terms of Fed rate hikes. So we expect dollar gains from here to be modest.”

Oxford Economics argues that a cap on the dollar is not only a boon for US consumers, who will see imported inflation peak at a lower level, but will also help economies such as Brazil, Turkey and Indonesia, which must borrow in dollars at rates set by the Fed. Much of the pain created by Reagan’s policies was exported to countries that relied on selling commodities to the west. Turkey will still suffer from higher borrowing costs, but its finance ministry will be relieved to find that the extremes of the Reagan era can be avoided.

The lesson for the UK is that Tory claims for deregulation as a route to riches have no precedent, not even from the Reagan era. Tax cuts can help, but both this government and the last have found themselves imposing more taxes than they cut, to a point where the ratio of tax income to GDP is at its highest in 30 years.

Reagan borrowed to spend, much to the disappointment of his free market friends, adding 3% of GDP to the US budget deficit. Such generosity with borrowed money is not an option for Philip Hammond, at least not on the scale used in 1980s America.

All Hammond can hope for is that the assessment of recent weeks that Trump is a benign force, who will neither emulate Reagan nor be a disaster, turns out to be true. Given the parlous state of the UK’s public finances after eight years of austerity, he needs all the help he can get.