IN AN effort to understand their new reality, many American bosses have been studying “The Art of the Deal”. Donald Trump’s autobiography, published in 1987, begins by describing his working week, which mainly consists of frequent calls with his stockbroker, sitting in his office as other businesspeople pay him lavish tribute, and drinking tomato juice for lunch.

If Mr Trump’s routine is anything like the same today, he must be delighted. The broker has good news: the S&P 500 index has returned 6% since his election and on January 25th the Dow Jones Industrial Average closed above 20,000 for the first time. There have been chief executives-a-plenty lavishing praise on him both in public and in private. Their devotion seems extraordinary. Before the vote, many of the same C-suiters lambasted him as a menace to capitalism and much else.

One theory is that executives are simply terrified of Mr Trump. But many are supportive of him in private, too. They offer two explanations: that they can’t help but respond to his personal charm offensive to big business, and that they are persuaded that there is some substance there. Consider the personal touch, first. On paper the Obama years were glorious for big firms. Their profits soared and many built oligopolies through big takeovers. But most CEOs viewed Mr Obama’s presidency with dismay. Their firms’ sales stagnated along with the economy, and, reluctant to invest, they spent profits on share buy-backs. Mr Obama was aloof, caring little for the company of businesspeople. Antitrust enforcement was lax, but other elements of regulation got tighter.

The new era could not be more different. Since winning, Mr Trump has had personal contact with the bosses of firms with a collective market value of $5trn, or a fifth of America’s stockmarket. He has either met or appointed them as advisers or officials. The list includes eight of America’s ten most valuable firms. The exceptions are Berkshire Hathaway, run by Warren Buffett, a backer of Hillary Clinton, and Wells Fargo, which faced a mis-selling scandal in 2016. Most CEOs are status-conscious and see no harm in pressing the flesh. An invitation to Trump Tower or the White House to discuss how to run America goes down well.

Once the cameras are switched off, the president lays on the flattery. He tells bosses how important their firms are to the country and that he will pave the way for them to invest. Those he has fallen out with get a chance to make up. In January Randall Stephenson, the boss of AT&T, which is trying to buy Time Warner in a deal Mr Trump denounced during his campaign, paid his respects. Elon Musk of Tesla, an electric-car firm, criticised Mr Trump in 2016, but has since become an adviser and attended a meeting on manufacturing at the White House on January 23rd. Also present was the head of Lockheed Martin, whom Mr Trump has previously roasted for ripping off the Pentagon. The next day Mr Trump met the heads of Detroit’s three big car firms, whom he has, in the past, beaten up for investing in Mexico.

Few bosses are deluded enough to think an hour with the fickle Mr Trump can secure lasting favour, however. They also say that his economic plans will unleash corporate America. Four substantial changes are afoot. Firms will be allowed to repatriate foreign profits without paying a border levy: they have $1trn of cash stashed overseas. A Republican-controlled Congress will ram through tax reforms this spring to cut corporate tax from a headline rate of 35% now to 20% or less. A state-backed splurge on crumbling airports and roads will go ahead. And there will be an all-out war on regulation. In the meeting on January 23rd Mr Trump promised to eliminate three-quarters of all red tape.

The combination of all this, bosses say, will create a virtuous cycle of investment and growth. But in each of the four areas there are grounds for caution. Mr Trump will demand that environmental and financial regulators enforce rules with less zeal, but unwinding red tape will take years. The infrastructure spending spree may run up against deficit-averse Republicans. And look more closely at corporate taxes. Big firms already pay far less than the official rate. The constituents of the S&P 500 index paid in total a cash tax rate of 23% in the last reported year, based on Bloomberg data (and excluding loss-making firms). If the tax rate were slashed to 15%, the bump would be worth 8% of pre-tax profits—nice to have but hardly transformative. The reduction might also be offset by other changes, such as new limits on the tax break that firms receive on their interest costs.

Hail to the chief

As for the cash that American firms hold abroad, half of it is owned by tech firms such as Google and Microsoft, which already invest less than one-third of their total cashflow and which might carry on buying back lots of stock. For the rest of the firms in the S&P 500, the cash that is stranded offshore amounts to only nine months’ worth of capital expenditure, or 2% of their market valuations. These figures are too small to make much difference.

And then there is Mr Trump’s attitude to trade, which matters greatly to big firms, since a third of their collective sales are abroad. Many bosses forgive Mr Trump’s threats to start trade wars with China and Mexico as a form of price discovery. He makes bombastic opening demands, they say, but businesspeople expect him to reach rational arrangements with both countries that allow commerce to flourish. One well-thumbed section in the autobiography explains how he aims high, pushes and pushes but then settles for less than he originally sought.

But dealing with countries is a higher-stakes game than bargaining over Manhattan building plots. The president is erratic, ill-informed and advised by hardline protectionists. American bosses’ volte-face on Mr Trump seems uncharacteristically excitable. Perhaps they would be better following another piece of advice from “The Art of the Deal”: “I believe in the power of negative thinking…always go into the deal expecting the worst.”