At the close on Wednesday, the Dow finished at 19,804.72, fewer than 170 points from its December 20 record.
The question is worrying investors. Yet Trump's initial steps may not offer clear answers.
Since Trump's victory, major stock indices in New York have experienced two phases: they rallied for a month, repeatedly smashing records, and then stalled toward the New Year, though holding on to unprecedented gains.
At the close on Wednesday, the Dow finished at 19,804.72, fewer than 170 points from its December 20 record, which brought it close to the 20,000-point milestone. The broader S&P 500, often seen as more representative, closed at 2,271.89, just under six points from its own all-time high set on January 6.
Since the election, the Dow and S&P 500 have gained 8.0 percent and 6.1 percent respectively.
Nevertheless, Wall Street analysts have not been so pessimistic about the outlook for the S&P 500 in 10 years, forecasting a mere five percent gain for 2017, according to a consensus set by Bespoke Investment.
"That signals an odd dichotomy," said Nicholas Colas of Convergex. "US stocks are at/near all-time highs but there is still considerable uncertainty about the core fundamentals that keep the market revving this deep into the red line."
Numerous explanations have been put forward to justify the rally, perhaps glossing over the fact that it was unexpected. After all, before the vote, conventional wisdom held that markets were expecting Democrat Hillary Clinton to win the presidency.
Analysts now repeat a different conventional wisdom, that investors are counting on a pro-growth Trump agenda, in other words, tax cuts, deregulation and spending to stimulate the economy.
Yet since winning the election, the future president has offered few details on any of these hoped-for policies, or how he plans to pay for them. Some observers are warning the market may have been running on wishful thinking since November, closing its eyes to nettlesome questions like Trump's very public penchant for protectionism.
"We sort of have been living in the fantasy world of the last two months on the expectations of what he will do," said Karl Haeling of Landesbank Baden-Wuerttemberg. "Once he gets in there, the risk of not going as quickly and smoothly as we had hoped, that goes up."
In a research note published early this month which received considerable comment, investment bank Morgan Stanley spoke of an impetus to "sell the inauguration" after having "bought" the election.
"After all, what incrementally positive and exciting outcomes could be produced in the first few weeks after that?" the analysts wrote.
Trump certainly has shown his ability to influence markets in the short-term by using mere words -- he sent the US dollar diving at the start of the week, for example, saying it was "too strong."
But whatever economic policies Trump decides to put in place, they will take months if not longer to have any direct impact.
"Now investors must mix patience with hope," said Gregori Volokhine of Meeshcaert Financial Services.
"The only question is how long their patience will last."
"Any tax cuts won't take effect or any have any fallout in the first six months," he added, echoing similar sentiment by JP Morgan CEO Jamie Dimon.
In presenting the bank's quarterly results this week, Dimon declined to celebrate any "Trump effect" for the near-term.
And ultimately some analysts put Trump's significance into context, noting that the stock rally may be justified by the rather solid state of the US economy.
"I expect over the next month or two the market will continue to move higher, because the economic data has been accelerating over the last couple of quarters," said Tom Cahill of Ventura Wealth Management.
"I don't think there is any reason that won't continue to be the case. In general this is a healthy economic environment."