By Fred Imbert and Yun Li, CNBC–

Stocks ended lower Tuesday, giving up big rally from earlier in the day, as Wall Street assessed the latest news on the coronavirus outbreak.

The Dow closed 26 points lower after rising as much as 937 points, or 4.1%, at its session high. The S&P 500 ended the day 0.16% lower after jumping more than 3%. The Nasdaq fell 0.3% after a 3% rally.

Some investors believed stock prices were getting ahead of the reality where coronavirus shutdowns are likely to weigh on the economy significantly beyond the second quarter. The major averages have rallied about 20% from their March 23 lows.

“Risk to the downside is greater than the opportunity to the upside from this point where we stand today,” said David Kostin, Goldman Sachs chief equity strategist, on CNBC’s “Squawk on the Street.” “I would just remind you that in 2008 in the fourth quarter there were many different rallies, I call them bear market rallies, some of which almost 20% a couple of times — but the market did not bottom until March of 2009.”

In the U.S., the number of new cases appears to have fallen in recent days from their recent peak. On Tuesday, New York Gov. Andrew Cuomo reported the state’s biggest one-day jump in deaths, but also said hospitalizations are slowing. Italy and Spain, two of the hardest-hit countries, are also seeing new cases fall off.

In Asia, South Korea reported less than 50 new cases of infection for the second day running. China also posted no new deaths as of April 6 for the first time since January when it started publishing daily updates. The two Asian countries were among those which saw spikes in infection rates earlier in the outbreak, with the first cases being reported out of China.

Stocks surged on Monday as a slew of coronavirus headlines pointed to a potential stabilization in the U.S. The Dow soared 1,600 points, posting its third biggest point gain ever. The S&P 500 jumped 7% to its highest level since March 13.

The S&P 500 is up 24.7% from its 52-week low set March 23 while the Dow has bounced 28% from its low.

Keith Lerner, chief market strategist at Truist/SunTrust Advisory, said the market reached its peak of indiscriminate selling after hitting its late March lows.

“That’s the first part of any type of bottoming process,” Lerner said. “Then you start seeing differentiation in the market; you start to see winners and losers as opposed to wholesale selling.”

President Donald Trump said in a press conference Monday there’s “tremendous light at the end of the tunnel’ with ten different therapeutic agents in active trials. Trump echoed comments by World Health Organization officials who said the research to develop vaccines and treatments has “accelerated at incredible speed.”

“The apex in New York state is likely imminent as opposed to one month out,” Marko Kolanovic, JPMorgan’s global head of macro quantitative and derivatives strategy, said in a note on Monday. “Big data indicated very early on that social distancing is working overall.”

Kolanovic also said in a conference call he expects a “limited” re-opening of the economy in two weeks.

Still, the cases in the U.S., the world’s most affected country, topped 368,000 with at least 10,000 deaths, according to data from Johns Hopkins University.

Stocks are still in bear-market territory with the S&P 500 about 20% off its record high. Many on Wall Street believe stocks haven’t fully priced in the potential corporate earnings collapse as the coronavirus outbreak has virtually shut down the global economy.