Stocks jumped on Tuesday, resuming the market's sharp rebound from last month's lows, as investors grew more optimistic about the coronavirus outlook. The Dow Jones Industrial Average rallied 558.99 points, or 2.4%, to 23,949.76. The S&P 500 climbed 3.1% to 2,846.06 while the Nasdaq Composite advanced nearly 4% to 8,515.74. The tech-heavy Nasdaq notched its first four-day winning streak since early February. The S&P 500 was led higher by 4% rallies in tech, consumer discretionary and consumer staples. Amazon rose to an all-time high to lead the Nasdaq higher. "When you look at the facts, I think there's reason to be more hopeful than we have been," CNBC's Jim Cramer said. "The worst-case scenario's been taken off the table, and if Apple and Google can do contact tracing that we all embrace ... while we continue to roll out more testing, the economy could reopen a lot sooner than we thought even, say, three weeks ago." Tuesday's gains come after a sharp drop in the previous session. The Dow lost 328 points, or 1.4%, on Monday while the S&P 500 declined by 1%.

New York virus deaths leveling off

New York Gov. Andrew Cuomo struck an optimistic tone about the outbreak in his state, the epicenter of the pandemic in the United States. He said Tuesday deaths related to the virus in the state are leveling off, adding the coronavirus hospitalization rate in New York remains low. President Donald Trump said in a press conference Monday night that growth in new coronavirus infections stabilized, providing "clear evidence" that mitigation is working in the country. "Financial markets have started to take a more positive view of the outlook," said Jan Hatzius, chief economist at Goldman Sachs, in a note. "The initial improvement was mostly policy-driven, but the greater optimism

of the past week seems to be at least partly related to the virus itself. " "To be clear, the health situation remains very bad in absolute terms, especially in the US which is now ahead of Italy and Spain in terms of coronavirus-related fatalities (though still much lower on a per-capita basis)." The number of coronavirus cases continues to rise globally. Data from Johns Hopkins University shows there are more than 1.9 million cases around the world, with over 598,000 in the U.S.

Tuesday's rally resumes a sharp rebound from the market lows set on March 23. Since then, the S&P 500 is up 27.5%. Investors have been cheering the apparent progress in the fight against the coronavirus along with unprecedented stimulus from the Federal Reserve. "The Fed has really pulled out all stops in terms of keeping markets liquid and fluid," said Gibson Smith, founder of Smith Capital. "My expectation is over the next three to six months, assuming we get the virus contained ... we'll look back on this period of time and realize it was just a moment in time with a lot of volatility and we probably have better times in front of us than worse times."

Earnings season kicks off