Cautious optimism swept investors Monday as governments across the globe tiptoed toward reopening and reports of expanded coronavirus research and testing proliferated.

The Dow Jones industrial average advanced 358 points, about 1.5 percent, to 24,133.78 as investors awaited White House guidelines on the phased reopening of schools, certain workplaces, mass transit and more. The Standard & Poor’s 500-stock index climbed 1.5 percent to 2,878.48, and the tech-heavy Nasdaq composite index rose 1.1 percent to 8,730.16.

All 11 stock market sectors were positive, led by financials and real estate, two beleaguered industries sniffing for any good news after being hit hard by the shutdown. 3M, Walt Disney, JPMorgan Chase and Goldman Sachs were among the Dow’s best performers.

“It’s all about uncertainty,” said Brad McMillan, chief investment officer for Commonwealth Financial Network. “The good news is that the number of daily tests for the coronavirus has picked up significantly. If we can test, we will know who is sick and be able to manage around that. The market loves the idea of less uncertainty.”

The United States has so far tested about 5 million people — or less than 2 percent of the population. Last week, Congress approved an additional $25 billion for testing as part of the latest funding bill, which scientists say is a good start but should expand significantly to ensure public safety.

CVS Health said Monday it will expand to 1.5 million tests a month at 1,000 locations around the country. The Trump administration is preparing to send enough kits to the states to enable them to test 2 percent of the population, according to a report in the Wall Street Journal.

Bill Gates, co-founder of Microsoft, said over the weekend that his Gates Foundation will devote its “total attention” to the coronavirus pandemic.

Georgia — the fastest-moving state — allowed barber shops, nail salons, tattoo parlors and gyms to reopen Friday. On Monday, people in Tennessee were allowed to dine in at restaurants. Texas said it will allow its stay-at-home order to expire Thursday. Missouri is planning to allow “almost every business” to open next week. On Sunday, New York Gov. Andrew M. Cuomo (D) laid out a plan for a gradual reopening of low-risk businesses starting in mid-May.

“Early signs of ‘return to work’ are promising, but the process is likely to be slow and nonlinear,” Lauren Goodwin, economist at New York Life Investments, wrote in a commentary Monday.

These steps come even as U.S. covid-19 deaths surged past 55,000 and confirmed cases surpassed 980,000. Deborah Birx, the White House’s coronavirus task force coordinator, said some form of social distancing will remain in place through the summer. But protesters and some business groups are calling for a faster timeline amid the economic pain the lockdowns have caused, including more than 22.5 million job losses within weeks.

“The biggest risk to the stock market is a premature reopening of the U.S. economy which results in an increase in COVID-19 cases and requires an abrupt reversal of these efforts to awaken the economy out of its engineered coma,” Marc Chaikin, founder of Chaikin Analytics, wrote in a commentary Monday. “There are so many things that can go wrong in the next six months that I continue to believe that investors should maintain sufficient cash levels to emotionally withstand whatever unfolds in the economy and the stock market.”

This week is the biggest for second-quarter earnings, with 150 firms on the S&P 500 reporting. Investors are looking toward reports from major oil companies and tech giants Apple, Tesla, Microsoft and Amazon to see how some of the nation’s most powerful companies are weathering the coronavirus storm.

European and Asian stocks closed on an upswing Monday as investors warily eye national economies as they exit the lockdown. Germany, the continent’s economic powerhouse, has been slowly easing its coronavirus shutdown curbs for several days.

Germany’s DAX finished above a 3 percent gain, while France’s CAC40 advanced 2.5 percent on the day. Britain’s FTSE 100 was up 1.6 percent following Prime Minister Boris Johnson’s return, and Europe’s benchmark Stoxx 600 index climbed 1.7 percent. Asian markets rose broadly Monday as China reported a record low of just three new infections. Japan’s Nikkei 225 closed up more than 2.7 percent, while Hong Kong’s Hang Seng Index ended the day up 1.88 percent.

As the global coronavirus infection count neared 3 million, hard-hit Italy and Spain announced plans to gradually reopen their economies in the coming week. And Johnson made his first public appearance since battling covid-19, but he used his time to urge Britons to hunker down awhile longer.

Oil prices sank Monday as a worldwide glut has swamped pipelines and storage capacity everywhere even as producers continued to send tens of millions of barrels of new oil into the market every day. That glut and ensuing shortage of storage space suggests that agreed-upon production cuts may not be enough to counterbalance cratering demand.

West Texas Intermediate, the U.S. oil benchmark, plunged 26 percent to trade at roughly $12.50 a barrel. Brent crude, the global benchmark, shed more than 7.3 percent, to $23 a barrel. Most oil producers lose money at those prices.

“The harsh reality is setting in that over the next month the world is about to hit crude storage capacity,” Ed Moya, an analyst with OANDA, wrote in a commentary Monday. “It is very expensive to shut-in production and the risks of damaging the well will keep many producers waiting to the last moment to act. Oil is in for another wild ride and energy traders should not be surprised if we see prices continue to remain heavy.”

Crude prices have dropped more than 50 percent since January because of an oversupply and a drop in demand. Global commerce, automobile use and jet travel have come to a virtual standstill because of the shutdown.

A price war between Saudi Arabia and Russia, two of the world’s largest producers, also flooded the oil market, driving prices down further. So much oil is sloshing around the globe that supertankers are doubling as oil storage tanks, floating offshore waiting to disgorge their product.