Major U.S. stock indexes jumped sharply higher on Monday as investors grew optimistic that the Federal Reserve and other central banks would soon intervene and limit the coronavirus's economic impact.

Coming off Wall Street's worst week since the 2008 financial crisis, the Dow Jones industrial average rose roughly 1,300 points, or close to 5%. The Standard & Poor's 500 and Nasdaq composite also roared higher, particularly in late-day trading. Both finished up more than 4%, one of their biggest daily gains in years.

All 11 S&P 500 stock market sectors were positive on Monday, led by utilities and consumer staples, as investors acted on a belief that the Fed and other central banks will take some action. The Dow's big gainers were Walmart and Apple.

"The market is anticipating major responses from global central banks, including multiple rate cuts by the U.S. Federal Reserve," said Dan Ivascyn, who oversees $1.9 trillion as the group chief investment officer of Pimco.

The gains were welcome news after last week, when all three indexes dropped into correction territory. A correction is a 10% reversal from recent highs. The Dow shed 12.36%, the S&P 500 erased 11.49% and the Nasdaq lost 10.54% over last week.

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Simeon Hyman, global investment strategist at ProShares said the volatility was due to uncertainty.

"Investors don't know what the ultimate impact of the coronavirus will be," Hyman said. "But if history is a guide, this will eventually pass and markets will recover."

Japan's Nikkei, which plunged last week as officials declared a state of emergency in the northern island of Hokkaido and schools closed through early April, was up roughly 1%. The markets were no doubt lifted by remarks from Bank of Japan Gov. Haruhiko Kuroda, who said the central bank "will monitor developments carefully, and strive to stabilize markets and offer sufficient liquidity via market operations and asset purchases."

"Even though no one knows for sure how far this decline will go, Friday's market action pointed to the likelihood of a near-term reflex rally, as many of the 'loose hands' may have been shaken free," said Sam Stovall of CFRA Research.

Hong Kong's Heng Seng was up roughly 0.6% and the Shanghai composite was 3.15% in the green.

European markets also entered corrections last week. They were only slightly steadier on Monday, with Britain's FTSE 100 gaining nearly 1.2%. Germany's DAX was trading down about 0.3%.

As last week's sell-off fueled anxiety that coronavirus could trigger a recession, central banks around the world faced calls to find ways to intervene, even when it wasn't clear that their traditional methods for staving off an economic downturn would be a match for the flu-like virus. Wall Street traders are now predicting at least three rate cuts this year, including one reduction when the Federal Reserve meets next on March 18. Interest rates are currently just below 1.75%, a low level by historical standards, but higher than the rates in much of the rest of the world.

On Monday, President Donald Trump criticized the Federal Reserve for being "slow to act" and continued his attacks on Fed Chair Jerome Powell.

"As usual, Jay Powell and the Federal Reserve are slow to act," Trump tweeted. "Germany and others are pumping money into their economies. Other Central Banks are much more aggressive. The U.S. should have, for all of the right reasons, the lowest Rate. We don't, putting us at a competitive disadvantage. We should be leading, not following!"

On Friday, Powell said the central bank would act if the economy takes a toll from coronavirus.

"The fundamentals of the U.S. economy remain strong. However, the coronavirus poses evolving risks to economic activity," Powell said. "The Fed is closely monitoring developments and their implications for the economic outlook. We will use our tools and act as appropriate to support the economy."

There were concerns that last week's Wall Street rout could push consumers to pull back on their spending and for companies to put a pause on hiring. Consumer spending has propped up not just the U.S. economy but also the global economy for a decade. Yet with painful memories of the 2008 financial crisis fresh in many Americans' minds, fear around coronavirus could prompt shoppers to rein it in.

"Declining consumer confidence, potentially severe retail traffic declines and temporary store closures are evolving risk factors that depend on uncertain variables like the geographic spread of the virus and the timing of containment [or] eradication solutions," analysts at Cowen wrote Monday morning.

That threat to consumer confidence, coupled with coronavirus' blow to the manufacturing and production of toys, medical equipment, auto parts and smartphones from China, has the business community on high alert and has raised the chance of a recession, economists say.

Two deaths were reported over the weekend in the U.S., and a genetic analysis suggested that the coronavirus has probably been spreading undetected for about six weeks in Washington state. The U.S. Food and Drug Administration on Saturday took steps to sharply expand testing. Meanwhile, cases continue to rise in South Korea, Italy and Iran.

"It is no longer possible to absolutely prevent new cases coming in," Brendan Murphy, Australia's Chief Medical Officer, told reporters on Monday. British Prime Minister Boris Johnson said the day before that he expected the outbreak to "spread a bit more" in Britain, where there are 39 confirmed cases.

The global death toll has passed 3,000, and South Korea said Monday it had confirmed 599 new cases, far higher than the daily tally reported in China. Italy now has more than 1,600 confirmed cases, while Iran surpassed 1,500, with 66 deaths.It looks like the start of another messy week for stocks.

This article was written by Rachel Siegel and Thomas Heath, reporters for The Washington Post.