All three major indexes jumped nearly 5% the day after equities markets suffered their biggest one-day losses since the 2008 financial crisis.
Still, the S&P 500 and the Nasdaq ended the session about 15% below the record closing highs reached on Feb. 19. Sinking beyond the 20% mark would confirm a bear market.
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"Coming off yesterday, you've got short-term bargain-hunters coupled with potential fiscal stimulus hopes," said Chuck Carlson, chief executive officer at Horizon Investment Services in Hammond, Indiana.
"It may be the biggest benefit is not actually what's getting done - it's that there appears to be a plan," Carlson added. "There does appear to be a willingness to do something, and that's probably what's helping the market." Market participants largely expect the US Federal Reserve to cut interest rates for the second time this month at the conclusion of next week's two-day monetary policy meeting.
Outside the United States, major world economies took steps to cushion the effects of the fast spreading COVID-19.
Global markets have been rattled in recent weeks by the rapidly spreading coronavirus, which has caused widespread supply chain disruption, hobbled the travel industry and prompted drastic containment measures in Italy and elsewhere.
Market uncertainties surrounding COVID-19 were exacerbated over the weekend as Saudi Arabia and Russia scrapped their supply pact and pledged to increase crude oil production.
But oil prices rebounded from Monday's largest percentage drop since the 1991 Gulf War, with front-month Brent crude rising 10.0% after Russia indicated it was open to talks with OPEC.
Energy stocks bounced back from their worst decline on record, advancing 5.0%.
The Dow Jones Industrial Average rose 1,167.14 points, or 4.89%, to 25,018.16, the S&P 500 gained 135.67 points, or 4.94%, to 2,882.23 and the Nasdaq Composite added 393.58 points, or 4.95%, to 8,344.25.
All 11 major sectors of the S&P 500 closed higher, led by tech and rate-sensitive financial shares.
Financials jumped 6.0% after suffering their worst day in more than a decade as US Treasury yields rebounded from record lows.
United Parcel Service Inc gained 6.5% as Stifel upgraded its shares to "buy," while Amazon.com Inc rose 5.1% on Cowen & Co's price target increase.
Shares of Chevron Corp and Marathon Oil Corp rose 5.3% and 21.2%, respectively, after the oil companies and their peers announced cost reduction efforts to combat plunging crude prices.
Advancing issues outnumbered declining ones on the NYSE by a 2.61-to-1 ratio; on Nasdaq, a 2.06-to-1 ratio favored advancers.
The S&P 500 posted three new 52-week highs and 100 new lows; the Nasdaq Composite recorded eight new highs and 578 new lows.
Volume on US exchanges was 15.81 billion shares, compared with the 11.52 billion average over the last 20 trading days.
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