In an after-hours statement Monday, aluminum company Alcoa said strong demand for lightweight aluminum in autos and airplanes helped it cope with weak metal prices. Though the second-quarter loss was wider than a year ago, the results beat Wall Street expectations once costs for closing smelters and other one-off costs were stripped out.
Alcoa has customers in many industries, making it a gauge of the global economy's health. And as the first member of the Dow index to report quarterly results, its results draw extra attention from investors.
"Investors appear to be taking what news there is in better stride as earnings season gets under way," said Andrew Wilkinson, chief economic strategist at Miller Tabak & Co.
Also shoring up confidence was the news that Greece's eurozone partners have agreed to give the country the next batch of bailout cash it needs to avoid bankruptcy. That potentially gets rid of one of the risks that could have afflicted trading.
There was widespread relief in Europe, with the FTSE 100 index of leading British shares closing up 0.9 percent at 6,513 while Germany's DAX rose 1.1 percent to 8,057. The CAC-40 in France finished Tuesday 0.52 percent higher at 3,843.
In the U.S., the Dow Jones industrial average was up 0.4 percent at 15,287 while the broader S&P 500 index rose 0.6 percent to 1,650.
The gains seen over recent sessions suggest that some of the concerns over an imminent scaling back of the Federal Reserve's monetary stimulus have eased. Rather than fearing the end of the stimulus, investors appear to be applauding the prevailing trend of improving U.S. economic news.
"Normality appears to have returned to the markets, with investors buying on good news and selling on bad," said Craig Erlam, market analyst at Alpari.
Over the past few weeks, markets have been extremely volatile due to expectations of an imminent reduction in the Fed's monetary stimulus. The consensus in the markets is now that the Fed will first reduce the amount of financial assets it buys in September.
The publication on Wednesday of the minutes of the last Fed policy meeting in June and an ensuing speech by the central bank's chairman, Ben Bernanke, will be monitored in that context.
Earlier, Asian markets recovered their poise following Monday's big retreat. Japan's Nikkei 225 index surged 2.6 percent to 14,472.90 and Australia's S&P/ASX 200 was up 1.5 percent to 4,881.70.
Other regional markets rose only moderately, reflecting continued caution. South Korea's Kospi inched up 0.7 percent to 1,830.35 while Hong Kong's Hang Seng added 0.5 percent to 20,683.01.
Mainland Chinese shares made small gains, with the Shanghai Composite up 0.4 percent to 1,965.45. The smaller Shenzhen Composite Index rose 0.4 percent to 892.93.
Elsewhere, markets were fairly settled.
In currencies, the euro was down 0.1 percent at $1.2771 while the dollar rose 0.2 percent to 101.08 yen. The price for crude oil was up 13 cents at $103.26 a barrel in New York.