The gyrations come a day after panic coursed through Wall Street, with the Dow plunging a record 1,175 points on Monday.
The Dow Jones Industrial Average fell 1,175.21 points (4.6 percent) to 24,345.75, the S&P 500 lost 113.19 points (4.10 percent) to 2,648.94, and the Nasdaq Composite dropped 273.42 points (3.78 percent) to 6,967.53.
The CBOE Volatility index, a measure of expected swings in the S&P 500, jumped 8 points to 45.29, its highest level since August 2015, on Tuesday. The Nasdaq climbed 148, or 2.1 per cent, to 7115.
With Monday's declines, the S&P 500 erased its gains for 2018 and is now down 0.9 per cent in 2018.
"We can all admit that the market went parabolic in the first 4 weeks of 2018 and we're just back to square one", Peter Boockvar, chief investment officer at Bleakley Advisory Group, wrote in a report on Tuesday.
Major indexes in Asia and Europe fell following Monday's drop in the Dow Jones industrial average. Investors remain fearful that signs of rising inflation and higher interest rates could bring an end to the bull market that has sent stocks to record high after record high in recent years. Exchange-traded funds that focus on junk bonds suffered a third day of losses.
The Dow opened with a 2 percent loss a day after losing 1,175 points.
The Dow has now pulled back about 10 percent since reaching a record high of 26,616 on January 26, 2018 - putting it in correction territory.
Price gyrations are nothing new on Wall Street.
The market is coming off its worst week in two years. The stock market has been unusually calm for more than a year.
This results in higher borrowing costs for companies, including the healthcare industry when it looks for capital to expand or acquire.
Other key indexes in the Pacific Rim also saw drops when they closed Tuesday, including a 5.1% skid for the Hang Seng in Hong Kong and a 3.2% decrease for Australia's S&P ASX 200. On Tuesday it rallied another $5.22, or 14.7 percent, to $40.84. Energy companies, banks, and industrial firms are taking some of the worst losses.
Energy companies were also moving lower as the price of crude oil slipped.
"The declines in markets are steep and vicious and are fostering a feeling of fear which begets irrational behaviour".
Some strategists viewed the recent selloff, which began last week amid concerns over higher interest rates and lofty valuations, as a healthy pullback after a rapid run-up at the start of the year.
"But more importantly, it is because the bull market has been due to the willingness of central banks to supply copious amounts of money to the markets at ultra-low interest rates". "Corrections are caused by people having to reposition for new environments". Experts do think the global economy will keep growing this year even though that is likely to bring more inflation.
US crude oil fell 76 cents, or 1.2 percent, to close at $63.39 a barrel in NY. Brent crude, the standard for worldwide oil prices, lost 96 cents, or 1.4 percent, to $67.62 a barrel in London. Late Friday the Fed said it will freeze Wells Fargo's assets at the level where they stood at the end of a year ago until it can demonstrate improved internal controls.
Another safe haven - gold - was up for the fourth day in the last five, to $1,340 USA an ounce.
Among the biggest losers on Tuesday was Tokyo's Nikkei 225 stock average, which ended 4.7 per cent lower. Yesterday, it lost 4.1 per cent, which was its biggest daily percentage drop since August 2011. The euro was up 0.3 percent at $1.2435 while the dollar rose 0.3 percent to 109.38 yen.
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