NEW YORK (Reuters) - Shaken out of many months of calm, Wall Street braced for a higher level of volatility in the days ahead, after a roughly 2 percent rebound in U.S. stocks on Tuesday followed the biggest one-day selloff in more than six years.

The question that vexed traders: were the wild swings of the past two days the start of a deeper move down or just clearing the way to the resumption of the aging bull market, which would turn nine on March 9.

“Today’s market action is a classic of a market that has searched for a bottom,” said Peter Cardillo, chief market economist at First Standard Financial In New York, who predicted a rebound back to record levels.

Bulls argue that strong U.S. corporate earnings, including a boost from the Trump administration’s tax cuts, will ultimately support market valuations. Bears, including short sellers that bet on the market decline, say that the market is over-stretched in the context of rising bond yields as central banks withdraw their easy money policies of recent years.

“The markets went into being religiously over-bought to deeply over-sold in a matter of four trading days,” said Adam Sarhan, chief executive of 50 Park Investments, an investment advisory service. “New buyers are showing up, who were waiting for the prices to go down.”

Tuesday’s wild trading session saw the Dow swing more than 1,100 points from its low to its high and ended with the benchmark S&P 500 tallying its best day since just before President Donald Trump’s November 2016 election.

“I don’t think the volatility is over,” said JJ Kinahan, chief market strategist at TD Ameritrade in Chicago. “These types of moves tend to take about three weeks to get through the system ... and volatility just doesn’t suddenly settle down.”

Investors were eyeing the recent steep slide as an opportunity, an extreme example of the “buying the dip” that has symbolized the market’s steady climb to record highs.

“We’ve been looking at this as an opportunity to incrementally add a little bit of risk - not get over our skis, but a little bit,” said Erin Browne, head of asset allocation at UBS Asset Management in New York.

During the trading day, stocks swung from negative to positive after indexes started the session 2 percent lower. The S&P 500 ended 6.2 percent below its Jan. 26 peak.

The sharp declines in recent days marked a pullback that had been long awaited by investors after the market minted record high after record high in a relatively calm ascent.

The Dow Jones Industrial Average rose 567.02 points, or 2.33 percent, to 24,912.77, the S&P 500 gained 46.2 points, or 1.74 percent, to 2,695.14 and the Nasdaq Composite added 148.36 points, or 2.13 percent, to 7,115.88.

After the end of regular trading on Tuesday, S&P 500 e-mini futures were down 0.4 percent.

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Technology, materials and consumer discretionary were the top-performing sectors on Tuesday. Defensive sectors utilities and real estate were the only major S&P groups to end negative.

Apple climbed 4.2 percent, while Microsoft and Amazon gained 3.8 percent each.

The U.S. stock market has climbed to record peaks since Trump’s election on the prospect of tax cuts and corporate deregulation as well as optimism over corporate earnings.

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The S&P 500 remains up 26 percent since his election, and on Tuesday clawed back into positive territory for 2018, up 0.8 percent.

“We had gone very far, very fast,” Matthew Cheslock, a trader at Virtu Financial, said from the floor of the New York Stock Exchange. “But I don’t think anyone expected the velocity or the ferocity that we saw on the downside.”

The market’s pullback came amid concerns about rising bond yields and higher inflation. These were reinforced by Friday’s January U.S. jobs report that prompted worries the Federal Reserve will raise benchmark interest rates at a faster pace than expected this year.

Traders had speculated that Monday’s selling was spurred by automated programs, and had called Monday’s session busy but orderly.

Market experts also attributed the selloff, including the overnight slide in S&P 500 futures, to the violent unwind of a trade betting on volatility in U.S. stocks staying low as the CBOE Volatility index, known as the VIX, notched its biggest one-day jump on Monday in over two years.

U.S. Securities and Exchange Commission Chairman Jay Clayton said he “can’t really say” what caused the dramatic drop in stock prices during recent trading sessions, but that all signs indicate financial markets are functioning normally.

U.S. Treasury Secretary Steven Mnuchin said recent volatility was not enough to rock market fundamentals.

Tuesday’s rebound came a day after a steep selloff that brought the biggest percentage daily declines for the S&P 500 and the Dow since August 2011 and a near 1,600 point intraday loss for the Dow.

Trading volume of more than 12.3 billion shares marked the busiest trading day since just after the November 2016 election, and topped Monday’s volume of 11.7 billion.