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Market volatility, largely absent until last week, picked up in the final days of Janet Yellen's tenure, with interest rates suddenly breaking out of a long-running range. Long dormant, inflation expectations suddenly started to rise and triggered a sell-off in the Treasury market.

Yields, which move opposite price, shot higher, spooking stocks. The Dow, after a bruising 666 point loss Friday, was sharply lower Monday in volatile trading, dropping more than 1,500 points at one point before coming back.

The market action can't all be blamed on Powell's ascension to Fed chair, but he will have little or no honeymoon period before being expected to raise interest rates and continue the unwind of the Fed's balance sheet. Yellen didn't raise interest rates for nearly two years into her term, but then did hike five times as well as initiating the program late last year to scale back the central bank's massive balance sheet.

"There's a confluence of factors, one of them being we have a new Fed chair," said Ward McCarthy, chief financial economist at Jefferies. "There was the feeling Janet Yellen would always bail out the market. That was the notion during her tenure. Powell seems more inclined to let markets do what they do."

But in fact, the S&P 500 has fallen on the first days of the past couple of Fed chairs. Powell's first day on Monday coincided with a 4.1 percent drop Monday. The index fell 0.9 percent on Yellen's first day, and it was down 2.2 percent on Ben Bernanke's first day.

Jim Caron, fixed income portfolio manager at Morgan Stanley Investment Management, said he does not believe the market sell-off has anything to do with Powell's appointment. "It could add some uncertainty but it's not like anything we haven't known about," he said.

McCarthy also noted the long period of time since the last market sell-off and the tax cuts being an inflection point. In addition, "there was a wide range of indications that inflation is accelerating which is what causes rates to rise," he said.

Coincidental or not, during the first months of each of the past few Fed chairs there was a fairly significant stock market sell-off, the most pronounced of which was the1987 market crash just two months after Alan Greenspan became chair. In the case of Powell, the market is anticipating tighter Fed policy, both from higher interest rates and the balance sheet unwinding.

When Yellen began her term Feb. 3, 2014, the market had already been selling off for nearly two weeks, and it bottomed out early on, with a 5.4 percent drop by the S&P 500 over 14 days. The market then swooned again that year, falling 9.3 percent from Sept. 18 to Oct. 15 on an intraday basis.

Bernanke's term as chair was greeted by a 7.8 percent sell-off, starting May 5, 2006, through June 13, but Bernanke also had to suffer through the stock market collapse during the 2008 financial crisis, so his first sell-off was a minor trial.

Paul Volcker, who waged a battle with inflation with dramatic rate hikes, began his tenure in August 1979, and by October, the S&P 500 began a sell-off that ended in an 11 percent decline by Nov. 7, 1979. The next year, there was a more than 20 percent drop.

Greenspan was tested the most by markets in his first weeks. He started as chair Aug. 11, 1987, and by Aug. 25, the market had started a sell-off that would include the Oct. 19, 1987, stock market crash. All told, the S&P 500 plunged into a bear market, losing 34.5 percent by the time it reached a bottom on Dec. 4.

Sam Stovall, chief equity strategist at CFRA, said some of these declines could be normal for the market, and not the result of uncertainty around a new Fed chair.

But Powell's job could be tricky. The new Fed chair may be faced with a hotter-than-expected economy after the tax legislation, and higher inflation. That could force Powell's Fed to raise rates more than the three times the central bank currently forecasts for this year. That could continue to rattle the markets, potentially causing the Fed to pull back if the market moves are dramatic enough or affect credit conditions too much.

Analysts said the Fed's challenge this year is also that other central banks are now moving toward tightening, with the European Central Bank paring its bond buying. U.S. Treasury yields have been moving higher with bonds, as a result. Japan is also looking to reduce stimulus at some point.