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Volatility has taken hold of the Treasury market, with yields swinging back and forth to a degree not seen since the “Taper Tantrum” of 2013.

It’s at “historically high” levels, according to a Bank of America Merrill Lynch analysis. Put it this way, says BofA rates strategist Priya Misra: If daily moves over the last few months have been “X” basis points, lately, “we are getting many days of moves greater than 1.5-times ‘X.’ ” (A basis point is one hundredth of a percent.)

That kind of whipsawing is surprising, Misra says, because U.S. data reports haven’t been all that volatile, the Federal Reserve still has key interest rates set at zero, and even though the central bank is making noise about raising rates–perhaps as early as June–it’s suggesting a very gradual process of getting policy back to normal–not exactly a recipe for wild swings in the market.

This week, we’ll get a sense of just how gradual the Fed intends to be when it comes to backing off its zero-rate policy. The Federal Open Market Committee, which makes the decision on rates, will release a statement on Wednesday at 2 p.m. Eastern time. Fed Chair Janet Yellen will take questions from the press after the statement’s release.

If Yellen doesn’t sound dovish—that is, if she keeps a sooner-rather-than-later rate hike on the table—yields could rise. “The risk is that a more balanced set of comments by Yellen results in greater volatility and higher yields as the market puts more weight on a June move,” BofA economists say. On the other hand, if the Fed says it will still be “patient”—its current promise du jour—on raising rates, Treasury yields could fall sharply, with investors putting their money on rates not rising anytime soon.

Investors will pay close attention to the Fed’s forward guidance–what it says it will do in the future–to help determine when it might press the button on raising rates. Treasuries have become very sensitive to this guidance, the BofA analysts say, so look for volatility after the two-day Fed meeting.

Also contributing to big swings in Treasuries lately: a lack of liquidity in the market, the BoA strategists say. Among other factors, BofA cites regulatory pressures that make the Treasury-dealing business less attractive for large banks. This has limited supply, they contend, which means smaller transactions can have outsize effects on the market. In this environment, “we believe that even small events and volumes can cause big market moves,” they say.

The 10-year benchmark Treasury yielded around 2.1% late last week, down from the 2.239% it fetched the prior week, when the yield hit its peak so far this year. Still, yields have risen steadily as of late: At the end of January, the 10-year yielded around 1.68%. Bond prices rise as yields fall.

IT’S NOT JUST THE FED that bond investors should pay attention to. The price of oil, down more than 50% in the past seven months, is reverberating beyond energy markets.

Moody’s Investors Service analysts flag the falling price of oil’s possible effect on the asset-backed securities market. In particular it points to securities tied to sectors that might benefit from the increased consumer-purchasing power generated from people who will have more in their pockets because they’re spending less at the pump.

As a result, investors might take a look at the asset-backed securities of unsecured consumer credit like credit cards and student loans, which stand to benefit from the oil-induced windfall to consumers’ pocketbooks.

“The average U.S. household will spend about $550 less on gas in 2015 than in 2014,” the Moody’s analysts say, citing data from the U.S. Energy Information Administration. “Oil price declines act like a tax cut, enabling consumers to spend a greater percentage of their incomes on nonenergy goods and services.”

The International Energy Agency said Friday that prices could fall further as the U.S. keeps pumping more oil than it has in the past. That might make these oil-influenced asset-backeds even more attractive.

BRADLEY DAVIS is the digital editor for markets and finance at The Wall Street Journal.

E-mail: editors@barrons.com