Investors are hunkering down in bonds, fearful that events such as North Korea tensions, the French election and strained Russian-American relations could turn out badly.

Treasurys and gold rose in early trading Tuesday as investors bought the traditional global safe havens over these emerging geopolitical risks. Stock futures were slightly lower.

When the stock market gets nervous, all hell breaks loose, but a jittery bond market can look quite different.

In fact it may not look like much at all. Take the 10-year note, for instance. There are all kinds of worries being talked about in the market, and the yield, which moves opposite to price, has been stuck in a band of roughly 2.30 to 2.60 percent for weeks.

That is significant. Some bond market pros believe the yield will break that range and move higher, only on some very good news — or it could fall below it, but only on some very bad news.

For now, however, several strategists expect the 10-year to stay closer to the low end of the range, because a number of near-term factors are raising the level of uncertainty — and fear — for markets.

"If you're betting on higher yields, a lot of things have to go well. But if you're betting on lower yields, only one of those things has to show up," said Aaron Kohli, fixed income strategist at BMO.

Here are the five big risks in the market right now:

French Election

Strategists expect market volatility to pick up around France's presidential election, the first round of which is April 23. The spread between the French 10-year yield and the 10-year German bund has been widening, and U.S. traders are watching that as a measure of how much discomfort there is around the election.

Nationalist candidate Marine Le Pen is the big worry because she would like France to leave the euro zone. She is not expected to ultimately win, but the market has its doubts after the British vote in favor of Brexit and the long-shot election of President Donald Trump.

"Consistently people said Le Pen does pretty well in the first round and gets blown out in the second round. Maybe there's too much complacency there. We think markets could get a little jittery after the first round," said Michael Schumacher, head of interest rate strategy at Wells Fargo Securities. The second round is May 7.

Government shutdown

When Congress returns from its spring break, it will have just a few days until the April 28 deadline to pass a continuing resolution to keep the government funded. If it fails to pass the resolution, the government will be shut down. The fight, not the shutdown, could rattle the bond market.

Strategists expect the resolution to be approved, but the unexpected fight that broke out around replacing Obamacare in March has created doubt around whether the Republican Congress will really be able to cooperate.

"Once they get back, they only have a week to do the CR. In my view, it's low odds [of failing]," said John Briggs, head of strategy at NatWest Markets. Congress will ultimately have to address the debt ceiling in the fall, when the government gets close to running out of money.

Kohli said he's concerned that if the shutdown is averted, "they're going to be in a situation where you have a more bruising fight in October."

Trump tantrum

Trump's election helped drive bond yields higher, as traders bet on a hotter economy and rising inflation. But that trade has faded, and Schumacher said it's about a third gone. But the trade that's not faded is the bid in the stock market that drove it more than 10 percent higher

"It [stock market] sure looks like its trading on tax reform," said Schumacher. The big concern around stocks is that the market begins to doubt the Trump agenda and sell off. He added that if stocks take a hit because of a slower legislative agenda, that could send buyers straight into bonds. Those doubts have already been showing up in the bond market.

Hans Mikkelsen of Bank of America Merrill Lynch also sees stocks as a potential catalyst for a bond rally, if tax reform doesn't materialize.

"This year we have seen a notable gap between positive equity market performance and a more skeptical bond market where yields have not gone up. We continue to think that the biggest near term risk to our bullish outlook for credit spreads is a correction in equities, should the Trump administration disappoint on tax reform," Mikkelsen wrote in a note.

Another risk is that the economy does not get the boost that's expected from some of Trump's policies, and confidence fades and economic activity declines.

Federal Reserve factor

The Federal Reserve is a factor that could surprise the markets, either with its hawkishness or dovishness, should the economy soften.

The market was surprised last week when the Fed's minutes from its March meeting revealed that Fed officials would like to begin unwinding the Fed's balance sheet this year. That was sooner than expected, and it would be another major step away from the easy policies the Fed adopted in the financial crisis. It's still unclear how the Fed would proceed.

Schumacher said the Fed is also a risk because it has changed the way it operates. Ahead of the March rate hike, he said the Fed spent just two weeks convincing the market it would seriously look at raising rates at that meeting. The move was unexpected by markets until numerous Fed officials made direct comments about it.

What's unusual was that the Fed usually does not act on such a tight time frame.

"If you look at a 20-odd year history of the Fed, normally the Fed tees things up a month in advance. Every 25 basis point rate hike since 1991, before last month … the market was pricing the 60 percent probability one month out," he said. "It was a big shift."

There is also a risk that the Fed doesn't raise rates, as expected. Right now, the market expects a hike in June.

Jim Caron, fixed income portfolio manager at Morgan Stanley Investment Management, said there's a chance the Fed could hold off in June just because of all of the uncertainty around the French election, the economy and geopolitical risks.

He said the second quarter data could be inconsistent, before improving in the second half.

"Inflation data should be weaker as year-over-year oil price comparisons decline and thus do not contribute to a rise in headline inflation. True for U.S. and Europe," he wrote in an email. He also added that confidence data is at high levels and could fall.

"I question if the Fed will want to hike rates in June amid this uncertainty, downturn in inflation and sagging confidence," he notes.

Geopolitical event risk

Trump's first military foray into Syria last week was a bit of a surprise to the market, but it has taken it in stride. The bond market, however, could see a flight to safety if the situation escalates or becomes more uncertain. The same is true of North Korea.

While the weekend was still several days away, bond traders Monday were already talking about adding to positions for more financial security ahead of the three-day weekend. On Monday, speculation circulated the market that North Korea could be ready to launch another missile on April 15 for its Sun Day, celebrating the birth of its founder and first leader Kim Il Sung.

Higher or lower yields?

The 10-year was yielding 2.35 percent late Monday, and some strategists believe it will hover in that area.

Kohli sees yields moving lower, and he points to how investors have been buying dips. "It does suggest the market is focused on some of the negative things," he said. He expects the 10-year to hold the range but move lower.

Briggs said in the near term, yields could drift and perhaps move a little higher based on technicals. "Big picture, I don't think we break the range. There's a lot of cross currents," he said.

Caron expects the 10-year yield to stay in a range of 2.20 to 2.65 percent, but he expects after the second quarter, it could move higher into the end of the year.