The list of big money bond market bashers is growing

Warren Buffett
Andrew Harrer | Bloomberg | Getty Images
Warren Buffett

The bond market has turned into a punching bag for big investors, but strategists don't see Treasury yields moving much higher for now.

Both Warren Buffett and Omega Advisors' Leon Cooperman Monday called the bond market overvalued relative to stocks. David Tepper of Appaloosa Management, at the Ira Sohn conference, was also bearish on bonds, calling them "horrific" with quantitative easing.

"If I had an easy way, and a non-risk way, of shorting a lot of 20-year or 30-year bonds, I would do it. But that's not my game. It can't be done in the quantity that would make sense for us," Buffett said on CNBC Monday morning.

Read MoreBuffett: Stocks versus bonds

Cooperman, chairman of Omega Advisors, said the stock market "isn't priced to perfection," but it's fairly valued, unlike the bond market. "I think the bond market is overvalued, but the stock market is about 16½ times earnings and [it] seems about right," Cooperman told CNBC's "Halftime Report."

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But bond valuations are in the eye of the beholder. Fixed income strategists say factors that have added richness to Treasury prices – and inversely held rates low – have not gone away, and bond yields should not rise all that much in the near future even if they do edge higher.

"I would agree Treasurys look like they're expensive, but are fundamentals really driving the Treasury market or is it really something else? I'm in the camp that says it's something else," said Jim Caron, global portfolio strategist in global fixed income at Morgan Stanley Investment Management.

The 10-year yield last week broke back above 2 percent, as European yields moved higher and some U.S. economic data – like employment costs - were seen as supportive. Low European yields, driven by European Central Bank (ECB) easing, have been a factor keeping a lid on U.S. rates.

The investor comments follow a call last week by DoubleLine's Jeff Gundlach to short bunds. Janus Capital's Bill Gross is also negative on European sovereigns. Gundlach Monday reiterated his position that interest rates have already bottomed.

Treasury yields have been held down by soft first quarter data and unease about whether the economy will spring back as expected. The stronger dollar, which dampened corporate earnings and U.S. exports, and lower oil prices, adding to low inflation, are all seen as factors behind lower rates. Caron said many of the factors pushing yields lower have now reversed, such as oil prices, but yields should still not rise that much.

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"I do think they're expensive, but the thing that's primarily driving the expensiveness in bonds is just that the risk premium is very low," he said. "I do think yields will rise." But he expects the move higher to be relatively slow for now.

"It's not like as a fixed income investor, you're going to get carried out of your investment. You do have to pick your spots," said Caron. "We were at 2.25 percent in March and we could get up to that level again...If the data doesn't really change, I think it's going to be hard to get sustainably above 2.5 percent."

The big wild card for rates is the Federal Reserve and when it might pull the trigger on its first rate hike. But since it is also data dependent, the Fed is watching for the same clues as the bond market.

Read MoreCooperman: Bond market is overvalued

"The 10-year is doing what I thought it would do...just drifting sideways," said Ward McCarthy, chief financial economist at Jefferies. He said the U.S. market has been reacting to the "mercurial effects" of quantitative easing program of the ECB, and he could see the 10-year yield pushing 2.5 percent, but not much more.

"The secondary effects of the ECB QE are going to affect Treasurys. Part of the problem is you had such a run on the dollar and it caused the Fed to soften its rhetoric and since then the dollar weakened... The expectation was money would flow from Europe into the U.S. both because the rates were higher and the anticipation the dollar would rise," he said.

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One of the criticisms leveled at the bond market is that has bubble-like attributes, but at the same time there is a shortage of liquidity. Bond market participants blame the liquidity issues on several factors, including new banking industry regulations that resulted in less capital in the markets, the huge stock pile of Treasurys that the Fed has on its balance sheet and the cutback in primary dealing desk staffing.

Some fear the liquidity problems could rise to the surface if rates move quickly, and the reaction could be violent, like the 40-basis point whipsaw in Treasurys on Oct. 15.

"If it's a liquidity event and nothing fundamental changes in the market, we believe prices will come back, but you want to be positioned so you can survive a shock like that. I believe liquidity in the market is a systemic risk," Caron said. He said one way to protect against a liquidity event is to put money closer to the front end of the curve. "If rates go up for a liquidity reason, then back end rates go up the most."

Liquidity issues have been increasingly highlighted, and J.P. Morgan CEO Jamie Dimon used his annual letter to shareholders to warn about it.

Read MoreSummers agrees with Dimon, there's a liquidity problem

"I think that's a pretty big topic right now," said Caron. "It's something that sort of lurks beneath the surface." He said it becomes a bigger factor should rates start to rise rapidly.

"I think it's more of an issue when rates rise and if people all of a sudden have to liquidate positions. That's when you can have an outsized move," he said. For that reason, investors should not be too aggressively positioned when rates do start to rise. "There could be a more violent event that's lurking in the future," he said.

Chris Rupkey, chief financial economist at Bank of Tokyo-Mitsubishi, does think rates could get higher than some strategists expect by the end of the year. He said the 10-year yield could have a 3-percent handle before the end of the year. "I don't want to take the number 3 off the table simply because we haven't seen the market reaction to the actual liftoff," he said.

He also expects the two-year yield to move more quickly to a much higher level, possibly as much as 1.9 percent. "When rate hikes come, the curve flattens," he said.