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.
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"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.