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It's a conundrum: bonds aren't likely to win a popularity contest any time soon, but analysts don't expect investor demand will slack off.
"There are two things going on that are offsetting each other. One is that there is quite a lot of concern about what happens to bonds when Federal Reserve starts to raise interest rates; that's behind the lack of enthusiasm," said Richard Jerram, chief economist at Bank of Singapore. "On the flip side, there is still globally a search for yield taking place."
"There's sort of a concern the market is overextended, but also recognition that there's a lot of underlying demand," Jerram said.
Demand is firm
That demand doesn't look like it'll slack off anytime soon. Bond demand is likely to outstrip supply globally by around $450 billion this year on a notional basis, widening from $384 billion last year, JPMorgan said in a note earlier this month.
Much of that buying may come from retail investors, it said, estimating they will pour around $350 billion into bond funds this year after buying $500 billion last year. In the fourth quarter of last year, bond mutual funds received higher inflows than equity funds for a third quarter, JPMorgan said, citing ICI data.
"In other words, the supply/demand picture for 2015 continues to look supportive for bonds globally," JPMorgan said.
For the week ending April 11, global bond funds saw a net $4.7 billion worth of inflows, marking a 15th week of injections, according to data from Jefferies.
But all that money isn't making bond funds well-liked. A net 54 percent of fund managers remain underweight on the segment in April, according to Bank of America-Merrill Lynch's monthly survey. A net 84 percent say bonds are overvalued, the highest in the survey's history, it said.
"The people who are buying bonds today are not price sensitive buyers," said Hans Goetti, head of investment for Asia at Banque Internationale a Luxembourg. "If I [buy bonds at low or negative yields] for my clients, seriously, I'd have some explaining to do."
He calls buying bonds at negative yields "a greater fool theory," of hoping to sell it later at a higher price.
A healthy balance
To be sure, some bond buyers might just be taking prudent steps to balance their portfolios.
"The large capital appreciation of equities in recent years, by 50 percent in the U.S. and by 30 percent globally over the past three years, has made retail investors more overweight equities vs. bonds even as they bought more bond than equity funds over the same period," JPMorgan said.
Assets under management in equity mutual funds and exchange-traded funds (ETFs) accounted for 47 percent of all assets of all fund assets in the fourth quarter of last year, JPMorgan noted.
—By CNBC.Com's Leslie Shaffer; Follow her on Twitter