Government bonds are a "very problematic" investment right now because of the large number of issuances and because they have been pushed down by the latest rally in stocks, said Uwe Parpart, chief economist and strategist at Asia Cantor Fitzgerald.
"For the moment, be very, very careful with government bonds," Parpart advised CNBC viewers Monday.
Last week's better-than-expected US unemployment figure means some aspects of the stimulus program are working, but the benefit is "a one-off," and the world economy is still fragile, he added.
All eyes will be on the Federal Reserve this week to see what it will announce on Wednesday, after a two-day policy meeting.
The Fed is seen ending its plan to buy $300 billion of longer-dated Treasurys in September; analysts expect the Fed to hold the fed funds rate at 0-0.25 percent.
The Fed's balance sheet has been shrinking, and if markets perceive this as tightening, "it will be very negative both for equities and for bond markets," according to Parpart.
Nobel Prize winner Paul Krugman earlier told CNBC that the first stimulus program in the US was not enough to avoid a Japan-style "lost decade," though it managed to help the world economy skirt a depression. He added that a second stimulus is needed.
Although the latest data point to a rebound in activity, the rally in risky assets could continue for two or three months, but then question marks will rise regarding the sustainability of the revival, said Jonathan Cavenagh, currency strategist Westpac Bank, in an interview on CNBC.
"I think the market will start to get a little bit disappointed with the recovery," Cavenagh said, adding that U.S. unemployment was likely to stabilize but not come down soon.