According to Jinshi, global bonds rose on Tuesday, echoing the overnight rise in U.S. Treasuries. Bets that the Federal Reserve may cut interest rates early have increased the appeal of sovereign debt. The yields on 10-year bonds in Australia and New Zealand fell by at least 8 basis points after data showed that the pace of contraction in U.S. factory activity accelerated in May.

Japan's 10-year bond yield fell two basis points, while South Korean bonds also rose. The renewed optimism in the bond market may be tested in the coming days when non-farm payrolls data will reveal whether the U.S. job market has cooled enough to warrant easing policy.

Royal Bank of Canada said it's not just the Fed. This week the focus is of course on the Canadian and European central banks, which are expected to start a rate cut cycle. U.S. job openings data will be released on Tuesday, which may also stimulate new demand for bonds if it is lower than market expectations.