European Central Bank President Mario Draghi has been the bond market's best friend, but investors aren't expecting the same support from his successor, Christine Lagarde.

Since Draghi took the helm of the ECB eight years ago, Europe's sovereign bonds have surged, with German debt returning 27 percent and that of Ireland almost 90 percent, Bloomberg Barclays indexes show. It has been a dream trade. Draghi cut rates two days after his tenure began and went on to live up to his famous pledge in 2012 to do "whatever it takes" to hold the euro area together. He oversaw trillions in bond buying, the introduction of negative rates and measures to support banks.

Thursday's gathering of the bank's governing council will be Draghi's last before his time as president ends on Oct. 31. Lagarde arrives just as monetary policy appears to be reaching its limits. The former head of the International Monetary Fund has praised the ECB's stimulus but may ask governments for fiscal support to help energize the euro-area economy. While sweeping increases in public spending are doubtful, the prospect of greater supply that any such measures would bring could threaten the record-breaking rally for the region's bonds.