That rare advice came in a note to clients this week, which said that the bank now favors European stocks over US shares.

The argument? After two years of outflows, European stocks look like a good deal. And with support from the European Central Bank, as well as growing expectations for fiscal stimulus, they could be poised for a rebound.

"We now believe that there is an opportunity for Eurozone [stocks] to bounce back," wrote Mislav Matejka, the firm's head of global and European equity strategy.

JPMorgan's recommendation is a bold one. Since last spring, eurozone stocks have underperformed US shares by more than 20% in dollar terms, per the bank's own analysis. And Matejka concedes plenty of reasons to worry about the path ahead for the region's riskier assets.

Chief among them is the disappointing economic data coming out of Europe. Germany's Ifo business expectations index is at its lowest point since June 2009. The Purchasing Managers' Index for the eurozone, a closely-watched gauge of manufacturing, is at its weakest level since October 2012.

Then there's the potential for political instability to resurface in Italy, along with Britain's pending exit from the European Union.

Due to an intervention by Parliament, analysts now see a much lower probability of a disorderly UK departure on or before the October 31 deadline. The expectation is that Prime Minister Boris Johnson will be forced to ask for an extension to make way for a general election. In the meantime, it's difficult to predict how Brexit will play out, with the lack of clarity acting as a drag on stocks.

Despite all this, Matejka and his team see room for optimism.

Much of that has to do with stimulus measures taken by the ECB, which last month pushed interest rates further into negative territory and announced that it would resume its bond-buying program indefinitely.

The latter, which generally works to lower borrowing costs, could be a "big support" for eurozone assets, Matejka wrote.

Expectations of fiscal stimulus could also push stocks higher, even if the political will to enact flashy spending packages still hasn't materialized.

"Meaningfully stronger fiscal support is unlikely anytime soon, [but] we believe that equity markets could start to price in increasing odds of this happening," the bank said, noting that Europe has lower debt levels than Japan and the United States, giving it more room to maneuver.

Central bankers, fearing they've depleted their toolkits, have been applying pressure on European governments to step up to the plate.

On this front, incoming ECB president Christine Lagarde could be helpful, JPMorgan pointed out.

"She might be seen as more politically connected, having previously served as the finance minister for France, and has also spoken clearly about the need for fiscal easing," Matejka said. CNN