European shares are "significantly underpriced" and could double within five years, with a 27 percent total return likely by the end of 2014, bringing stocks back to their 2007 highs, Barclays said.
"European stock markets appear significantly cheap relative to history, relative to other regions globally, and relative to other asset classes," Barclays said in a note.
"Investors in European equities remain unduly risk-averse," even though the 2011-12 crisis environment is now gone, Barclays said. "While the past few months have seen a movement towards a less risk averse set of prices, we suggest that this process has quite a bit further to go."
(Read more: Why Europe may not get much cheaper)
Price-to-book ratios have historically been good indicators of European stock returns, it said, noting the current 1.82 level is generally followed by shares doubling over the next five years.
"The relative price/book on European indices relative to U.S. indices is now at one of the cheapest levels seen since 1975," at around a 30 percent discount, it said. It set a Stoxx 600 index target of 400 for the end of 2014, compared with its current level around 322.42 and its 2007 high around 400.
Expectations for the region's shares to double in five years may not be far-fetched.
(Read more: Why the euro area remains a good investment bet)
"Unless one holds a bearish view on the Eurozone – that it does go back into crisis – it does seem plausible that it will get good gains," said Shane Oliver, head of investment strategy at AMP Capital.
"A return to more normal valuations would push shares up by about a third," he said. "It might get to a doubling in five years, depending on how long it takes to get profits back up," from their current level below the long-term trend.
While U.S. shares continue to set fresh records, "European stocks are still a long way from record highs. It tells you a lot about the upside potential," he said. He noted the Euro Stoxx index is at 307.62, about 44 percent away from its high of 442.87 in 2007.