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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.
Eurozone shares are trading around 11 times earnings, while U.S. shares are at 15 times, an around 36 percent discount, he noted. "The starting point in Europe is far more attractive," he said.
(Read more: Sell US, buy European assets: Strategist)
Institutional investors appear to be heading toward European shares, as well, with 30.9 percent of long-only and hedge funds choosing continental Europe as their favorite developed equity region in a survey at a conference in Beijing, conducted by Bank of America-Merrill Lynch. Only around 12 percent said they believed the key risk to markets in 2014 would be European issues re-surfacing, well behind the more than 50 percent who felt the key risk was U.S. policy uncertainty.
Peter Oppenheimer, European equities strategist at Goldman Sachs believes investors are transitioning from a period of "hope" or a valuation-driven phase into a slower, but longer, "growth" phase driven by earnings growth.
This pace of growth would be enough to generate a total return through 2014 of about 15 percent, he said in a research note on Thursday.
HSBC is also positive on Europe, citing attractive valuations, signs the earnings cycle is near its bottom, prospects of a policy boost from the European Central Bank and few signs investors are becoming overconfident.
(Read more: Why we like European currencies right now: Goldman)
While many investors are beginning to sound more positive about Europe, HSBC doesn't believe they've already reacted to the view.
"We see no signs that either retail or mutual fund investors have moved aggressively into European equities. Rather it seems to be a case of all talk, no action."
The MSCI Europe ex-U.K. index is trading at a trailing price-to-book ratio of 1.6 times, compared with its average over the past 16 years of 2.3 times, while on a 12-month forward price-to-earnings basis, the index is at 13.6 times, compared with its average of 14.7 times over the past 16 years, according to data from HSBC.
But it does caution, "We are close to the point when further appreciation in European equities will require an improvement in the earnings cycle."
— By CNBC's Leslie Shaffer. Follow her on Twitter: