"The European market place, particularly for equities, is following very much what the U.S. did a couple of years ago because obviously the U.S. monetary authority loaded up our system with accommodative capital...and now you are almost seeing a mirror image of that occurring here in Europe," Mike Thompson, the managing director and head of global markets intelligence at S&P Capital IQ, told CNBC last week.
Read MoreEurope's bulls run…but for how long?
The S&P 500 outperformed most advanced markets last year as the U.S. Federal Reserve begun dialing back its own quantitative easing (QE) program but has posted slim gains of just 0.7 percent year-to-date. Unthinkably, an article by Reuters last week quoted some analysts already speculating that the ECB might also "taper" the pace of its bond purchases, possibly even before the end of 2015 and way before initial expectations. This comes as business activity data has produced better-than-expected results and euro zone inflation figures have edged ever so slightly higher.
Buyers might also be a little wary of the price-to-earnings ratio - a popular calculation used by many market participants to gauge the value of a stock. The ratio for the Euro Stoxx 600 is now above the S&P 500 after years of it being the other way around, with a higher ratio meaning the more overvalued its likely to be.
Read MoreEurope's best stocks this quarter
If you are buying European stocks you are now part of a consensus trade. This should ring alarm bells but there are ways to ride out this bull run in style. Piers Curran, head of trading at Amplify Trading, told CNBC via email that he would favor cyclical stocks in this environment.
Martin Todd, co-manager of the Hermes Sourcecap European Alpha fund, detailed his five hidden "growth gems" in a research note last week. He named Spanish airport operator Aena, Zurich-based food business Aryzta, financial services firm Wirecard, Spanish manufacturer Gamesa and Telecom Italia as having "strong long-term growth potential."
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