This paper examines the profitability of four European higher return stock portfolios and their linkages between the value premium factor return, high-minus-low (HML), developed by Fama and French. Our fundamental analyses and quantitative examinations using Markov switching models derive the following findings. First, in the four higher return stock portfolios in Europe, the smallest and the highest momentum portfolio shows the highest return. Second, the second smallest and the highest book-to-market (BM) portfolio, the second smallest and the highest operating profitability portfolio, and the second smallest and the second lowest investment portfolio for Europe also demonstrate higher excess returns than the overall stock market in Europe. Furthermore, we also clarify that for all the four European stock portfolios, there clearly exist two regimes: one is positively associated with the value premium factor return, HML, and the other is negatively associated with HML. We further reveal that recently, for all the four portfolios, the high value premium factor loading regimes shift to the other regimes that are uncorrelated with HML. This indicates that, in the recent periods, hedging and risk-diversification effects can be recognized in investing value stocks and the four higher return stock portfolios in Europe.