This work aims to exploit the so-called "Beta anomaly" regarding the risk-reward relationship, and set up rules and methodologies in order to build new efficient portfolios. It is well known in literature, and among practitioners, that "Low Beta strategies" generate good performances exploiting alpha opportunities. In this paper we focus on β parameters: we analyze this one and its components (Correlation and Standard Deviation) in order to better understand the drivers and contributions behind

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... the "Low Beta strategies", and eventually exploit them. We perform an extensive empirical analysis on the S&P500 and the relative sectors, covering more than 10 years. In addition we follow Long/Short strategies in building portfolios based on β and their components where we compare results against the benchmark. We also introduce "Walking Beta" approach in order to give a deep and innovative view on the market risk/reward relationship, illustrating different time frames and the evolution of risk parameters.