In this thesis, we perform a robustness test of the interesting ndings by in particular Artavanis (2013), but also Ang et al. (2006) and others, who nd evidence that a downside beta outperforms the CAPM beta in its ability to explain excess stock returns in a test developed by Fama and French (1992). Stating that the CAPM beta is outperformed by the less known downside beta is a bold statement, and could indicate that information of a downside beta can be used to achieve abnormal excess returns on the stock market. These ndings deserve robustness tests to either strengthen their case or show that the results are inconsistent across di¤erent markets or time periods, which is the motivation for writing this thesis. Our main ndings show that there is no di¤erence in the ability of the CAPM beta and the downside beta to explain excess returns in a Fama and French (1992) test during the years 2000-2014 on the Frank- furt, London and Stockholm stock exchanges. Thus, the results of the robustness test are demotivating, weakening the case for the downside beta rather than accepting its superiority.