Risk is an essential factor to consider when investing in the capital markets. The question of how one should define and manage risk is one that has gained a lot of attention and remains a popular topic in both the academic and professional world. With substantial evidence that returns are asymmetric and that investors do not exhibit quadratic utility, downside risk has been gaining increasing attention, and numerous magnitudes that capture downside risk are now well known and widely used. The present study considers six different downside risk measures and tests their relationship with the cross-section of returns as well as their performance in portfolio optimization compared to variance. Results from previous studies in this field are quite disparate and the question remains whether downside risk measures lead to more efficient allocations than variance.