This study analyzes various measures of the downside beta of stocks. Downside beta is sometimes defined and estimated in different ways. Theoretically, an approach based on the mean-semi-variance equilibrium model appears superior. Two known alternative approaches are not consistent with the basic principles of coherent risk measures and the properties of a well-behaved pricing kernel. Moreover, to achieve superior out-of-sample predictive power, it is essential to estimate the downside beta definition that follows from the theory. Using monthly stock-level data, the downside beta premium, if properly defined and estimated, is roughly four to seven percent per annum, depending on the model specification and sample period, compared with a premium of zero to three percent for regular market beta.