Sorting Out Downside Beta

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