An alternative perspective on the relationship between downside beta and CAPM beta

In this paper we derive relationships between the CAPM beta and three measures of downside risk discussed in the literature. The relationships are derived assuming data generating processes in the mean-variance and mean-semivariance frameworks. In a sample of emerging market index returns we highlight that the association between the CAPM beta and downside beta depends on the standard deviation, skewness and kurtosis of the market portfolio return distribution. Therefore choice of risk measure may depend on the market being investigated. We argue that the derived relationships may also help explain anomalous results in empirical investigations.