An Analytical Framework for Explaining Relative Performance of CAPM Beta and Downside Beta

Even though investors' view of risk is generally regarded as related to the downside of the return distribution the CAPM beta is still a widely used measure of systematic risk. A number of studies compare the empirical performance of CAPM beta and downside beta in explaining the variation in portfolio returns and report mixed results. This paper provides a basis for explaining such mixed results. Using data generating processes in the mean-variance and mean-lower partial moment frameworks, analytical relationships between the CAPM beta and downside beta are derived. The derived relationships reveal that the association between the two systematic risk measures is to a great extent dependent on the volatility of the market portfolio returns and the deviation of the target rate from the risk-free rate. How the relationships derived here may be used in practice is demonstrated using empirical data