Conditional Downside Risk and the CAPM

The mean-semivariance CAPM strongly outperforms the traditional mean-variance CAPM in terms of its ability to explain the cross-section of US stock returns. If regular beta is replaced by downside beta, the traditional risk-return relationship is restored. The downside betas of low-beta stocks are substantially higher than the regular betas, while high-beta stocks involve less systematic downside risk than suggested by their regular betas. This pattern is especially pronounced during bad states-of-the-world, when the market risk premium is high. In sum, our results provide evidence in favor of market portfolio efficiency, provided we account for conditional downside risk.