We analyze if the value-weighted stock market portfolio is second-order stochastic dominance (SSD) efficient relative to benchmark portfolios formed on size, value, and momentum. In the process, we also develop several methodological improvements to the existing tests for SSD efficiency....

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...

Downside risk, when properly defined and estimated, helps to explain the cross-section of US stock returns. Sorting stocks by a proper estimate of downside market beta leads to a substantially larger cross-sectional spread in average returns than sorting on regular market beta. This result...