Bollerslev, T., Patton, \AndrewJ.\ and Quaedvlieg, R. (2021). Realized semibetas: Disentangling “good” and “bad” downside risks Journal of Financial Economics, 144(1):227--246.

We propose a new decomposition of the traditional market beta into four semibetas that depend on the signed covariation between the market and individual asset returns. We show that semibetas stemming from negative market and negative asset return covariation predict significantly higher future returns, while semibetas attributable to negative market and positive asset return covariation predict significantly lower future returns. The two semibetas associated with positive market return variation do not appear to be priced. The results are consistent with the pricing implications from a mean-semivariance framework combined with arbitrage risk driving a wedge between the risk premiums for long and short positions. We conclude that rather than betting against the traditional market beta, it is better to bet on and against the “right” semibetas.