This paper proposes a generalization of the class of realized semivariance and semicovariance measures introduced by Barndorff-Nielsen, Kinnebrock and Shephard (2010) and Bollerslev, Li, Patton and Quaedvlieg (2020a) to allow for a finer decomposition of realized (co)variances. The new "realized...

Under the CAPM assumptions, the market capitalization weighted portfolio is mean-variance efficient. In real world applications it has been shown by various authors that low risk portfolios outperform the market capitalization weighted portfolio. We revisit this anomaly using high-frequency data...