A note on semivariance

In a recent paper (Jin, Yan, and Zhou 2005), it is proved that efficient strategies of the continuous-time mean-semivariance portfolio selection model are in general never achieved save for a trivial case. In this note, we show that the mean-semivariance efficient strategies in a single period are always attained irrespective of the market condition or the security return distribution. Further, for the below-target semivariance model the attainability is established under the arbitrage-free condition. Finally, we extend the results to problems with general downside risk measures.