Portfolio optimization under lower partial risk measures

Portfolio management using lower partial risk (downside risk) measures is attracting more attention of practitioners in recent years. The purpose of this paper is to review important characteristics of these risk measures and conduct simulation using four alternative measures, lower semi-variance, lower semi-absolute deviation, first order below target risk and conditional value-at-risk. We will show that these risk measures are useful to control downside risk when the distribution of assets is non-symmetric. Further, we will propose a computational scheme to resolve the difficulty associated with solving a large dense linear programming problems resulting from these models. We will demonstrate that this method can in fact solve problems consisting of 10⁴ assets and 10⁵ scenarios within a practical amount of CPU time.