Uncertain Mean-LPMs Model

Downside risk is a class of risk measures which focuses on the asymmetry of returns about some target level of return (Harlow 1991). It has gradually attracted more and more attentions since investors are often sensitive to downside losses, relative to upside gains. Moreover, it requires simpler theoretical assumptions to justify its application. In portfolio management, investors always prefer securities with smaller downside risk. In the situation with symmetrically distributed returns, some downside risks are consistent with general risk measures. For example, semivariance is exactly proportional to variance for normal distribution, which implies they are equivalent in measuring risk.