Conditional Mean-Variance and Mean-Semivariance models in portfolio optimization.

Summary It is known that the historical observed returns used to estimate the expected return provide poor guides to predict the future returns. Consequently, the optimal portfolio weights are extremely sensitive to the return assumptions used. Getting information about the future evolution of different asset returns, could help the investors to obtain more efficient portfolio. The solution will be reached by estimating the portfolio risk by conditional variance or conditional semivari-ance. This strategy allows us to take advantage of returns prediction which will be obtained by nonparametric univariate methods. Prediction step uses kernel estimation of conditional mean. Application on the Chinese and the American markets are presented and discussed.