Mean-semivariance portfolio optimization using minimum average partial

Mean-semivariance and minimum semivariance portfolios are a preferable alternative to mean-variance and minimum variance portfolios whenever the asset returns are not symmetrically distributed. However, similarly to other portfolios based on downside risk measures, they are particularly affected by parameter uncertainty because the estimates of the necessary inputs are less reliable than the estimates of the full covariance matrix. We address this problem by performing PCA using Minimum Average Partial on the downside correlation matrix in order to reduce the dimension of the problem and, with it, the estimation errors. We apply our strategy to various datasets and show that it greatly improves the performance of mean-semivariance optimization, largely closing the gap in out-of-sample performance with the strategies based on the covariance matrix.