Improved Estimates of Higher-Order Comoments and Implications for Portfolio Selection

In the presence of nonnormally distributed asset returns, optimal portfolio selection techniques require estimates for variance-covariance parameters, along with estimates for higher-order moments and comoments of the return distribution. This is a formidable challenge that severely exacerbates the dimensionality problem already present with mean-variance analysis. This article extends the existing literature, which has mostly focused on the covariance matrix, by introducing improved estimators for the coskewness and cokurtosis parameters. We find that the use of these enhanced estimates generates a significant improvement in investors' welfare. We also find that it is only when improved estimators are used that portfolio selection with higher-order moments dominates mean-variance analysis from an out-of-sample perspective.