Mean-Variance-Skewness-Kurtosis efficiency of portfolios computed via moment-based bounds

We analyze moment-based bounding approximations on the expected value of a utility function. We show that optimizing these bounds yields a solution, which is mean-variance (MV) or MV-skewness-kurtosis (MVSK) efficient depending on how many moments are included in the approximation. To illustrate the approach we apply it to an asset allocation model with a shortfall utility function. Numerical results are presented for an out of sample trading strategy using sixteen years of daily trading for a portfolio of six assets. The strategy significantly outperforms a standard market index, Dow Jones Industrial Average.