Higher Order Moments Resampling

This paper develops a set of portfolio optimization models that involve a resampling approach of the higher order moments of financial assets return distributions. Specifically, the first four moments are examined. The Resampled Efficiency (RE) techniques introduce Monte Carlo methods to properly represent investment information uncertainty in computing minimum variance (MV) portfolio optimality. Notwithstanding the central limit theorem, for both the academic and financial communities it is a well known fact that stock market returns exhibit latent higher moment risk in the form of negative skewness and high kurtosis. Taking cue from these considerations we have added higher-order moments to the resampling rule. We discuss the solution of the higher order moments resampling approach by replaying an investment game. The game compares the performance of a player using four portfolio schemes for determining portfolio weights using a Monte Carlo based resampling approach. Extensive computational results are obtained on a real-world dataset with two different resampling approaches. Surprisingly, when higher moments of stock return distributions are accounted for in the resampling optimisation algorithm success is mixed.