Higher Order Moments and Beyond

As we skip behind the normality world, many desirable properties fall short. Specifically, the central moments of linear combinations of random variables do not preserve the features of the addenda. For example, not even null-correlated returns preserve the sign of odd central moments as the returns are combined into a portfolio. A mathematical explanation of this counter-intuitive phenomenon is provided. However, a way to overcome these drawbacks exist. Advantages in using one-sided higher order moments instead of higher order moments are highlighted. First of all, one-sided moments are coherent measures of risk. Thanks to this feature a number of desirable marginal ordering preservations is guaranteed.