Portfolio Selection in Multidimensional General and Partial Moment Space

This paper develops a general approach for the single period portfolio optimization problem in a multidimensional general and partial moment space. A shortage function is defined that looks for possible increases in odd moments and decreases in even moments. A main result is that this shortage function ensures sufficient conditions for global optimality. It also forms a natural basis for developing tests on the influence of additional moments. Furthermore, a link is made with an approximation of an arbitrary order of a general indirect utility function. This nonparametric efficiency measurement framework permits to differentiate mainly between portfolio efficiency and allocative efficiency. Finally, information can, in principle, be inferred about the revealed risk aversion, prudence, temperance and other higher-order risk characteristics of investors. A mean-variance-skewness-kurtosis example on a small sample of assets serves as an empirical illustration. We also compare the relative fit of a series of lower partial moment models.