LPM Density Functions for the Computation of the SD Efficient Set

The equivalence between partial moments and stochastic dominance dates back to Bawa and Fishburn. We present a test for first, second, and third degree stochastic dominance between two variables using Lower Partial Moments. The results uphold Hadar and Russell's original conclusions about the odd moments of preferred prospects. We recall Nawrocki's research comparing Mean/Variance portfolios against the continuum of risk-averse investors using Lower Partial Moments. The excess skewness of the LPM portfolios clearly demonstrates the preference of positive skewness for risk-averse investors. Finally, we provide an algorithm for efficiently determining stochastic dominance efficient sets among large numbers of variables