I have been trying to find a way to create the efficient frontier using Post Modern Portfolio Theory (PMPT), but have failed to come across a source that mentions how to do so. I know PMPT uses downside risk as opposed variance (MPT), so somehow I need to find a method to minimize downside risk I suppose.
According to this research paper: http://www.ecocyb.ase.ro/nr_2013_pdf/Geambasu%20Cristina,%20Robert%20Sova.pdf,
"It is simple to compute for a share or for a portfolio already formed, for historical or predictive data, but things became more complicated if we intend to use the PMPT model in determining the portfolio assets structure"
So is there not a way to find an optimal set of asset weights to minimize downside risk?
In this paper by Rom and Ferguson, http://www.actuaries.org/AFIR/Colloquia/Orlando/Ferguson_Rom.pdf, they mention
"The PMPT efficient frontier is calculated using an algorithm for downside risk developed by The Pension Research Institute applied to the expected return, standard deviation and skewness values" and they also provide an efficient frontier calculated by using PMPT on p.12, but the algorithms I'm assuming have not been made public.
So my question is, does anyone know what the algorithm is/might be or how can I go about creating it?