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?

  • 2
    $\begingroup$ I haven't read the paper, but can you not simply set up an MV optimization and then replace the SD/variance portion with downside risk? It should operate nearly identically, only with different inputs. $\endgroup$
    – Chris
    Commented Oct 31, 2019 at 17:31
  • $\begingroup$ Have you had any progress? I'm interested in exactly the same problem. My naive approach would be to use DR instead of STD and then optimize for best Sortino ratio. $\endgroup$
    – ruslaniv
    Commented May 25, 2020 at 7:29

1 Answer 1


Hi: Footnote 15 of the paper at this link explains what the formulation is (in brief: it is based on the Sortino Ratio). It sounds like something that can be programmed as a quadratic optimization. R has a lot of facilities for doing that sort of thing.

Addendum: I didn't read it but this paper provides a lot more detail than the one above.

  • 1
    $\begingroup$ Note: the second paper you mention is just a different copy of the first paper the OP mentioned. $\endgroup$
    – Alex C
    Commented Oct 31, 2019 at 17:13
  • 1
    $\begingroup$ @Alexc: Thanks for heads up. Let me know if I should delete that. Fortunately, the second one looks more useful anyway. $\endgroup$
    – mark leeds
    Commented Nov 1, 2019 at 13:39

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