Portfolio optimization in an upside potential and downside risk (UPM-LPM) framework

In the process of evolving portfolio theory, In order to eliminate the defects and basic assumptions limitation of the traditional model, the concept of downside risk and the Mean-LPM model has been introduced.
The Lower Partial Moment (LPM) has been the downside risk measure that is most commonly used in portfolio analysis. Its major disadvantage is that its underlying utility functions are linear above some target return. As a result, the upper partial moment (UPM)/lower partial moment (LPM) analysis has been suggested in the recent researches. The UPM-LPM framework is powerful because it implements the full richness of economic utility theory such as Morgenstern economic utility function and prospect theory.
In this study, using by stock market Sector indexes over 3 years period since 2010 to 2012, the mean-variance and UPM/LPM optimal portfolio has been calculated in different degrees of potential and risk aversion. In the next step, the optimal portfolio performance of both model has been measured over second period from 2013 to 2015. This research used MATLAB software for optimizing and analyzing of portfolio selection models.
The Jobson-Korkie test has been used to measure the portfolio performance difference between Mean-Variance and UPM-LPM model. It was found that there is significant difference between results of Sharp ratio in Markowitz portfolio and UPM-LPM portfolio, and in the different risk/potential aversion approaches the UPM-LPM portfolio are significantly better than the traditional Markowitz model