Some researchers and many practitioners have move from the classic mean-variance (Markowitz, 1959) portfolio theory to a new portfolio optimization framework based on downside-risk measures that are more appropriate to the investor’s preferences. Moreover, several studies (Friedman and Savage, 1952; Kahneman and Tversky, 1979) have point out the existence of S-shape utility functions in investors, which mean, investors are risk-averse and risk-seeking. In this paper we propose a new portfolio optimization framework based on minimizing the Lower-Partial-Moment (LPM) and maximizing the upper-partial-moment (UPM) returns that is more in accordance to the investor’s behavior and the S-shape utility function found in real world. Given the complexity of the optimization problem, and the high nonlinearities and discontinuities, we use a metaheuristic (genetic algorithm) to achieve our goal. We find that, in general, the UPM-LPM portfolio optimization beats the classical mean-variance optimization and the mean-downside risk portfolios. Also, we find that the bigger differences happen close to the portfolio of minimum downside-risk and the smallest differences are in the area of the efficient frontier where the potential upside return is maximize.
