Investors have long sought to manage losses when they construct portfolios in a given investment environment. It has been particularly crucial for institutional investors, such as pension funds, to manage downside risks because they are often exposed to risks inherent in establishing strategic asset allocations over a long-term investment horizon. Therefore, many previous studies by practitioners and academics in the investment world have examined risk measurement and management with a downside risk perspective. In this study, we propose a portfolio management strategy that could maximize a downside risk-adjusted return, the Sortino ratio, utilizing the genetic algorithm and three downside risk measurements, namely semi-deviation, win-loss ratio, and skewness. Using this investment strategy, we aim to reduce the frequency of negative returns to the extent possible so that the portfolio return distributions ultimately become more positively skewed. For this empirical study, we used six asset classes, and compared six different investment strategies. From the experimental results using data from June 8, 2007 to June 30, 2017, we find that the proposed model can successfully increase downside risk-adjusted returns and construct right-skewed portfolios, which are desirable properties for loss-averse long-term investors.