Markowitz median variance and fuzzy median variance in portfolio selection problem

The mean-variance Markowitz model assumes that historical data can accurately predict the condition of the securities market in the future. However, this may not be true due to the high volatility in the financial market, leading to imprecise information. Fuzzy approaches are deemed to be a sound alternative when dealing with indefinite information and abnormal data. This paper compares three models which are the mean-variance Markowitz model, the median-variance model, and the fuzzy median variance model. The median is one of the robust statistics less affected by deviations than the mean. Both approaches are demonstrated on shares of the KLCI Bursa Malaysia. The empirical result shows that the fuzzy median variance employing the trapezoidal fuzzy numbers model presents lower risk and better performance than the Markowitz mean-variance and median-variance models.