An empirical comparison of different risk measures in portfolio optimization

Risk is one of the important parameters in portfolio optimization problem. Since the introduction of the mean-variance model, variance has become the most common risk measure used by practitioners and researchers in portfolio optimization. However, the mean-variance model relies strictly on the assumptions that assets returns are multivariate normally distributed or investors have a quadratic utility function. Many studies have proposed different risk measures to overcome the drawbacks of variance. The purpose of this paper is to discuss and compare the portfolio compositions and performances of four different portfolio optimization models employing different risk measures, specifically the variance, absolute deviation, minimax and semi-variance. Results of this study show that the minimax model outperforms the other models. The minimax model is appropriate for investors who have a strong downside risk aversion.