Mean-Variance-VaR portfolios: MIQP formulation and performance analysis

Abstract Value-at-risk is one of the most popular risk management tools in financial industry. Over past 20 years, several attempts to include VaR portfolio selection process have been proposed. However, using as a measure optimization models leads problems that are computationally hard solve. In view this, few practical applications appeared literature up now. this paper, we propose add criterion classical Mean-Variance approach order better address typical regulatory constraints We thus obtain model characterized by three criteria: expected return, variance, and at specified confidence level. The resulting problem consists minimizing variance with parametric on levels return VaR. This can be formulated mixed-integer quadratic programming (MIQP) problem. An extensive empirical analysis seven real-world datasets demonstrates applicability proposed approach. Furthermore, out-of-sample performance more binding optimal Mean-Variance-VaR portfolios seems generally than Equally Weighted Mean-Variance-CVaR portfolios.