A novel multi period mean-VaR portfolio optimization model considering practical constraints and transaction cost

The portfolio optimization literature has spent a little effort to consider the fat tail characteristic of asset returns as well as their extreme events. To remove such shortcomings, in this paper, a novel portfolio optimization model is developed in which Value at Risk (VaR) is utilized as a risk measure to account extreme risk so that VaR is estimated use of Extreme Value Theory (EVT). To enrich the practicality of our proposed model, set of real trading constraints are considered such as cardinality, budget, floor and ceiling constraints. Since these modifications lead to a non-convex NP-hard problem which is computationally difficult, a new design of Non-dominated Sorting Genetic Algorithm (NSGA-II) is proposed to solve it. To evaluate the performance of EVT approach in our proposed mean-VaR model, three well-known alternative VaR estimation methods are also considered such as historical simulation, GARCH and t-student GARCH. Experimental results using historical daily financial market data from S & P 100 indices demonstrates that our proposed NSGA-II has great capability of treating the mean-VaR portfolio optimization problem. In addition, the validation study confirmed that our enhanced NSGA-II not only offers superior result compared with that of delivered by benchmark problem in a much lower solving time, but its performance is better than the original NSGA-II. Also, the results indicate that our proposed model outperforms other mean-VaR models especially in low risk area of Pareto front. Finally, the proposed algorithm is compared with set of Non-dominated-based algorithms including SPEA-II, NSPSO and NSACO which results illustrated that our enhanced NSGA-II suggests superior solutions rather than other algorithms. (C) 2018 Elsevier B.V. All rights reserved.