Mean-VaR Portfolio Optimization Based on the Improved Knapsack Problem: Parametric and Nonparametric Approaches

One of the most important problems in portfolio selection models is the ability to provide the optimal number of each share. Therefore, in some cases, it interferes with portfolio optimization in converting the desired weight per share to the desired number per share, unless the results are an integer. Moreover, by applying the appropriate strategy, it seems possible to discover the optimal stock allocation for significant cases with comparatively large stock value. In this regard, this study presents a multi- objective portfolio selection model considering cardinality, quantity and budget constraints based on a new improved knapsack problem. Value-at-Risk (VaR) is considered as the second objective function of risk assessment in the knapsack-based portfolio selection model. We consider parametric (variance- covariance matrix) and non-parametric (historical) approaches to measure VaR. The study also uses the best GARCH family models to estimate the conditional volatility of return in the variance- covariance matrix, which is based on measuring and comparing different criteria under various types of GARCH family models. Finally, a Non-dominated Sorting Genetic Algorithm II (NSGA II) is planned to solve the problem. An actual portfolio of the Iran stock market is solved to demonstrate the application of the suggested model.