An algorithm based on Mean-CVaR for selecting efficient portfolio with cardinality constraints

Subject Areas : International Journal of Industrial Mathematics

فرهاد حسین زاده لطفی ¹ , Fatemeh Fattahi ² , سعید محرابیان ³ , علی هادی ⁴

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Faculty of Mathematics and Computer Sciences, Kharazmi University, Tehran, Iran
3 - Department of Mathematics, Faculty of Mathematical Science Computer, Kharazmi University, Tehran, Iran.
4 - Department of Mathematics, Science and Research Branch, Islamic Azad University Tehran, Iran.

Received: 2021-01-19 Accepted : 2024-08-05 Published : 2024-09-21

Keywords: Portfolio selection, Cardinality Constraint, Conditional Value-at-Risk, Linear Model, NP-Hard,

Abstract :

Investors usually hold only a small number of stocks to construct portfolio because of the cardinality constrained portfolio selection problem which arises due to the transaction cost and other market frictions. The cardinality constrained portfolio selection with the traditional mean-variance criteria (Mixed-integer and quadratic programming) and mean-CVaR (linear Mixed-integer) are an NP-Hard optimization problem. To solve this mixed-integer nonlinear programming (NP-Hard), a corresponding genetic algorithm (GA) is utilized. In this paper, we presented an algorithm that implements the model mean-CVaR as a linear model for solving this problem. Furthermore, this algorithm can be suggested all possible optimal and find the exact solution. Additionally, a numerical example, which includes an application of the algorithm by considering the stock’s price of the 15 stocks, during the period from 8/16/2019 to 8/14/2020 that obtained from a real datasets, is presented in order to demonstrate that the algorithm is useful for portfolio detection.