Three steps method for portfolio optimization by using Conditional Value at Risk measure

Subject Areas : Statistics

S. Navidi ¹ , sh. Banihashemi ² , M. Sanei ³

1 - Department of Applied Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran
2 - Department of Mathematics, Mathematics and Computer Science, Allameh Tabataba’I University, Tehran, Iran
3 - Department of Applied Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran

Received: 2016-02-20 Accepted : 2016-05-20 Published : 2016-05-21

Keywords: بهینه سازی سبد سهام, تحلیل پوششی داده ها, تصمیم گیری چند هدفه, ارزش در معرض خطر شرطی, داده‌های منفی,

Abstract :

Comprehensive methods must be used for portfolio optimization. For this purpose, financial data of stock companies, inputs and outputs variable, the risk measure and investor’s preferences must be considered. By considering these items, we propose a method for portfolio optimization. In this paper, we used financial data of companies for screening the stock companies. We used Conditional Value at Risk (CVaR) as a risk measure, because of its advantages. Data Envelopment Analysis (DEA) can be used to calculate the efficiency of stock companies. Conventional DEA models assume non-negative data. However, many of these data take the negative value, therefore we propose the MeanSharp- CVaR (MSh CV) model and the Multi Objective MeanSharp- CVaR (MOMSh CV) model base on Range Directional Measure (RDM) that can take positive and negative values. By using Multi Objective Decision Making (MODM) model, investors can allocate their capital to the stocks of portfolio as they like. Finally, a numerical example of the purposed method is applied to Iran’s financial market.