Portfolio Optimization (The Application of Value at Risk Model on Cross Efficiency)

Abstract

Markowitz model is the base for modern approach to portfolio optimization problem. Markowitz model is formulated based on mean and variance of portfolio that is calculated based of historical return. Since this model was proposed many effort have been done to improve formulation of portfolio optimization problem. One of the most important improvement is substituting variance by downside risk measure. Downside risk measure account for fluctuation that just occurs below the mean of returns .The other improvement that recently proposed is data generation based on data envelopment analysis (DEA) and using generated data instead of historical returns. This new improvement that essentially changed basis of portfolio optimization problem provide an opportunity for researcher to examine kinds risk measure based on generated data instead of historical return. In this paper data envelopment analysis is used for generating cross efficiencies based on financial ratios. Then Value at Risk (VaR) as a downside risk measure is redefined for using on cross efficiencies. A well known linear model is used for determining weighs of portfolio based on minimization of Value at Risk. Performance method is evaluated by applying on 185 stock from Tehran Stock Exchange and comparing Sharp criteria proposed portfolios, market portfolio and application of Markowitz model on cross efficiencies during 2011 to 2015. Sharp criteria reveals that proposed method has better performance than the other methods.

Keywords

• Portfolio Optimization
• Value at Risk
• Data Envelopment Analysis
• Cross Efficiency