Portfolio Optimization Based on Cross Efficiencies By Linear Model of Conditional Value at Risk Minimization

Markowitz model is the first modern formulation of portfolio optimization problem. Relying on historical return of stocks as basic information and using variance as a risk measure are tow drawbacks of this model. Since Markowitz model has been presented, many efforts have been done to remove theses drawbacks. On one hand several better risk measures have been introduced and proper models have been developed to detect optimized portfolio based on them. On the other hand the idea of using generated data by data envelopment analysis instead of historical return of stocks has been presented. In this paper, both improvements are collected by applying a conditional value at risk minimization linear model on cross efficiencies, generated by a proper model of data envelopment analysis model, called range adjusted model. Performance of proposed method, market portfolio as a benchmark and method of applying Markowitz model on cross efficiencies calculated according to sharp ratio using next year real return of each portfolio during years of study. Results support proper performance of proposed method.