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

Abstract

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