Robust conditional value–at–risk under parallelpipe uncertainty: an application to portfolio optimization

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2016
Kara, Güray
In markets with high uncertainties, the trade–off between maximizing expected return and minimizing the risk is one of the main challenges in modeling and decision making. Since investors mostly shape their invested amounts towards certain assets and their risk version level according to their returns; scientists and practitioners has done studies on this subject since the beginning of the stock markets’ establishment. Developments and inventions in the mathematical optimization provide a wide range of solutions to handle this problem. Mean–Variance Approach by Markowitz is one the oldest and best known approaches to the risk–return trade–off in the markets. However, it is a one time–step model and not very much prepared for highly volatile markets. After Markowitz, different optimization approaches have been invented for portfolio Optimization, especially, in the tradition of Conditional Value–at–Risk. In this study, we modeled a Robust Optimization problem based on the data and used Robust Optimization approach to find a robust optimal solution to our portfolio optimization problem. This approach includes the use of Robust Conditional Value–at–Risk (RCVaR) under Parallelpipe Uncertainty sets, an evaluation and a numerical finding of the robust optimal portfolio allocation. We obtained and then traced back our robust linear programming model to the Standard Form of a Linear Programming model; then we solved it by a well–chosen algorithm and software package. The main idea is modeling a robust portfolio optimization problem that includes our development of RCVaR based on uncertainty–set–valued data. Our aim is, by considering the return–risk trade–off analysis under uncertain data, to obtain more robust, in fact, lower, risk–level under worst–case scenario by using RCVaR. Uncertainty in parameters, based on uncertainty in the prices, and a risk–return analysis are crucial parts of this study. Hence, the trade–off (antagonism) between accuracy and risk (variance), and robustness are our main issue. A numerical experiment is presented containing real–world data from stock markets. The thesis ends with a conclusion and an outlook to future studies. 

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Citation Formats
G. Kara, “Robust conditional value–at–risk under parallelpipe uncertainty: an application to portfolio optimization,” M.S. - Master of Science, Middle East Technical University, 2016.