Robust optimization of conditional value at risk and portfolio selection

This paper deals with a portfolio selection model in which the methodologies of robust optimization are used for the minimization of the conditional value at risk of a portfolio of shares. Conditional value at risk, being in essence the mean shortfall at a specified confidence level, is a coherent risk measure which can hold account of the so called "tail risk" and is therefore an efficient and synthetic risk measure, which can overcome the drawbacks of the most famous and largely used VaR. An important feature of our approach consists in the use of techniques of robust optimization to deal with uncertainty, in place of stochastic programming as proposed by Rockafellar and Uryasev. Moreover we succeeded in obtaining a linear robust copy of the bi-criteria minimization model proposed by Rockafellar and Uryasev. We suggest different approaches for the generation of input data, with special attention to the estimation of expected returns. The relevance of our methodology is illustrated by a portfolio selection experiment on the Italian market.