Robust Mean-Conditional Value at Risk Portfolio Optimization

In the portfolio optimization, the goal is to distribute the fixed capital on a set of investment opportunities to maximize return while managing risk. Risk and return are quantities that are used as input parameters for the optimal allocation of the capital in the suggested models. But these quantities are not known at the time of the formulation and solving the problem. Thus they should be estimated to solve the problem which might lead to large error. One of the widely used approaches to deal with such a situation, is robust optimization. In this paper we study the robust models of the mean-Conditional Value at Risk (M-CVaR) portfolio selection problem under the estimation risk in mean return for both interval and ellipsoidal uncertainty sets. The corresponding robust models are a linear programming problem and a second order conic programming problem (SOCP) respectively. At end an example is given to demonstrate the impact of uncertainty.