Portfolio Selection Based on Modified CoVaR in Gaussian Framework

We study a Mean-Risk model, where risk is measured by a Modified CoVaR (Conditional Value at Risk): CoVaRα,β≤(X|Y)=VaRβ(X|Y+VaRα(Y)≤0). We prove that in a Gaussian setting, for a sufficiently small β, such a model has a solution. There exists a portfolio that fulfills the given constraints and for which the risk is minimal. This is shown in relation to the mean–standard deviation portfolio, and numerical examples are provided.