Several risk measures in portfolio selection: Is it worthwhile?

This paper is concerned with asset allocation using a set of three widely used risk measures, which are the variance or deviation, Value at Risk and the Conditional Value at Risk. Our purpose is to evaluate whether solving the asset allocation problem under several risk measures is worthwhile or not, given the added computational complexity. The main contribution of the paper is the solution of two models that consider several risk measures: the mean-VaR-CVaR model and the mean-variance-VaR model. The inclusion of VaR as one of the objectives to minimize leads to nonconvex problems, therefore the approach we propose is based on a heuristic: multi-objective genetic algorithms. Our results show the adequacy of the multi-objective approach for the portfolio optimization problem and emphasize the importance of dealing with mean-variance-VaR or mean-VaR-CVaR models as opposed to mean-variance-CVaR.